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https://www.physicsforums.com/threads/1-1.237716/ | # 1 = -1
1. May 29, 2008
### _Mayday_
Hey Everyone,
A while back I found this cool little proof that showed 1 = -1. Now I am fully aware there was a little cheat in there somewhere, but I have lost the little proof. Has anyone come across it, or have anything similar? I just think it's cool, even though in one of the steps there is a mistake. I know it starts with like rooting one, and then putting 1 = (-1)(-1) etc.
Cheers.
_Mayday_
2. May 29, 2008
### dirk_mec1
I got another version:
$$\frac{-1}{1}=-1$$ and $$\frac{1}{-1}=-1$$
so:
$$\frac{-1}{1}=\frac{1}{-1}$$
if $$\sqrt{-1}=i$$
then
$$\sqrt{\frac{-1}{1}}=\sqrt{\frac{1}{-1}}$$
so:
$$\frac{\sqrt{-1}}{\sqrt{1}}=\frac{\sqrt{1}}{\sqrt{-1}}$$
$$\frac{1}{2}(\frac{i}{1})=\frac{1}{2}(\frac{1}{i})$$
becomes
$$\frac{i}{2}=\frac{1}{2i}$$
$$\frac{i}{2} + \frac{3}{2i} = \frac{1}{2i} + \frac{3}{2i}$$
$$i(\frac{i}{2} + \frac{3}{2i}) = i(\frac{1}{2i} + \frac{3}{2i})$$
$$\frac{-1}{2}+\frac{3}{2}=\frac{1}{2}+\frac{3}{2}$$
$$\frac{2}{2} = \frac{4}{2}$$
$$1 = 2$$
3. May 29, 2008
### robert Ihnot
YOu got a problem right here: $$\frac{\sqrt{-1}}{\sqrt{1}}=\frac{\sqrt{1}}{\sqrt{-1}}$$ Since this gives i=1/i.
$$\sqrt{\frac{-1}{1}}=\sqrt{\frac{1}{-1}}$$
Just because a=b doesn't mean that $$\sqrt a = \sqrt b.$$
Last edited: May 29, 2008
4. May 29, 2008
### LukeD
yes it does (as long as we've agreed on some convention so that $$\sqrt{x}$$ is a function, which we have)
And that line is correct. The problem is that in the complex numbers $$\sqrt{\frac{a}{b}} = \sqrt{\frac{c}{d}}$$ does not imply that $$\frac{\sqrt{a}}{\sqrt{b}}=\frac{\sqrt{c}}{\sqrt{d}}$$. This is true for the positive real numbers, but not for complex numbers in general.
But the poster was just asking for "proofs" that 1 = -1. Of course they are all flawed. But to the OP: There are a lot of "proofs" of this, so any more description, if you could remember any part of it, would be useful.
Last edited: May 29, 2008
5. May 29, 2008
### Diffy
Hey Mayday,
You pretty much have a proof in the one that Dirk_mec1 posted.
Once you get to this step:
$$\frac{\sqrt{-1}}{\sqrt{1}}=\frac{\sqrt{1}}{\sqrt{-1}}$$
you now have
i/1 = 1/i
multiply both sides by i
you have (i^2)/1 = i/i --> -1/1 = 1/1 --> -1 = 1.
6. May 29, 2008
### _Mayday_
Thank you! Wait till my class see this stuff!
7. May 30, 2008
### Alex48674
Another one that freaks people out
a=b
aa=ab
aa-bb=ab-bb
(a+b)(a-b)=b(a-b)
divide by a-b
a+b=b
since a=b then
2b=b
2=1
Naturally this is completely fake, the error in this logic is that when you divide by a-b you are dividing by zero. If you want to can keep repeating this and get like 1=4 and stuff. Kinda freaks people out but make sure you explain it to them in the end =P. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8107119202613831, "perplexity": 1279.7442886022752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743110.55/warc/CC-MAIN-20181116173611-20181116195611-00192.warc.gz"} |
https://brilliant.org/problems/functions-problem-2406/ | # Swapping in and out
Algebra Level 1
If $$f(x)=x+\frac{1}{x}$$ and $$g(x)=x-\frac{1}{x}$$, $$f \big( g(3) \big) = \frac{a}{b}$$, where $$a$$ and $$b$$ are positive, coprime integers. What is $$a+b$$?
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https://www.physicsforums.com/threads/limit-calculation.443258/#post-2961565 | # Limit Calculation
• #1
CalculusHelp1
22
0
## Homework Statement
Calculate the limit as x-->pi/4 of [tan(x-pi/4)+1]/x-pi/4
## Homework Equations
lim h-->0 of [f(x+h)-f(x)]/h = f'(x)
lim x--->a [f(x)-f(a)]/(x-a) = f'(x)
## The Attempt at a Solution
I've attempted to turn this equation into the form f(x)-f(a)/x-a by letting f(x)=tanx and a=pi/4
This turns into -[-tan(x+a)-tan(a)]/x-a...which isn't the correct derivative form. .I've tried other methods which also turn into similar garble (a minus sign backwards, x-h rather than x+h and the like).
Can anyone see what the problem is? Thanks
## Answers and Replies
• #2
Staff Emeritus
Homework Helper
22,178
3,317
The limit
$$\lim_{x\rightarrow \pi/4}{\frac{\tan(x-\pi/4)+1}{x-\pi/4}}$$
Is of the form "1/0". Thus the limit is always $$+\infty$$ or $$-\infty$$ or it doesn't exist (if the left limit does not equal the right limit). Which one is it?
• #3
CalculusHelp1
22
0
Oh is is actually this easy?
In that case, I would think since the numerator will always be positive regardless of which side the limit approaches from, and the denominator will switch signs depending on which side it approaches from, then the limit from the left will be -infinity and will be +infinite from the right, then the limit will not exist.
Are you sure there isn't a way to do this with derivatives? I thought this is what the question was getting at
• #4
Staff Emeritus
Homework Helper
22,178
3,317
Yes, I know it looks a lot like a derivative. But this method is definitely simpler then to change the limit into a derivative (if there is a way of doing that).
I don't think that you can change this limit into a derivative-limit. A derivative will yield "0/0", while this is "1/0".
• #5
Staff Emeritus
Homework Helper
22,178
3,317
Well, if the question was
$$\lim_{x\rightarrow \pi/4}{\frac{\tan(x)-1}{x-\pi/4}}$$
Then you can do some derivative-stuff. But I don't really see a possibility here...
• #6
CalculusHelp1
22
0
Okay that makes sense. Thanks for the help
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410 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9506087303161621, "perplexity": 2092.703484943705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00322.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=134630 | ## Pressure of gasses
$PV=nRT$
305174946
Posts: 61
Joined: Fri Sep 28, 2018 12:17 am
### Pressure of gasses
On page 151 of the 6th edition of our textbook there is an equation: P=dhg which solves for the pressure of a gas based on the height of a column of liquid and its density and gravity. I was wondering if we would need to know this calculation, if so can someone please explain it in depth because the explanation in the textbook slightly confuses me.
Kenan Kherallah 2C
Posts: 78
Joined: Fri Sep 28, 2018 12:17 am
### Re: Pressure of gasses
I dont think we will be using this equation since he hasnt mentioned it in lecture and all HW problems are solvable without the equation.
904914909
Posts: 60
Joined: Fri Sep 28, 2018 12:26 am
### Re: Pressure of gasses
I think stick to the formulas he has given us in lecture so far, bc this one hasn't been mentioned yet.
Mhun-Jeong Isaac Lee 1B
Posts: 54
Joined: Fri Sep 28, 2018 12:17 am
### Re: Pressure of gasses
Yeah just to confirm the above responses, Dr. Lavelle hasn't gone over that equation so I don't think we have to know that one. For now at least.
Jasmine Chow 1F
Posts: 60
Joined: Fri Sep 28, 2018 12:16 am
Been upvoted: 1 time
### Re: Pressure of gasses
I don't think we will be using it. He hasn't mentioned it in lecture yet.
Chem_Mod
Posts: 17238
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 367 times
### Re: Pressure of gasses
This is more of a physics topic but if your interested this is the general idea:
To calculate the weight of the liquid we use the equation: weight (force)=mg (mass x gravity constant). The mass of the liquid can be determined using both the volume of the liquid and its density (m=Vd : where V=volume and d=density). Combining these equations we now get F=Vdg.The volume of a cylinder of liquid can be determined using the geometric formula V=A (of the circle) x h (height of the liquid). Using this equation we now get: F=Ahdg
Now, the definition of pressure is Force/Area, so combining the equations above we get P=(Ahdg)/A which when simplified yield P=hdg Tadaaaaa. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9153250455856323, "perplexity": 1949.8399476516806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575596.77/warc/CC-MAIN-20190922160018-20190922182018-00279.warc.gz"} |
https://www.physicsforums.com/threads/infinite-series-question.94507/ | # Infinite series question
1. Oct 13, 2005
### happyg1
Hello,
Here's the question:
Does the series SUM log(1+1/n) converge or diverge?
I wrote out the nth partial sums like this:
log(1+1) + log(1+1/2) + log(1+1/3)+..........+log(1+1/n)
It looks to me like the limit of the thing inside the parentheses goes to 1 as n goes to infinity, making the limit of the entire thing 0. So I say it converges.
One of my classmates says that SUM 1/n diverges, so this one does too. I can't disagree with him, but I fail to see the relevance.
I'm confused. Any clarification will be appreciated.
CC
2. Oct 13, 2005
### shmoe
The terms going to zero is a necessary but not sufficient condition for convergence of the series (1/n is your basic counterexample).
They probably have the limit comparison test in mind. You can also look at the integral comparison test, you can find an antiderivative of log(1+1/n) easily enough.
3. Oct 13, 2005
### Ali 2
The series diverges ..
Take the sequance of partial sums ..
$$S_n = \sum_{k=1} ^n\log \left( 1 + \frac 1k \right) = \sum_{k=1} ^n \log \left ( \frac { k+1} { k} \right ) = \sum_{k=1} ^n \log (k+1) - \log (k) \mbox{ ( Telescoping series }$$
$$= (\log 2 - \log 1) + (\log 3 - \log 2) +....... + (\log n - \log (n-1) ) + (\log (n+1) - \log n)$$
$$= - \log 1 + \log ( n+1 ) = \log (n+1)$$
$$\lim _ { n \rightarrow \infty } S_n = \lim _ { n \rightarrow \infty } \log ( n+1) = \infty \Longrightarrow \sum_{n=1} ^ {\infty}\log \left( 1 + \frac 1n \right) \mbox{ diverges }$$
Last edited: Oct 13, 2005
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https://socratic.org/questions/how-do-you-find-all-solutions-to-x-6-64i-0 | Precalculus
Topics
# How do you find all solutions to x^6-64i=0?
##### 1 Answer
Aug 20, 2016
Use de Moivre's theorem to find all $6$ Complex roots.
#### Explanation:
Given:
${x}^{6} - 64 i = 0$
Add $64 i$ to both sides to get:
${x}^{6} = 64 i$
$\textcolor{w h i t e}{{x}^{6}} = {2}^{6} \left(0 + 1 i\right)$
$\textcolor{w h i t e}{{x}^{6}} = {2}^{6} \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)$
From de Moivre's theorem, we have:
${\left(\cos \theta + i \sin \theta\right)}^{n} = \cos n \theta + i \sin n \theta$
Hence principal root:
${x}_{1} = \sqrt[6]{64 i} = 2 \left(\cos \left(\frac{\pi}{12}\right) + i \sin \left(\frac{\pi}{12}\right)\right)$
The other $5$ roots can be found by multiplying by the primitive Complex $6$th root of $1$, i.e. $\left(\cos \left(\frac{\pi}{3}\right) + i \sin \left(\frac{\pi}{3}\right)\right)$ to find:
${x}_{2} = 2 \left(\cos \left(\frac{5 \pi}{12}\right) + i \sin \left(\frac{5 \pi}{12}\right)\right)$
${x}_{3} = 2 \left(\cos \left(\frac{9 \pi}{12}\right) + i \sin \left(\frac{9 \pi}{12}\right)\right)$
${x}_{4} = 2 \left(\cos \left(\frac{13 \pi}{12}\right) + i \sin \left(\frac{13 \pi}{12}\right)\right)$
${x}_{5} = 2 \left(\cos \left(\frac{17 \pi}{12}\right) + i \sin \left(\frac{17 \pi}{12}\right)\right)$
${x}_{6} = 2 \left(\cos \left(\frac{21 \pi}{12}\right) + i \sin \left(\frac{21 \pi}{12}\right)\right)$
These trigonometric values can be expressed in terms of square roots:
$\cos \left(\frac{\pi}{12}\right) = \frac{1}{4} \left(\sqrt{6} + \sqrt{2}\right) \text{ } \sin \left(\frac{\pi}{12}\right) = \frac{1}{4} \left(\sqrt{6} - \sqrt{2}\right)$
$\cos \left(\frac{5 \pi}{12}\right) = \frac{1}{4} \left(\sqrt{6} - \sqrt{2}\right) \text{ } \sin \left(\frac{5 \pi}{12}\right) = \frac{1}{4} \left(\sqrt{6} + \sqrt{2}\right)$
$\cos \left(\frac{9 \pi}{12}\right) = - \frac{\sqrt{2}}{2} \text{ } \sin \left(\frac{9 \pi}{12}\right) = \frac{\sqrt{2}}{2}$
$\cos \left(\frac{13 \pi}{12}\right) = - \frac{1}{4} \left(\sqrt{6} + \sqrt{2}\right) \text{ } \sin \left(\frac{13 \pi}{12}\right) = - \frac{1}{4} \left(\sqrt{6} - \sqrt{2}\right)$
$\cos \left(\frac{17 \pi}{12}\right) = - \frac{1}{4} \left(\sqrt{6} - \sqrt{2}\right) \text{ } \sin \left(\frac{17 \pi}{12}\right) = - \frac{1}{4} \left(\sqrt{6} + \sqrt{2}\right)$
$\cos \left(\frac{21 \pi}{12}\right) = \frac{\sqrt{2}}{2} \text{ } \sin \left(\frac{21 \pi}{12}\right) = - \frac{\sqrt{2}}{2}$
So here are the $6$ roots in the Complex plane:
graph{((x-1/2(sqrt(6)+sqrt(2)))^2 + (y-1/2(sqrt(6)-sqrt(2)))^2 - 0.01)((x-1/2(sqrt(6)-sqrt(2)))^2 + (y-1/2(sqrt(6)+sqrt(2)))^2 - 0.01)((x+sqrt(2))^2+(y-sqrt(2))^2-0.01)((x+1/2(sqrt(6)+sqrt(2)))^2 + (y+1/2(sqrt(6)-sqrt(2)))^2 - 0.01)((x+1/2(sqrt(6)-sqrt(2)))^2 + (y+1/2(sqrt(6)+sqrt(2)))^2 - 0.01)((x-sqrt(2))^2+(y+sqrt(2))^2-0.01) = 0 [-5, 5, -2.5, 2.5]}
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https://www.docsity.com/en/anisotropy-chemical-engineering-previous-solved-exam/297536/ | # Anisotropy - Chemical Engineering - Previous Solved Exam, Exams for Engineering Chemistry. The National Centre for Biological Sciences
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Microsoft Word - ChE_179 exam 2 s12_soln.doc
1
Name:____________________
CHEMICAL ENGINEERING 179
Exam 2 Wednesday, April 11 2012 Closed Book with 3x5 Card
kB = 1.381 x 10-23 J K-1; R = 8.314 J (mole K)-1 = 1.987 cal (mole K)-1 ; NA = 6.022 x 1023 (mole)-1; e = 1.602
x 10-19 C; mp = 1.673 x 10-27kg = 1.007 amu ; 1 liter = 1000 cm3 ; STP = 273 K, 760 torr (1 atm); 1 atm = 1.013 x 105 Pa; 1 Pa = 1 J/m3; 1 eV = 1.602 x 10-19 J Short Answer. 5 pts. each. 1.What is the chief advantage of plasma etching over wet liquid etching in semiconductor manufacturing? Anisotropy is possible in the etch profile. 2. A measurement of Si etch rate is made with F atoms only hitting the surface, then F atoms plus Ar+ (500 eV), then only Ar+ (500eV). Sketch the expected etch rate vs. time for this experiment, labeling the different regions. Low etch rate, followed by a high etch rate, followed by a low rate again. 3. Chemical vapor deposition (CVD) reactor design calculations usually require chemical kinetics rather than chemical thermodynamics. Why is this? The chemical processes are not at equilibrium, which is required to use chemical thermodynamics. 4. In semiconductor manufacturing, CVD processes are usually conducted at reduced pressure. List 2 reasons why low pressure is preferred to atmospheric pressure for CVD. - higher diffusivity leads to better film deposition uniformity; lower pressure reduces particle formation;
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5. For cylindrical, isothermal LPCVD (low pressure CVD) reactors with multiple wafers and flow in the annular region, what is the expected axial profile (that is, along the length of the reactor) in reactant concentration? The expected profile will be an exponential decline in concentration. 6. What is the definition of the effectiveness factor (in terms of a ratio of reaction rates)? Ratio of actual rate divided by maximum possible rate in absence of mass transfer limitations. 7. For best growth rate uniformity results, should the LPCVD reactor be operated in the reaction rate limited or mass transfer limited regimes? Why? Reaction rate limited regime implies no mass transfer limitations, leading to film deposition rate uniformity. 8. How do ‘magnetron’ plasma sputtering systems work? They use magnets above the target electrode to intensify the plasma, reducing electron losses and allowing higher deposition rates at lower pressure than conventional sputtering systems. 9. What is the source of light emitted by ‘glow discharge plasma?’ Electron impact excitation leads to emission of photons and light emission. 10. List 3 ways that plasmas are used in thin film processing. Etching; deposition, photoresist stripping; surface cleaning
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Problem. (50) 1. Consider a rectangular-shaped atmospheric pressure CVD reactor. The reaction occurs only on the bottom interior surface of the reactor and the reaction is controlled by the rate of mass transfer through the boundary layer. The gas enters at 273K, 1 atmosphere pressure, and the reacting (lower) surface is maintained at a high temperature. Assume the gas diffusivity is 1 cm2/s in the boundary layer. Ignore pressure drop in the reactor and any effects of gas temperature on properties. The reactor length is 20 cm, the height is 5 cm and the width is 10 cm. The flowrate of the gas entering is 50 standard liters per minute and the inlet mole fraction of reactive component is 0.001. Assume the flow remains laminar down the length of the reactor, and the boundary layer
above the reactive surface increases down the length (x) as ! (x) =1.5 x" Ugas
Sc !1 3 , where the
symbols have their normal meaning (as in the HW). Solve for and plot the relative rate of reaction (rate divided by some scaling rate) as a function of length down the reactor. Solution.
The rate of film deposition in the limit of mass transfer control is r(x) = DAB ! (x)
(CA ! 0) .
Since we want relative rate of deposition, we only need to plot a normalized function. So all we need is to get the gas velocity Ugas and the minor Sc correction, recognizing that Sc ~1. This comes from the inlet volumetric flow (we are at standard conditions) and the cross sectional area of the inlet rectangle. The gas velocity does not change down the length and we are ignoring the effects of gas temperature changes, so it is fairly straightforward. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8269413113594055, "perplexity": 2794.0191839045483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824912.16/warc/CC-MAIN-20181213145807-20181213171307-00073.warc.gz"} |
https://deepai.org/publication/projected-iterative-soft-thresholding-algorithm-for-tight-frames-in-compressed-sensing-magnetic-resonance-imaging | # Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging
Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image representations, e.g. tight frames, can significantly improve the image quality. But how to efficiently solve the reconstruction problem with these redundant representation systems is still challenging. This paper attempts to address the problem of applying iterative soft-thresholding algorithm (ISTA) to tight frames based magnetic resonance image reconstruction. By introducing the canonical dual frame to construct the orthogonal projection operator on the range of the analysis sparsity operator, we propose a projected iterative soft-thresholding algorithm (pISTA) and further accelerate it by incorporating the strategy proposed by Beck and Teboulle in 2009. We theoretically prove that pISTA converges to the minimum of a function with a balanced tight frame sparsity. Experimental results demonstrate that the proposed algorithm achieves better reconstruction than the widely used synthesis sparse model and the accelerated pISTA converges faster or comparable to the state-of-art smoothing FISTA. One major advantage of pISTA is that only one extra parameter, the step size, is introduced and the numerical solution is stable to it in terms of image reconstruction errors, thus allowing easily setting in many fast magnetic resonance imaging applications.
## Authors
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Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offe...
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• ### Fast Iteratively Reweighted Least Squares Algorithms for Analysis-Based Sparsity Reconstruction
In this paper, we propose a novel algorithm for analysis-based sparsity ...
11/18/2014 ∙ by Chen Chen, et al. ∙ 0
• ### A Convergence Proof of Projected Fast Iterative Soft-thresholding Algorithm for Parallel Magnetic Resonance Imaging
The boom of non-uniform sampling and compressed sensing techniques drama...
09/17/2019 ∙ by Xinlin Zhang, et al. ∙ 18
• ### Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction
Objective: Improve the reconstructed image with fast and multi-class dic...
03/10/2015 ∙ by Zhifang Zhan, et al. ∙ 0
This short article presents a class of projection-based solution algorit...
03/08/2011 ∙ by Xin Li, et al. ∙ 0 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9166152477264404, "perplexity": 2118.563684562372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655887046.62/warc/CC-MAIN-20200705055259-20200705085259-00564.warc.gz"} |
https://www.physicsforums.com/threads/universal-quantifier.537550/ | # Homework Help: Universal quantifier
1. Oct 6, 2011
### gotjrgkr
1. The problem statement, all variables and given/known data
In a book "How to prove it" by velleman, universal quantifier is defined as follows;
To say that P(x) is true for every value of x in the universe of discourse U, we will write $\forall$xP(x). This is read "For all x, P(x)". The symbol $\forall$ is called the universal quantifier.
And in this book, universe of discourse is defined as a set of all possible values for the variables relating with a statement.
Then, what I want to know is if under a special condition like that the universe of discourse of a statement is not a set, the universal quantifier can't be used to express such the statement.
For example, since there's no set which contains all ordinal numbers, I expect that a statement like "for all ordinal numbers x, P(x)" can't be expressed by using universal quantifier.
In a book " introduction to set theory" by karel hrbacek, the set of all natural numbers is
defined as $\left\{$ x : x$\in$ I for every inductive set I$\right\}$.
In this case, the universe of discourse of the statement is the set of all inductive set.
But , i can't convince of the existence of such a set of all inductive set.
2. Relevant equations
3. The attempt at a solution
In some books described by NBG set theory, universal quantifier is just defined without the use of universe of discourse. I thought that this is because the notion class can be replaced with it. I mean, I thought that the definition of universal quatifier is such that for all x contained in a specified class, P(x).
I'm very confused about this notion and I doubt myself whether asking this question is meaningful or not....
I wanna know what is wrong in my argument and I ask you the exact definition of universal quantifier and also wanna know if the notion universe of discourse is needed in defining universal quantifier.
Please tell me about the truth if you know .
Thakns..
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https://www.masterbuilder.co.in/behaviour-sand-reinforced-plastic-3d-reinforcements/ | Behaviour of Sand Reinforced With Plastic 3D Reinforcements
# Behaviour of Sand Reinforced With Plastic 3D Reinforcements
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The concept of mechanically stabilized earth has been widely used in various geotechnical applications such construction of embankments, pavements, bridge abutments, soft ground improvement and so on. Addition of reinforcements to soil have been performed by either incorporating continuous reinforcement inclusions such as sheet, bar or strip within a soil mass in a well defined pattern, or by randomly mixing discrete fibres with a soil fill. The effect of conventional reinforcements on soil has been extensively investigated by Fleming et al. (2006), Iizuka et al. (2004), Katarzyna (2006), Latha and Murthy (2006), Park and Tan (2005), Patra, Das and Atalar (2005), Varuso, Grieshaber and Nataraj (2005), Yetimoglu, Inanir and Inanir (2005). The concept of three dimensional reinforcement was first introduced by Lawton et al. (1993), who performed laboratory investigations on sand reinforced with geo-jacks. They also observed that use of geo-jacks on top of the geogrid substantially improved the performance of the soil foundation and that the combination of geogrid and geo-jacks performed better than a combination of geogrid and gravel. Zhang et al.(2008) investigated the use of three dimensional reinforcements in the form of rings with varying heights of vertical elements.
In this investigation, results from laboratory plate load tests conducted on square footing on sand bed reinforced with single and multiple layers of multi-directional reinforcements are presented, in order to determine the feasibility of using multi-directional reinforcements to improve the bearing capacity of soil and to investigate the significance of parameters such as volume ratio of reinforcements, depth to first layer, spacing between reinforcements in a layer, spacing between layers and number of layers.
Locally available clean river sand obtained from the premises of NIT Calicut, Kerala, India was oven dried and was used for the present study. Reinforcing elements were manufactured from injection moulding of ABS plastic granules. ABS is derived from acrylonitrile, butadiene, and styrene. Acrylonitrile is a synthetic monomer produced from propylene and ammonia; butadiene is a petroleum hydrocarbon obtained from the C4 fraction of steam cracking; styrene monomer is made by dehydrogenation of ethyl benzene, which is a hydrocarbon. ABS combines the strength and rigidity of acrylonitrile and styrene polymers with the toughness of polybutadiene rubber. ABS has superior properties in terms of hardness, gloss, toughness, and electrical insulation. The properties of sand and reinforcements are mentioned in Table 1 and Table 2 respectively. The reinforcements consisted of four legs or protrusions in a single plane (x–y) and two protrusions in plane perpendicular to this plane (z), with an average length of 30 mm and a diameter of 5 mm were used for the study, as shown in Fig.1. The effect of parameters such as volume ratio of reinforcements, depth to first layer, spacing between reinforcements in a layer, spacing between layers and number of layers are investigated vide plate load test performed on a 150 mm square MS plate placed in an MS tank of size 75cm x 75 cm x 75 cm. The test setup is shown in Fig.2.
The general nomenclature adopted for the study are as follows:
b= width of reinforcing element
B= width of plate
u=depth to first layer
d= spacing between layers
s= spacing between reinforcing elements in a single layer
N= number of layers.
Depth to first layer of reinforcement
Typical pressure vs. settlement curves for the model footing on unreinforced and reinforced sand bed is shown Fig.3. The reinforcing elements were placed, close to each other, such that the spacing between them, s/b=0.This corresponds to a volume ratio of 0.3%. Each test was performed twice and the average of the settlement values was taken into consideration, to account for accuracy. It can be seen that placement of a single layer of reinforcement, too close to the surface (u/B=0.1), does not improve the settlement response significantly. As the depth to first layer increases beyond 0.1B, the response improved drastically. This is due to the fact that at shallow depths of placement, the magnitude of mobilized frictional resistance at the sand-reinforcement interface is relatively less, due to the smaller overburden pressure. Placing the first reinforcement layer at a depth greater than 0.7B, had an adverse effect on bearing capacity and settlement values, since the settlements began to increase, although better than the unreinforced case. This behaviour is due to increased thickness of sand layer over the reinforcements, resulting in higher settlement. Surface heave reduces with increasing depth of placement of reinforcement upto u/B=0.5, and thereafter decreases.
The improvements in bearing capacity and settlement behaviour are quantified using three factors viz. Bearing capacity ratio (BCR), Settlement reduction factor (SRF) and Heave ratio (dx100/B). BCR is calculated as the ratio between the ultimate bearing capacity of reinforced sand to that of unreinforced sand. The ultimate bearing capacity in all cases, in the study is calculated, corresponding to a settlement of 25 mm.
where,
s0 is the settlement of unreinforced sand bed at a given pressure and sr represents settlement of reinforced sand bed at the same pressure. Heave ratio is defined as the ratio between the maximum heave, observed at a distance of 1B from the edge of the plate for unreinforced sand bed to the maximum heave observed in reinforced sand bed.
Fig.4 shows the variation in BCR corresponding to 25 mm settlement. For a single layer of reinforcement, the bearing capacity improved by as much as 1.3 times, corresponding at a depth of placement, 0.5B. Settlement reduction factor was calculated for various depths to first layer of reinforcement, as shown in Fig.5.
A maximum reduction of 0.72 was obtained corresponding to u/B=0.5 with zero spacing between reinforcing elements. The variation of heave ratio with depth of first reinforcement layer is shown in Fig.6. Similar to the trends observed, the maximum reduction in heave corresponds to a depth of 0.5B.
The general ground displacement profile in terms of settlement and heave with variation in depth of first reinforcement layer is described in Fig.7.
Spacing between reinforcing elements
The optimum depth of placement of the first layer of reinforcement was determined as 0.5B. The reinforcing elements were placed close to one another, so that there was zero spacing between them (s/b=0; b being the width of the reinforcing element).
The next phase involved the determination of optimum spacing between the reinforcing elements. Two different configurations of reinforcement arrangement, viz. s/b=0.5 and s/b=1. were tested. The corresponding volume ratios are 0.135% and 0.084%. As expected, placing the reinforcing elements close to one another, with zero spacing between them, accounts for maximum improvement in the strength parameters, on account of increased volume ratio of reinforcement. However, it is to be noted that the reduction in strength improvement, when the reinforcements are arranged at a spacing of s/b=0.5 and s/b=1 is only marginal. Considering the practical difficulties in placing the reinforcing elements one by one, at zero spacing between them in field applications, and the economical aspects of the project, the placement of reinforcements at a spacing of s/b=1, proves to be feasible. Thus, considering a balance between the strength improvement and the overall economic benefits, an intra-layer spacing of s/b=1 is adopted for the study.
Number of layers and spacing between layers
The next phase of tests involved determining the influence of number of reinforcing layers on the bearing capacity and settlement. In all tests conducted in this phase, the depth to first reinforcement layer is fixed at 0.5B. The number of reinforcement layers is varied from one to four, the final layer being kept at a depth of 2B. The reinforcement layers were placed in such a way that they were spaced evenly between 0.5B and 2B depths. The thickness of the reinforcing elements was around 0.2B. Hence, it was not possible to place the reinforcements at spacing less than 0.5B, due to practical difficulties in ensuring the correct placement of reinforcing elements and compaction of the sand above. Placing a layer above 0.5B depth was not considered in this phase, as the optimum depth for a single reinforcement layer was obtained as 0.5B. Also, if a reinforcement layer was placed above this level, providing due allowance for the thickness of the reinforcing element, the depth of placement would be less than 0.3B and would not contribute significantly to the improvement in strength parameters, as discussed in the previous sections. The bearing capacity was found to increase with an increase in number of reinforcing layers, coupled with a decrease in settlements. This is due to the ability of reinforcements to spread the superimposed load to larger depths, where the confining and overburden pressures are higher. It was observed that as the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR and SRF, whereas this improvement reduced to about 14% and 3% for BCR and SRF respectively, when the number of layers increased beyond 3.Similarly, the reduction in heave observed was about 10% when the number of layers increased from 2 to 3, and only 0.6% when the number of layers increased from 3 to 4. Since the tests are conducted on laboratory scale models, the effect of confinement and scaling play a significant role. Further large scale field studies are required to be performed in this regard to determine the exact behaviour of multi-directional reinforcements.
A comparison of the improvements in bearing capacities imparted by conventional reinforcing elements such as geogrids and the multi-directional elements developed in this study are provided in Table 3. It can be seen that the multi-directional reinforcements perform on par with the conventional reinforcing systems. Additionally for a given aerial coverage, the cost of these elements is about 50% less. compared to the existing methods of conventional reinforcements.
Conclusions
Based on the results from experimental investigations on the behaviour of model footing, resting on sand bed reinforced with plastic multi-directional reinforcements, the following conclusions can be drawn:
a. An appreciable increase in bearing capacity was observed as the depth to the first layer of reinforcement increased beyond 0.1B. The optimum depth of placement of the first layer was 0.5B. Placing reinforcements beyond 0.5B depth, in a single layer, resulted in a reduction in increase of bearing capacity. The bearing capacity increased by 1.3 times and the settlements reduced by almost 72%.
b. Within a single layer of reinforcement, the maximum improvement in BCR was obtained corresponding to zero spacing between the inclusions. However, considering a balance between the strength improvement and economical aspects, an optimum spacing of 1b was adopted, where b is the width of the reinforcing element.
c. BCR increased with increase in number of reinforcement layers. As the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR, whereas this improvement reduced to about 14 % when the number of layers increased beyond 3. SRR showed similar trends, the improvements being 43% and 3% respectively. A similar trend was observed in case of Heave factor also.
d. Owing to the size of the reinforcing elements and the practical difficulties in laying and compacting sand layers between the reinforcing elements, a minimum spacing of 0.2B was required to be maintained between the reinforcement layers. Hence, considering these factors, the optimum layer spacing was maintained as 0.5B.
References
1. Fleming, I.R., Sharma, J.S., Jogi, M.B., (2006), “Shear strength of geomembrane–soil interface under unsaturated conditions”, Geotextiles and Geomembranes 24 (5), 274–284. DOI:10.1016/j.geotexmem.2006.03.009
2. Iizuka, A., Kawai, K., Kim, E.R., Hirata, M., (2004), “Modeling of the confining effect due to the geosynthetic wrapping of compacted soil specimens”, Geotextiles and Geomembranes 23 (5), 329–358.DOI: 10.1016/j.geotexmem.2004.01.001
3. Katarzyna, Z.A., (2006), “Shear strength parameters of compacted fly ash–HDPE geomembrane interfaces”. Geotextiles and Geomembranes, 24 (2), 91–102. DOI: 10.1016/j.geotexmem.2005.11.006
4. Latha, M.G., Murthy, V.S., (2006), “Investigations on sand reinforced with different geosynthetics”, Geotechnical Testing Journal 29 (6), 474–481. DOI: 10.1520/GTJ100439
5. Park, T., Tan, S.A., (2005), “Enhanced performance of reinforced soil walls by the inclusion of short fiber”, Geotextiles and Geomembranes 23 (4), 348–361. DOI: 10.1016/j.geotexmem.2004.12.002
6. Patra, C.R., Das, B.M., Atalar, C., (2005), “Bearing capacity of embedded strip foundation on geogrid-reinforced sand”, Geotextiles and Geomembranes 23 (5), 454–462. DOI: 10.1016/j.geotexmem.2005.02.001
7. Varuso, R.J., Grieshaber, J.B., Nataraj, M.S., (2005), “Geosynthetic reinforced levee test section on soft normally consolidated clays”, Geotextiles and Geomembranes 23 (4), 362–383. DOI: 10.1016/j.geotexmem.2004.11.001
8. Yetimoglu, T., Inanir, M., Inanir, O.E., (2005), “A study on bearing capacity of randomly distributed fiber-reinforced sand fills overlying soft clay”, Geotextiles and Geomembranes 23 (2), 174–183. DOI: 10.1016/j.geotexmem.2004.09.004
9. Lawton E.C, Khire M.V, Fox N.S.,(1993), “Reinforcement of Soils by Multioriented Geosynthetic Inclusions”, Journal of Geotechnical Engineering 119 (2). DOI: 10.1061/(ASCE)0733-9410(1993)119:2(257)
10. Zhang M.X., Zhou H., Javadi A.A, Wang Z.W., (2008), “Experimental and Theoretical Investigation of Strength of Soil Reinforced with Multi-Layer Horizontal Vertical Orthogonal elements”, Geotextiles and Geomembranes 26, 1–13. DOI: 10.1016/j.geotexmem.2007.06.001
11. Phanikumar, B. R., Prasad, R., Singh, A. (2009), “Compressive load response of geogrid-reinforced fine, medium and coarse sands”, Geotextiles and Geomembranes, 27(3), 183–186. http://doi.org/10.1016/j.geotexmem.2008.11.003
12. Latha G.M, Somwanshi A., (2009), “Bearing capacity of square footings on geosynthetic reinforced sand”. Geotextiles and Geomembranes 27,281–294 DOI:10.1016/j.geotexmem.2009.02.001
13. M Harikumar, N Sankar, S Chandrakaran, 2016, Behaviour of model footing resting on sand bed reinforced with multi-directional reinforcing elements, Geotextiles and Geomembranes 44 (4), 568-578 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8170503377914429, "perplexity": 3890.921484353632}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891750.87/warc/CC-MAIN-20180123052242-20180123072242-00101.warc.gz"} |
http://book.caltech.edu/bookforum/showpost.php?s=65a60731ea6a3758c5e828d65a834c82&p=12418&postcount=3 | View Single Post
#3
08-01-2016, 01:18 PM
jeffjackson Junior Member Join Date: Jun 2016 Posts: 5
Re: Section 1.3 argument for feasibility of learning is fundamentally flawed
Malik, I'm glad to hear that we agree that Section 1.3 is not a valid defense of learning. Now let me sketch what I believe is a reasonable defense.
Essentially, the idea is to extend the argument of Section 1.3 with two additional observations:
1. The sample size of the Hoeffding bound depends only logarithmically on the desired probability bound.
2. Most computer scientists "trust" randomized algorithms when the probability of error of such an algorithm is extremely small, such as, say, .
The first observation implies that we can drive the probability of seeing a misleading training set down to extremely small values with a relatively modest increase in training set size and/or in the allowable error of the hypothesis. For instance, in the standard (1-hypothesis) Hoeffding bound, we want the product to be greater than . For the lower bound on is approximately 2, while for the bound is approximately 17, an increase of less than a factor of 9. To be sure, such an increase in might not be feasible for many learning problems. But for those problems where something like this increase is feasible, we may be able to say something stronger than Hoeffding alone says about the outcome of learning.
Regarding the second observation, randomized algorithms are procedures for solving problems much as regular (deterministic) algorithms are. However, any given run of a randomized algorithm makes random choices and has a small chance that these random choices will cause it to produce an incorrect answer. Probably the best-known randomized algorithm, and one of the earliest to be discovered, is the Miller-Rabin primality testing algorithm, which has been widely used in browsers in support of secure communication. If this algorithm is used as part of secure communication of, say, credit card information, and if the algorithm incorrectly certifies that a number is prime, then the result could be insecure communication of that credit card information. So, since Miller-Rabin has a small chance of error, why would browser manufacturers take a chance with my credit card information by using this potentially faulty algorithm? Because, in practice, the probability of randomization error can be driven so small that it is in effect more likely that the hardware running the algorithm will incorrectly execute the algorithm and thereby produce an erroneous output than it is that the randomization of the algorithm will lead to an erroneous output. Thus, since it is generally considered reasonable to ignore the small--but nonzero--possibility of hardware errors producing incorrect outputs, it should similarly be considered reasonable to ignore the unlikely possibility of sufficiently small randomization error producing incorrect outputs.
What does this discussion of randomized algorithms have to do with learning? A learning algorithm can in some sense be viewed as a form of randomized algorithm in which the randomization comes from a presumed random choice of the training data rather than from any random choices made by the algorithm itself. Hoeffding bounds the probability that the algorithm will be misled by its random input and therefore produce an erroneous output, that is, will output a hypothesis with a claim that it approximates the target when in fact the hypothesis is far from the target. Thus, given that it is reasonable to accept the results of randomized algorithms run with sufficiently low probability of error, it would seem to also be reasonable to accept the results of running a learning algorithm with sufficiently low Hoeffding probability bound (and given the standard assumption that the training data is drawn at random). That is, it would seem that if for a given learning problem we have such that is sufficiently small, and if the learning algorithm run on this problem claims that its hypothesis is a good approximation to the target, then we should accept this claim.
However, it should be noted that this position has proved to be controversial, as ultimately it runs counter to the widely-held belief that Bayesian decision theory is the preferred way to make rational decisions. In particular, see Section 5.6 of David Wolpert's paper The Lack of A Priori Distinctions Between Learning Algorithms (Neural Computation 8, pp. 1341-90, 1996), which tacitly assumes that the Bayesian view is the only reasonable view in the learning setting and then, based on this assumption, shows that an argument such as the one above fails to establish the feasibility of learning.
So, in the end, to accept the defense of learning outlined above is to accept that Bayesian decision theory is not (always) the preferred approach to rational decision making, despite the apparently strong theoretical foundations for Bayesian theory, its success in many practical applications, and its widespread acceptance. I believe that I can, in fact, show that there is a better theory that encompasses both traditional Bayesian decision theory and the defense of learning presented above. But that discussion won't fit in the margins of this post ;-) So, for now, I leave it to the reader to decide which he or she prefers: the argument above which implies that learning free of target assumptions can be feasible for problems with sufficiently large , or strict adherence to Bayesian decision theory which implies that target-assumption-free learning is impossible. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9119793772697449, "perplexity": 353.05074803872327}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359497.20/warc/CC-MAIN-20210227204637-20210227234637-00430.warc.gz"} |
http://mathhelpforum.com/algebra/190736-logarithmic-equations.html | # Math Help - Logarithmic equations
1. ## Logarithmic equations
Having some troubles figuring out these two logarithmic equations
First is 4^m+2=32
And the second is
6^2-r=50
Thanks in advance would love to know how to solve
2. ## Re: Logarithmic equations
Originally Posted by DjNito
Having some troubles figuring out these two logarithmic equations
First is 4^m+2=32
And the second is
6^2-r=50
Thanks in advance would love to know how to solve
I suppose you mean ...
$4^{m+2} = 32$
you can solve this equation w/o logs ... note that $4 = 2^2$ and $32 = 2^5$
$6^{2-r} = 50$
$\log(6^{2-r}) = \log(50)$
use the power property of logarithms and finish it ...
3. ## Re: Logarithmic equations
Thank you for this help!! really help man | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9026036858558655, "perplexity": 4496.4674074706745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999678977/warc/CC-MAIN-20140305060758-00035-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://asmedigitalcollection.asme.org/dynamicsystems/article-abstract/94/4/315/400879/Direct-and-Inverse-Transformations-Between-Phase?redirectedFrom=fulltext | A complete, general treatment of the transformations, direct and inverse, between the phase variable form and the canonical or Jordan canonical form of the system matrix is presented. Analytical expressions are obtained for the matrices and all combinations of real, complex, distinct, and repeated eigenvalues are covered.
This content is only available via PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8310700058937073, "perplexity": 497.80064704630286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986702077.71/warc/CC-MAIN-20191020024805-20191020052305-00476.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=84325 | ## deltaG and deltaS(sys) at zero
$\Delta G^{\circ}= \Delta H^{\circ} - T \Delta S^{\circ}$
$\Delta G^{\circ}= -RT\ln K$
$\Delta G^{\circ}= \sum \Delta G_{f}^{\circ}(products) - \sum \Delta G_{f}^{\circ}(reactants)$
Clement Ng
Posts: 73
Joined: Sat Jul 22, 2017 3:00 am
Been upvoted: 3 times
### deltaG and deltaS(sys) at zero
A sample of 1 mole of gas initially at 1 atm and 298 K is heated at constant pressure to 350 K, then the gas is compressed isothermally to its initial volume and is then cooled to 298 K at constant volume.
Why are deltaS(sys) and deltaG zero in this case? Which equations would you use to figure what factors are at zero?
ZoeHahn1J
Posts: 63
Joined: Sat Jul 22, 2017 3:01 am
Been upvoted: 1 time
### Re: deltaG and deltaS(sys) at zero
delta S is zero because change in entropy is a state function, and the final and initial volumes are the same. delta G is zero when a reaction is at equilibrium. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8998151421546936, "perplexity": 1856.7610145514554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250606975.49/warc/CC-MAIN-20200122101729-20200122130729-00228.warc.gz"} |
https://piping-designer.com/index.php/properties/fluid-mechanics/183-avogadro-s-law | Written by Jerry Ratzlaff on . Posted in Fluid Dynamics
According to Avogadro's gas law, when temperature and pressure are held constant, the volume of a gas is proportional to the number of moles of gas present.
$$\large{ \frac {V_i} {n_i} = \frac { V_f } { n_f } }$$
### Where:
$$\large{n_i }$$ = initial number of moles
$$\large{n_f }$$ = final number of moles
$$\large{V_f }$$ = final volume
Tags: Equations for Gas | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9005102515220642, "perplexity": 1240.0838191044095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739211.34/warc/CC-MAIN-20200814100602-20200814130602-00350.warc.gz"} |
https://www.yutaka-kamegaya.com/2019/02/16/%E7%92%B0%E5%A2%83%E3%82%92%E5%A4%89%E3%81%88%E3%82%8B/ | ·
# 環境を変える
それは自分の気持ちや姿勢を改善するのである。
でも、自分は変わる事が出来る。
--------------------------------------------------------------------------------------------------------------------------------
Change the environment
If the environment given to you is painful, you will need to improve it.
What will be improved?
It improves one 's feelings and attitudes.
It is very difficult to change only the environment on our own.
The world is covered with various barriers, which is actually the case.
But I can change myself.
My feelings and attitude are the maximum actions that can be changed depending on myself.
Although it is paradoxical, it is because it changes with respect to the environment, and the environment actually changes comfortably.
The mind that I can forgive and my intention to change,
both humanly and physically,
In the end it will change to the environment. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9591072797775269, "perplexity": 1906.6380476240925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400213454.52/warc/CC-MAIN-20200924034208-20200924064208-00481.warc.gz"} |
http://math.stackexchange.com/users/52816/matem%c3%a1ticos-chibchas?tab=summary | Matemáticos Chibchas
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Mathematics 4,301 rep 1925 Science Fiction & Fantasy 284 rep 114 Anime & Manga 136 rep 15 Mathematica 118 rep 5 TeX - LaTeX 111 rep 3 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9383201599121094, "perplexity": 2224.721322474811}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246642037.57/warc/CC-MAIN-20150417045722-00312-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-and-graph-the-compound-inequality-3x-9-or-8x-8 | Algebra
Topics
# How do you solve and graph the compound inequality 3x < -9 or 8x > -8 ?
May 8, 2015
(1) 3x < -9 -> x < -3
(2) 8x > -8 -> x > -1
On a number line, plot the 2 points (-1) and (-3). These 2 points create a segment (-1, -3) and 2 rays.
Try the origin x = 0 on the right ray,. -> 0 > -1 . OK . Then O is located on the true ray. It means the right ray belongs to the solution set. By symmetry, the left ray also belongs to the solution set.
Finally, the solution set is the 2 open intervals (-infinity, -3) and (-1, +infinity)
##### Impact of this question
1676 views around the world
You can reuse this answer | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8851673007011414, "perplexity": 1804.904990305405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558015.52/warc/CC-MAIN-20220523101705-20220523131705-00164.warc.gz"} |
https://cris.bgu.ac.il/en/publications/falling-through-the-black-hole-horizon-3 | # Falling through the black hole horizon
Ram Brustein, A. J.M. Medved
Research output: Contribution to journalArticlepeer-review
4 Scopus citations
## Abstract
Abstract: We consider the fate of a small classical object, a “stick”, as it falls through the horizon of a large black hole (BH). Classically, the equivalence principle dictates that the stick is affected by small tidal forces, and Hawking’s quantum-mechanical model of BH evaporation makes essentially the same prediction. If, on the other hand, the BH horizon is surrounded by a “firewall”, the stick will be consumed as it falls through. We have recently extended Hawking’s model by taking into account the quantum fluctuations of the geometry and the classical back-reaction of the emitted particles. Here, we calculate the train exerted on the falling stick for our model. The strain depends on the near-horizon state of the Hawking pairs. We find that, after the Page time when the state of the pairs deviates significantly from maximal entanglement (as required by unitarity), the induced strain in our semiclassical model is still parametrically small. This is because the number of the disentangled pairs is parametrically smaller than the BH entropy. A firewall does, however, appear if the number of disentangled pairs near the horizon is of order of the BH entropy, as implicitly assumed in previous discussions in the literature.
Original language English 89 Journal of High Energy Physics 2015 6 https://doi.org/10.1007/JHEP06(2015)089 Published - 19 Jun 2015
## Keywords
• Black Holes
• Models of Quantum Gravity
## Fingerprint
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http://blog.geomblog.org/2015/01/ | ## Thursday, January 29, 2015
### More FOCS 2014-blogging
In the spirit of better late than never, some more updates from Amirali Abdullah from his sojourn at FOCS 2014. Previously, he had blogged about the higher-order Fourier analysis workshop at FOCS.
I'll discuss now the first official day of FOCS, with a quick digression into the food first: the reception was lovely, with some nice quality beverages, and delectable appetizers which I munched on to perhaps some slight excess. As for the lunches given to participants, I will think twice in future about selecting a kosher option under dietary restrictions. One hopes for a little better than a microwave instant meal at a catered lunch, with the clear plastic covering still awaiting being peeled off. In fairness to the organizers, once I decided to revert to the regular menu on the remaining days, the chicken and fish were perfectly tasty.
I will pick out a couple of the talks I was most interested in to summarize briefly. This is of course not necessarily a reflection of comparative quality or scientific value; just which talk titles caught my eye.
The first talk is "Discrepancy minimization for convex sets" by Thomas Rothvoss. The basic setup of a discrepany problem is this: consider a universe of $n$ elements, $[n]$ and a set system of $m$ sets ($m$ may also be infinite), $S = \{S_1, S_2, \ldots, S_m \}$, where $S_i \subset [n]$. Then we want to find a $2$-coloring $\chi : [n] \to \{-1, +1 \}$ such that each set is as evenly colored as possible. The discrepany then measures how unevenly colored some set $S_i \in S$ must be under the best possible coloring.
One fundamental result is that of Spencer, which shows there always exists a coloring of discrepancy $O(\sqrt{n})$. This shaves a logarithmic factor off of a simple random coloring, and the proof is non-constructive. This paper by Rothvoss gives the first algorithm that serves as a constructive proof of the theorem.
The first (well-known) step is that Spencer's theorem can be recast as a problem in convex geometry. Each set $S_i$ can be converted to a geometric constraint in $R^n$, namely define a region $x \in R^n : \{ \sum_{j \in S_i} | x_j | \leq 100 \sqrt{n} \}$. Now the intersection of these set of constraints define a polytope $K$, and iff $K$ contains a point of the hypercube $\{-1 , +1 \}^n$ then this corresponds to the valid low discrepancy coloring.
One can also of course do a partial coloring iteratively - if a constant fraction of the elements can be colored with low discrepancy, it suffices to repeat.
The algorithm is surprisingly simple and follows from the traditional idea of trying to solve a discrete problem from the relaxation. Take a point $y$ which is generated from the sphercial $n$-dimensional Gaussian with variance 1. Now find the point $x$ closest to $y$ that lies in the intersection of the constraint set $K$ with the continuous hypercube $[-1, +1]^n$. (For example, by using the polynomial time ellipsoid method.) It turns out some constant fraction of the coordinates of $x$ are actually tight(i.e, integer valued in $\{-1, +1 \}$) and so $x$ turns out to be a good partial coloring.
To prove this, the paper shows that with high probability all subsets of $[-1 +1]^n$ with very few tight coordinates are far from the starting point $y$. Whereas with high probability, the intersection of $K$ with some set having many tight coordinates is close to $y$. This boils down to showing the latter has sufficiently large Gaussian measure, and can be shown by standard tools in convex analysis and probabilitiy theory. Or to rephrase, the proof works by arguing about the isoperimetry of the concerned sets.
The other talk I'm going to mention from the first day is by Karl Bringmann on the hardness of computing the Frechet distance between two curves. The Frechet distance is a measure of curve similarity, and is often popularly described as follows: "if a man and a dog each walk along two curves, each with a designated start and finish point, what is the shortest length leash required?"
The problem is solvable in $O(n^2)$ time by simple dynamic programming, and has since been improved to $O(n^2 / \log n)$ by Agarwal, Avraham, Kaplan and Sharir. It has long been conjectured that there is no strongly subquadratic algorithm for the Frechet distance. (A strongly subquadratic algorithm being defined as $O(n^{2 -\delta})$ complexity for some constant $\delta$, as opposed to say $O(n^2 / polylog(n))$.)
The work by Bringmann shows this conjecture to be true, assuming SETH (the Strongly Exponential Time Hypothesis), or more precisely that there is no $O*((2- \delta)^N)$ algorithm for CNF-SAT. The hardness result holds for both the discrete and continuous versions of the Frechet distance, as well as for any $1.001$ approximation.
The proof works on a high level by directly reducing an instance of CNF-SAT to two curves where the Frechet distance is smaller than $1$ iff the instance is satisfiable. Logically, one can imagine the set of variables are split into two halves, and assigned to each curve. Each curve consists of a collection of "clause and assignment" gadgets, which encode whether all clauses are satisfied by a particular partial assignment. A different such gadget is created for each possible partial assignment, so that there are $O*(2^{N/2})$ vertices in each curve. (This is why solving Frechet distance by a subquadratic algorithm would imply a violation of SETH.)
There are many technical and geometric details required in the gadgets which I won't go into here. I will note admiringly that the proof is surprisingly elementary. No involved machinery or complexity result is needed in the clever construction of the main result; mostly just explicit computations of the pairwise distances between the vertices of the gadgets.
I will have one more blog post in a few days about another couple of results I thought were interesting, and then comment on the Knuth Prize lecture by the distinguished Dick Lipton.
## Tuesday, January 27, 2015
### Streaming @ SODA: Part II
This is the second of two posts by Samira Daruki on the streaming sessions at SODA 2015. For the first post, see here.
In the third paper from the streaming graph family in SODA15: "Parameterized Streaming: Maximal Matching and Vertex Cover", Chitnis, Cormode, Hajiaghayi and Monemizadeh introduce a new approach to handling graph streams called parameterized streaming algorithms. Also, in addition to insertion-only model, they consider the dynamic model of streaming graphs in which the input is a sequence of insertion/deletion on the edges.
This dynamic model of streaming graph processing is popular when the graph size is changing, and has recently received much attention due to breakthroughs by Ahn, Guha and McGregor (one, and two). Over these two papers, they showed the first results for a number of graph problems over dynamic streams. This has provoked much interest into what can be computed over dynamic graph streams, although still there is not much work on solving graph optimization problems in this model. The challenge here is that when an edge is deleted, sometimes it requires a substantial work to repair the solution again, so we need to make sure that the algorithm has enough information to do so, while keeping only a bounded amount of working space. (ed: not surprisingly, some of these ideas are useful for non-streaming dynamic graph algorithms: witness the paper by Kapron, King and Mountjoy on dynamic connectivity in (randomized) worst-case polylog time from SODA a few years ago)
Returning to parametrized streaming, in this paper instead of solving exactly the optimization problem on the graph stream, the goal is to solve the “parametrized” version of the problem, where the parameter $k$ is given and we want to solve the following decision problem:
Is there a solution with size bounded by $k$?
The motivation behind parametrizing the problem comes from real world applications in which the solution of the graph problems is small comparing to the size of the input (i.e. sublinear in the size of input). In these cases, the interesting challenge is to solve the optimization graph problems in streaming fashion using space bounded by some function of the “solution size” instead of the “input size”.
To solve the parameterized problems, one of the techniques which is used is kernelization, which uses a polynomial time preprocessing to map the input to another equivalent input of smaller size $f(k)$ (called a kernel) with a new parameter value $k’ \le g(k)$, for a computable function $g$.
In this paper, by combining kernelization techniques with randomized sketch structures, the first streaming algorithms for the parameterized versions of the Vertex Cover problem is obtained. The main idea here is to maintain a maximal matching of underlying graph in a streaming fashion. Then run the well-known kernelization algorithm for Vertex Cover on the maintained maximal matching. The data structure to maintain the maximal matching use the $k$-sample recovery sketching algorithm, which is a generalization of linear sketching for $\ell_0$-sampling, as the main tool and apply it to the neighborhood of each vertex (incident edges) in the resulted matching. So as the edges are inserted or deleted, these sketches can be updated without needing knowledge of the full neighborhood of nodes. However, there are some challenges with deletion of edges: as the edges are deleted we need to have an intelligent mechanism to ensure the matching remains maximal using only limited stored information.
Another nice result here is showing a tight lower bound of $\Omega(k^2)$ (by reducing from the INDEX problem in communication complexity) for the space complexity of any (randomized) streaming algorithms for parameterized Vertex Cover, which holds even in the insertion-only model.
Besides the general models of insert-only and dynamic, another restricted model in dynamic framework is also discussed in which we know for sure that at time $i$, the size of the vertex cover of underlying graph induced by the edges till that point is at most $k$. With this promise, they develop a dynamic parameterized streaming algorithm whose space usage matches the proved lower bound.
It is interesting to think about other NP-hard problems in the framework of parameterized streaming and explore how kernelization can be helpful in this direction or see whether we can find other powerful hammers to overcome the challenges which arises in designing algorithms for hard problems in streaming setting.
Coda:
Along with the three papers discussed above, there was another paper on streaming presented at SODA (by Naumovitz and Saks) which provides a deterministic polylogarithmic-space streaming algorithm for approximating distance to monotonicity for a sequence of $n$ numbers, compared to the corresponding randomized result presented at SODA two years ago.
While I won't discuss this work here so as to keep these posts just about streaming graph algorithms, I encourage the interested readers to take a look at this paper as well, as the last one in the streaming family of SODA15.
### Streaming @ SODA: Part I
This two part series is written by my student Samira Daruki
Modern graph data sets are too large to fit in the memory. And so the streaming model is one of the more popular and attractive ones for analyzing massive graphs: in this model, for an input graph $G = (V, E)$ with $n$ vertices and $m$ edges, the edges arrive in an arbitrary order in a stream and the algorithm can only use $\tilde{O}(n)$ space. The algorithm is allowed to have several passes over the stream but usually the ideal case is to have just one pass.
For many graph problems such as matching, spanning tree, graph sparsification, approximate distance and counting subgraphs there now exist streaming algorithms with space complexity $O(n \text{poly} (\log n))$. In these algorithms, usually we assume that the nodes of the graphs can be stored in memory but edges cannot. Notice that for constructing matchings, spanners and sparsifiers, the output size is often $\Omega(n)$, so it forces the streaming algorithm to use $\Omega(n)$ space.
But if you don't need to report the output, then this can be avoided. For an example, see the work of Kapralov, Khanna and Sudan from SODA 2014 which approximates the matching size to a $\text{poly}(\log n)$ factor using $\text{poly}(\log n)$ space in a random stream (where edges appear in a random order rather than arbitrarily)
Thus, the question now is:
can we obtain a $\text{poly}\log$ space streaming algorithm for approximating the solution cost for other graph problems?
Consider for instance MAX-CUT. There are several results on approximating the maximum cut in graphs in a non-streaming model; the trivial approach is to take a random cut. This selects half of the edges in expectation, resulting in a factor $1/2$-approximation.
Thus implies that in a streaming model we can just count the number of edges $m$ and output $\frac{m}{2}$ which results in a $O(\log n)$-space algorithm. By keeping a sample of the edge set we can get a different tradeoff: a $(1+\epsilon)$-approximation algorithm which uses $O(\frac{n}{\epsilon^2})$ space.
Can we get a streaming algorithm with better than factor-$2$ approximation using just $poly(\log n)$ space?
A paper by Kapralov, Khanna and Sudan in the streaming session of SODA15 this year answers this question. This is the latest in a line of results on streaming graph problems by Kapralov and others from SODA 2012, 2013 and 2014 (mentioned above)
Here is their main result
For any constant $\epsilon > 0$ a single pass streaming algorithm for approximating the value of MAX-CUT to a factor $2 − \epsilon$ requires $\Omega(\sqrt{n})$ space, even in the random order model.
This result rules out the possibility of $\text{poly}(\log n)$ space, but suggests that $\tilde{O}(\sqrt{n})$ space cost might be possible in some specific settings.
Another major result of this paper is as follows:
For any constant $\epsilon > 0$ a single pass streaming algorithm for approximating MAX-CUT value to factor $1 + \epsilon$ requires $n^{1−O(\epsilon)}$ space in adversarial streams.
The main fact they use here is the connection between the MAX CUT value and (distance from) bipartiteness:
if a graph $G$ with $m$ edges is $\beta$-far from being bipartite, then maxcut value of $G$ is at most $(1-\beta)m$.
The other simple observation is that any algorithm that computes a $\gamma$-approximation to MAX CUT distinguishes between bipartite graphs and graphs that are $1-\frac{1}{\gamma}$-far from being bipartite. Thus to show that no streaming algorithm using space $c$ can achieve a $\gamma$- approximation with failure probability at most $\delta$, it's enough enough to show no streaming algorithm using space $c$ can distinguish between bipartite graphs and graphs which are $1- \frac{1}{\gamma}$-far from being bipartite with probability at least $1- \delta$.
Given these facts, now the core idea to prove the main result here is exhibiting a distribution over inputs where $(2-\epsilon)$ approximation to MAX-CUT requires $\Omega(\sqrt{n})$ space.
More precisely, the input graph instances are based on random Erdos-Renyi graphs, which are either bipartite in YES case or non-bipartite in the NO case. In order to achieve a $(2-\epsilon)$-factor gap for the MAX CUT in this structure, we choose the expected degree of vertices to be $\Theta(\frac{1}{\epsilon^2})$.
This way, the input streaming graph can be partitioned and given to the algorithm in $\Omega(\frac{1}{\epsilon^2})$ phases, which can be simulated as a $\frac{1}{\epsilon^2}$-party one-way communication game.
Then, by giving a reduction from a variation of Boolean Hidden Matching(BHM) called Distributional Boolean Hidden Partition(D-BHP) to the MAX-CUT on the input instance of the problem, and showing that $\Omega(\sqrt{n})$ space is necessary to differentiate between these two cases, the main streaming lower bound result for obtaining approximate MAX-CUT is straightforward.
There are many technical details in performing this reduction, but roughly speaking they show that any algorithm that solves MAX-CUT on the constructed instances must solve the two-party communication problem in at least one of the phases.
There are still some main open problems left in this paper:
• One is whether breaking $2$-approximation barrier in $\sqrt{n}$ space is possible if we are allowed to have $poly(\log n)$ passes over the input stream?
• Also it is interesting to think about designing streaming algorithms for other graph problems using $o(n)$ space.
This brings us to another paper presented in this session. In Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond (by Esfandiari, Hajiaghayi, Liaghat, Monemizadeh and Onak), this latter question is answered about finding the maximum matching for planar graphs using $o(n)$ space.
Here is the main result:
If the underlying graph is planar, then there is a streaming algorithm which provides a $O(1)$-approximation solution to maximum matching with high probability using $O(n^{\frac{2}{3}})$ space.
The main idea for proving the result here is to use a known structural graph property:
If we characterize the nodes of the input graph based on the degrees to two groups of light (deg < 9) and heavy (deg > 9) vertices and then define the shallow edges as the ones with two light endpoints, then we have the following nice property: (Assuming |maximum matching| = m, |shallow edges| = s and | heavy vertices| = h):
$$\frac{\max (s, h)}{12} \leq m \leq h + s$$
Then using this structural fact as the main tool, constructing a small size matching (bounded by $c n^{\frac{2}{3}}$) as we read the edges in a greedy manner, and estimating the number of shallow edges and heavy vertices in the induced subgraph by a subset of sampled vertices with size $c n^{\frac{2}{3}}$, we can approximate the size of the maximum matching by a constant factor.
In addition to planar case, they show that similar results for approximating maximum matching in other graph structures such as $d$-degenerate graphs and forests are achievable.
Coming up: parametrized streaming and VERTEX COVER.
## Thursday, January 15, 2015
### Brief Review of the post-SODA workshop on algorithmic challenges in machine learning.
My student +John Moeller attended the workshop on algorithmic challenges in machine learning organized by +Shachar Lovett and +Kamalika Chaudhuri after SODA. He wrote up a brief report of some papers that he liked.
## Monday, January 12, 2015
### FOCS Workshop on higher-order Fourier analysis: A Review
This is a guest post by my student Amirali Abdullah. Amirali attended FOCS 2014 and has a number of interesting reflections on the conference.
2014 was my first experience of attending a FOCS conference, and finally seeing the faces* (attached to some of the cutting edge as well as classical results in theoretical computer science. Not only did I get to enjoy the gentle strolls between conference halls, and hearing about fields I'd never known existed, I had the pleasure of doing so while revisiting historic Philadelphia.
With the talk videos now available, I thought now would be a good time to revisit some of the talks and my thoughts on the event. The usual disclaimers apply - this will be by no means comprehensive, and I won't go into the technicalities in much depth.
I'll begin with the first day, where I chose to attend the workshop on Higher-Order Fourier analysis. The starting point is that for the study of a function $f$, it is standard to consider its correlations with the Fourier basis of exponential functions (i.e., of the form $e(x) = e^{2 \pi \iota x}$) (also called as linear phase functions). This basis is orthonormal and has many nice analytic properties.
A standard technique is to decompose a function $f$ into the heavy components of its Fourier basis, and then argue that the contribution of the lower weight components is negligible. This gives a decompositon $f= f_1+ f_2$, where $f_1$ has few non-zero Fourier coefficients, and $f_2$ has all Fourier coefficients close to 0. Another way to view this under certain perspectives is $f_1$ representing the structured part of $f$ and $f_2$ the pseudorandom part.
However for some applications, the analysis of correlation with quadratic (or even higher order) phase functions of the form $e(x) = e^{2 \pi \iota x^2}$ is more powerful and indeed required. (An example of such a problem is where given a function on the integers, one desires to study its behavior on arithmetic progressions of length four or more.)
A subtlety in the study of higher order Fourier analysis is that notions such as "tail" and "weight" now have to be redefined. For regular Fourier analysis (at least on the Hamming cube) the natural notion corresponds with the $\ell_2^2$ norm or the linear correlation of a function and a linear basis element. However, in higher order Fourier analysis one has to define norms known as the Gowers uniformity norms which capture higher order correlations with these higher degree functions. This yields a decomposition of $f = f_1 + f_2 + f_3$, where $f_1$ consists of few non-zero higher order phase functions, $f_2$ has small $\ell_2$ norm and $f_3$ has small \emph{Gower's norm} under the right notion.
There were several talks discussing the various subfields of higher order Fourier analysis. Madhur Tulsiani discussed some of the algorithmic questions, including computing such a decomposition of the function into higher order Fourier terms in an analog of the Goldreich-Levin algorithm. Yui Yoshida discussed applications to algebraic property testing.
Abhishek Bhowmick discussed his very interesting paper with Lovett showing that the list-decoding radius of the Reed-Muller code over finite prime fields equals (approximately) the minimum distance of the code. The application of Fourier order analysis here is essentially to decompose the input space of the code by high-degree polynomials so that any random distribution is well-spread over these partition atoms.
I thought the workshop was an interesting exposure to some deep mathematics I had not previously seen, and gave some good pointers to the literature/work I can consult if I ever want a richer understanding of the toolset in the field.
Note: Thanks to Terry Tao's book on the subject for some useful background and context. All mistakes in this post are entirely mine. For a much more comprehensive, mathematically correct and broad view on the subject, do check out his blog.
* One can of course claim that 'seeing faces' could also include the digital images on faculty and student websites snapped in haste or misleading poses, but I choose to ignore this subtlety.
### Privacy is dead, but not because Scott McNealy said so.
I decided to experiment with using Medium for a long-form not-quite technical post on the evolution of research in data privacy.
The idea of privacy has driven much of our concerns over data for the last few years, and has been the driver of extremely successful research efforts, most notably in differential privacy.What we’re seeing now though is a pivot away from the undifferentiated and problematic notion of privacy in data towards a more subtle and nuanced notion of how data is actually used, and how it should be used.
Here's the post: Medium allows this nifty way of commenting inline, so comment away there, or here. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8133829832077026, "perplexity": 557.8835561726578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00609.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-asymptotes-for-y-7x-2-x-2-3x-4 | Precalculus
Topics
# How do you find the asymptotes for y= (7x-2) /( x^2-3x-4)?
Jan 14, 2016
The asymptotes of any expression are found by defining what happens to the expression when $x \to \infty$ or $x \to - \infty$ or when $y \to \infty$
#### Explanation:
The asymptotes of any expression are found by defining what happens to the expression when $x \to \infty$ or $x \to - \infty$ or when $y \to \infty$
In this case $y = \frac{7 x + 2}{{x}^{2} - 3 x - 4}$ or $\frac{7 x - 2}{\left(x - 4\right) \left(x + 1\right)}$
Hence when $x \to 4$ or $x \to - 1$ then $y \to \infty$. Therefore there are vertical asymptotes at $x = 4$ and at $x = - 1$
${\lim}_{x \to \pm \infty} \frac{7 x - 2}{{x}^{2} - 3 x - 4} = {\lim}_{x \to \pm \infty} \frac{7}{x} = 0$
##### Impact of this question
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You can reuse this answer | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 14, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8521686792373657, "perplexity": 598.7058891740787}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999263.6/warc/CC-MAIN-20190620165805-20190620191805-00139.warc.gz"} |
https://www.zora.uzh.ch/id/eprint/69972/ | Abstract
The paper states that the subject of irrigation in Roman Hispania is often neglected in modern scholarship, and points out the problems and questions arising from this subject, such as the general importance of irrigation on the Iberian Peninsula, the role of the arabic conquest in it, and the interpretation of archaeological evidence. By providing a possible classification of irrigation systems, a case study of the Ebro valley and an overview of irrigation infrastructure in the remaining parts of the Iberian Peninsula, the authors draw preliminary conclusions on the relation of irrigation infrastructure and privileged Roman settlements and suggest that irrigation played a bigger role in the economy of Roman Hispania than generally assumed.
Abstract
The paper states that the subject of irrigation in Roman Hispania is often neglected in modern scholarship, and points out the problems and questions arising from this subject, such as the general importance of irrigation on the Iberian Peninsula, the role of the arabic conquest in it, and the interpretation of archaeological evidence. By providing a possible classification of irrigation systems, a case study of the Ebro valley and an overview of irrigation infrastructure in the remaining parts of the Iberian Peninsula, the authors draw preliminary conclusions on the relation of irrigation infrastructure and privileged Roman settlements and suggest that irrigation played a bigger role in the economy of Roman Hispania than generally assumed. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8072624206542969, "perplexity": 2230.5146159154533}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335124.77/warc/CC-MAIN-20220928051515-20220928081515-00205.warc.gz"} |
https://www.genealogy.math.ndsu.nodak.edu/id.php?id=48886 | ## Morton Raymond Dubman
Ph.D. University of California, Los Angeles 1970
Dissertation: Estimates of the Renewal Function When the Second Moment Is Infinite | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9189598560333252, "perplexity": 1964.3180198836185}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103639050.36/warc/CC-MAIN-20220629115352-20220629145352-00076.warc.gz"} |
https://www.tutorialspoint.com/converting_decimals_to_fractions/converting_decimal_to_mixed_number_and_an_improper_fraction_in_simplest_form_basic_online_quiz.htm | Converting a decimal to a mixed number and an improper fraction in simplest form: Basic Online Quiz
Following quiz provides Multiple Choice Questions (MCQs) related to Converting a decimal to a mixed number and an improper fraction in simplest form: Basic. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Explanation
Step 1:
The decimal 4.6 is read as 4 and 6 tenths. So, it is written as a mixed number $4\frac{6}{10}$
Step 2:
In simplest form $4\frac{29}{100} = 4\frac{3}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 4 × 5 + 3 = 23. This the numerator of the improper fraction and 5 is the denominator.
So, $4\frac{3}{5} = \frac{23}{5}$
Explanation
Step 1:
The decimal 5.8 is read as 5 and 8 tenths. So, it is written as a mixed number $5\frac{8}{10}$
Step 2:
In simplest form $5\frac{8}{10} = 5\frac{4}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 5 × 5 + 4 = 29. This the numerator of the improper fraction and 5 is the denominator.
So, $5\frac{4}{5} = \frac{29}{5}$
Explanation
Step 1:
The decimal 6.6 is read as 6 and 6 tenths. So, it is written as a mixed number $6\frac{6}{10}$
Step 2:
In simplest form $6\frac{6}{10} = 6\frac{6}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 6 × 5 + 3 = 33. This the numerator of the improper fraction and 5 is the denominator.
So, $6\frac{3}{5} = \frac{33}{5}$
Explanation
Step 1:
The decimal 7.2 is read as 7 and 2 tenths. So, it is written as a mixed number $7\frac{2}{10}$
Step 2:
In simplest form $7\frac{2}{10} = 7\frac{1}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 7 × 5 + 1 = 36. This the numerator of the improper fraction and 5 is the denominator.
So, $7\frac{1}{5} = \frac{36}{5}$
Explanation
Step 1:
The decimal 8.2 is read as 8 and 2 tenths. So, it is written as a mixed number $8\frac{2}{10}$
Step 2:
In simplest form $8\frac{2}{10} = 8\frac{1}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 8 × 5 + 1 = 41. This the numerator of the improper fraction and 5 is the denominator.
So, $8\frac{1}{5} = \frac{41}{5}$
Explanation
Step 1:
The decimal 9.6 is read as 9 and 6 tenths. So it is written as a mixed number $9\frac{6}{10}$
Step 2:
In simplest form $9\frac{6}{10} = 9\frac{3}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 9 × 5 + 3 = 48. This the numerator of the improper fraction and 5 is the denominator.
So, $9\frac{3}{5} = \frac{48}{5}$
Explanation
Step 1:
The decimal 10.2 is read as 10 and 2 tenths. So, it is written as a mixed number $10\frac{2}{10}$
Step 2:
In simplest form $10\frac{2}{10} = 10\frac{1}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 10 × 5 + 1 = 51. This the numerator of the improper fraction and 5 is the denominator.
So, $10\frac{1}{5} = \frac{51}{5}$
Explanation
Step 1:
The decimal 12.4 is read as 12 and 4 tenths. So, it is written as a mixed number $12\frac{4}{10}$
Step 2:
In simplest form $12\frac{4}{10} = 12\frac{2}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 12 × 5 + 2 = 62. This the numerator of the improper fraction and 5 is the denominator.
So, $12\frac{2}{5} = \frac{62}{5}$
Explanation
Step 1:
The decimal 15.8 is read as 15 and 8 tenths. So, it is written as a mixed number $15\frac{8}{10}$
Step 2:
In simplest form $15\frac{8}{10} = 15\frac{4}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 15 × 5 + 4 = 64. This the numerator of the improper fraction and 5 is the denominator.
So, $15\frac{4}{5} = \frac{64}{5}$
Explanation
Step 1:
The decimal 16.4 is read as 16 and 4 tenths. So, it is written as a mixed number $16\frac{4}{10}$
Step 2:
In simplest form $16\frac{4}{10} = 16\frac{2}{5}$
Step 3:
The same number is converted into an improper fraction as follows. 16 × 5 + 2 = 82. This the numerator of the improper fraction and 5 is the denominator.
So, $16\frac{2}{5} = \frac{82}{5}$
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http://en.wikipedia.org/wiki/Greisen%E2%80%93Zatsepin%E2%80%93Kuzmin_limit | # Greisen–Zatsepin–Kuzmin limit
The Greisen–Zatsepin–Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays (high energy charged particles from space) coming from "distant" sources. The limit is 5×1019 eV, or about 8 joules. The limit is set by slowing-interactions of cosmic ray protons with the microwave background radiation over long distances (~160 million light-years). The limit is at the same order of magnitude as the upper limit for energy at which cosmic rays have experimentally been detected. For example, one extreme-energy cosmic ray has been detected which appeared to possess a record 3.12×1020 eV (50 joules) of energy (about the same as the kinetic energy of a 60 mph baseball).
Cosmologists and theoretical physicists have regarded such observations as key in the search for explorations of physics in the energy realms which would require new theories of quantum gravity and other theories which predict events at the Planck scale. This is because protons at these extreme energies (3×1018 eV) are much closer to the Planck energy (about 1.22×1028 eV, or 2 billion joules) than any particles that can be made by current particle accelerators (2×1013 eV, or 3 millionths of a joule). They are thus suitable as a probe into realms where the theory of special relativity breaks down. Physicist Lee Smolin has written that if such cosmic rays which violate the GZK limit can be confirmed, and other possible explanations discounted, it "would be the most momentous discovery of the last hundred years—the first breakdown of the basic theories comprising the twentieth century's scientific revolution."[1]
## Computation of the GZK-limit
The limit was independently computed in 1966 by Kenneth Greisen,[2] Vadim Kuzmin, and Georgiy Zatsepin,[3] based on interactions between cosmic rays and the photons of the cosmic microwave background radiation (CMB). They predicted that cosmic rays with energies over the threshold energy of 5×1019 eV would interact with cosmic microwave background photons $\gamma_{\rm CMB}$, relatively blueshifted by the speed of the cosmic rays, to produce pions via the $\Delta$ resonance,
$\gamma_{\rm CMB}+p\rightarrow\Delta^+\rightarrow p + \pi^0,$
or
$\gamma_{\rm CMB}+p\rightarrow\Delta^+\rightarrow n + \pi^+.$
Pions produced in this manner proceed to decay in the standard pion channels—ultimately to photons for neutral pions, and photons, positrons, and various neutrinos for positive pions. Neutrons decay also to similar products, so that ultimately the energy of any cosmic ray proton is drained off by production of high energy photons plus (in some cases) high energy electron/positron pairs and neutrino pairs.
The pion production process begins at a higher energy than ordinary electron-positron pair production (lepton production) from protons impacting the CMB, which starts at cosmic ray proton energies of only about 1017eV. However, pion production events drain 20% of the energy of a cosmic ray proton as compared with only 0.1% of its energy for electron positron pair production. This factor of 200 is from two sources: the pion has only about ~130 times the mass of the leptons, but the extra energy appears as different kinetic energies of the pion or leptons, and results in relatively more kinetic energy transferred to a heavier product pion, in order to conserve momentum. The much larger total energy losses from pion production result in the pion production process becoming the limiting one to high energy cosmic ray travel, rather than the lower-energy light-lepton production process.
The pion production process continues until the cosmic ray energy falls below the pion production threshold. Due to the mean path associated with this interaction, extragalactic cosmic rays traveling over distances larger than 50 Mpc (163 Mly) and with energies greater than this threshold should never be observed on Earth. This distance is also known as GZK horizon.
Why is it that some cosmic rays appear to possess energies that are theoretically too high, given that there are no possible near-Earth sources, and that rays from distant sources should have scattered off the cosmic microwave background radiation?
A number of observations have been made by the AGASA experiment that appeared to show cosmic rays from distant sources with energies above this limit (called extreme-energy cosmic rays, or EECRs). The observed existence of these particles was the so-called GZK paradox or cosmic ray paradox.
These observations appear to contradict the predictions of special relativity and particle physics as they are presently understood. However, there are a number of possible explanations for these observations that may resolve this inconsistency.
• The observations could be due to an instrument error or an incorrect interpretation of the experiment, especially wrong energy assignment.
• The cosmic rays could have local sources well within the GZK horizon (although it is unclear what these sources could be).
• Heavier nuclei could possibly circumvent the GZK limit.
### Weakly interacting particles
Another suggestion involves ultra-high energy weakly interacting particles (for instance, neutrinos) which might be created at great distances and later react locally to give rise to the particles observed. In the proposed Z-burst model, an ultra-high energy cosmic neutrino collides with a relic anti-neutrino in our galaxy and annihilates to hadrons. This process proceeds via a (virtual) Z-boson:
$\nu + \bar{\nu}\rightarrow Z\rightarrow \text{hadrons}$
The cross section for this process becomes large if the center of mass energy of the neutrino antineutrino pair is equal to the Z-boson mass (such a peak in the cross section is called "resonance"). Assuming that the relic anti-neutrino is at rest, the energy of the incident cosmic neutrino has to be:
$E = \frac{m_{Z}^{2}}{2 m_{\nu}}= 4.2\times 10^{21} \left(\frac{\text{eV}}{m_{\nu}}\right)\text{eV}$
where $m_{Z}$ is the mass of the Z-boson and $m_{\nu}$ the mass of the neutrino.
### Proposed theories for particles above the GZK-cutoff
A number of exotic theories have been advanced to explain the AGASA observations, including doubly special relativity. However, it is now established that standard doubly special relativity does not predict any GZK suppression (or GZK cutoff), contrary to models of Lorentz symmetry violation involving an absolute rest frame.[4] Other possible theories involve a relation with dark matter, decays of exotic super-heavy particles beyond those known in the Standard Model.
## Conflicting evidence for GZK-cutoff
In July 2007, during the 30th International Cosmic Ray Conference in Mérida, Yucatán, México, the High Resolution Fly's Eye Experiment (HiRes) and the Auger International Collaboration presented their results on ultra-high-energy cosmic rays. HiRes has observed a suppression in the UHECR spectrum at just the right energy, observing only 13 events with an energy above the threshold, while expecting 43 with no suppression. This result has been published in the Physical Review Letters in 2008 and as such is the first observation of the GZK Suppression.[5] The Auger Observatory has confirmed this result:[6] instead of the 30 events necessary to confirm the AGASA results, Auger saw only two, which are believed to be heavy nuclei events. According to Alan Watson, spokesperson for the Auger Collaboration, AGASA results have been shown to be incorrect, possibly due to the systematical shift in energy assignment.
### Extreme Universe Space Observatory on Japanese Experiment Module (JEM-EUSO)
EUSO which was scheduled to fly on the International Space Station (ISS) in 2009, was designed to use the atmospheric-fluorescence technique to monitor a huge area and boost the statistics of UHECRs considerably. EUSO is to make a deep survey of UHECR-induced extensive air showers (EASs) from space, extending the measured energy spectrum well beyond the GZK-cutoff. It is to search for the origin of UHECRs, determine the nature of the origin of UHECRs, make an all-sky survey of the arrival direction of UHECRs, and seek to open the astronomical window on the extreme-energy universe with neutrinos. The fate of the EUSO Observatory is still unclear since NASA is considering early retirement of the ISS.
### The Fermi Gamma-ray Space Telescope to resolve inconsistencies
Launched in June 2008, the Fermi Gamma-ray Space Telescope (formerly GLAST) will also provide data that will help resolve these inconsistencies.
• With the Fermi Gamma-ray Space Telescope, one has the possibility of detecting gamma rays from the freshly accelerated cosmic-ray nuclei at their acceleration site (the source of the UHECRs).[7]
• UHECR protons accelerated in astrophysical objects produce secondary electromagnetic cascades during propagation in the cosmic microwave and infrared backgrounds, of which the GZK-process of pion production is one of the contributors. Such cascades can contribute between ≃1% and ≃50% of the GeV-TeV diffuse photon flux measured by the EGRET experiment. The Fermi Gamma-ray Space Telescope may discover this flux.[8]
## Possible sources of UHECRs
In November 2007, researchers at the Pierre Auger Observatory announced that they had evidence that UHECRs appear to come from the active galactic nuclei (AGNs) of energetic galaxies powered by matter swirling onto a supermassive black hole. The cosmic rays were detected and traced back to the AGNs using the Véron-Cetty-Véron catalog. These results are reported in the journal Science.[9] Nevertheless, the strength of the correlation with AGNs from this particular catalog for the Auger data recorded after 2007 has been slowly diminishing.[10]
## Pierre Auger Observatory and HiRes results on UHECRs above GZK-limit
According to the analysis made by the AUGER collaboration, the existence of the GZK cutoff may have been confirmed, but important uncertainties remain in the interpretation of the experimental results and further work is required.[11]
In 2010 final results of The High Resolution Fly's Eye (HiRes) experiment reconfirmed earlier results of the GZK cutoff from the HiRes experiment.[12] The results were previously brought into question when the AGASA experiment hinted at suppression of the GZK cutoff in their spectrum. The AUGER collaboration results agree with some parts of the HiRes final results on the GZK cutoff, but some discrepancies still remain.
## References
1. ^ Smolin, Lee. The Trouble With Physics Houghton Mifflin Harcourt. 2006, p. 222 (pbk) ISBN 978-0-618-55105-7. dewey= 530.14 22
2. ^ Greisen, Kenneth (1966). "End to the Cosmic-Ray Spectrum?". Physical Review Letters 16 (17): 748–750. Bibcode:1966PhRvL..16..748G. doi:10.1103/PhysRevLett.16.748.
3. ^ Zatsepin, G. T.; Kuz'min, V. A. (1966). "Upper Limit of the Spectrum of Cosmic Rays". Journal of Experimental and Theoretical Physics Letters 4: 78–80. Bibcode:1966JETPL...4...78Z.
4. ^ Luis González-Mestres (February 2009), AUGER-HiRes results and models of Lorentz symmetry violation, http://arxiv.org/abs/0902.0994 , Proceedings of CRIS (Cosmic Ray International Seminar), La Malfa, September 15–19, 2008, Nuclear Physics B - Proc. Suppl., Volume 190, May 2009, Pages 191-197, and references therein
5. ^ Abbasi, R. U.; et al. (2008). "First Observation of the Greisen-Zatsepin-Kuzmin Suppression". Physical Review Letters 100 (10): 101101. arXiv:astro-ph/0703099. Bibcode:2008PhRvL.100j1101A. doi:10.1103/PhysRevLett.100.101101. PMID 18352170.
6. ^ Abraham, J.; et al. (2008). "Observation of the suppression of the flux of cosmic rays above 4×1019 eV". Physical Review Letters 101 (6): 061101–1–061101–7. arXiv:0806.4302. Bibcode:2008PhRvL.101f1101A. doi:10.1103/PhysRevLett.101.061101.
7. ^ Ormes, Jonathan F.; et al. (2000). "The origin of cosmic rays: What can the Fermi Gamma-ray Telescope say?". AIP Conference Proceedings 528: 445–448. arXiv:astro-ph/0003270. doi:10.1063/1.1324357.
8. ^ Kalashev, Oleg E.; Semikoz, Dmitry V.; Sigl, Guenter (2007). "Ultra-High Energy Cosmic Rays and the GeV-TeV Diffuse Gamma-Ray Flux". ArΧiv e-prints. arXiv:0704.2463v1.
9. ^ The Pierre Auger Collaboration (2007). "Correlation of the Highest-Energy Cosmic Rays with Nearby Extragalactic Objects". Science 318 (5852): 938–943. arXiv:0711.2256. Bibcode:2007Sci...318..938T. doi:10.1126/science.1151124. PMID 17991855.
10. ^ The Pierre Auger Collaboration (2010). "Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter". Astropart. Phys. 34 (5): 314–326. arXiv:1009.1855. Bibcode:2010APh....34..314A. doi:10.1016/j.astropartphys.2010.08.010.
11. ^ The Pierre Auger Collaboration (2010). "Measurement of the energy spectrum of cosmic rays above 1018 eV using the Pierre Auger Observatory". Phys. Lett. B 685 (4–5): 239–246. arXiv:1002.1975. Bibcode:2010PhLB..685..239A. doi:10.1016/j.physletb.2010.02.013.
12. ^ Sokolsky; for the HiRes Collaboration (2010). "Final Results from the High Resolution Fly's Eye (HiRes) Experiment". arXiv:1010.2690 [astro-ph.HE]. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9301538467407227, "perplexity": 1849.5815670154689}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500815050.22/warc/CC-MAIN-20140820021335-00314-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/13/lesson/13.2.2/problem/13-77 | ### Home > PC3 > Chapter 13 > Lesson 13.2.2 > Problem13-77
13-77.
The Gladiator van travels $20t + 18$ miles per hour for $0\le t\le3$ hours.
1. Draw a graph of the situation. Label the axes carefully.
2. Compute the exact area under the curve.
Use the formula for the area of a trapezoid.
3. How far did the Gladiator travel during those three hours?
It is the area under the curve. | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9016214609146118, "perplexity": 2007.9293264258044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00268.warc.gz"} |
https://ir.lib.uwo.ca/etd/5137/ | #### Degree
Doctor of Philosophy
Computer Science
Prof. Lila Kari
#### Abstract
DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction.
Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language.
Moreover, we investigate the computational power of some variants of the Signal-passing Tile Assembly Model (STAM), as well as propose the concept of {\it Smart Tiles}, i.e., tiles with glues that can be activated or deactivated by signals, and which possess a limited amount of local computing capability. We demonstrate the potential of smart tiles to perform some robotic tasks such as replicating complex shapes.
COinS | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8865973353385925, "perplexity": 2453.0673530940603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215523.56/warc/CC-MAIN-20180820023141-20180820043141-00275.warc.gz"} |
http://nccr-swissmap.ch/research/publications/string-topology-and-configuration-spaces-two-points | # String topology and configuration spaces of two points
Thursday, 14 November, 2019
## Published in:
arXiv:1911.06202
Given a closed manifold M. We give an algebraic model for the Chas-Sullivan product and the Goresky-Hingston coproduct. In the simply-connected case, this admits a particularly nice description in terms of a Poincaré duality model of the manifold, and involves the configuration space of two points on M. We moreover, construct an IBL_\infty-structure on (a model of) cyclic chains on the cochain algebra of M, such that the natural comparison map to the S^1-equivariant loop space homology intertwines the Lie bialgebra structure on homology. The construction of the coproduct/cobracket depends on the perturbative partition function of a Chern-Simons type topological field theory. Furthermore, we give a construction for these string topology operations on the absolute loop space (not relative to constant loops) in case that M carries a non-vanishing vector field and obtain a similar description. Finally, we show that the cobracket is sensitive to the manifold structure of M beyond its homotopy type. More precisely, the action of {\rm Diff}(M) does not (in general) factor through {\rm aut}(M).
## Author(s):
Florian Naef
Thomas Willwacher | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9171804785728455, "perplexity": 614.1941336652849}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540518627.72/warc/CC-MAIN-20191209093227-20191209121227-00278.warc.gz"} |
http://tex.stackexchange.com/questions/129538/how-to-line-break-cites-correctly-hanging-over-problem | How to line-break cites correctly (hanging-over problem)?
while using Bibtex, I experienced an frustrating issue with line-breaks on cites in my block text.
I have chosen to use the following bibtex implementation:
``````\bibliographystyle{plain}
\bibliography{library}
``````
No voodoo here. Nevertheless, this leads to the following composition:
The cite is not line-broken correctly. I assume many other users have already experienced that hanging-over problem either.
Can someone help me how to fix that LaTeX is compiling the cite correctly in a way that it nicely integrates itself into block structure?
EDIT: Rephrasing makes it hard to monitor the whole 300 pages every time I recompile the document due to some minor modifications. I know that many use suggest to rephrase the text but I would like to ask for a more professional solution here.
-
Have you tried to rephrase the sentence including the cite? Adding or deleting a word can do it ... – Kurt Aug 22 '13 at 10:14
I thought about a more elegant way instead of making my sentence sounding not so nice anymore ;). Honestly, I think rephrasing makes it hard to monitor the whole 300 pages every time I recompile the document due to some minor modifications. – Robiston Aug 22 '13 at 10:17
I think we are talking about the last fine tuning of your document. I do this usually only one time, after I have finished writing my text with the final proofread of the document. With option `draft` you can find the hanging-over lines easily and rephrase them or insert (depends on the situation) a hyphenation mark. The algorithm of LaTeX is very good, but some times it needs the help of you. Until today a good typography needs the help of a person, the program allone can not manage it in the same way a learned typographer can ... – Kurt Aug 22 '13 at 11:12
plain style alone doesn't give such citations. Beside this what do you want latex to do to handle the problem? – Ulrike Fischer Aug 22 '13 at 11:12
You should load microtype and you can loosen the settings of latex regarding line breaking see tex.ac.uk/cgi-bin/texfaq2html?label=overfull. – Ulrike Fischer Aug 22 '13 at 11:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8558979630470276, "perplexity": 1529.4011591755523}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278389.62/warc/CC-MAIN-20160524002118-00236-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://www.yogakuhack.com/entry/saved_khalid | # 【洋楽歌詞和訳】Saved ／ Khalid （カリード）
Khalid （カリード）の Saved の英語歌詞と日本語和訳をご紹介します。 Khalid （カリード）の洋楽歌詞和訳一覧はこちら Amazon Musicでは、好きな洋楽アーティストが聴き放題。
### Saved の英語歌詞と和訳
1, 2, 3, 4
The hard part always seems to last forever
Sometimes I forget that we aren't together
Deep down in my heart, I hope you're doing alright
But from time to time I often think of why you aren't mine
ときどきどうして君が俺のものじゃないのか分からなくなる
But I'll keep your number saved
でも君の電話番号は消さないよ
Cause I hope one day you'll get the sense to call me
だってまた君が電話する気になるかもしれないだろ
I'm hoping that you'll say
You're missing me the way I'm missing you
So I'll keep your number saved
だから君の電話番号は消さない
Cause I hope one day I'll get the pride to call you
また君に電話できる日が来るかもしれないから
To tell you that no one else
Is gonna hold you down the way that I do
Now, I can't say I'll be alright without you
And I can't say that I haven't tried to
But, all your stuff is gone
I erased all the pictures from my phone
Of me and you
Here's what I'll do
これが俺のやり方なんだ
Cause I hope one day you'll get the sense to call me
だってまた君が電話する気になるかもしれないだろ
I'm hoping that you'll say
You're missing me the way I'm missing you
So I'll keep your number saved
だから君の電話番号は消さない
Cause I hope one day I'll get the pride to call you
また君に電話できる日が来るかもしれないから
To tell you that no one else
Is gonna hold you down the way that I do
I hope you think of all the times we shared
I hope you'll finally realize I was the only one who cared
It's crazy how this love thing seems unfair
この恋は不公平すぎる
You won't find a love like mine anywhere
But I'll keep your number saved
でも君の電話番号は消さないよ
Cause I hope one day you'll get the sense to call me
だってまた君が電話する気になるかもしれないだろ
I'm hoping that you'll say
You're missing me the way I'm missing you
So I'll keep your number saved
だから君の電話番号は消さない
Cause I hope one day I'll get the pride to call you
また君に電話できる日が来るかもしれないから
To tell you that no one else
Is gonna hold you down the way that I do
But I'll keep your number saved
でも君の電話番号は消さないよ
Cause I hope one day you'll get the sense to call me
だってまた君が電話する気になるかもしれないだろ
I'm hoping that you'll say
You're missing me the way I'm missing you
So I'll keep your number saved
だから君の電話番号は消さない
Cause I hope one day I'll get the pride to call you
また君に電話できる日が来るかもしれないから
To tell you that I'm finally over you
やっと君を忘れることができたって
I'm finally over you | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.829649806022644, "perplexity": 3952.523195083659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743353.54/warc/CC-MAIN-20181117102757-20181117124757-00241.warc.gz"} |
https://www.mathkplus.com/I-Math/Fractions/Multiplying-Fractions.aspx | ]]>
Math K-Plus
# How To Use Multiplying Fractions Calculator
## Solve Any Fraction Multiplication Problem And Show Step-By-Step Detail
Look below the calculator to see a real fraction multiply problem solved.
Please Read! Instructions to input proper fractions, improper fractions, whole numbers, and mixed numbers into the Calculator:
• Example to enter a fraction "1/3", and example to enter a whole number "3".
• Enter a whole number and a fraction - put a space between them: "3 1/3".
• Enter both fractions in the calculator you want to multiply plus your answer. Now press MULTIPLY button and compare your answer with the calculator.
• Or test example already typed in to the calculator. Just press the MULTIPLY button or enter a new problem and press the MULTIPLY button.
Multiplying Fractions Calculator
Name Multiply Value
Enter Fraction One. You can enter up to 10 digits/characters
Enter Fraction Two. You can enter up to 10 digits/characters
×
Your Answer. You can enter up to 12 digits/characters
## HERE IS AN EXAMPLE OF FRACTION MULTIPLICATION
$3 1/3 × 5 1/2 =$ Problem Statement. Convert mixed number 3 1/3 to improper fraction. $3 1/3 = (3 × 3) + 1 3 = 103$ Convert mixed number 5 1/2 to improper fraction. $5 1/2 = (5 × 2) + 1 2 = 112$ $103 × 112 =$ Solve this fraction problem. $103 × 112 =$ $10 × 113 × 2 =$ $1106 =$ $+1106 =$ $+553$ The fraction can be reduced by dividing the numerator and denominator by the Greatest Common Factor ... 2 Problem Answer. $(+18) + (1)3 =$ Group whole numbers and fractions. $(18) + (1)3 =$ $(18) + (1)3 =$ $18 13$ Problem Answer.
The calculator above has a number of valuable features:
• Math Practice The student can solve a fraction multiplication problem and compare their answer to the calculator. The calculator shows each step to solve the math problem entered. If the student has made a mistake, they can study the calculator results to understand where and avoid the mistake in the future. By using the tool for practicing, students can sharpen their skills. Use the New Problem button to create random problems to practice solving.
• Math Problem Solver The calculator is also a useful tool for a student to verify their homework is correct. Again an opportunity to learn from mistakes.
• Math Quizzes The student can at anytime take a five question test to validate the level of their current skills. Further these tests help prepare the student for classroom tests. The quickest test is the five question Test. It is recommended you see Help
Recommended reading: How To Multiply Fractions, Adding Fractions, Subtracting Fractions, and Dividing Fractions.
_ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9212977886199951, "perplexity": 1506.8281000255554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056974.30/warc/CC-MAIN-20210920010331-20210920040331-00081.warc.gz"} |
https://arxiv.org/abs/1401.5968 | astro-ph.IM
(what is this?)
# Title: Simulation study of the plasma brake effect
Abstract: The plasma brake is a thin negatively biased tether which has been proposed as an efficient concept for deorbiting satellites and debris objects from low Earth orbit. We simulate the interaction with the ionospheric plasma ram flow with the plasma brake tether by a high performance electrostatic particle in cell code to evaluate the thrust. The tether is assumed to be perpendicular to the flow. We perform runs for different tether voltage, magnetic field orientation and plasma ion mass. We show that a simple analytical thrust formula reproduces most of the simulation results well. The interaction with the tether and the plasma flow is laminar (i.e., smooth and not turbulent) when the magnetic field is perpendicular to the tether and the flow. If the magnetic field is parallel to the tether, the behaviour is unstable and thrust is reduced by a modest factor. The case when the magnetic field is aligned with the flow can also be unstable, but does not result in notable thrust reduction. We also fix an error in an earlier reference. According to the simulations, the predicted thrust of the plasma brake is large enough to make the method promising for low Earth orbit (LEO) satellite deorbiting. As a numerical example we estimate that a 5 km long plasma brake tether weighing 0.055 kg could produce 0.43 mN breaking force which is enough to reduce the orbital altitude of a 260 kg object mass by 100 km during one year.
Comments: 15 pages, 17 figures, 2 tables, in press in Annales Geophysicae Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Plasma Physics (physics.plasm-ph) DOI: 10.5194/angeo-32-1207-2014 Cite as: arXiv:1401.5968 [astro-ph.IM] (or arXiv:1401.5968v2 [astro-ph.IM] for this version)
## Submission history
From: Pekka Janhunen [view email]
[v1] Thu, 23 Jan 2014 13:37:14 GMT (11554kb,D)
[v2] Fri, 29 Aug 2014 06:47:57 GMT (2400kb,D) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8296805620193481, "perplexity": 1840.8525098737705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815934.81/warc/CC-MAIN-20180224191934-20180224211934-00670.warc.gz"} |
http://mathhelpforum.com/calculus/65365-inverse-x-sin-x.html | We can show the inverse exists by working with the fact that $( x + \sin x) ' > 0$ for $x\not = \pi n$ and $0$ for $x=\pi n$. Therefore, the function is increasing. But to since the inverse you need to be able to solve the equation $y + \sin (y) = x$. I do not think there is a "nice" way to solve this equation. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9898546934127808, "perplexity": 26.649376731700073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806310.85/warc/CC-MAIN-20171121021058-20171121041058-00466.warc.gz"} |
https://jmlr.org/papers/v6/goldsmith05a.html | ## New Horn Revision Algorithms
Judy Goldsmith, Robert H. Sloan; 6(64):1919−1938, 2005.
### Abstract
A revision algorithm is a learning algorithm that identifies the target concept, starting from an initial concept. Such an algorithm is considered efficient if its complexity (in terms of the measured resource) is polynomial in the syntactic distance between the initial and the target concept, but only polylogarithmic in the number of variables in the universe. We give efficient revision algorithms in the model of learning with equivalence and membership queries. The algorithms work in a general revision model where both deletion and addition revision operators are allowed. In this model one of the main open problems is the efficient revision of Horn formulas. Two revision algorithms are presented for special cases of this problem: for depth-1 acyclic Horn formulas, and for definite Horn formulas with unique heads.
[abs][pdf][bib] | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9475777745246887, "perplexity": 1186.9030560679698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949689.58/warc/CC-MAIN-20230331210803-20230401000803-00409.warc.gz"} |
https://www.scribd.com/document/64225489/Bayesian-Macro | # Bayesian Macroeconometrics
Marco Del Negro Federal Reserve Bank of New York Frank Schorfheide∗ University of Pennsylvania CEPR and NBER April 18, 2010
Prepared for Handbook of Bayesian Econometrics
Correspondence: Marco Del Negro: Research Department, Federal Reserve Bank of New York,
33 Liberty Street, New York NY 10045: [email protected]. Frank Schorfheide: Department of Economics, 3718 Locust Walk, University of Pennsylvania, Philadelphia, PA 19104-6297. Email: [email protected]. The views expressed in this chapter do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. Ed Herbst and Maxym Kryshko provided excellent research assistant. We are thankful for the feedback received from the editors of the Handbook John Geweke, Gary Koop, and Herman van Dijk as well as comments by Giorgio Primiceri, Dan Waggoner, and Tao Zha.
Del Negro, Schorfheide – Bayesian Macroeconometrics: April 18, 2010
2
Contents
1 Introduction 1.1 1.2 1.3 Challenges for Inference and Decision Making . . . . . . . . . . . . . How Can Bayesian Analysis Help? . . . . . . . . . . . . . . . . . . . Outline of this Chapter . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 4 7 8 10 14 16 29 29 30 32 35 38 39 41 44 49 51 52 54 61
2 Vector Autoregressions 2.1 2.2 2.3 2.4 2.5 A Reduced-Form VAR . . . . . . . . . . . . . . . . . . . . . . . . . . Dummy Observations and the Minnesota Prior . . . . . . . . . . . . A Second Reduced-Form VAR . . . . . . . . . . . . . . . . . . . . . . Structural VARs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further VAR Topics . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 VARs with Reduced-Rank Restrictions 3.1 3.2 3.3 Cointegration Restrictions . . . . . . . . . . . . . . . . . . . . . . . . Bayesian Inference with Gaussian Prior for β . . . . . . . . . . . . . Further Research on Bayesian Cointegration Models . . . . . . . . .
4 Dynamic Stochastic General Equilibrium Models 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 A Prototypical DSGE Model . . . . . . . . . . . . . . . . . . . . . . Model Solution and State-Space Form . . . . . . . . . . . . . . . . . Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extensions I: Indeterminacy . . . . . . . . . . . . . . . . . . . . . . . Extensions II: Stochastic Volatility . . . . . . . . . . . . . . . . . . . Extension III: General Nonlinear DSGE Models . . . . . . . . . . . . DSGE Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . DSGE Models in Applied Work . . . . . . . . . . . . . . . . . . . . .
Del Negro, Schorfheide – Bayesian Macroeconometrics: April 18, 2010 5 Time-Varying Parameters Models 5.1 5.2 5.3 Models with Autoregressive Coefficients . . . . . . . . . . . . . . . . Models with Markov-Switching Parameters . . . . . . . . . . . . . . Applications of Bayesian TVP Models . . . . . . . . . . . . . . . . .
0 62 63 68 73 74 75 78 90 91 95 99
6 Models for Data-Rich Environments 6.1 6.2 Restricted High-Dimensional VARs . . . . . . . . . . . . . . . . . . . Dynamic Factor Models . . . . . . . . . . . . . . . . . . . . . . . . .
7 Model Uncertainty 7.1 7.2 7.3 Posterior Model Probabilities and Model Selection . . . . . . . . . . Decision Making and Inference with Multiple Models . . . . . . . . . Difficulties in Decision-Making with Multiple Models . . . . . . . . .
obtained from theoretical considerations. Some questions require high-dimensional empirical models. Answers to some questions. such as what are the main driving forces of business cycles.1 Challenges for Inference and Decision Making Unfortunately. 2010 1 1 Introduction One of the goals of macroeconometric analysis is to provide quantitative answers to substantive macroeconomic questions. for instance. require at least a minimal set of restrictions. because of changes in economic policies. The study of international comovements is often based on highly parameterized multicountry vector autoregressive models. High-dimensional models are also necessary in applications in which it is reasonable to believe that parameters evolve over time. Other questions. Thus. For instance. Thus. such as whether gross domestic product (GDP) will decline over the next two quarters. can be obtained with univariate time-series models by simply exploiting serial correlations. Many macroeconomists have a strong preference for models with a high degree of theoretical coherence such as dynamic stochastic general equilibrium (DSGE) models. 1.Del Negro. For instance. that allow the identification of structural disturbances in a multivariate time-series model. In these models. macroeconometricians often face a shortage of observations necessary for providing precise answers. documenting the uncertainty associated with empirical findings or predictions is of first-order importance for scientific reporting. but they do demand identification restrictions that are not selfevident and that are highly contested in the empirical literature. macroeconometricians might be confronted with questions demanding a sophisticated theoretical model that is able to predict how agents adjust their behavior in response to new economic policies. the analysis of domestic business cycles might involve processing information from a large cross section of macroeconomic and financial variables. sample information alone is often insufficient to enable sharp inference about model parameters and implications. Schorfheide – Bayesian Macroeconometrics: April 18. an unambiguous measurement of the quantitative response of output and inflation to an unexpected reduction in the federal funds rate remains elusive. Finally. such as changes in monetary or fiscal policy. Other questions do not necessarily require a very densely parameterized empirical model. decision rules of economic agents are derived from assumptions .
In any sample of realistic size. In the context of time-varying coefficient models. rational expectations.2 How Can Bayesian Analysis Help? In Bayesian inference. and competitive equilibrium. to the extent that the prior is based on nonsample information. Thus. but a theoretically coherent model is required for the analysis of a particular economic policy. Thus. likelihood functions for empirical models with a strong degree of theoretical coherence tend to be more restrictive than likelihood functions associated with atheoretical models. This combination of information sets is prominently used in the context of DSGE model inference in Section 4. this means that the functional forms and parameters of equations that describe the behavior of economic agents are tightly restricted by optimality and equilibrium conditions. there will be a shortage of information for determining the model coefficients. Schorfheide – Bayesian Macroeconometrics: April 18. Examples include the vector autoregressions (VARs) with time-varying coefficients in Section 5 and the multicountry VARs considered in Section 6. a prior distribution is updated by sample information contained in the likelihood function to form a posterior distribution. it provides the ideal framework for combining different sources of information and thereby sharpening inference in macroeconometric analysis. but only gradually.Del Negro. Many macroeconometric models are richly parameterized. or that they change frequently. These sources might include microeconometric panel studies that are informative about aggregate elasticities or long-run averages of macroeconomic variables that are not included in the likelihood function because the DSGE model under consideration is too stylized to be able to explain their cyclical fluctuations. Through informative prior distributions. leading to very imprecise inference and diffuse predictive distributions. 2010 2 about agents’ preferences and production technologies and some fundamental principles such as intertemporal optimization. A challenge arises if the data favor the atheoretical model and the atheoretical model generates more accurate forecasts. Bayesian DSGE model inference can draw from a wide range of data sources that are (at least approximately) independent of the sample information. but by a potentially large amount. Such assumptions can be conveniently imposed by treating the sequence of model parameters as a . In practice. it is often appealing to conduct inference under the assumption that either coefficient change only infrequently. 1.
which might be undesirable. the lack of identification poses no conceptual problem in a Bayesian framework. which enter the likelihood function. Schorfheide – Bayesian Macroeconometrics: April 18. Predictive distributions of future observations such as aggregate output. Unfortunately. and an orthogonal matrix Ω. as long as the joint prior distribution of reduced-form and nonidentifiable parameters is proper. 2010 3 stochastic process. Ω is not identifiable based on the sample information. inflation. variance. In this sense.Del Negro. To the extent that the substantive analysis requires a researcher to consider multiple theoretical and empirical frameworks. which does not enter the likelihood function. so is the joint posterior distribution. which is of course nothing but a prior distribution that can be updated with the likelihood function. namely as random variables. Identification issues also arise in the context of DSGE models. Since shocks and parameters are treated symmetrically in a Bayesian framework. one could of course set many coefficients equal to zero or impose the condition that the same coefficient interacts with multiple regressors. However. which can be easily incorporated through probability distributions for those coefficients that are “centered” at the desired restrictions but that have a small. the conditional distribution of Ω given the reduced-form parameters will not be updated. accounting for these two sources of uncertainty simultaneously is conceptually straightforward. An extreme version of lack of sample information arises in the context of structural VARs. An important and empirically successful example of such a prior is the Minnesota prior discussed in Section 2. which are studied in Section 2. To reduce the number of parameters in a high-dimensional VAR. yet nonzero. meaning that the total probability mass is one. In this case. Conceptually more appealing is the use of soft restrictions. it does pose a challenge: it becomes more important to document which aspects of the prior distribution are not updated by the likelihood function and to recognize the extreme sensitivity of those aspects to the specification of the prior distribution. such hard restrictions rule out the existence of certain spillover effects. Thus. These distributions need to account for uncertainty about realizations of structural shocks as well as uncertainty associated with parameter estimates. Bayesian analysis allows the researcher to assign probabilities to competing model specifications . and its conditional posterior is identical to the conditional prior. and interest rates are important for macroeconomic forecasts and policy decisions. Structural VARs can be parameterized in terms of reduced-form parameters. In general.
This idea is explored in more detail in Section 4. to center a prior distribution on a more flexible reference model. While many macroeconomic time series are well described by stochastic trend . distinguishing between reduced-form and structural VARs. With posterior model probabilities in hand. Bayesian methods offer a rich tool kit for linking structural econometric models to more densely parameterized reference models. For instance. The DSGE models discussed in Section 4 provide an example. Schorfheide – Bayesian Macroeconometrics: April 18. As an empirical illustration. 2010 4 and update these probabilities in view of the data. one could use the restrictions associated with the theoretically coherent DSGE model only loosely.3 Outline of this Chapter Throughout this chapter. we devote the remainder of Section 2 is devoted to a discussion of advanced topics such as inference in restricted or overidentified VARs. Reduced-form VARs essentially summarize autocovariance properties of vector time series and can also be used to generate multivariate forecasts. changes in monetary policy unanticipated by the public. Nonetheless. in practice posterior model probabilities often favor more flexible. we will emphasize multivariate models that can capture comovements of macroeconomic time series. 1.Del Negro. More useful for substantive empirical work in macroeconomics are so-called structural VARs. Throughout this chapter. nonstructural time-series models such as VARs. inference and decisions can be based on model averages (section 7). Predictions of how economic agents would behave under counterfactual economic policies never previously observed require empirical models with a large degree of theoretical coherence. After discussing various identification schemes and their implementation. Section 3 is devoted to VARs with explicit restrictions on the long-run dynamics. we will encounter a large number of variants of VARs (sections 2 and 3) and DSGE models (section 4) that potentially differ in their economic implications. We will begin with a discussion of vector autoregressive models in Section 2. As mentioned earlier. that is. Much of the structural VAR literature has focused on studying the propagation of monetary policy shocks. in which the innovations do not correspond to one-step-ahead forecast errors but instead are interpreted as structural shocks. we measure the effects of an unanticipated change in monetary policy using a four-variable VAR.
Schorfheide – Bayesian Macroeconometrics: April 18. Eichenbaum. This observation is consistent with a widely used version of the neoclassical growth model (King. Plosser. output and investment data. and Rebelo (1988)). as pointed out by Sims and Uhlig (1991).S. written as so-called vector error correction models (VECM). One can impose such common trends in a VAR by restricting some of the eigenvalues of the characteristic polynomial to unity. uses them to regularize or smooth the likelihood function of a cointegration model in areas of the parameter space in which it is very nonelliptical. Modern dynamic macroeconomic theory implies fairly tight cross-equation restrictions for vector autoregressive processes.Del Negro. Plosser. instead of using priors as a tool to incorporate additional information. While frequentist analysis of nonstationary time-series models requires a different set of statistical tools. and in Section 4 we turn to Bayesian inference with DSGE models. Most of the controversies are related to the specification of prior distributions. in many countries the ratio (or log difference) of aggregate consumption and investment is stationary. The term DSGE model is typically used to refer to a broad class that spans the standard neoclassical growth model discussed in King. Moreover. and Evans (2005). However. these stochastic trends are often common to several time series. we also discuss an important strand of the literature that. agents potentially face uncertainty with respect to total factor productivity. Nonetheless. the DSGE model generates a joint probability distribution for the endogenous model variables such . given the specification of preferences and technology. for instance. VARs with eigenvalue restrictions. For example. the shape of the likelihood function is largely unaffected by the presence of unit roots in autoregressive models. or the nominal interest rate set by a central bank. This uncertainty is generated by exogenous stochastic processes or shocks that shift technology or generate unanticipated deviations from a central bank’s interest-rate feedback rule. Conditional on the specified distribution of the exogenous shocks. the Bayesian literature has experienced a lively debate about how to best analyze VECMs. 2010 5 models. A common feature of these models is that the solution of intertemporal optimization problems determines the decision rules. and Rebelo (1988) as well as the monetary model with numerous real and nominal frictions developed by Christiano. in which the exogenous technology process follows a random walk. have been widely used in applied work after Engle and Granger (1987) popularized the concept of cointegration. We will focus on the use of informative priors in the context of an empirical model for U. Our prior is based on the balancedgrowth-path implications of a neoclassical growth model.
Schorfheide – Bayesian Macroeconometrics: April 18. we augment the VAR models of Section 2 and the DSGE models of Section 4 with time-varying parameters. output and hours worked data. consumption. one has to take into account that agents are aware that parameters are not constant over time and hence adjust their decision rules accordingly. We study empirical models for so-called data-rich environments in Section 6. As an illustration. We distinguish between models in which parameters evolve according to a potentially nonstationary autoregressive law of motion and models in which parameters evolve according to a finite-state Markov-switching (MS) process. investment. or they might be caused by the introduction of new economic policies or the formation of new institutions. These changes might be a reflection of inherent nonlinearities of the business cycle. which in the context of a DSGE model could be interpreted as the most important economic state variables. Section 4 discusses inference with linearized as well as nonlinear DSGE models and reviews various approaches for evaluating the empirical fit of DSGE models. such as the number of lags in a VAR. Parsimonious empirical models for large data sets can be obtained in several ways. an additional layer of complication arises. discussed in Section 5. the presence of timevariation in coefficients. the importance of certain types of propagation mechanisms in DSGE models. we will encounter uncertainty about model specifications. or the number of factors in a dynamic factor model. A . We consider restricted large-dimensional vector autoregressive models as well as dynamic factor models (DFMs).Del Negro. The dynamics of macroeconomic variables tend to change over time. These factors are typically unobserved and follow some vector autoregressive law of motion. When solving for the equilibrium law of motion. Because of the rapid advances in information technologies. macroeconomists now have access to and the ability to process data sets with a large cross-sectional as well as a large time-series dimension. Throughout the various sections of the chapter. Much of the empirical work with DSGE models employs Bayesian methods. and inflation. The key challenge for econometric modeling is to avoid a proliferation of parameters. Thus.S. The latter class of models assumes that the comovement between variables is due to a relatively small number of common factors. we conduct inference with a simple stochastic growth model based on U. If time-varying coefficients are introduced in a DSGE model. 2010 6 as output. Such changes can be captured by econometric models with time-varying parameters (TVP).
Sims (1980) proposed that VARs should replace large-scale macroeconometric models inherited from the 1960s.) ) to denote the j’th column (row) of a matrix A. more generally. we sometimes drop the time subscripts and abbreviate Y1:T by Y . VARs have been used for macroeconomic forecasting and policy analysis to investigate the sources of business-cycle fluctuations and to provide a benchmark against which modern dynamic macroeconomic theories can be evaluated. we say that (X. tr[A] is the trace of the square matrix A. If no ambiguity arises. we follow the Appendix of this Handbook. and vec(A) stacks the columns of A. in Section 4 it will become evident that the equilibrium law of motion of many dynamic stochastic equilibrium models can be well approximated by a VAR. we let A = tr[A A]. I{x ≥ a} is the indicator function equal to one if x ≥ a and equal to zero otherwise. Finally. With respect to notation for probability distributions. p(Y |θ) is the likelihood function. . We use Yt0 :t1 to denote the sequence of observations or random variables {yt0 . The remainder of this section is organized as follows. |A| is its determinant. p(θ) is the density associated with the prior distribution. ν). decision making under model uncertainty is provided in Section 7. . ν) has an Inverted Wishart distribution. We derive the likelihood function of a reduced-form VAR in Section 2. If X|Σ ∼ M Np×q (M. Σ) ∼ M N IW (M. If A is a vector.2 discusses how to use dummy observations to construct prior distributions and reviews the widely . Section 2. Since then. . We use iid to abbreviate independently and identically distributed. In fact. which were largely inconsistent with the notion that economic agents take the effect of today’s choices on tomorrow’s utility into account. VARs appear to be straightforward multivariate generalizations of univariate autoregressive models. Here ⊗ is the Kronecker product. 2 Vector Autoregressions At first glance. S. they turn out to be one of the key empirical tools in modern macroeconomics.Del Negro. At second sight.1. yt1 }. . Finally.j) (A(j. θ often serves as generic parameter vector. and p(θ|Y ) the posterior density. 2010 7 treatment of Bayesian model selection and. P. Moreover. Σ ⊗ P ) is matricvariate Normal and Σ ∼ IWq (S. We use A(. a word on notation. because the latter imposed incredible restrictions. √ then A = A A is its length. Schorfheide – Bayesian Macroeconometrics: April 18. We use I to denote the identity matrix and use a subscript indicating the dimension if necessary.
2010 8 used Minnesota prior. Insert Figure 1 Here 2. The evolution of yt is described by the p’th order difference equation: yt = Φ1 yt−1 + . Let yt be an n × 1 random vector that takes values in Rn . Φc ] . we consider a reduced-form VAR that is expressed in terms of deviations from a deterministic trend. In Section 2. over the period from 1964:Q1 to 2006:Q4: percentage deviations of real GDP from a linear time trend. designed to capture the joint dynamics of multiple time series. Figure 1 depicts the evolution of three important quarterly macroeconomic time series for the U. . (1) We refer to (1) as the reduced-form representation of a VAR(p).S. . The joint density of Y1:T . where n = 3 in our empirical illustration. .3. annualized inflation rates computed from the GDP deflator. yT . To characterize the conditional distribution of yt given its history. .Del Negro. We shall proceed under the assumption that the conditional distribution of yt is Normal: ut ∼ iidN (0. These series are obtained from the FRED database maintained by the Federal Reserve Bank of St. Louis.1 A Reduced-Form VAR Vector autoregressions are linear time-series models. because the ut ’s are simply one-step-ahead forecast errors and do not have a specific economic interpretation. . . conditional on Y1−p:0 and the coefficient matrices Φ and . Section 2. .4 is devoted to structural VARs in which innovations are expressed as functions of structural shocks with a particular economic interpretation. (2) We are now in a position to characterize the joint distribution of a sequence of observations y1 . We will subsequently illustrate the VAR analysis using the three series plotted in Figure 1. Finally. Let k = np + 1 and define the k × n matrix Φ = [Φ1 . Schorfheide – Bayesian Macroeconometrics: April 18. Section 2. + Φp yt−p + Φc + ut . Σ). . and the effective federal funds rate. one has to make a distributional assumption for ut . . an unanticipated change in monetary policy. Φp . for example.5 provides some suggestions for further reading. .
(7) (6) ˆ ˆ Φ is the maximum-likelihood estimator (MLE) of Φ. . Σ. the T × n matrices Y y1 . . . Draws from this posterior can be easily obtained by direct Monte Carlo sampling. . S. . and S is a matrix with sums of squared residuals. Σ): 1 ˆ p(Y |Φ. we abbreviate p(Y1:T |Φ. Σ) ∝ |Σ|−T /2 exp − tr[Σ−1 S] 2 1 ˆ ˆ × exp − tr[Σ−1 (Φ − Φ) X X(Φ − Φ)] . Σ. nsim : ˆ 1. Σ. . T − k) distribution. (3) The conditional likelihood function can be conveniently expressed if the VAR is written as a multivariate linear regression model in matrix notation: Y = XΦ + U. . . Σ)|Y ∼ M N IW Φ. . 1]. Σ) ∝ |Σ|−(n+1)/2 . ˆ ˆ ˆ S = (Y − X Φ) (Y − X Φ). It can be factorized as T p(Y1:T |Φ. . . xt = [yt−1 . Draw Σ(s) from an IW (S. . Y1−p:t−1 ). . If we combine the likelihood function with the improper prior p(Φ.1: Direct Monte Carlo Sampling from Posterior of VAR Parameters For s = 1. (X X)−1 . Y = . Y1−p:0 ) by p(Y |Φ. yt−p . is called (conditional) likelihood function when it is viewed as function of the parameters. . we can deduce immediately that the posterior distribution is of the form ˆ ˆ (Φ. T − k . xT uT (4) (5) In a slight abuse of notation. (8) Detailed derivations for the multivariate Gaussian linear regression model can be found in Zellner (1971). Y1−p:0 ) = t=1 p(yt |Φ. . .Del Negro. U = . X = . Here. 2 where ˆ Φ = (X X)−1 X Y. yT and U and the T × k matrix X are defined as x1 u1 . Algorithm 2. 2010 9 Σ. Schorfheide – Bayesian Macroeconometrics: April 18.
Suppose T ∗ dummy observations are collected in matrices Y ∗ and X ∗ . T − k). the sample size shrinks to 96 observations. and each equation of a VAR with p = 4 lags has 13 coefficients. and Sims (1984). which dates back to Litterman (1980) and Doan. inflation. Σ(s) ⊗ (X X)−1 ). In . X ] . S. Using the same arguments that lead to (8). T ∗ − k) prior for Φ and Σ. Notice that all three series are fairly persistent. Informative prior distributions can compensate for lack of sample information. Y ] . ¯ ¯ ¯ ¯ ¯ then we deduce that the posterior of (Φ. Provided that T ∗ > k+n ¯ and X ∗ X ∗ is invertible. or observations generated from introspection. This insight dates back at least to Theil and Goldberger (1961). in which yt is composed of output deviations. and we will subsequently discuss alternatives to the improper prior used so far. observations generated by simulating a macroeconomic model. and the Euro Area on post-1982 data. depicted in Figure 1. Σ) · |Σ|−(n+1)/2 can be interpreted as a M N IW (Φ. Consider our lead example. 10 An important challenge in practice is to cope with the dimensionality of the parameter matrix Φ. S. Litterman. Now imagine estimating a two-country VAR for the U. we deduce that up to a constant the product p(Y ∗ |Φ. after the disinflation under Fed Chairman Paul Volcker. Our exposition follows the more recent description in Sims and Zha (1998). Schorfheide – Bayesian Macroeconometrics: April 18. 2. with the exception that for now we focus on a reduced-form rather than on a structural VAR. and we use the likelihood function associated with the VAR to relate the dummy observations to the parameters Φ and Σ.2 Dummy Observations and the Minnesota Prior Prior distributions can be conveniently represented by dummy observations. If the sample is restricted to the post-1982 period. Consider the data depicted in Figure 1. Σ) is M N IW (Φ. 2010 ˆ 2. the use of dummy observations leads to a conjugate prior. and interest rates. These dummy observations might be actual observations from other countries. where Φ and S are obtained ˆ ˆ from Φ and S in (7) by replacing Y and X with Y ∗ and X ∗ . Thus. (X X)−1 . ¯ ¯ ¯ ¯ ˆ ˆ Y = [Y ∗ . Our sample consists of 172 observations.Del Negro. which doubles the number of parameters. (X ∗ X ∗ )−1 . and let Φ and S be the analogue of Φ and S in (7). Prior and likelihood are conjugate if the posterior belongs to the same distributional family as the prior distribution. Now let T = T + T ∗ . the prior distribution is proper. X = [X ∗ . Draw Φ(s) from the conditional distribution M N (Φ. A widely used prior in the VAR literature is the so-called Minnesota prior.S.
Schorfheide – Bayesian Macroeconometrics: April 18. Let Y−τ :0 be a presample. The dummy observations are interpreted as observations from the regression model (4). In turn. the rows of U are normally distributed. We begin with dummy observations that generate a prior distribution for Φ1 . The Minnesota prior is typically specified conditional on several hyperparameters. While it is fairly straightforward to choose prior means and variances for the elements of Φ.Del Negro. For instance. there are nk(nk + 1)/2 of them.t . The use of dummy observations provides a parsimonious way of introducing plausible correlations between parameters. To simplify the exposition. would be fairly well described by a random-walk model of the form yi. possibly with the exception of post-1982 inflation rates. 2010 11 fact. it tends to be difficult to elicit beliefs about the correlation between elements of the Φ matrix. Thus.t−1 + ηi. the dummy observations are plugged into (4): λ1 s1 0 0 λ1 s2 = λ1 s1 0 0 0 0 0 Φ+ u11 u12 u21 u22 . alternatively. We will pursue the latter route for the following reason. the univariate behavior of these series. For illustrative purposes. we will specify the rows of the matrices Y ∗ and X ∗ . through dummy observations. if some series have very little serial correlation because they have been transformed to induce stationarity – for example log output has been converted into output growth – then an iid approximation might be preferable. and let y and s be n × 1 vectors of means and standard deviations. 0 = λ1 s1 φ21 + u12 . we will discuss how DSGE model restrictions could be used to construct a prior. suppose that n = 2 and p = 2. The random-walk approximation is taken for convenience and could be replaced by other representations. After all. The remaining hyperparameters are stacked in the 5 × 1 vector λ with elements λi . The idea behind the Minnesota prior is to center the distribution of Φ at a value that implies a random-walk behavior for each of the components of yt . In Section 4. we can rewrite the first row of (9) as λ1 s1 = λ1 s1 φ11 + u11 .t = yi. At the same time. The Minnesota prior can be implemented either by directly specifying a distribution for Φ or. (9) λ1 s2 0 0 0 According to the distributional assumption in (2). setting all these correlations to zero potentially leads to a prior that assigns a lot of probability mass to parameter combinations that imply quite unreasonable dynamics for the endogenous variables yt .
A prior for the covariance matrix Σ. and they tend to improve VAR forecasting performance. Suppose we assume that φj ∼ N (0. The sums-of-coefficients dummy observations.1 The prior for Φ2 is implemented with the dummy observations 0 0 0 0 = 0 0 λ1 s1 2λ2 0 0 0 0 λ1 s2 2λ2 0 0 Φ + U. can be obtained by stacking the observations s1 0 λ3 times. which is consistent with the beliefs of many applied macroeconomists. 2010 and interpret it as φ11 ∼ N (1. λ2 ). They favor unit roots and cointegration.t /sj . If we define φj = φj sj and xj. The remaining sets of dummy observations provide a prior for the intercept Φc and will generate some a priori correlation between the coefficients. then the transformed parameters ˜ ˜ interact with regressors that have the same scale. The sj terms that appear in the definition of the dummy observations achieve j this scale adjustment. (13) Consider the regression yt = φ1 x1. .t +ut . the same value y i is likely to be a good forecast of yi. regardless of the value of other variables: λ4 y 1 0 0 λ4 y 2 = λ4 y 1 0 0 λ4 y 2 λ4 y 1 0 0 0 Φ + U. 1 1 φ21 ∼ N (0.t is sj . j of the matrix Φ. (12) 0 s2 = 0 0 0 0 0 0 0 0 0 0 Φ+U (11) λ4 y 2 0 The co-persistence dummy observations. (10) where the hyperparameter λ2 is used to scale the prior standard deviations for coefficients associated with yt−l according to l−λ2 .Del Negro. The hyperparameter λ1 controls the tightness of the prior. ut ∼ iidN (0.t . j of Σ. introduced in Doan. and suppose that the standard ˜ deviation of xj. λ2 /s2 ). Litterman. Σ22 /(λ2 s2 )). Schorfheide – Bayesian Macroeconometrics: April 18. 1). 1 1 12 φij denotes the element i. and Σij corresponds to element i. then φj ∼ N (0.t are at the level y i . Σ11 /(λ2 s2 )). yt tends to persist at that level: λ5 y 1 λ5 y 2 1 = λ 5 y 1 λ 5 y 2 λ5 y 1 λ5 y 2 λ 5 Φ + U. centered at a matrix that is diagonal with elements equal to the presample variance of yt .t = xj. proposed by Sims (1993) reflect the belief that when all lagged yt ’s are at the level y. and Sims (1984).t +φ2 x2. capture the view that when lagged values of a variable yi.
If the prior distribution is constructed based on T ∗ dummy observations. which is commonly done in hierarchical Bayes models. we let T = T ∗ + T . A potential drawback of the dummy-observation prior is that one is forced to treat all equations symmetrically when specifying a prior. Methods for relaxing this restriction and alternative approaches of implementing the Minnesota prior (as well as other VAR priors) are discussed in Kadiyala and Karlsson (1997). if the prior variance for the lagged inflation terms in the output equation is 10 times larger than the prior variance for the coefficients on lagged interest rate terms. then it also has to be 10 times larger in the inflation equation and the interest rate equation. an empirical Bayes approach of choosing λ based on the marginal likelihood function pλ (Y ) = p(Y |Φ. s. including the intercept. Schorfheide – Bayesian Macroeconometrics: April 18. Y = [Y ∗ . The hyper¯ parameters (¯. These two sets of dummy observations introduce correlations in prior beliefs about all coefficients. From a a practitioner’s view. If λ = 0. the more weight is placed on various components of the Minnesota prior vis-´-vis the likelihood function. S ∗ (S) is y ¯ ˆ ¯ ¯ obtained from S in (7) by replacing Y and X with Y ∗ and X ∗ (Y and X). Y ] . then an analytical expression for the marginal likelihood can be obtained by using the normalization constants for the MNIW distribution (see Zellner (1971)): pλ (Y ) = (2π) −nT /2 ¯ ¯ n ¯ T −k |X X|− 2 |S|− 2 |X ∗ X ∗ |− 2 |S ∗ | n ∗ −k −T 2 ¯ 2 2 ¯ n(T −k) 2 n(T ∗ −k) 2 n ¯ i=1 Γ[(T − k + 1 − i)/2] . Σ) (14) tends to work well for inference as well as for forecasting purposes. then all the dummy observations are zero. one could specify a prior distribution for λ and integrate out the hyperparameter. A more detailed discussion of selection versus averaging is provided in Section 7. The larger the elements of λ.Del Negro. and the VAR is estimated under an improper prior. VAR inference tends to be sensitive to the choice of hyperparameters. . Σ|λ)d(Φ. Instead of conditioning on the value of λ that maximizes the marginal likelihood function pλ (Y ). in a given equation. Σ)p(Φ. 2010 13 The strength of these beliefs is controlled by λ4 and λ5 . We will provide an empirical illustration of this hyperparameter selection approach in Section 2.4. n Γ[(T ∗ − k + 1 − i)/2] i=1 (15) ¯ ¯ ¯ As before. In other words. X ] . the prior covariance matrix for the coefficients in all equations has to be proportional to (X ∗ X ∗ )−1 . For instance. λ) enter through the dummy observations X ∗ and Y ∗ . and X = [X ∗ .
. 2010 14 2. Γ0 +Γ1 t. as long as the prior for Φ and Σ conditional on Γ is M N IW .Del Negro. Lj t Wt (Φ) = I− j=1 Φj . the posterior of I− j=1 Φj Lj (yt − Γ0 − Γ1 t) = ut . . Thus. let Y (Γ) be the T × n matrix with rows (yt − Γ0 − Γ1 t) and X(Γ) be the T × (pn) matrix with rows [(yt−1 − Γ0 − Γ1 (t − 1)) . studied. This alternative specification makes it straightforward to separate beliefs about the deterministic trend component from beliefs about the persistence of fluctuations around this trend. (16) Here Γ0 and Γ1 are n×1 vectors. . Y1−p:0 ) ∝ exp − 1 2 T (18) (zt (Φ) − Wt (Φ)Γ) Σ−1 (zt (Φ) − Wt (Φ)Γ) . Using this operator. yt = Φ1 yt−1 + . this unconditional mean also depends on the autoregressive coefficients Φ1 . Thus. . captures stochastic fluctuations around the deterministic trend. Γ. Γ. zt (Φ) = Wt (Φ)Γ + ut and the likelihood function can be rewritten as p(Y1:T |Φ. The first term. in Villani (2009): yt = Γ0 + Γ1 t + yt . . Φp . Moreover. I− j=1 Φj Lj t with the understanding that = t − j. Σ. Suppose we define Φ = [Φ1 . for instance. . Φp ] and Γ = [Γ1 . However. Σ)|Γ is of the M N IW form. one can use the following representation. Y1−p:0 ) 1 ∝ |Σ|−T /2 exp − tr Σ−1 (Y (Γ) − X(Γ)Φ) (Y (Γ) − X(Γ)Φ) 2 (Φ. . t=1 . whereas the second part. (yt−p − Γ0 − Γ1 (t − p)) ]. Let L denote the temporal lag operator such that Lj yt = yt−j . . These fluctuations could either be stationary or nonstationary. then the conditional likelihood function associated with (16) is p(Y1:T |Φ. ut ∼ iidN (0. . one can rewrite (16) as p (17) . Now define p p p zt (Φ) = I− j=1 Φj Lj yt . . the law of motion of yt . . . . Schorfheide – Bayesian Macroeconometrics: April 18. Alternatively. captures the deterministic trend of yt . Γ2 ] . + Φp yt−p + ut . . Σ). Σ.3 A Second Reduced-Form VAR The reduced-form VAR in (1) is specified with an intercept term that determines the unconditional mean of yt if the VAR is stationary.
2. 1). ut ∼ iidN (0. Schorfheide – Bayesian Macroeconometrics: April 18.2: Gibbs Sampling from Posterior of VAR Parameters For s = 1. If φ1 = 1. Conditional on φc . Σ(s) . 1). 1 − ξ] and φc ∼ N (φc . Σ(s) ) from the MNIW distribution of (Φ. Schotman and van Dijk (1991) make the case that the representation (20) is more appealing. . as the parameter is now capturing the drift in a unit-root process instead of determining the long-run mean of yt . 2010 15 Thus. λ2 ). and Kohn (This Volume) discuss evidence that in many instances the so-called centered parameterization of (20) can increase the efficiency of MCMC algorithms. it is assumed that ξ > 0 to impose stationarity. Y ). In empirical work researchers often treat parameters as independent and might combine (19) with a prior distribution that implies φ1 ∼ U [0. In turn. whereas the first allows only for fluctuations around a constant mean. this prior for φ1 and φc E[y has the following implication.2 Since the initial level of the latent process y0 is ˜ unobserved. which is an example of a so-called Markov chain Monte Carlo (MCMC) algorithm discussed in detail in Chib (This Volume): Algorithm 2. in practice it is advisable to specify a proper prior for γ0 in (20). characterized by (20). E[y 2 Giordani. . Thus. we consider the special case of two univariate AR(1) processes: yt = φ1 yt−1 + φc + ut . Draw Γ(s) from the Normal distribution of Γ|(Φ(s) . . ut ∼ iidN (0. γ0 in (20) is nonidentifiable if φ1 = 1. . the interpretation of φc in model (19) changes drastically. Since the expected value of I t ] = φc /(1 − φ1 ). the (conditional) posterior distribution of Γ is also Normal. The second process. if the goal of the empirical analysis is to determine the evidence in favor of the hypothesis that φ1 = 1. For the subsequent argument. yt = γ0 + γ1 t + yt . To illustrate the subtle difference between the VAR in (1) and the VAR in (16). nsim : 1.Del Negro. Posterior inference can then be implemented via Gibbs sampling. allows for stationary fluctuations around a linear time trend. it is straightforward to verify that as long as the prior distribution of Γ conditional on Φ and Σ is matricvariate Normal. the prior mean and variance of the population mean I t ] increases (in absolute value) as φ1 −→ 1 − ξ. . If |φ1 | < 1 both AR(1) processes are stationary. (19) (20) yt = φ1 yt−1 + ut . Y ). Pitt. Σ)|(Γ(s−1) . Draw (Φ(s) .
2010 16 this prior generates a fairly diffuse distribution of yt that might place little mass on values of yt that appear a priori plausible. We will consider two ways of adding economic content to the VAR specified in (1). Shocks to these equations can in turn be interpreted as monetary policy shocks or as innovations to aggregate supply and demand. With these dummy observations. the co-persistence dummy observations discussed in Section 2. and γ1 = 0 – avoids the problem of an overly diffuse data distribution. but the notion of an aggregate demand or supply function is obscure. money demand equation.4 Structural VARs Reduced-form VARs summarize the autocovariance properties of the data and provide a useful forecasting tool. More generally. these models are specified in terms of preferences of economic agents and production technologies. γ0 ∼ N (γ 0 . A second way of adding economic content to VARs exploits the close connection between VARs and modern dynamic stochastic general equilibrium models. researchers often assume that shocks to the aggregate supply and demand equations are independent of each other. aggregate supply equation. the implied prior distribution of the population mean of yt conditional on φ1 takes the form I t ]|φ1 ∼ N (y. The optimal solution of agents’ decision problems combined with an equilibrium concept leads to an autoregressive law of motion for . 1 − ξ]. As we will see in Section 4. Treating the parameters of Model (20) as independent – for example. φ1 ∼ U [0. one can turn (1) into a dynamic simultaneous equations model by premultiplying it with a matrix A0 .Del Negro. it is natural to assume that the monetary policy shocks are orthogonal to the other innovations. but they lack economic interpretability. a monetary policy rule might be well defined. for instance. at least the location reE[y mains centered at y regardless of φ1 . (λ5 (1 − φ1 ))−2 ). First. To the extent that the monetary policy rule captures the central bank’s systematic reaction to the state of the economy. In the context of a DSGE model. monetary policy rule. such that the equations could be interpreted as. In this case I t ] has a priori mean γ 0 and variance λ2 for E[y every value of φ1 . 2. For researchers who do prefer to work with Model (19) but are concerned about a priori implausible data distributions. While the scale of the distribution of E[y I t ] is still dependent on the autoregressive coefficient. λ2 ).2 are useful. and aggregate demand equation. Schorfheide – Bayesian Macroeconometrics: April 18.
To summarize. preferences. We now express the one-step-ahead forecast errors as a linear = Σtr Ω t . 2010 17 the endogenous model variables.4. Σ)p(Φ. Σ). The identification problem arises precisely from the absence of Ω in this likelihood function.4. Σ. One reason for this independence assumption is that many researchers view the purpose of DSGE models as that of generating the observed comovements between macroeconomic variables through well-specified economic propagation mechanisms. denoted by p(Y |Φ. Σtr refers to the unique lower-triangular Cholesky factor of Σ with nonnegative diagonal elements. Σ).1 Reduced-Form Innovations and Structural Shocks A straightforward calculation shows that we need to impose additional restrictions to identify a structural VAR. or fiscal policy. or policies. Schorfheide – Bayesian Macroeconometrics: April 18. one can think of a structural VAR either as a dynamic simultaneous equations model. preferences. 2. our structural VAR is parameterized in terms of the reduced-form parameters Φ and Σ (or its Cholesky factor Σtr ) and the orthogonal matrix Ω.4. monetary policy. Σ)p(Ω|Φ. Φ. Φ has to satisfy the restriction Σ = Φ Φ . (21) Here. . the likelihood function here is the same as the likelihood function of the reduced-form VAR in (6). rather than from correlated exogenous shocks. (22) Since the distribution of Y depends only on the covariance matrix Σ and not on its factorization Σtr ΩΩ Σtr . these kinds of dynamic macroeconomic theories suggest that the one-step-ahead forecast errors ut in (1) are functions of orthogonal fundamental innovations in technology. These shocks are typically assumed to be independent of each other. Thus. Thus.2. We adopt the latter view in Section 2.1 and consider the former interpretation in Section 2. The second equality ensures that the covariance matrix of ut is preserved. that is. in which the forecast errors are explicitly linked to such fundamental innovations. Economic fluctuations are generated by shocks to technology. Ω) = p(Y |Φ. The joint distribution of data and parameters is given by p(Y. and Ω is an n×n orthogonal matrix.Del Negro. in which each equation has a particular structural interpretation. or as an autoregressive model. Let combination of structural shocks ut = Φ t t be a vector of orthogonal structural shocks with unit variances.
Algorithm 2. (23) Thus. Φ. and Moon and Schorfheide (2009).Del Negro. . For the remainder of this subsection. 1 (25) . reduces to a point mass. Σ). for instance.3: Posterior Sampler for Structural VARs For s = 1. Integrating the joint density with respect to Ω yields p(Y. nsim : 1. it is assumed that the eigenvalues of Φ1 are all less than one in absolute value. Σ(s) ). Christiano. Σ)p(Φ. Ω|Y ) can in principle be obtained in two steps. the relationship between the forecast errors ut and the structural shocks surveys. given the reduced-form parameters. Most authors use dogmatic priors for Ω such that the conditional distribution of Ω. . Kadane (1974). Σ. Σ)p(Ω|Φ. Σ|Y ). Schorfheide – Bayesian Macroeconometrics: April 18. Σ) = p(Y |Φ. much of the literature on structural VARs reduces to arguments about the appropriate choice of p(Ω|Φ. . Σ)dΩ (24) The conditional distribution of the nonidentifiable parameter Ω does not get updated in view of the data. conditional on Ω. Φ. . the calculation of the posterior distribution of the reduced-form parameters is not affected by the presence of the nonidentifiable matrix Ω. Φ. Priors for Ω are typically referred to as identification schemes because. Not surprisingly. see. Eichenbaum. Σ). p = 1. Σ) = p(Ω|Φ. Draw Ω(s) from the conditional prior distribution p(Ω|Φ(s) . This eigenvalue restriction guarantees that the VAR can be written as infinite-order moving average (MA(∞)): ∞ t is uniquely determined. we consider a simple bivariate VAR(1) without intercept. Cochrane (1994). Σ(s) ) from the posterior p(Φ. p(Y. To present various identification schemes that have been employed in the literature. Σ) = p(Y. Σ)p(Ω|Φ. Φ. 2. The conditional posterior density of Ω can be calculated as follows: p(Ω|Y. Poirier (1998). Σ). and Evans (1999). that is. We can deduce immediately that draws from the joint posterior distribution p(Φ. 2010 18 We proceed by examining the effect of the identification problem on the calculation of posterior distributions. and Φc = 0. This is a well-known property of Bayesian inference in partially identified models. Draw (Φ(s) . and Stock and Watson (2001) provide detailed yt = j=0 Φj Σtr Ω t . we set n = 2.
In the stationary bivariate VAR(1). rotating the two vectors by 180 degrees simply changes the sign of the impulse responses to both shocks. each triplet (Φ(s) .Del Negro. Handling these nonlinear transformations of the VAR parameters in a Bayesian framework is straightforward. s = 1. 1 (i) (27) Thus. Σ(s) . Notice that Ω(ϕ) = −Ω(ϕ + π). . macroeconomists are often interested in so-called variance decompositions. Then we can define the contribution of the i’th structural shock to the variance of yt as ∞ Γ(i) yy = j=0 Φj Σtr ΩI (i) Ω Σtr (Φj ) .0 ](jj) /[Γyy. Switching from ξ = 1 to ξ = −1 changes . the (unconditional) covariance matrix is given by ∞ Γyy = j=0 Φj Σtr ΩΩ Σtr (Φj ) . 1}: Ω(ϕ. . In addition. 2010 We will refer to the sequence of partial derivatives ∂yt+j = Φj Σtr Ω. . The determinant of Ω equals ξ. . 19 (26) as the impulse-response function. nsim . A variance decomposition measures the fraction that each of the structural shocks contributes to the overall variance of a particular element of yt . it is straightforward to compute posterior moments and credible sets. Using (26) or (27). because one can simply postprocess the output of the posterior sampler (Algorithm 2. Schorfheide – Bayesian Macroeconometrics: April 18. π]. Thus. and the two vectors are orthogonal. can be converted into a draw from the posterior distribution of impulse responses or variance decompositions. the set of orthogonal matrices Ω can be conveniently characterized by an angle ϕ and a parameter ξ ∈ {−1.3). Based on these draws. i is equal to one and all other elements are equal to zero. 1 Let I i be the matrix for which element i.t explained by shock i is [Γyy. . Each column represents a vector of unit length in R2 . ξ) = cos ϕ −ξ sin ϕ sin ϕ ξ cos ϕ (28) where ϕ ∈ (−π. 1. . 1 ∂ t j = 0. For n = 2. .0 ](jj) . Ω(s) ). Variance decompositions based on h-step-ahead forecast error covariance matrices j h j j=0 Φ1 Σ(Φ ) can be constructed in the same manner. the fraction of the variance of yj.
and output growth: yt = [πt .2 (Long-Run Identification): Now suppose yt is composed of inflation. for instance.t in cases (i) and (ii). the desired long-run response is given by − Φ1 ) = (I [(I − Φ1 )−1 Σtr ](2. The long-run response of the loglevel of output to a monetary policy shock can be obtained from the infinite sum of growth-rate responses implies that j ∞ j=0 Φ1 ∞ ˜ j=0 ∂∆ ln yt+j /∂ R. This identification scheme has been used. We now use the following identification restriction: unanticipated changes in monetary policy shocks do not raise output in the long run.1) (ϕ. for instance. t z. after imposing the identi- fication and normalization restrictions.t ] .t . ξ). ∆ ln yt ] . we need to determine the ϕ and ξ . we ˜ maintain the assumption that business-cycle fluctuations are generated by monetary policy and technology shocks. by Nason and Cogley (1994) and Schorfheide (2000). For instance. A short-run identification scheme was used in the seminal work by Sims (1980). R. and the vector ˜ t consists of innovations to technology. considering responses to expansionary monetary policy and technology shocks. Rt ] and y =[ z. Rt . Such a restriction on Ω is typically referred to as a short-run identification scheme. but now reverse the ordering: t = [ R. Since by construction Σtr ≥ 0. output 11 increases in response to z. and (iv) ϕ = π and ξ = −1. 2010 20 the sign of the impulse responses to the second shock. That is.t . following an earlier literature.t ] . since Σtr ≥ 0.t . πt . Identification can be achieved by imposing restric- tions on the informational structure. Likewise. (ii) ϕ = 0 and ξ = −1. R. Σ) assigns probability one to the matrix Ω that is diagonal with elements 1 and -1. (iii) ϕ = π and ξ = 1. We will now consider three different identification schemes that restrict Ω conditional on Φ and Σ. yt = [˜t .j) (A(j. Example 2. Thus. (29) where A(. The former could be defined as shocks that lower interest rates upon impact. the prior p(Ω|Φ. Since the stationarity assumption −1 . z. As in the previous example. Schorfheide – Bayesian Macroeconometrics: April 18.) Ω(. It is common in the literature to normalize the direction of the impulse response by. To obtain the orthogonal matrix Ω.) ) is the j’th column (row) of a matrix A.t . interest rates fall in response 22 to a monetary policy shock in cases (ii) and (iii). yt . Example 2.t . Boivin and Giannoni (2006b) assume in a slightly richer setting that the private sector does not respond to monetary policy shocks contemporaneously. and that the federal funds rate.Del Negro.1 (Short-Run Identification): Suppose that yt is composed of output deviations from trend. This assumption can be formalized by considering the following choices of ϕ and ξ in (28): (i) ϕ = 0 and ξ = 1. and monetary policy.
and Uhlig (2005) propose to be more o agnostic in the choice of Ω. the sign will be different. Eichenbaum. and Vigfusson (2007) and Chari. similar to Example 2. ∆ ln yt ] and ˜ [ R. ξ) ≥ 0 and is referred to as a sign-restriction identification scheme.1) (ϕ. z. 2010 21 such that the expression in (29) equals zero. structural VARs identified with long-run schemes often lead to imprecise estimates of the impulse response function and to inference that is very sensitive to lag length choice and prefiltering of the observations. A long-run identification scheme was initially used by Blanchard and Quah (1989) to identify supply and demand disturbances in a bivariate VAR. By rotating the vector Ω(.t . Σ) in the two preceding examples were degenerate. ξ) are composed of orthonormal vectors. However. To implement this normalization. Canova and De Nicol´ (2002). where we used ϕ = 0 and ξ = −1 regardless of Φ and Σ. Schorfheide – Bayesian Macroeconometrics: April 18. Σ) remains a point mass. output rises. ξ) such that the long-run effect (29) of a monetary policy shock on output is zero. once the normalization has been imposed. and McGrattan (2008). ξ) by 180 degrees. this implies that Σtr Ω(. we ˜ ˜ can find a second angle ϕ such that the long-run response in (29) equals zero. We could use the same normalization as in Example 2. While the shapes of the response functions are the same for each of these pairs. that is. Example 2. it only changes the sign of the response to the second shock.1. This point dates back to Sims (1972) and a detailed discussion in the structural VAR context can be found in Leeper and Faust (1997). The priors for Ω|(Φ.3 (Sign-Restrictions): As before. the usefulness of long-run restrictions has been debated in the papers by Christiano. It will become clear subsequently that sign restrictions only partially identify impulse responses in the sense that they deliver (nonsingleton) sets. ξ) that is perpendicular to [(I − Φ1 )−1 Σtr ](2.1) (ϕ.1 by considering the effects of expansionary technology shocks (the level of output rises in the long run) and expansionary monetary policy shocks (interest rates fall in the short run). Unlike in Example 2.Del Negro. In addition. we can find four pairs (ϕ. Faust (1998).1. Since long-run effects of shocks in dynamic systems are intrinsically difficult to measure. here the choice depends on Φ and Σ. one has to choose one of the four (ϕ. Notice that ξ does not affect the first column of Ω. p(Ω|Φ. Formally.1) (ϕ. ξ) pairs. Kehoe.t ] t = . we can deduce 11 . we normalize the monetary policy shock to be expansionary. Thus. Since the columns of Ω(ϕ. Suppose we restrict only the direction of impulse responses by assuming that monetary policy shocks move inflation and output in the same direction upon impact. Suppose that (29) equals zero for ϕ. let yt = [πt . Since by construction Σtr ≥ 0.) . we need to find a unit length vector Ω(. More recently.
3. the error bands typically reported in the literature have to be interpreted point-wise. say a monetary policy shock. For each triplet (Φ. Σ). Ω). In an effort to account for the correlation between responses at different horizons. sign restrictions are imposed not . The parameter ξ can be determined conditional on Σ and ϕ by normalizing the technology shock to be expansionary. To implement Bayesian inference. suitable generalizations of (26) and (27) can be used to convert parameter draws into draws of impulse responses or variance decompositions. in which Ω(s) is calculated directly as function of (Φ(s) . which is a unit-length vector. they delimit the credible set for the response of a particular variable at a particular horizon to a particular shock. 2010 22 from (28) and the sign restriction on the inflation response that ϕ ∈ (−π/2. π/2] and a prior for ξ|(ϕ. In this case. restrict their attention to one particular shock and parameterize only one column of the matrix Ω. researchers are interested only in the response of an n-dimensional vector yt to one particular shock. For short. the inequality restriction for the output response can be used 22 to sharpen the lower bound: Σtr cos ϕ + Σ22 sin ϕ ≥ 0 21 implies ϕ ≥ ϕ(Σ) = arctan − Σ21 /Σ22 . a researcher now has to specify a prior distribution for ϕ|Σ with support on the interval [ϕ(Σ). standard deviations. Other authors. π/2]. With these draws in hand. Σ). In practice. researchers have often chosen a uniform distribution for ϕ|Σ as we will discuss in more detail below. medians. Bayesian inference in sign-restricted structural VARs is more complicated because one has to sample from the conditional distribution of p(Ω|Φ.Del Negro.1) . one can approximate features of marginal posterior distributions such as means. Σ(s) ). Some authors. that is. or credible sets.and long-run identification schemes. one can simply replace Ω in the previous expressions by its first column Ω(. construct responses for the full set of n shocks. it is straightforward to implement Bayesian inference. However. One can use a simplified version of Algorithm 2. like Uhlig (2005). In many applications. including the empirical illustration provided below. It is important to keep in mind that impulse-response functions are multidimensional objects. Σ. Sims and Zha (1999) propose a method for computing credible bands that relies on the first few principal components of the covariance matrix of the responses. Since Σtr ≥ 0 as well. Schorfheide – Bayesian Macroeconometrics: April 18. like Peersman (2005). Credible sets for impulse responses are typically plotted as error bands around mean or median responses. In practice.
this uniform distribution is obtained by letting ϕ ∼ U (−π. specifying a prior distribution for (the columns of) Ω can be viewed as placing probabilities on a Grassmann manifold. The sample used for posterior inference is restricted to the period from 1965:I to 2005:I. . We then remove a linear trend from log inverse velocity and scale the deviations from trend by 100. Louis. in case of Example 2. and λ5 = 1.1 and the marginal likelihood formula (15) which do not allow for equation-specific parameter restrictions. Detailed descriptions of algorithms for Bayesian inference in sign-restricted structural VARs for n > 2 can be found. restricting it to the interval [−ϕ(Σ). We consider 3 This deterministic trend could also be incorporated into the specification of the VAR. We use the dummy-observation version of the Minnesota prior described in Section 2. we add our measure of detrended per capita real GDP to obtain real money balances. Illustration 2. and Zha (2010). Any r columns of Ω can be interpreted as an orthonormal basis for an r-dimensional subspace of Rn .3. interest rates. Schorfheide – Bayesian Macroeconometrics: April 18. π] in (28) and. for instance. λ4 = 1.3 The deviations from the linear trend are scaled by 100 to convert them into percentages. A uniform distribution can be defined as the unique distribution that is invariant to transformations induced by orthonormal transformations of Rn (James (1954)). A similar problem arises when placing prior probabilities on cointegration spaces. scaled by 400 to obtain annualized percentage rates. λ3 = 1. We take the natural log of per capita output and extract a deterministic trend by OLS regression over the period 1959:I to 2006:IV.Del Negro. Finally. and we will provide a more extensive discussion in Section 3. and real money balances.n−r . Waggoner.3. in Uhlig (2005) and Rubio-Ram´ ırez. π/2]. Most authors use a conditional prior distribution of Ω|(Φ. We divide sweep-adjusted M2 money balances by quarterly nominal GDP to obtain inverse velocity. in this illustration we wanted (i) to only remove a deterministic trend from output and not from the other variables and (ii) to use Algorithm 2. However. Thus. The data are obtained from the FRED database of the Federal Reserve Bank of St. Our measure of nominal interest rates corresponds to the average federal funds rate (FEDFUNDS) within a quarter. inflation. 2010 23 just on impact but also over longer horizons j > 0.1: We consider a VAR(4) based on output.2 with the hyperparameters λ2 = 4. Per capita output is defined as real GDP (GDPC96) divided by the civilian noninstitutionalized population (CNP16OV). The set of these subspaces is called Grassmann manifold and denoted by Gr. For n = 2. Inflation is defined as the log difference of the GDP deflator (GDPDEF). Σ) that is uniform. Database identifiers are provided in parentheses.
2010 24 Table 1: Hyperparameter Choice for Minnesota Prior λ1 πi.00 0. According to the posterior mean estimates.20 -888.00 1. The subsequent analysis is conducted conditional on this hyperparameter setting.00 0. the second step of Algorithm 2. described at the beginning of Section 2. Schorfheide – Bayesian Macroeconometrics: April 18.18 0.20 -898. using the appropriate modification of S.4 percent. with a weight of approximately one on λ1 = 0. We assign equal prior probability to each of these values and use (15) to compute the marginal likelihoods pλ (Y ).1. Φ and X. Results are reported in Table 1.0 ln pλ (Y ) πi. a one-standard deviation shock raises interest rates by 40 basis points upon impact. In response. Proposal draws ˜ ˜ Ω are obtained by sampling Z ∼ N (0.50 0.32 0.35 0. Posterior means and credible sets for the impulse responses are plotted in Figure 2. The posterior mean of the output response is slightly positive. Σ). and real money balances fall by 0.20 -914.00 0. we focus on the first column of the orthogonal matrix Ω. indicating substantial uncertainty about the sign and magnitude of the real effect of unanticipated changes in monetary policy . I) and letting Ω = Z/ Z .3.2. This uniform distribution is truncated to enforce the sign restrictions given (Φ. we use the sign-restriction approach described in Example 2.71 1. we assume that a contractionary monetary policy shock raises the nominal interest rate upon impact and for one period after the impact.43 0. which controls the overall variance of the prior.20 -902.01 0.20 -868.3 is implemented with an acceptance sampler that rejects proposed draws of Ω for which the sign restrictions are not satisfied.00 five possible values for λ1 .10 0.00 2.1. In particular. We specify a prior for Ω(.00 0. but the 90% credible set ranges from -50 to about 60 basis points.1) that implies that the space spanned by this vector is uniformly distributed on the relevant Grassman manifold.T 0. During these two periods. Thus. the (annualized) inflation rate drops by 30 basis points. To identify the dynamic response to a monetary policy shock. Draws from the posterior distribution of the reduced-form parameters Φ and Σ ˆ ˆ can be generated with Algorithm 2. Since we are identifying only one shock.Del Negro. the shock also lowers inflation and real money balances. The posterior probabilites of the hyperparameter values are essentially degenerate.
define A = [A1 . . For instance. then we obtain tr A0 yt = A1 yt−1 + .t would Finally. Schorfheide – Bayesian Macroeconometrics: April 18. Ac ] such that (30) can be expressed as a multivariate regression of the form Y A0 = XA + E with likelihood function 1 p(Y |A0 . yt−p . Sims and Zha (1998) propose prior distributions that share the Kronecker structure of the likelihood function and hence lead to posterior distributions that can . . the posterior of A is matricvariate Normal. . correspond to unanticipated deviations from the expected policy.Del Negro. p. A detailed discussion of the Bayesian analysis of (30) is provided in Sims and Zha (1998). . .1) . conditional on A0 . tr tr tr j = 1. (30) Much of the empirical analysis in the Bayesian SVAR literature is based on this alternative parameterization (see. Moreover. 2010 under our fairly agnostic prior for the vector Ω(. xt . As in (5). 1. . Accordingly. . . Sims and Zha (1998)). 1] and Y and X be matrices with rows yt . . Ap . . one could impose identifying restrictions on A0 such that the first equation in (30) corresponds to the monetary policy rule of the central bank. we use E to denote the T × n matrix with rows t. Notice that. . Insert Figure 2 Here 2. for instance. A) ∝ |A0 |T exp − tr[(Y A0 − XA) (Y A0 − XA)] .2 An Alternative Structural VAR Parameterization 25 We introduced structural VARs by expressing the one-step-ahead forecast errors of a reduced-form VAR as a linear function of orthogonal structural shocks. . 2 (32) (31) The term |A0 |T is the determinant of the Jacobian associated with the transformation of E into Y . . the likelihood function is quadratic in A.4. meaning that under a suitable choice of prior. The advantage of (30) is that the coefficients have direct behaviorial interpretations. respectively. Aj = Ω Σ−1 Φj . Ap yt−p + Ac + t . let xt = [yt−1 . I). . and Ac = Ω Σ−1 Φc . t ∼ iidN (0. Suppose we now premultiply both sides of (1) by Ω Σ−1 and define A0 = Ω Σ−1 .
is provided next. λ−1 I ⊗ V (A0 ) . M2. that is. Each row in the table corresponds to a behavioral equation labeled on the left-hand side of the row. The first equation represents an information market. real GDP interpolated to monthly frequency (˜). without having to invert matrices of the dimension nk × nk.4: Suppose yt is composed of a price index for industrial commodities (PCOM). V (A0 ) = (X ∗ X ∗ )−1 . and the remaining three equations characterize the production sector of the economy. Specifically. for instance. An example of such restrictions. Schorfheide – Bayesian Macroeconometrics: April 18. where −1 (34) ¯ A(A0 ) = ¯ V (A0 ) = λV −1 (A0 ) + X X −1 λV −1 (A0 )A(A0 ) + X Y A0 .2.2: A(A0 ) = (X ∗ X ∗ )−1 X ∗ Y ∗ A0 . Example 2. y The exclusion restrictions on the matrix A0 used by Robertson and Tallman (2001) are summarized in Table 2. The matrices A(A0 ) and V (A0 ) can.Del Negro. be constructed from the dummy observations presented in Section 2. the second equation is the monetary policy rule. the federal funds rate (R). Combining the likelihood function (32) with the prior (33) leads to a posterior for A that is conditionally matricvariate Normal: ¯ ¯ A|A0 . based on a structural VAR analyzed by Robertson and Tallman (2001). Y ∼ M N A(A0 ). λV −1 (A0 ) + X X The specific form of the posterior for A0 depends on the form of the prior density p(A0 ). The entries in the table imply that the .4. The prior distribution typically includes normalization and identification restrictions. the consumer price index (CPI). and the unemployment rate (U). 2010 26 be evaluated with a high degree of numerical efficiency. I ⊗ V (A0 ) . the third equation describes money demand. it is convenient to factorize the joint prior density as p(A0 )p(A|A0 ) and to assume that the conditional prior distribution of A takes the form A|A0 ∼ M N A(A0 ). (33) where the matrix of means A(A0 ) and the covariance matrix V (A0 ) are potentially functions of A0 and λ is a hyperparameter that scales the prior covariance matrix.
ii < 0. n by −1. . whereas the matrix A0 has only 18 free elements. In practice. 2010 27 Table 2: Identification Restrictions for A0 Pcom Inform MP MD Prod Prod Prod X 0 0 0 0 0 M2 X X X 0 0 0 R X X X 0 0 0 Y X 0 X X X X CPI X 0 X 0 X X U X 0 0 0 0 X Notes: Each row in the table represents a behavioral equation labeled on the lefthand side of the row: information market (Inform). this normalization can be imposed by postprocessing the output of the posterior sampler: for all draws (A0 . Ac ) multiply the i’th row of each matrix by −1 if A0. . because the covariance matrix of the one-step-ahead forecast errors of a VAR with n = 6 has in principle 21 free elements.Del Negro. A1 . Waggoner and Zha (2003) developed an efficient MCMC algorithm to generate draws from a restricted A0 matrix. consumer price index (CPI). . Ap . federal funds rate (R). Schorfheide – Bayesian Macroeconometrics: April 18. . A 0 entry denotes a coefficient set to zero. with the restriction that A(A0 ) = M A0 for some matrix M and that V (A0 ) = V does not depend on A0 . only variables that enter contemporaneously into the monetary policy rule (MP) are the federal funds rate (R) and M2. assume that the prior for A|A0 takes the form (33). the system requires a further normalization. . and three equations that characterize the production sector of the economy (Prod). A common normalization scheme is to require that the diagonal elements of A0 all be nonnegative. monetary aggregate (M2). as is the case for our . This normalization works well if the posterior support of each diagonal element of A0 is well away from zero. money demand (MD). The column labels reflect the observables: commodity prices (Pcom). Otherwise. . Despite the fact that overidentifying restrictions were imposed. . this normalization may induce bimodality in distributions of other parameters. monetary policy rule (MP). and unemployment (U). without changing the distribution of the endogenous variables. real GDP (Y). One can multiply the coefficients for each equation i = 1. . For expositional purposes. The structural VAR here is overidentified.
. independently across i. . 2010 28 dummy-observation prior. bi−1 . . Choose w2 . . qi is the number of unrestricted elements of A0(. . . (36) ¯ where Si = Ui (S + Ω−1 )Ui and A0 can be recovered from the bi ’s. Un bn ]|T exp − bi Si bi . bn ): T p(bi |Y. b1 . . . j = i. . . . . wqi such that w1 . . . wqi form an orthonormal basis for Rqi and we can introduce the parameters β1 . . . β1 has a Gamma . . . j = i and define w1 = Vi Ui w/ Vi Ui w . wqi by construction falls in the space spanned by Uj bj . Under the assumption that bi ∼ N (bi . . . Schorfheide – Bayesian Macroeconometrics: April 18. and Ui is an n × qi matrix. let w be an n × 1 vector perpendicular to each vector Uj bj . bi+1 . . . . . Let Vi be a qi × qi matrix such that Vi Si Vi = I.i) = Ui bi where bi is a qi × 1 vector. we can verify that the conditional posterior of the βj ’s is given by p(β1 . . . its distribution is not Normal. . . . bn ) ∝ |[U1 b1 . (37) By the orthonormal property of the wj ’s. . bi+1 . . . .Del Negro. . . . bi−1 . . .i) . . all βj ’s are independent of each other. composed of orthonormal column vectors. bi−1 . Now consider the i conditional density of bi |(b1 . . . . βqi and reparameterize the vector bi as a linear combination of the wj ’s: qi bi = V i j=1 βj wj . . 2 j=1 The last line follows because w2 . . Moreover. bi+1 . . . . . Then the marginal likelihood function for A0 is of the form p(Y |A0 ) = 1 ¯ p(Y |A0 . . . we obtain p(b1 . . . . bn ) T (38) qi 2 βj j=1 qi T ∝ |[U1 b1 . . 2 (35) ¯ where S is a function of the data as well as M and V . . 2 Since bi also appears in the determinant. . βj Vi wj . b1 . Un bn ]|T exp − T 2 n bi S i bi i=1 . . . . . Ωi ). A)p(A|A0 )dA ∝ |A0 |T exp − tr[A0 SA0 ] . βqi |Y. . Characterizing the distribution of bi requires a few additional steps. Thus. . . Un bn ]| exp − 2 j=1 T qi 2 ∝ |β1 |T exp − βj . Waggoner and Zha (2003) write the restricted columns of A0 as A0(. . bn |Y ) ∝ |[U1 b1 .
. in Pelloni and Polasek (2003). The left panel of Figure 3 . . and investment exhibit clear trends and tend to be very persistent. . .Del Negro. (s) 2. define bi (s) 2. 3 VARs with Reduced-Rank Restrictions It is well documented that many economic time series such as aggregate output. Y ) from the matricvariate Normal distribution in (34).5 Further VAR Topics The literature on Bayesian analysis of VARs is by now extensive. bi−1 . n generate (s) (s) (s−1) (s−1) β1 . are normally distributed.4: Gibbs Sampler for Structural VARs For s = 1. . A complementary survey of Bayesian analysis of VARs including VARs with time-varying coefficients and factor-augmented VARs can be found in Koop and Korobilis (2010). We will discuss VAR models with stochastic volatility in Section 5. for instance. Waggoner. Our exposition was based on the assumption that the VAR innovations are homoskedastic. Draw A0 (s) conditional on (A(s−1) . possibly conditional on the future path of a subset of variables. Draws from the posterior of A0 can be obtained by Gibbs sampling. . . Algorithm 2. . Readers who are interested in using VARs for forecasting purposes can find algorithms to compute such predictions efficiently. Extensions to GARCHtype heteroskedasticity can be found. it has long been recognized that linear combinations of macroeconomic time series (potentially after a logarithmic transformation) appear to be stationary. bn according to (37). For i = 1. . . consumption. .i) = Ui bi . and βj . Y ) as follows. . 2 ≤ j ≤ qi . . . Examples are the so-called Great Ratios. such as the consumption-output or investment-output ratio (see Klein and Kosobud (1961)). 2010 29 distribution. βqi from (38) conditional on (b1 . Rubio-Ram´ ırez. Uhlig (1997) proposes a Bayesian approach to VARs with stochastic volatility. bi+1 . . . and our presentation is by no means exhaustive. nsim : 1. . At the same time. and let A0(. . and Zha (2010) provide conditions for the global identification of VARs of the form (30). in Waggoner and Zha (1999). . (s) (s) ). Draw A(s) conditional on (A0 . . Schorfheide – Bayesian Macroeconometrics: April 18.
1 Cointegration Restrictions Consider the reduced-form VAR specified in (1). (39) . . Schorfheide – Bayesian Macroeconometrics: April 18. Cointegration implies that the series have common stochastic trends that can be eliminated by taking suitable linear combinations. and the fluctuations look at first glance mean-reverting. we discuss Bayesian inference in cointegration systems under various types of prior distributions. For now. Subtracting yt−1 from both sides of the equality leads to ∆yt = (Φ1 − I)yt−1 + Φ2 yt−2 + . then yt is nonstationary. the dynamic behavior of a univariate autoregressive process φ(L)yt = ut . then these series are said to be cointegrated.Del Negro. which takes the form of a reduced-rank regression. crucially depends on the roots of the characteristic polynomial φ(z). Johansen (1991). where φ(L) = 1 − p p j=1 φj L and L is the lag operator. Unit-root processes are often called integrated of order one. we will show in Section 3. Such restricted VARs have become a useful and empirically successful tool in applied macroeconomics. The observation that particular linear combinations of nonstationary economic time series appear to be stationary has triggered a large literature on cointegration starting in the mid 1980’s. it exhibits no apparent trend. we will discuss how such cointegration relationships arise in a dynamic stochastic general equilibrium framework. 2010 30 depicts log nominal GDP and nominal aggregate investment for the United States over the period 1965-2006 (obtained from the FRED database of the Federal Reserve Bank of St. . This leads to the so-called vector error correction model.1 that one can impose cotrending restrictions in a VAR by restricting some of the eigenvalues of its characteristic polynomial to unity. + Φp yt−p + Φc + ut . and Phillips (1991). If the smallest root is unity and all other roots are outside the unit circle. In Section 4. Johansen (1988). Engle and Granger (1987).2. ut ∼ iidN (0. In Section 3. Louis) and the right panel shows the log of the investment-output ratio. 3. Σ). While the ratio is far from constant. I(1). Insert Figure 3 Here More formally. If a linear combination of univariate I(1) time series is stationary. because stationarity can be induced by taking first differences ∆yt = (1 − L)yt . for example. see.
2010 For j = 1. Thus. where α and β are n × r matrices of full column rank. for instance. Ψ(L)ut = ∞ Ψj ut−j is a stationary linear process. it is useful to define a matrix α⊥ and β⊥ of full column rank and dimension n × (n − r) such that α α⊥ = 0 and β β⊥ = 0. (42) p−1 j=1 Πj . yt has n − r common stochastic trends given by (α⊥ Γβ⊥ )−1 α⊥ t τ =1 (ut + Πc ). then (41) implies that yt can be expressed as (Granger’s Representation Theorem): t (41) yt = β⊥ (α⊥ Γβ⊥ ) Γ=I− and −1 α⊥ τ =1 (ut + Πc ) + Ψ(L)(ut + Πc ) + Pβ⊥ y0 . according to (41) the growth rates of output and investment should be modeled as functions of lagged growth rates as well as the log investment-output ratio.Del Negro. It follows immediately j=0 that the r linear combinations β yt are stationary. |Φ(1)| = 0 – then the matrix Π∗ is of reduced rank. Then we can rewrite (39) (40) Φj z j . . This reparameterization leads to the so-called vector error correction or vector equilibrium correction (VECM) representation: ∆yt = αβ yt−1 + Π1 ∆yt−1 + . Moreover. A detailed exposition can be found. + Πp−1 ∆yt−p+1 + Πc + ut . . studied by Engle and Granger (1987). Φ(z) is the characteristic polynomial of the VAR. we can reparameterize the matrix as Π∗ = αβ . Since in this example β⊥ is . . If no root of Φ(z) = 0 lies inside the unit circle and α⊥ β⊥ has full rank. . . – that is. . we ˜ can define α and β such that Π∗ = αAA−1 β = αβ . If yt is composed of log GDP and investment. If the rank of Π∗ equals r < n. . Schorfheide – Bayesian Macroeconometrics: April 18. The columns of β are called cointegration vectors. in the monograph by Johansen (1995). In addition to the matrices α ˜ ˜˜ and β. + Πp−1 ∆yt−p+1 + Πc + ut . −1] . Pβ⊥ is the matrix that projects onto the space spanned by β⊥ . It can be easily verified that the parameterization of Π∗ in terms of α and β is not unique: for any nonsingular r × r matrix A. a visual inspection of Figure 3 suggests that the cointegration vector β is close to [1. p−1 define Πj = − as ∆yt = Π∗ yt−1 + Π1 ∆yt−1 + . If the VAR has unit roots. A few remarks are in order. where Π∗ = −Φ(1) and Φ(z) = I − j=1 p p i=j+1 Φp 31 and Πc = Φc . .
Br×(n−r) ] . nsim : 1. β) is MNIW. . we will focus on inference for Π∗ = αβ conditional on Π and Σ for the remainder of this section (Step 2 of Algorithm 3. Throughout this subsection we normalize β = [Ir×r . . Σ)|(α. and ut . Σ)|(Y. We will examine various approaches to specifying a prior distribution for Π∗ and discuss Gibbs samplers to implement posterior inference. In this section. β) is also of the MNIW form and can easily be derived following the calculations in Section 2. ut ∼ iidN (0.2 Bayesian Inference with Gaussian Prior for β Define Π = [Π1 . To simplify the subsequent exposition. In particular. . Inspection of (41) suggests that conditional on α and β. Let ∆Y . Σ|Π∗ (s) (s−1) . Equation (42) highlights the fact that output and investment have a common stochastic trend. X. Draw Π∗ from the posterior p(Π∗ |Π(s) . Σ). the VECM reduces to a multivariate linear Gaussian regression model. Schorfheide – Bayesian Macroeconometrics: April 18. . To do so. . Geweke (1996) used such priors to study inference in the reduced-rank regression model. 2. α. Πc ] and let ut ∼ N (0. yt−1 . it is convenient to write the regression in matrix form. As before. Y ). if (Π. 2010 2 × 1 and the term (α⊥ Γβ⊥ )−1 α⊥ t τ =1 (ut + Πc ) 32 is scalar. A Gibbs sampler to generate draws from the posterior distribution of the VECM typically has the following structure: Algorithm 3. Y ). Π∗ = αβ . we study the simplified model ∆yt = Π∗ yt−1 + ut . we consider independent priors p(α) and p(β) that are either flat or Gaussian. and U denote the T × n matrices with rows ∆yt . Πp−1 . Σ(s) . Σ). Σ(s) ) from the posterior p(Π. respectively. The remainder of Section 3 focuses on the formal Bayesian analysis of the vector error correction model. In practice.Del Negro. A discussion of model selection and averaging approaches is deferred to Section 7.1). the researcher faces uncertainty about the number of cointegration relationships as well as the number of lags that should be included.1: Gibbs Sampler for VECM For s = 1. such that ∆Y = XΠ∗ + U . . (43) and treat Σ as known. . 3. then we can deduce immediately that the posterior (Π. Draw (Π(s) . .
β) ∝ p(α) exp 1 ˜ ˜ ˜ − tr[Σ−1 (αX Xα − 2αX ∆Y )] . β) ∝ |Σ|−T /2 exp 1 − tr[Σ−1 (∆Y − Xβα ) (∆Y − Xβα )] . In the context of our output-investment illustration. Then p(α|Y. If the prior has the same Kronecker structure as the likelihood function. For brevity. The following steps are designed to eliminate the α term. An informative prior for α could be constructed from beliefs about the speed at which the economy returns to its balanced-growth path in the absence of shocks. Partition X = [X1 . 2 (45) Thus. Schorfheide – Bayesian Macroeconometrics: April 18. as long as the prior of vec(α ) is Gaussian. 2010 33 The prior distribution for β is induced by a prior distribution for B. then the posterior is matricvariate Normal. We will discuss the consequences of this normalization later on. We will encounter a DSGE model with such a balanced-growth-path property in Section 4. We begin with the posterior of α. we will derive conditional posterior distributions for α and β based on the ˜ likelihood (44). we refer to this class of priors as balanced-growth-path priors. This normalization requires that the elements of yt be ordered such that each of these variables appears in at least one cointegration relationship. reflecting either presample evidence on the stability of the investment-output ratio or the belief in an economic theory that implies that industrialized economies evolve along a balanced-growth path along which consumption and output grow at the same rate. Post-multiplying (46) by the matrix . The derivation of the conditional posterior of β is more tedious. Define X = Xβ. Now define Z = ∆Y − X1 α and write Z = X2 Bα + U. X2 ] such that the partitions of X conform to the partitions of β = [I. the likelihood function is of the form p(Y |α. the posterior of vec(α ) is multivariate Normal. 2 (44) In turn. (46) The fact that B is right-multiplied by α complicates the analysis. one might find it attractive to center the prior for the cointegration coefficient B at −1.Del Negro. B ] and rewrite the reduced-rank regression as ∆Y = X1 α + X2 Bα + U. Conditional on an initial observation and the covariance matrix Σ (both subsequently omitted from our notation).
respectively.S. We use an improper prior of the form p(Π. ˜ Z2 = Zα⊥ . Draws from the posterior distribution are generated through a Gibbs sampler in which Step 2 of Algorithm 3. let Σ = C ΣC and partition Σ conforming ˜ ˜ ˜ ˜ ˜ with U = [U1 . α) ∝ p(β(B)) exp 1 ˜ ˜ ˜ − tr Σ−1 (Z1|2 − X2 B) (Z1|2 − X2 B) 1|2 2 . . 0. if the prior distribution for B is either flat or Normal. (48) Thus. Then we can deduce 22 p(B|Y. 2λ where λ ∈ {0. The posterior is similar for all three choices of λ. The mean and variance of Z1 conditional on Z2 are given −1 ˜ −1 ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ by (Σ12 Σ22 Z2 + X2 B) and Σ1|2 = Σ11 − Σ12 Σ22 Σ21 .1: We use the VECM in (41) with p = 4 and the associated movingaverage representation (42) to extract a common trend from the U. 0 + U1 . 2010 C = [α(α α)−1 . ˜ U2 = U α⊥ . . indicating that the data .1 is replaced by the two steps described in Algorithm 3.01. Σ. B) ∝ |Σ|−(n+1)/2 exp − 1 (B − (−1))2 . −1] . U2 ]. The posterior density for B is plotted in Figure 4 for the three parameterizations of the prior variance λ. Z2 = X2 B. 1}. Define Z1|2 = ˜ ˜ ˜ ˜ Z1 − Σ12 Σ−1 Z2 . which sharp˜ ˜ ens the inference for B. B] is centered at the balanced-growth-path values [1. Algorithm 3. α. Formally. Draw α(s) from p(α|β (s−1) . Y ) given in (45). Illustration 3.Del Negro. The prior distribution for the cointegration vector β = [1. then the conditional posterior of B given α is Normal. ˜ U1 = U α(α α)−1 . where ˜ Z1 = Zα(α α)−1 . investment and GDP data depicted in Figure 3. . nsim : 1. 2. . α⊥ ] yields the seemingly unrelated regression ˜ ˜ ˜ ˜ Z1 . Schorfheide – Bayesian Macroeconometrics: April 18.2: Gibbs Sampler for Simple VECM with Gaussian Priors For s = 1.1.2. Draw B (s) from p(B|α(s) . U2 . Through Z2 . 34 (47) ˜ ˜ Notice that we cannot simply drop the Z2 equations. we obtain ˜ ˜ information about U2 and hence indirectly information about U1 . Y ) given in (48) and let β (s) = [I. B (s) ] .
ϕ ∈ (0. For each prior. and Villani (2006). the posterior mean of B is about −1.1. We begin by reviewing the first strand. The second strand uses prior distributions to regularize or smooth the likelihood function of a cointegration model in areas of the parameter space in which it is very nonelliptical. Using posterior draws based on λ = 0. Our discussion focuses on the output-investment example with n = 2 and r = 1. Figure 5 plots the decompositions of log nominal aggregate investment and log nominal GDP into common trends and stationary fluctuations around those trends. National Bureau of Economic Research (NBER) recession dates are overlayed in gray.10. which we previously encountered in the context of structural VARs in Section 2. The plots in the left column of the Figure display the common trend β⊥ (α⊥ Γβ⊥ )−1 α⊥ t τ =1 (ut + Πc ) for each series.3 Further Research on Bayesian Cointegration Models The Bayesian analysis of cointegration systems has been an active area of research. 2010 35 are quite informative about the cointegration relationship.07. indicating a slight violation of the balanced-growth-path restriction. Rather than normalizing one of the ordinates of the cointegration vector β to one. Insert Figure 4 Here Insert Figure 5 Here 3. van Dijk. we can alternatively normalize its length to one and express it in terms of polar coordinates. . we let β(ϕ) = [cos(−π/4 + π(ϕ − 1/2)).n−r ). Schorfheide – Bayesian Macroeconometrics: April 18. Subsequently.Del Negro. sin(−π/4 + π(ϕ − 1/2))] . Strachan and Inder (2004) and Villani (2005) emphasize that specifying a prior distribution for β amounts to placing a prior probability on the set of r-dimensional subspaces of Rn (Grassmann manifold Gr. while the plots in the right column show the demeaned stationary component Ψ(L)ut . In this case the Grassmann manifold consists of all the lines in R2 that pass through the origin. and a detailed survey is provided by Koop. with most of the mass of the distributions placed on values less than −1. 1]. Strachan.4. For reasons that will become apparent subsequently. The first strand points out that the columns of β in (41) should be interpreted as a characterization of a subspace of Rn and that priors for β are priors over subspaces. we consider two strands of this literature.
for general n and r. B ]. B ]. we can choose a Beta distribution for ϕ and let ϕ ∼ B(γ. if γ = 1. and it turns out that the subspaces associated with β(ϕ) are uniformly distributed on the Grassmann manifold (see James (1954)). B becomes nonidentifiable. For n = 2. caused by local nonidentifiability of α and B under the ordinal normalization β = [I. As the loadings α for the cointegration relationships β yt−1 approach zero. then the prior is fairly dogmatic. we used a balanced-growth-path prior that was centered at the cointegration vector [1. Instead. 1]. If γ >> 1. γ). to generate prior distributions that are centered at the balanced-growth-path restriction. the marginal posterior density of α can be written as p(α|Y ) ∝ p(α) p(Y |α. which rotate the subspace spanned by β(ϕ) around the origin. derives the posterior distribution for α and β using the ordinal normalization β = [I. As γ approaches 1 from above it becomes more diffuse. Thus. B ] favors the cointegration spaces near the region where the linear normalization is invalid. and its density integrates to infinity. B)dB. Kleibergen and van Dijk (1994) and Kleibergen and Paap (2002) use prior distributions to correct irregularities in the likelihood function of the VECM. meaning that some of the first r variables do not appear in any cointegration vector. We now turn to the literature on regularization. In fact. Under this prior. then the conditional posterior of B given α = 0 is improper. this group is given by the set of orthogonal matrices specified in (28). 2010 36 The one-dimensional subspace associated with β(ϕ) is given by λβ(ϕ). In our empirical illustration. because a flat and apparently noninformative prior on B in β = [I. −1] . these authors propose to normalize β according to β β = I and develop methods of constructing informative and diffuse priors on the Grassmann manifold associated with β. . where λ ∈ R. This vector lies in the space spanned by β(1/2). Strachan and Inder (2004) are very critical of the ordinal normalization. then ϕ ∼ U (0. Villani (2005) proposes to use the uniform distribution on the Grassman manifold as a reference prior for the analysis of cointegration systems and. This uniform distribution is defined to be the unique distribution that is invariant under the group of orthonormal transformations of Rn . If the highly informative balanced-growth-path prior discussed previously were replaced by a flat prior for B – that is p(B) ∝ constant – to express diffuse prior beliefs about cointegration relationships. Schorfheide – Bayesian Macroeconometrics: April 18.Del Negro.
B. (51) Here. D11 . α and B. This prior has the property that as α −→ 0 its density vanishes and counteracts the divergence of p(Y |α. W21 ]. The matrix Λ is chosen to obtain a convenient functional form for the prior density below: Λ = (V22 V22 )−1/2 V22 D22 W22 (W22 W22 )−1/2 . p(Π∗ ) ∝ constant. For Λ = 0 the rank of the unrestricted Π∗ in (50) reduces to r and we obtain the familiar expression Π∗ = βα . They proceed by deriving a conditional distribution for Π∗ given Λ = 0. and D is a diagonal n × n matrix. Regardless of the rank of Π∗ . Schorfheide – Bayesian Macroeconometrics: April 18. Kleibergen and Paap (2002) propose the following alternative. Λ). α = 0)dB determines the marginal density at α = 0. Λ)) is the Jacobian associated with the mapping between Π∗ and (α. −1 B = V21 V11 . B.Del Negro. B)dB. B) ∝ |JΛ=0 (Π∗ (α. . B. and α = V11 D11 [W11 . and W11 are of dimension r×r. 2010 Since 37 p(Y |B. where β= I B . Here Mα and Mβ are chosen such that the second equality in (50) holds. The partitions V11 . The starting point is a singular-value decomposition of a (for now) unrestricted n × n matrix Π∗ . ignoring the rank reduction generated by the r cointegration relationships. the matrices β⊥ and α⊥ take the form β⊥ = Mβ [V12 V22 ] and α⊥ = Mα [W12 W22 ]. Details of the implementation of a posterior simulator are provided in Kleibergen and Paap (2002). Finally. the posterior of α tends to favor near-zero values for which the cointegration relationships are poorly identified. it can be verified that the matrix can be decomposed as follows: Π∗ = V11 V21 D11 W11 W21 + V12 V22 D22 W12 W22 (50) = βα + β⊥ Λα⊥ . Thus. which takes the form: Π∗ = V DW = V11 V12 V21 V22 D11 0 0 D22 W11 W21 W12 W22 . The authors start from a flat prior on Π∗ : that is. JΛ=0 (Π∗ (α. Λ))| ∝ |β β|(n−r)/2 |αα |(n−r)/2 . respectively. and all other partitions conform. p(α. and finally use a change of variables to obtain a distribution for the parameters of interest. (49) V and W are orthogonal n × n matrices.
This uncertainty is generated by exogenous stochastic processes that shift technology. Conditional on distributional assumptions for the exogenous shocks. . 2010 38 4 Dynamic Stochastic General Equilibrium Models The term DSGE model is typically used to refer to a broad class of dynamic macroeconomic models that spans the standard neoclassical growth model discussed in King. Schorfheide – Bayesian Macroeconometrics: April 18. agents potentially face uncertainty with respect to total factor productivity.7 discusses numerous methods of documenting the performance of DSGE models and comparing them to less restrictive models such as vector autoregressions. we provide a brief discussion of some empirical applications in Section 4. Bayesian inference on the parameters of a linearized DSGE model is discussed in Section 4.Del Negro. the DSGE model generates a joint probability distribution for the endogenous model variables such as output. and analyzing the welfare effects of economic policies.1. This posterior is the basis for substantive inference and decision making.3. and inflation. or the nominal interest rate set by a central bank. and to models solved with nonlinear techniques are discussed in Sections 4. The model solution and state-space representation are discussed in Section 4.4. In a Bayesian framework.6. generating predictive distributions for key macroeconomic variables. for instance.5. Extensions to models with indeterminacies or stochastic volatility. and 4. taking both parameter and model uncertainty into account. investment. 4. consumption. Finally. We present a prototypical DSGE model in Section 4. A detailed survey of Bayesian techniques for the estimation and evaluation of DSGE models is provided in An and Schorfheide (2007a). for example. this likelihood function can be used to transform a prior distribution for the structural parameters of the DSGE model into a posterior distribution. Section 4. such as studying the sources of business-cycle fluctuations and the propagation of shocks to the macroeconomy. and Evans (2005).2. Moreover. DSGE models can be used for numerous tasks. respectively.8. Eichenbaum. Plosser. A common feature of these models is that decision rules of economic agents are derived from assumptions about preferences and technologies by solving intertemporal optimization problems. The remainder of this section is organized as follows. or generate unanticipated deviations from a central bank’s interest-rate feedback rule. and Rebelo (1988) as well as the monetary model with numerous real and nominal frictions developed by Christiano.
Finally. Both output and labor productivity are plotted in terms of percentage deviations from a linear trend. According to this model. and Bt is an exogenous preference shifter that can be interpreted as a labor supply shock. and log labor productivity for the US. where Wt is the hourly wage. If Bt increases. and Santaeulalia-Llopis (2009). The household receives the labor income Wt Ht . Fuentes-Albero. It owns the capital stock Kt and rents it to the firms at the rate Rt . an important source of the observed fluctuations in the three series is exogenous changes in total factor productivity. (53) where It is investment and δ is the depreciation rate. hours worked.1 A Prototypical DSGE Model Figure 6 depicts postwar aggregate log output. Schorfheide – Bayesian Macroeconometrics: April 18. (54) . The representative household maximizes the expected discounted lifetime utility from consumption Ct and hours worked Ht : ∞ I t E s=0 β t+s ln Ct+s − (Ht+s /Bt+s )1+1/ν 1 + 1/ν (52) subject to a sequence of budget constraints Ct + It ≤ Wt Ht + Rt Kt . 2010 39 Insert Figure 6 Here 4. We will illustrate the techniques discussed in this section with the estimation of a stochastic growth model based on observations on aggregate output and hours worked. The household uses the discount rate β. ν is the aggregate labor supply elasticity. The simplest DSGE model that tries to capture the dynamics of these series is the neoclassical stochastic growth model. The first-order conditions associated with the household’s optimization problem are given by a consumption Euler equation and a labor supply condition: 1 1 = βI E (Rt+1 + (1 − δ)) Ct Ct+1 and 1 1 Wt = Ct Bt Ht Bt 1/ν . then the disutility associated with hours worked falls. Capital accumulates according to Kt+1 = (1 − δ)Kt + It .Del Negro. Precise data definitions are provided in R´ ıos-Rull. Kryshko. The model consists of a representative household and perfectly competitive firms. Schorfheide.
Wt . Log technology evolves according to ln At = ln A0 +(ln γ)t+ln At . 1). respectively: Wt = α Yt . Firms solve a static profit maximization problem and choose labor and capital to equate marginal products of labor and capital with the wage and rental rate of capital. The solution to the rational expectations difference equations (53) to (59) determines the law of motion for the endogenous variables Yt . Kt (56) An equilibrium is a sequence of prices and quantities such that (i) the representative household maximizes utility and firms maximize profits taking the prices as given. (59) and 0 ≤ ρb < 1. Schorfheide – Bayesian Macroeconometrics: April 18. we specify a law of motion for the two exogenous processes. Ct = . Since we will subsequently solve the model by constructing a local approximation of its dynamics near a steady state. we assume ln A−τ = 0 and ln B−τ = 0. Ht .t ∼ iidN (0. consumption. Ht Rt = (1 − α) Yt . (55) The stochastic process At represents the exogenous labor augmenting technological progress.Del Negro. To initialize the exogenous processes. and produce final goods according to the following Cobb-Douglas technology: 1−α Yt = (At Ht )α Kt . 1). Wt = . hire labor services. and Rt . At At At At At (60) . It = . 1]. b.t ∼ iidN (0. (57) To close the model. 2010 40 Firms rent capital. If 0 ≤ ρa < 1. (58) where ρa ∈ [0. If ρa = 1. Kt+1 = . Kt . ln At = ρa ln At−1 +σa a. investment. The technology process ln At induces a common trend in output. a. Ct . then ln At is a random-walk process with drift. and wages.t . it is useful to detrend the model variables as follows: Yt = Ct It Kt+1 Wt Yt . and (ii) markets clear. capital. implying that Yt = Ct + It . the technology process is trend stationary.t . It . Exogenous labor supply shifts are assumed to follow a stationary AR(1) process: ln Bt = (1 − ρb ) ln B∗ + ρb ln Bt−1 + σb b.
and ln Wt . Schorfheide – Bayesian Macroeconometrics: April 18. γ. β K∗ Y∗ = (1 − α)γ . σa . (62) This log ratio is always stationary. and is a function of shocks dated t and earlier. Yt Kt eat Kt+1 = (1 − δ)Kt e−at + It . At = ln γ + (ρa − 1) ln At−1 + σa At−1 a. the model and b. ln A0 . δ. 4. we are detrending Kt+1 by At .t economy becomes deterministic and has a steady state in terms of the detrended variables. the detrended variables follow a stationary law of motion. which according to (60) are obtained by taking pairwise differences of ln Yt . ν.t (63) to zero. ln Ct .t . we stack the parameters of the DSGE model in the vector θ: θ = [α.2 Model Solution and State-Space Form The solution to the equilibrium conditions (59). even if the underlying technology shock is nonstationary. R∗ I∗ Y∗ = 1− 1−δ γ K∗ Y∗ . ρa . β. the model generates a number of cointegration relationships. if ρa = 1. and (62) leads to a probability distribution for the endogenous model variables.Del Negro. It is straightforward to rewrite (53) to (57) in terms of the detrended variables: 1 Ct = βI E Yt . the capital-output. Ht 1 Ct+1 e−at+1 (Rt+1 + (1 − δ)) . ln B∗ . because if ρa = 1 the ln At−1 term drops out. Finally. Moreover. For instance. Yt = Ct + It . and the investment-output ratios are given by R∗ = γ − (1 − δ). (61). the rental rate of capital. 2010 41 The detrended variables are mean reverting. indexed by the vector of structural . This bounds the probability of experiencing large deviations from the log-linearization point for which the approximate solution becomes inaccurate. (64) In a stochastic environment. ρb . 1 Ct Wt = 1 Bt Ht Bt 1/ν (61) Wt = α Rt = (1 − α) 1−α Yt = Htα Kt e−at The process at is defined as at = ln . σb ] . This steady state is a function of θ. Hence. If we set the standard deviations of the innovations a. According to our timing convention. ln It . ln Kt+1 . Kt+1 refers to capital at the end of period t/beginning of t + 1.
θ). This likelihood function can be used for Bayesian inference. where st is a vector of suitably defined state variables and the innovations for the structural shocks. a few remarks about the model solution are in order. at = At − At−1 . the intertemporal optimization problems of economic agents can be written recursively. In general. For now. Yt At Kt+1 = 1−δ I∗ 1−δ Kt + It − at . ignoring the discrepancy between the nonlinear model solution and the first-order approximation. A multitude of techniques are available for solving linear rational expectations models (see. using Bellman equations. γ γ K∗ C∗ I∗ Ct + It . Before turning to the Bayesian analysis of DSGE models. t . with the loose justification that any explosive solution would violate the transversality conditions associated with the underlying dynamic optimization problems. Yt = Y∗ Y∗ = ρa At−1 + σa a. Schorfheide – Bayesian Macroeconometrics: April 18. the solution takes the form st = Φ1 (θ)st−1 + Φ (θ) t . For the neoclassical growth model. Economists focus on solutions that guarantee a nonexplosive law of motion for the endogenous variables that appear in (66). then Xt = ln Xt − ln X∗ (Xt = ln Xt − ln X∗ ).t . We adopt the convention that if a variable Xt (Xt ) has a steady state X∗ (X∗ ).t . The solution of the DSGE model can be written as st = Φ(st−1 . for instance. (66) t (65) is a vector that stacks Ht = ν Wt − ν Ct + (1 + ν)Bt . = αHt + (1 − α)Kt − (1 − α)at . 2010 42 parameters θ. The log-linearized equilibrium conditions of the neoclassical growth model (61) are given by the following system of linear expectational difference equations: Ct = I t Ct+1 + at+1 − E R∗ Rt+1 R∗ + (1 − δ) Wt = Yt − Ht . we proceed under the assumption that the DSGE model’s equilibrium law of motion is approximated by log-linearization techniques. the value and policy functions associated with the optimization problems are nonlinear in terms of both the state and the control variables. In most DSGE models. Sims (2002b)).Del Negro. (67) . and the solution of the optimization problems requires numerical techniques. Bt = ρb Bt−1 + σb b. Rt = Yt − Kt + at .
and Ht are linear functions of st . In the subsequent illustration. At and Bt . or additional shocks as in Leeper and Sims (1995) and more recently Smets and Wouters (2003). The other endogenous variables. and where H∗ is the steady state of hours worked and the variables At . Ht . It . 2010 43 The system matrices Φ1 and Φ are functions of the DSGE model parameters θ. Thus. the trend generated by technology (ln γ)t + At is added in the measurement equation. Kt+1 . Yt . The model predicts that certain linear combinations of variables. Like all DSGE models. If the innovations Kohn (This Volume). Sargent (1989).Del Negro. and Rt can be expressed as linear functions of st . Wt . (68) Equations (67) and (68) provide a state-space representation for the linearized DSGE model. Pitt. the linearized neoclassical growth model has some apparent counterfactual implications. Yt . Equation (68) becomes ln GDPt ln Ht = ln Y0 ln H∗ + ln γ 0 t+ Yt + At Ht . as well as the two exogenous processes At and Bt . Ct . so that it matches the number of exogenous shocks. are constant. the likelihood function for more than two variables is degenerate. In the subsequent empirical illustration. which is clearly at odds with the data. and st is composed of three elements: the capital stock at the end of period t. it is instructive to examine the measurement equations that the model yields for output . Our measurement equation takes the form yt = Ψ0 (θ) + Ψ1 (θ)t + Ψ2 (θ)st . Since fluctuations are generated by two exogenous disturbances. and Ireland (2004). t are Gaussian. which is described in detail in Giordani. In this case. Schorfheide – Bayesian Macroeconometrics: April 18. then the likelihood function can be obtained from the Kalman filter. To cope with this problem authors have added either so-called measurement errors. Notice that even though the DSGE model was solved in terms of the detrended model variable Yt . Altug (1989). we let yt consist of log GDP and log hours worked. Although we focus on the dynamics of output and hours in this section. such as the labor share lsh = Ht + Wt − Yt . we restrict the dimension of the vector of observables yt to n = 2. we are able to use nondetrended log real GDP as an observable and to learn about the technology growth rate γ and its persistence ρa from the available information about the level of output.
Schorfheide – Bayesian Macroeconometrics: April 18. suppose the neoclassical growth model is estimated based on aggregate output and hours data over the period 1955 to 2006. even if ρa = 1.2 as justification of our informative prior for the cointegration vector. If the information is vague. the model implies the following cointegration relationship: −1 1 ln GDPt ln It = ln (1 − α)(γ − 1 + δ) + It − Yt . If ρa = 1 then the last line of (66) implies that At follows a random-walk process and hence induces nonstationary dynamics. the posterior estimates of the cointegration vector reported in Illustration 3. we can write ln GDPt ln It = ln Y0 ln Y0 + (ln I∗ − ln Y∗ ) + ln γ ln γ t+ At + Yt At + It . To the extent that this information is indeed precise. In contrast. such a model deficiency may lead to posterior distributions of the autoregressive coefficients associated with shocks other than technology that concentrate near unity. In this case. To the contrary. Then. the choice of prior should be properly documented. the use of a tight prior distribution is desirable.1 suggest that the balanced-growth-path implication of the DSGE model is overly restrictive. Suppose we use the GDP deflator to convert the two series depicted in Figure 3 from nominal into real terms. This representation highlights the common trend in output and investment generated by the technology process At . this should not be interpreted as “cooking up” desired results based on almost dogmatic priors. In practice. the spirit behind the prior elicitation is to use other sources of information that do not directly enter the likelihood function. There are three important sources of information that are approximately independent of the data that enter the likelihood function and therefore could be used for the elicitation of prior distribution: (i) information from macroeconomic time series other than . γ/β − 1 + δ Recall that both Yt and It are stationary. 4. 2010 44 and investment.3 Bayesian Inference Although most of the literature on Bayesian estimation of DSGE models uses fairly informative prior distributions. For concreteness. it should translate into a more dispersed prior distribution.Del Negro. We used this model implication in Section 3. Most important.
and (iii) macroeconomic data. to individuals moving in and out of unemployment. that is. microeconometric estimates of labor supply elasticities – an example of source (ii) – could be used to specify a prior for the Frisch elasticity ν. Since none of these variables directly enters the likelihood function. Let Σ be the inverse of the (negative) Hessian computed at the posterior mode ˜ θ. and Whiteman (2000). for instance. 0 . it is sensible to incorporate this information through the prior distribution. Schorfheide – Bayesian Macroeconometrics: April 18. ρb . and δ. which can be computed numerically. Consider source (i). (ii) micro-level observations that are. Hence. 2010 45 output and hours during the period 1955 to 2006. Because of the nonlinear relationship between the DSGE model parameters θ and the system matrices Ψ0 . Moreover. Finally. Denote the posterior mode by θ. The parameters ρa . Up to now. It is apparent from (64) that long-run averages of real interest rates. The basic RWM Algorithm takes the following form Algorithm 4. prior to 1955. the marginal and conditional distributions of the elements of θ do not fall into the well-known families of probability distributions. capital-output ratios. Ingram. Ψ2 . Φ1 and Φ in (67) and (68).Del Negro. that is. accounting for the fact that most of the variation in hours worked at the aggregate level is due to the extensive margin. prior distributions for these parameters can be chosen such that the implied dynamics of output and hours are broadly in line with presample evidence. and σb implicitly affect the persistence and volatility of output and hours worked. ˜ ˜ 3. Del Negro and Schorfheide (2008) provide an approach for automating this type of prior elicitation. ˜ 2. informative about labor-supply decisions. Ψ1 .1: Random-Walk Metropolis (RWM) Algorithm for DSGE Model 1. β. including observations on output and hours worked. c2 Σ) or directly specify a starting value. which up ˜ to a constant is given by ln p(Y |θ) + ln p(θ). Use a numerical optimization routine to maximize the log posterior. Draw θ(0) from N (θ. information from source (iii). and investment-output ratios are informative about α. the parameter α equals the labor share of income in our model. σa . the most commonly used procedures for generating draws from the posterior distribution of θ are the Random-Walk Metropolis (RWM) Algorithm described in Schorfheide (2000) and Otrok (2001) or the Importance Sampler proposed in DeJong.
Del Negro. For s = 1. . Thus. and replacing Σ in Step 4 with a matrix whose diagonal elements are equal to the prior variances of the DSGE model parameters and whose off-diagonal elements are zero. then the maximization in Step 1 can be implemented with a gradient-based numerical optimization routine. Here. standard deviations. and credible sets. ϑ|Y ) = p(Y |ϑ)p(ϑ) . Any inaccuracy in the computation of the steady states will translate into an inaccurate evaluation of the likelihood function that makes use of gradient-based optimization methods impractical. While the computation of the steady states is trivial in our neoclassical stochastic growth model. and ˜ then set θ to the value that attains the highest posterior density across optimization runs. . An and Schorfheide (2007b) describe a hybrid MCMC algorithm with transition mixture to deal with a bimodal posterior distribution. it is advisable to start the optimization routine from multiple starting values. . for example posterior means. Chib and Ramamurthy (2010) recommend using a simulated annealing algorithm for Step 1. In this case. nsim : draw ϑ from the proposal distribution N (θ(s−1) .1 tends to work well if the posterior density is unimodal. c2 Σ). 2010 46 ˜ 4. such as the mean of the prior distribution. The scale factor c0 controls the expected distance between the mode and the starting point of the Markov chain. (ii) the solution of the linear rational expectations system.000 iterations provide very similar approximations of the objects of interest.000. Schorfheide – Bayesian Macroeconometrics: April 18. The optimization is often not straightforward as the posterior density is typically not globally concave. The jump from θ(s−1) is accepted (θ(s) = ϑ) with probability min {1. it might require the use of numerical equation solvers for more complicated DSGE models. r(θ(s−1) . . Based on practitioners’ experience. The tuning parameter c is typically chosen to obtain a rejection rate of about 50%. reasonable perturbations of the starting points lead to chains that after 100. Chib and Ramamurthy . which could be drawn from the prior distribution. The evaluation of the likelihood typically involves three steps: (i) the computation of the steady state. Most recently. In some applications we found it useful to skip Steps 1 to 3 by choosing a reasonable ˜ starting value. p(Y |θ(s−1) )p(θ(s−1) ) If the likelihood can be evaluated with a high degree of precision. Algorithm 4. ϑ|Y )} and rejected (θ(s) = θ(s−1) ) otherwise. and (iii) the evaluation of the likelihood function of a linear state-space model with the Kalman filter.000 to 1. medians. r(θ(s−1) .
The use of a dogmatic prior can then be viewed as a (fairly good) approximation of a low-variance prior. Schorfheide. These choices yield values of α = 0.025 in quarterly terms. Fuentes-Albero. and δ to be consistent with a labor share of 0.Del Negro. it implies that the total factor productivity has a serial correlation between 0. We assume that α has a Beta distribution with a standard deviation of 0. an investmentto-output ratio of about 25%. we define ln Y0 = ln Y∗ + ln A0 and use fairly agnostic priors on the location parameters ln Y0 and ln H∗ . Our prior implies that the preference shock is slightly less persistent than the technology shock.2. Fixing these parameters is typically justified as follows.02.66. β = 0. A detailed discussion can be found in Chib (This Volume). and δ = 0. Based on National Income and Product Account (NIPA) data. we use such a low-variance prior for α.66. Finally. We use a Gamma distribution with parameters that imply a prior mean of 2 and a standard deviation of 1. we choose the prior means for α. Conditional on the adoption of a particular data definition. An important parameter for the behavior of the model is the labor supply elasticity. 2010 47 (2010) have developed a multiblock Metropolis-within-Gibbs algorithm that randomly groups parameters in blocks and thereby dramatically reduces the persistence of the resulting Markov chain and improves the efficiency of the posterior sampler compared to a single-block RWM algorithm. Kryshko. resulting in small prior variances. As is quite common in the literature. balanced-growth considerations under slightly different household preferences suggest a value of 2. Illustration 4.1: The prior distribution for our empirical illustration is summarized in the first five columns of Table 3. For illustrative purpose. a priori plausible values vary considerably. Schorfheide – Bayesian Macroeconometrics: April 18. and that the standard deviation of the shocks is about 1% each quarter. and SantaeulaliaLlopis (2009). and Rogerson (1988) model of hours’ variation along the extensive margin would lead to ν = ∞. Micro-level estimates based on middle-age white males yield a value of 0. and an annual interest rate of 4%. .99.0. the relevant long-run averages computed from NIPA data appear to deliver fairly precise measurements of steady-state relationships that can be used to extract information about parameters such as β and δ. we decided to use dogmatic priors for β and δ. As discussed in R´ ıos-Rull. β.99. Our prior for the technology shock parameters is fairly diffuse with respect to the average growth rate.91 and 0. published by the Bureau of Economic Analysis.
S. let lsh∗ (θ) be the model-implied labor share as a function of θ and lsh a sample average of postwar U.Del Negro. The posterior means of the labor supply elasticity are 0. Due to the fairly tight prior. where λ reflects the strength of the belief about the labor share. We used a logarithmic transformation of γ. which leads to a rejection rate of about 50%. Kryshko. Unlike in Figure 6. Del Negro and Schorfheide (2008) propose to multiply an initial prior p(θ) constructed from marginal distributions for the individual elements of θ by a ˜ function f (θ) that reflects beliefs about steady-state relationships and autocovariances. lsh∗ . we do not remove a deterministic trend from the output series. Alternatively. the autocorrelation parameter of the technology shock is estimated subject to the restriction that it lie in the interval [0. The scale parameter in the proposal density is chosen to be c = 0. We apply the RWM Algorithm to generate 100. FuentesAlbero. 2010 48 The distributions specified in the first columns of Table 3 are marginal distributions. 1). This function is generated by interpreting long-run averages of variables that do not appear in the model and presample autocovariances of yt as noisy measures of steady states and population autocovariances.000 draws from the posterior distribution of the parameters of the stochastic growth model. which is what we will do in the empirical illustration. and the innovation standard deviations of the shocks are 1. The estimated shock autocorrelations are around 0. Schorfheide – Bayesian Macroeconometrics: April 18. are summarized in the last four columns of Table 3. whereas it is fixed at 1 in the stochastic trend version. Schorfheide.70. A joint prior is typically obtained by taking the product of the marginals for all elements of θ. one could replace a subset of the structural parameters by. respectively. These relatively small values of ν imply that most of the fluctuations in hours worked are due to the labor supply shock.7% for the preference shock. which can be interpreted as the average quarterly growth rate of the economy and is estimated . For example. and then regard beliefs about these various steady states as independent.42 and 0. Then ln f (θ) could be defined as −(lsh∗ (θ) − lsh)2 /(2λ). R∗ . ˜ The prior distribution is updated based on quarterly data on aggregate output and hours worked ranging from 1955 to 2006. Posterior means and 90% credible intervals. I∗ /K∗ . In the deterministic trend version.5. and K∗ /Y∗ . the distribution of α is essentially not updated in view of the data. computed from the output of the posterior simulator. which is in line with the range of estimates reported in R´ ıos-Rull. The overall prior then takes the form p(θ) ∝ p(θ)f (θ). for instance.97. labor shares. and Santaeulalia-Llopis (2009). We consider two versions of the model.1% for the technology shock and 0.
(71) Here. described in detail in Lubik and Schorfheide (2004). on the one hand. (70) If. because this indeterminacy might arise if a central bank does not react forcefully enough to counteract deviations of inflation from its long-run target value. which is scalar. Schorfheide – Bayesian Macroeconometrics: April 18. the unique stable equilibrium law of motion of the endogenous variable yt is given by yt = t.1) process yt = θyt−1 + (1 + M ) t − θ t−1 . Clarida. From a macroeconomist’s perspective. the law of motion of yt is not uniquely determined. θ should be interpreted as the structural parameter. It can be verified that if. M captures an indeterminacy: based on θ alone. Once draws from the posterior distribution have been generated. The estimates of ln H∗ and ln Y0 capture the level of the two series. In an influential paper.3% to 0.Del Negro. but it does affect the law of motion of yt if θ ≤ 1. θ ∈ (0. The presence of indeterminacies raises a few complications for Bayesian inference. θ > 1. . they can be converted into other objects of interest such as responses to structural shocks.4%. Gali. 2010 49 to be 0. on the other hand. one obtains a much larger class of solutions that can be characterized by the ARMA(1. M is completely unrelated to the agents’ tastes and technologies characterized by θ. and this is referred to as indeterminacy. 4. 2]. postwar data and found that the policy rule estimated for pre-1979 data would lead to indeterminate equilibrium dynamics in a DSGE model with nominal price rigidities. Consider the following simple example. the scalar parameter M ∈ R is used to characterize all stationary solutions of (69). and Gertler (2000) estimated interest rate feedback rules based on U.S. (69) Here.4 Extensions I: Indeterminacy Linear rational expectations systems can have multiple stable solutions. Suppose that yt is scalar and satisfies the expectational difference equation 1 E yt = I t [yt+1 ] + t . θ ≤ 1. DSGE models that allow for indeterminate equilibrium solutions have received a lot of attention in the literature. θ t ∼ iidN (0. 1).
.16.01] [8.61.00 .007.03 8.04 0.010.93] 0.07.80 0. 0. 0.68] Mean 90% Intv.002.10 .02 1.99] [. Trend Domain [0. .011 [.22.98 . .93.003 [.77 0.08. s and ν for the Inverted Gamma distribution.65 [0. 1) I R I R I + R Beta InvGamma Beta InvGamma Normal Normal 0. [0.008] [-0.98 0. To estimate the stochastic growth version of the model we set ρa = 1. 0.004 1.01 4. 0.010. 0.012] [0. .98] I R I + R I R I R I R + + + Posterior Stoch.00 2.23] [. and Normal distributions.007 -0.00 .63. Schorfheide – Bayesian Macroeconometrics: April 18.10 0. Gamma. .01 4.004] 0.70 .67] 0.011 0.008] [-0. .95 0.025 50 are fixed.42 [0. 2010 Notes: Para (1) and Para (2) list the means and the standard deviations for Beta.66 Density Para (1) α ν 4 ln γ ρa σa ρb σb ln H∗ ln Y0 Del Negro. 0. .002.00 0.Table 3: Prior and Posterior Distribution for DSGE Model Parameters Prior Det.86] 90% Intv.62.00 .96.65 0.0 -0. 0.99 and δ = 0.008 0. Trend Mean 0. where pIG (σ|ν.39 [.00 10.95.69] [0. the upper and lower bound of the support for the Uniform distribution.02] [7. s) ∝ σ −ν−1 e−νs 2 /2σ 2 .96. The parameters β = 0.97 [0. Name Beta Gamma Normal 0.006.99] [.00 100 8. 0. 8.005] Para (2) 0.00 0. 1. 8.02 0.012] [0.
1) process (71) cancel. Their approach amounts to using (67) and .Del Negro. suppose ηt ∼ iidN (0. consider for instance the technology shock that a. The likelihood function has the following features. this irregular shape of the likelihood function does not pose any conceptual challenge.t ∼ N (0. Justiniano and Primiceri (2008) solved the linear rational expectational system obtained from the log-linearized equilibrium conditions of their DSGE model and then augmented the linear solution by equations that characterize the stochastic volatility of the exogenous structural shocks. 2010 51 From an econometrician’s perspective. According to (70). If θ ≤ 1 and M = 0 the likelihood function does not vary with θ because the roots of the autoregressive and the moving-average polynomial in the ARMA(1. 2] and ΘD = [0.S. 4. 1]) along the lines of the determinacyindeterminacy boundary. In a Bayesian framework. treated the subspaces as separate models. If θ ≤ 1 and M = 0. Schorfheide – Bayesian Macroeconometrics: April 18. generated posterior draws for each subspace separately. However. then the likelihood function exhibits curvature. one can combine proper priors for θ and M and obtain a posterior distribution. a. Justiniano and Primiceri (2008) allow the volatility of the structural shocks t in (67) to vary stochastically over time. Lubik and Schorfheide (2004) divided the parameter space into ΘD and ΘI (for model (69) ΘD = (1. vt ). 1). one needs to introduce this auxiliary parameter M to construct the likelihood function.t . (72) ln vt = ρv ln vt−1 + ηt . GDP data is the reduction in the volatility of output growth around 1984. To investigate the sources of this volatility reduction. An alternative approach would be to capture the Great Moderation with Markov-switching shock standard deviations (see Section 5). in more realistic applications the implementation of posterior simulation procedures require extra care. In principle. the likelihood function is completely flat (does not vary with θ and M ) for θ > 1 because all parameters drop from the equilibrium law of motion. The authors adopt a specification in which log standard deviations evolve according to an autoregressive process. Alternatively. In the context of the stochastic growth model.t 2 ∼ N (0. This phenomenon has been termed the Great Moderation and is also observable in many other industrialized countries. We previously assumed in (58) that a. ω 2 ). and used marginal likelihoods to obtain posterior probabilities for ΘD and ΘI .5 Extensions II: Stochastic Volatility One of the most striking features of postwar U.
ρv . As we will see in the next subsection.Del Negro. the RWM step described in Algorithm 4. Y ). The empirical model of Justiniano and Primiceri (2008) ignores any higher-order dynamics generated from the nonlinearities of the DSGE model itself on grounds of computational ease.2: Metropolis-within-Gibbs Sampler for DSGE Model with Stochastic Volatility For s = 1. and Kohn (This Volume). as can be seen from the equilibrium conditions (61) associated with our stochastic growth model. Y (s) (s−1) ). Y ) from the Normal-Inverse Gamma posterior obtained from the AR(1) law of motion for ln vt in (72). and Kohn (This Volume). nsim : 1.6 Extension III: General Nonlinear DSGE Models DSGE models are inherently nonlinear. 2. .t t evolves according to (72). ω . Schorfheide – Bayesian Macroeconometrics: April 18. The following Gibbs sampler can be used to generate draws from the posterior distribu- Algorithm 4. 4. Draw θ(s) conditional on (θ|v1:T .1:T conditional on (θ(s) . Pitt. Draw (s) a. many researchers take the stand that the equilibrium dynamics are .1 can be used to generate a draw θ(s) . v1:T . where is the observable and vt is the latent state.1:T . Draw (ρv . Given the sequence v1:T (s−1) (s−1) the likeli- hood function of the state-space model can be evaluated with the Kalman filter. . 2010 assuming that the element tion. Pitt. Shephard. and Rossi (1994) and Kim. Nonetheless. . Smoothing algorithms that generate draws of the sequence of stochastic volatilities have been developed by Jacquier. Bayesian inference is more difficult to implement for DSGE models solved with nonlinear techniques. given the magnitude of the business-cycle fluctuations of a country like the United States or the Euro area. Notice that (72) can be intera. described in Giordani. ω (s) ) conditional on (v1:T .t preted as a nonlinear state-space model. 3. in the shock vector 52 a. and Chib (1998) and are discussed in Jacquier and Polson (This Volume) and Giordani. . Y ) using the simulation smoother of (s−1) Carter and Kohn (1994). Draw v1:T conditional on ( (s) (s) (s) (s) a. Consequently. Polson. 4.
2010 53 well approximated by a linear state-space system. First. (74) Fern´ndez-Villaverde and Rubio-Ram´ (2007) and Fern´ndez-Villaverde and Rubioa ırez a Ram´ ırez (2008) show how a particle filter can be used to evaluate the likelihood function associated with a DSGE model. Bayesian analysis of nonlinear DSGE models is currently an active area of research and faces a number of difficulties that have not yet been fully resolved. Without errors in the measurement equation. the linearized consumption Euler equation takes the form Ct = I t Ct+1 + at+1 − Rj. It can be easily shown that for any asset j. log-linear approximations have the undesirable feature (for asset-pricing applications) that risk premiums disappear. θ). (67) and (68) are replaced by (65) and yt = Ψ(st . a and Rubio-Ram´ ırez (2004). the researcher has to introduce measurement errors in (74). Thus. The use of nonlinear model solution techniques complicates the implementation of Bayesian estimation for two reasons. the evaluation of the likelihood function becomes more costly because both the state transition equation and the measurement equation of the state-space model are nonlinear. t . A comparison of solution methods for DSGE models can be found in Aruoba. a proposed particle st has to satisfy ˜ the following two equations: yt = Ψ(˜t . However. θ). or if the goal of the analysis is to study asset-pricing implications or consumer welfare. yielding a gross return Rj.Del Negro. Thus. Pitt. this linear approximation becomes unreliable if economies are hit by large shocks.t+1 . as is often the case for emerging market economies. Second. The most common approach in the literature on estimated DSGE models is to use second-order perturbation methods. and Kohn (This Volume). Suppose that {st−1 }N is i=1 a collection of particles whose empirical distribution approximates p(st−1 |Y1:t−1 . it is computationally more demanding to obtain the nonlinear solution. Schorfheide – Bayesian Macroeconometrics: April 18. A detailed description of the particle filter is provided in Giordani. θ) s (i) st ˜ (i) (i) (i) (75) (76) = (i) (i) Φ(st−1 . . E (73) implying that all assets yield the same expected return.t . For the particle filter to work in the context of the stochastic growth model described above. θ). Fern´ndez-Villaverde.
Based on the ˜ s. Posterior odds of a model with adjustment costs versus a model without are useful for such an assessment. An efficient ˜ s implementation of the particle filter is one for which a large fraction of the N st ’s ˜ are associated with values of ηt that are small relative to Ση . Thus. θ) + ηt .Del Negro. First. the probability that (75) is satisfied ˜ is zero. 2010 (i) 54 If st is sampled from a continuous distribution. Finally. because the nonlinear equation might have multiple solutions. st needs to be sampled from a ˜ discrete distribution. θ). and then find all ˜ real solutions ˜ of for the equation yt = Ψ(Φ(st−1 . in the context of the stochastic growth model we could examine whether the model is able to capture the correlation between output and hours worked that we observe in the data. in the absence of measurement errors. it is important to realize that one needs to bound the magnitude of the measurement error standard deviations from below to avoid a deterioration of the particle filter performance as these standard deviations approach zero. eliminating st . Schorfheide – Bayesian Macroeconometrics: April 18. In this case. Such comparisons can be used to examine whether a particular . In practice. . then (75) turns into yt = Ψ(˜t . ˜ this calculation is difficult if not infeasible to implement. For instance. One can plug (76) into (75). one could examine to what extent a DSGE model is able to capture salient features of the data.7 DSGE Model Evaluation An important aspect of empirical work with DSGE models is the evaluation of fit. ˜. This type of evaluation can be implemented with predictive checks. Second. Some authors – referring to earlier work by Sargent (1989). If errors ηt ∼ N (0. a researcher might want to compare one or more DSGE models to a more flexible reference model such as a VAR. a researcher might be interested in assessing whether the fit of a stochastic growth model improves if one allows for convex investment adjustment costs. which in the context of our stochastic growth model amounts to a modification of the DSGE model. We consider three methods of doing so. We will distinguish three approaches. θ). θ). s (i) (i) (i) (77) This equation can be solved for any st by setting ηt = yt − Ψ(˜t . θ). or Ireland (2004) – make measurement errors part of the specification of their empirical model. (i) 4. Altug (1989). Ση ) are added to the measurement equation (74). one (i) (i) (i) (i) (i) can obtain the support points for the distribution of st as Φ(st−1 .
the methods proposed by Geweke (1999) and Chib and Jeliazkov (2001) can be used to obtain numerical approximations of the marginal likelihood. 2010 55 DSGE model captures certain important features of the data.1 Posterior Odds The Bayesian framework allows researchers to assign probabilities to various competing models. and Smets and Wouters (2007) use odds to determine the importance of a variety of real and nominal frictions in a medium-scale New Keynesian DSGE model. Schorfheide – Bayesian Macroeconometrics: April 18. Section 7 provides a more detailed discussion of model selection and model averaging based on posterior probabilities. 4. Predictive checks . Alternatively. These probabilities are updated through marginal likelihood ratios according to πi. 4.2 Predictive Checks A general discussion of the role of predictive checks in Bayesian analysis can be found in Lancaster (2004). Illustration 4. πj.0 p(Y |Mi ) = × . they can be used to rank different DSGE model specifications. respectively.8 and 1395.0 (79) is the marginal likelihood function.2: We previously estimated two versions of the neoclassical stochastic growth model: a version with a trend-stationary technology process and a version with a difference-stationary exogenous productivity process. these marginal data densities imply that the posterior probability of the difference-stationary specification is approximately 90%. If posterior draws for the DSGE model parameters are generated with the RWM algorithm. The key challenge in posterior odds comparisons is the computation of the marginal likelihood that involves a high-dimensional integral.0 p(Y |Mj ) (πi. and Geweke (2007).T πj. Geweke (2005).7.7. Mi )p(θ(i) )dθ(i) (78) Here.Del Negro. If the prior probabilities for the two specifications are identical. The log-marginal data densities ln p(Y |Mi ) are 1392. Posterior odds-based model comparisons are fairly popular in the DSGE model literature. πi.T πi. For instance. Rabanal and Rubio-Ram´ ırez (2005) use posterior odds to assess the importance of price and wage stickiness in the context of a small-scale New Keynesian DSGE model.2.T ) is the prior (posterior) probability of model Mi and p(Y |Mi ) = p(Y |θ(i) .
p(θ|FT ). In posterior predictive checks. The goal of prior predictive checks is to determine whether the model is able to capture salient features of the data. generate a parameter draw θ from p(θ|Ft ). Finally. The simulated trajectories can be converted into sample statistics of interest. Draws from the predictive distribu˜ tion can be obtained in two steps. to obtain an approximation for predictive distributions of sample moments. In its core. If S(Y1:T ) is located far in the tails. then the model is discredited. ∗ Second. the distribution of the parameters. Let Y1:T be a hypothetical sample of length T .Del Negro. similar to the . the prior predictive check replaces Y1:T in (80) with Y1:T and tries to measure whether the density that the Bayesian model assigns a priori to the observed data is high or low. The ∗ predictive distribution for Y1:T based on the time t information set Ft is ∗ p(Y1:T |Ft ) = ∗ p(Y1:T |θ)p(θ|Ft )dθ. 2010 56 can be implemented based on either the prior or the posterior distribution of the ∗ DSGE model parameters θ. Canova (1994) was the first author to use prior predictive checks to assess implications of a stochastic growth model driven solely by a technology shock. A comparison of (79) and (80) for t = 0 indicates that the two expressions are identical. If S(Y1:T ) falls into the tails (or lowdensity region) of the predictive distribution derived from the estimated model. Schorfheide – Bayesian Macroeconometrics: April 18. prior predictive checks can be very useful at an early stage of model development. Because the prior predictive distribution conveys the implications of models without having to develop methods for formal posterior inference. the posterior predictive check works like a frequentist specification test. is conditioned on the observed data Y1:T . First. Prior predictive distributions are closely related to marginal likelihoods. simulate a trajectory of observations Y1:T from the DSGE model conditional ˜ on θ. and Schorfheide (2007) use posterior predictive checks to determine whether a stochastic growth model. One can make the procedure more easily interpretable by replacing the high-dimensional data matrix Y with a low-dimensional statistic S(Y ). ∗ S(Y1:T ). Chang. such as the sample correlation between output and hours worked. one can compute the value of the statistic S(Y1:T ) based on the actual data and assess how far it lies in the tails of its predictive distribution. one concludes that the model has difficulties explaining the observed patterns in the data. (80) We can then use F0 to denote the prior information and FT to denote the posterior information set that includes the sample Y1:T . ∗ In its implementation. Doh.
which in turn is a function of the DSGE model parameters θ. which are transformations of model . Thus. if there is a strong overlap between the predictive densities for ϕ between DSGE model M1 and VAR M0 . 2010 57 one analyzed in this section.Del Negro. to examine asset-pricing implications of DSGE models. hours worked. the densities p(ϕ|Mi ) and p(ϕ|Y.7. In practice.0 π2. Let p(ϕ|Y. At the same time. Draws of ϕ can be obtained by transforming draws of the DSGE model and VAR parameters. M0 ) denote the posterior distribution of population characteristics as obtained from the VAR. The ratio formalizes the confidence interval overlap criterion proposed by DeJong. M0 )dϕ (81) can be interpreted as odds ratio of M1 versus M2 conditional on the reference model M0 . Loss-Function-Based Evaluation: Schorfheide (2000) proposes a Bayesian framework for a loss function-based evaluation of DSGE models. these models are designed to capture certain underlying population moments. is able to capture the observed persistence of hours worked.3 VARs as Reference Models Vector autoregressions play an important role in the assessment of DSGE models. since they provide a more richly parameterized benchmark. such as the volatilities of output growth. As in Geweke (2010)’s framework. for instance. the researcher considers a VAR as reference model M0 that is meant to describe the data and at the same time delivers predictions about ϕ. The numerator in (81) is large. respectively. the researcher is interested in the relative ability of two DSGE models to capture a certain set of population moments ϕ. Models of Moments: Geweke (2010) points out that many DSGE models are too stylized to deliver a realistic distribution for the data Y that is usable for likelihoodbased inference. and the correlation between these two variables. M0 ) can be approximated by Kernel density estimates based on draws of ϕ. We consider three approaches to using VARs for the assessment of DSGE models. Geweke (2010) shows that π1. and Whiteman (1996) and has been used. M0 )dϕ p(ϕ|M2 )p(ϕ|Y. Instead. denoted by p(ϕ|Mi ). a prior distribution for θ induces a model-specific distribution for the population characteristics. 4.0 p(ϕ|M1 )p(ϕ|Y. Ingram. Schorfheide – Bayesian Macroeconometrics: April 18. Suppose we collect these population moments in the vector ϕ.
We will refer to such a model as DSGE-VAR. one specifies a loss function L(ϕ. Mi ) and posterior model probabilities πi. the evaluation is loss-function dependent. say. ϕ) = ϕ − ϕ 2 . Mi ). then the predictive distribution is dominated by M1 . Third. 2.Del Negro. under which a ˆ ˆ ˆ point prediction ϕ of ϕ is to be evaluated. one can form a predictive density for ϕ by averaging across the three models p(ϕ|Y ) = i=0. Second. none of the DSGE models fits well. let I D [·] Eθ be the expectation under the DSGE model conditional on parameterization θ and define the autocovariance matrices ΓXX (θ) = I D [xt xt ]. Assuming that the data have been transformed such that yt is stationary. 1. the DSGE models are assumed to deliver a probability distribution for the data Y . Unlike in Geweke (2010). and a VAR that serves as a reference model M0 . Del Negro and Schorfheide (2004) link DSGE models and VARs by constructing families of prior distributions that are more or less tightly concentrated in the vicinity of the restrictions that a DSGE model implies for the coefficients of a VAR. DSGE-VARs: Building on work by Ingram and Whiteman (1994).T p(ϕ|Y. For each DSGE model. Mi )dϕ. Eθ ΓXY (θ) = I D [xt yt ]. Suppose there are two DSGE models. the prediction ˆ ϕ(i) is computed by minimizing the expected loss under the DSGE model-specific ˆ posterior: ϕ(i) = argminϕ ˆ ˜ L(ϕ. whereas the model ranking becomes effectively loss-function independent if one of the DSGE models has a posterior probability that is close to one. DSGE model M1 is well specified and attains a high posterior probability. XX Σ∗ (θ) = ΓY Y (θ) − ΓY X (θ)Γ−1 (θ)ΓXY (θ). Eθ A VAR approximation of the DSGE model can be obtained from the following restriction functions that relate the DSGE model parameters to the VAR parameters: Φ∗ (θ) = Γ−1 (θ)ΓXY (θ). ϕ)p(ϕ|Y )dϕ. ϕ). Finally one can compare DSGE models M1 and M2 based on the posterior expected loss L(ϕ(i) . (82) If. for example L(ϕ. 2. In this procedure. The first step of the analysis consists of computing model-specific posterior predictive distributions p(ϕ|Y. computed under the overall posterior distribution (82) ˆ that averages the predictions of the reference model and all DSGE models. i = 0. however. if the DSGE models are poorly specified. 2010 58 parameters θ. then the predictive density is dominated by the VAR. M1 and M2 . The starting point is the VAR specified in Equation (1). Schorfheide – Bayesian Macroeconometrics: April 18. ˜ i = 1.2 πi. XX (83) .T . ϕ)p(ϕ|Y. If.1.
With a QR factorization. λT Σ∗ (θ). Σ)pλ (Φ. see (21). 2010 59 To account for potential misspecification of the DSGE model. tr DSGE (85) where Σ∗ (θ) is lower-triangular and Ω∗ (θ) is an orthogonal matrix. is given by ∂yt ∂ t = Σtr Ω. allows for deviations of Φ and Σ from the restriction functions: Φ. Since Φ and Σ can be conveniently integrated out. the posterior short-run responses of the VAR with those from the DSGE model. and T denotes the actual sample size. Let A0 (θ) be the contemporaneous on yt according to the DSGE model. the DSGE’s and the DSGE-VAR’s impulse responses to all shocks approximately coincide. the initial response of yt to the structural shocks can be uniquely decomposed into ∂yt ∂ t = A0 (θ) = Σ∗ (θ)Ω∗ (θ). The initial tr impact of t on yt in the VAR. (87) with the understanding that the distribution of Ω|θ is a point mass at Ω∗ (θ). as opposed to the covariance matrix of innovations. that is ut = Σtr Ω t . θ) = p(Y |Φ. we now use a prior distribution that. the one-step-ahead forecast errors ut are functions of the structural shocks impact of t t. λT − k . Σ|θ ∼ M N IW Φ∗ (θ). the identification procedure can be interpreted as matching. The next step is to turn the reduced-form VAR into a structural VAR. we can first draw from the marginal . (84) This prior distribution can be interpreted as a posterior calculated from a sample of T ∗ = λT artificial observations generated from the DSGE model with parameters θ. in absence of misspecification. The final step is to specify a prior distribution for the DSGE model parameters θ. which can follow the same elicitation procedure that was used when the DSGE model was estimated directly. we obtain the hierarchical model pλ (Y. Schorfheide – Bayesian Macroeconometrics: April 18. [λT ΓXX (θ)]−1 . λ is a hyperparameter. Φ. Σ. The rotation matrix is chosen such that.Del Negro. while centered at Φ∗ (θ) and Σ∗ (θ). we maintain the triangularization of its covariance matrix Σ and replace the rotation Ω in (86) with the function Ω∗ (θ) that appears in (85). in contrast. V AR (86) To identify the DSGE-VAR. To the extent that misspecification is mainly in the dynamics. According to the DSGE model. Here. Σ|θ)p(Ω|θ)p(θ). at least qualitatively. Thus.
. then the normalized pλ (Y )’s can be interpreted as posterior probabilities for λ. then a comˆ parison between DSGE-VAR(λ) and DSGE model impulse responses can potentially yield important insights about the misspecification of the DSGE model. Del Negro. Define ˆ λ = argmaxλ∈Λ pλ (Y ). . . say. . compute Ω(s) = Ω∗ (θ(s) ). 2010 60 posterior of θ and then from the conditional distribution of (Φ. Σ) given θ. The framework has also been used as a tool for model evaluation and comparison in Del Negro. . Smets.5 and 2. The marginal likelihood pλ (Y |θ) is obtained by straightforward modification of (15). Moreover. . Schorfheide.Del Negro. Schorfheide – Bayesian Macroeconometrics: April 18. a natural criterion for the choice of λ is the marginal data density pλ (Y ) = pλ (Y |θ)p(θ)dθ. it is convenient to restrict the hyperparameter to a finite grid Λ. given by pλ (θ|Y ) ∝ pλ (Y |θ)p(θ). nsim . This leads to the following algorithm. Since the empirical performance of the DSGE-VAR procedure crucially depends on the weight placed on the DSGE model restrictions. nsim : draw a pair (Φ(s) . If one assigns equal prior probability to each grid point.2.1 to generate a sequence of draws θ(s) . For s = 1. (89) If pλ (Y ) peaks at an intermediate value of λ. . between 0.3: Posterior Draws for DSGE-VAR 1. Σ(s) ) from its conditional MNIW posterior distribution given θ(s) . The DSGEVAR approach was designed to improve forecasting and monetary policy analysis with VARs. Algorithm 4. . Schorfheide. s = 1. 2. and Wouters (2007) and for policy analysis with potentially misspecified DSGE models in Del Negro and Schorfheide (2009). it is useful to consider a datadriven procedure to select λ. The MNIW distribution can be obtained by the modification of (8) described in Section 2. (88) For computational reasons. Use Algorithm 4. As in the context of the Minnesota prior. from the posterior distribution of θ. and Wouters (2007) emphasize that the posterior of λ provides a measure of fit for the DSGE model: high posterior probabilities for large values of λ indicate that the model is well specified and that a lot of weight should be placed on its implied restrictions. . Smets.
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4.8
DSGE Models in Applied Work
Much of the empirical analysis with DSGE models is conducted with Bayesian methods. Since the literature is fairly extensive and rapidly growing, we do not attempt to provide a survey of the empirical work. Instead, we will highlight a few important contributions and discuss how Bayesian analysis has contributed to the proliferation of estimated DSGE models. The first published papers that conduct Bayesian inference in DSGE models are DeJong, Ingram, and Whiteman (2000), Schorfheide (2000), and Otrok (2001). Smets and Wouters (2003) document that a DSGE model that is built around the neoclassical growth model presented previously and enriched by habit formation in consumption, capital adjustment costs, variable factor utilization, nominal price and wage stickiness, behavioral rules for government spending and monetary policy, and numerous exogenous shocks could deliver a time-series fit and forecasting performance for a vector of key macroeconomic variables that is comparable to a VAR. Even though posterior odds comparison, literally taken, often favor VARs, the theoretical coherence and the ease with which model implications can be interpreted make DSGE models an attractive competitor. One reason for the rapid adoption of Bayesian methods is the ability to incorporate nonsample information, meaning data that do not enter the likelihood function, through the use of prior distributions. Many of the priors used by Smets and Wouters (2003) as well as in subsequent work are fairly informative, and over the past five years the literature has become more careful about systematically documenting the specification of prior distributions in view of the available nonsample information. From a purely computational perspective, this kind of prior information often tends to smooth out the shape of the posterior density, which improves the performance of posterior simulators. Once parameter draws have been obtained, they can be easily converted into objects of interest. For instance, Justiniano, Primiceri, and Tambalotti (2009) study the relative importance of investment-specific technology shocks and thereby provide posterior distributions of the fraction of the businesscycle variation of key macroeconomic variables explained by these shocks. A large part of the literature tries to assess the importance of various propagation mechanisms that are useful for explaining observed business-cycle fluctuations. Bayesian posterior model probabilities are widely employed to compare competing model specifications. For instance, Rabanal and Rubio-Ram´ (2005) compare the ırez relative importance of wage and price rigidities. Unlike standard frequentist likeli-
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hood ratio tests, posterior odds remain applicable, even if the model specifications under consideration are nonnested, for example, a DSGE model with sticky wages versus a DSGE model with sticky prices. DSGE models with nominal rigidities are widely used to analyze monetary policy. This analysis might consist of determining the range of policy rule coefficients that guarantees a unique stable rational expectations solution and suppresses selffulfilling expectations, of choosing interest-rate feedback rule parameters that maximize the welfare of a representative agent or minimizes a convex combination of inflation and output-gap volatility, or in finding a welfare-maximizing mapping between the underlying state variables of the economy and the policy instruments. The solution of these optimal policy problems always depends on the unknown taste and technology parameters. The Bayesian framework enables researchers and policy makers to take this parameter uncertainty into account by maximizing posterior expected welfare. A good example of this line of work is the paper by Levin, Onatski, Williams, and Williams (2006). Several central banks have adopted DSGE models as tools for macroeconomic forecasting, for example, Adolfson, Lind´, and e Villani (2007) and Edge, Kiley, and Laforte (2009). An important advantage of the Bayesian methods described in this section is that they deliver predictive distributions for the future path of macroeconomic variables that reflect both parameter uncertainty and uncertainty about the realization of future exogenous shocks.
5
Time-Varying Parameters Models
The parameters of the models presented in the preceding sections were assumed to be time-invariant, implying that economic relationships are stable. In Figure 7, we plot quarterly U.S. GDP-deflator inflation from 1960 to 2006. Suppose one adopts the view that the inflation rate can be decomposed into a target inflation, set by the central bank, and some stochastic fluctuations around this target. The figure offers three views of U.S. monetary history. First, it is conceivable that the target rate was essentially constant between 1960 and 2006, but there were times, for instance, the 1970s, when the central bank let the actual inflation deviate substantially from the target. An alternative interpretation is that throughout the 1970s the Fed tried to exploit an apparent trade-off between unemployment and inflation and gradually revised its target upward. In the early 1980s, however, it realized that the long-run
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Phillips curve is essentially vertical and that the high inflation had led to a significant distortion of the economy. Under the chairmanship of Paul Volcker, the Fed decided to disinflate, that is, to reduce the target inflation rate. This time-variation in the target rate could be captured either by a slowly-varying autoregressive process or through a regime-switching process that shifts from a 2.5% target to a 7% target and back. This section considers models that can capture structural changes in the economy. Model parameters either vary gradually over time according to a multivariate autoregressive process (section 5.1), or they change abruptly as in Markov-switching or structural-break models (section 5.2). The models discussed subsequently can be written in state-space form, and much of the technical apparatus needed for Bayesian inference can be found in Giordani, Pitt, and Kohn (This Volume). We focus on placing the TVP models in the context of the empirical macroeconomics literature and discuss specific applications in Section 5.3. There are other important classes of nonlinear time-series models such as threshold vector autoregressive models, Geweke and Terui (1993) and Koop and Potter (1999), for instance, in which the parameter change is linked directly to observables rather than to latent state variables. Due to space constraints, we are unable to discuss these models in this chapter.
5.1
Models with Autoregressive Coefficients
Most of the subsequent discussion is devoted to VARs with parameters that follow an autoregressive law of motion (section 5.1.1). Whenever time-varying parameters are introduced into a DSGE model, an additional complication arises. For the model to be theoretically coherent, one should assume that the agents in the model are aware of the time-variation, say, in the coefficients of a monetary policy rule, and form their expectations and decision rules accordingly. Hence, the presence of time-varying parameters significantly complicates the solution of the DSGE model’s equilibrium law of motion and requires the estimation of a nonlinear state-space model (section 5.1.2). 5.1.1 Vector Autoregressions
While VARs with time-varying coefficients were estimated with Bayesian methods almost two decades ago, see, for instance, Sims (1993), their current popularity in
2. Schorfheide – Bayesian Macroeconometrics: April 18. Consider the reduced-form VAR in Equation (1). Now let Xt = In ⊗ xt and φ = vec(Φ). Φc ] . We defined xt = [yt−1 . .Del Negro. arises from the interest in documenting time-varying features of business cycles in the United States and other countries. . unemployment. The ut innovations are also . We let the parameters evolve according to the random-walk process: φt = φt−1 + νt . yt−p . . (91) We restrict the covariance matrix Q to be diagonal and the parameter innovations νt to be uncorrelated with the VAR innovations ut . The rationale for their reduced-form specification is provided by models in which the policy maker and/or agents in the private sector gradually learn about the dynamics of the economy and consequently adapt their behavior (see Sargent (1999)). νt ∼ iidN (0. φt . as well as for the competing Markov-switching approach of Sims and Zha (2006) discussed in Section 5. To the extent that this adjustment occurs gradually in every period. Then we can write the VAR as yt = Xt φt + ut . They estimated a VAR in which the coefficients follow unit-root autoregressive processes. Q). Cogley and Sargent (2002) set out to investigate time-variation in US inflation persistence using a three-variable VAR with inflation. Cogley and Sargent (2005b) address this criticism of their earlier work by adding time-varying volatility to their model. 1] and Φ = [Φ1 . and the agents might slowly learn about the policy change. The central bank might adjust its target inflation rate in view of changing beliefs about the effectiveness of monetary policy. it can be captured by models in which the coefficients are allowed to vary in each period. . Φp . φ with a vector of time-varying coefficients. . and interest rates. . who took advantage of the MCMC innovations in the 1990s. The motivation for their work. Cogley and Sargent (2002)’s work was criticized by Sims (2002a). . 2010 64 empirical macroeconomics is largely due to Cogley and Sargent (2002). + Φp yt−p + Φc + ut . . . who pointed out that the lack of time-varying volatility in their VAR may well bias the results in favor of finding changes in the dynamics. (90) where we replaced the vector of constant coefficients. which we are reproducing here for convenience: yt = Φ1 yt−1 + . . Our subsequent exposition of a TVP VAR allows for drifts in both the conditional mean and the variance parameters.
(92) In the decomposition of Σt . .5 to make the innovation variances for shocks in DSGE models time varying. nsim : 1.4. If the prior distributions for φ0 .1: Gibbs Sampler for TVP VAR For s = 1. Algorithm 5. . then one can use the following Gibbs sampler for posterior inference. described in Giordani. . Σt = B −1 Ht (B −1 ) . σn (s−1) . σ1 (s−1) . σi ). Q(s−1) . Condi- tional on the VAR parameters φt . In practice these priors are chosen to ensure that the shocks to (91) and (93) are small enough that the short.2.t random walk: ln hi. σ1 (s−1) . their variance now evolves over time: ut ∼ N (0. . and the σi ’s are conjugate.t . . Q. H1:T (s) (s−1) . The prior distributions for Q and the σi ’s can be used to express beliefs about the magnitude of the period-to-period drift in the VAR coefficients and the changes in the volatility of the VAR innovations. . but unlike in Section 2. Y ).t = ln hi. B. (93) Notice that this form of stochastic volatility was also used in Section 4. and Kohn (This Volume). Pitt. and Ht is a diagonal matrix with elements h2 following a geometric i.t ∼ iidN (0. According to (92). . φ1:T can be sampled using the algorithm developed by Carter and Kohn (1994). But is normally distributed with variance Ht : 1 But = Ht2 t . the matrix B is a lower-triangular matrix with ones on the diagonal. Σt ). Schorfheide – Bayesian Macroeconometrics: April 18. Y ). Q(s−1) .and medium-run dynamics of yt are not swamped by the random-walk behavior of φt and Ht . (90) and (91) provide a state-space representation for yt . Draw B (s) conditional on (φ1:T . Thus. Thus. σn (s−1) .Del Negro. Draw φ1:T conditional on (B (s−1) . the innovations to equation (90) are known. 2. . 2010 65 normally distributed. 2 ηi. H1:T (s) (s−1) . where t (94) is a vector of standard normals. . the problem of sampling from the posterior distribution of B under a conjugate prior is identical to the problem of sampling from the posterior distribution of A0 in the structural VAR specification (30) described in detail in Section 2.t−1 + ηi.
V 0 ). Del Negro (2003) advocates the use of a shrinkage prior with tighter variance than Cogley and Sargent’s to partly overcome the problem of overfitting. . and Chib (1998) to draw the sequences hi. Draw H1:T conditional on (φ1:T . and unemployment to estimate a time-varying monetary policy rule for the postwar United States. 2010 3. A Bayesian analysis of a TVP cointegration model can be found in Koop. . i. H1:T . Y ) from the appro- priate Inverted Wishart distribution derived from (91). Koop and Potter (2008) discuss how to impose such a restriction efficiently. . φ0 .t:T . s 5. Finally. Q(s−1) . no cointegration restrictions are imposed on the VAR specified in (90).5. σn conditional on (φ1:T . Conditional on φt and B. Draw σ1 . where φ0 and V 0 are obtained by estimating a fixed-coefficient VAR with a flat prior on a presample.) ut ∼ N (0. the parameters of the VAR in equation (30). then this model generalizes the constant-coefficient structural SVAR discussed in Section 2.t which is identical to (72). Thus. H1:T . Primiceri (2005) extends the above TVP VAR by also allowing the nonzero offdiagonal elements of the contemporaneous covariance matrix B to evolve as randomwalk processes. h2 ). Schorfheide – Bayesian Macroeconometrics: April 18. Primiceri (2005) uses a structural TVP VAR for interest rates. B (s) . . . Polson. B (s) . 4. Q(s) . For the initial vector of VAR coefficients. B (s) . Y ). σ1 (s) (s) (s−1) . and Strachan (2008).Del Negro. Shephard. and Rossi (1994) or Kim. Cogley and Sargent (2002) and Cogley and Sargent (2005b) use a prior of the form φ0 ∼ N (φ0 . Leon-Gonzalez. inflation. we can write the i’th equation of (94) as zi. σn (s−1) . . σn (s−1) .t = B(i. σ1 (s) (s) (s−1) 66 . as in Section 4. Del Negro (2003) suggests an alternative approach where time-variation is directly imposed on the parameters of the structural model – that is. . one can use the algorithms of Jacquier. Draw Q(s) conditional on (φ1:T . Imposing the restriction that for each t all roots of the characteristic polynomial associated with the VAR coefficients φt lie outside the unit circle introduces a complication that we do not explore here.4 with Ω = I to a TVP environment. If one is willing to assume that the lower-triangular Bt ’s identify structural shocks. Y ) from the appropriate (s) (s) (s) Inverted Gamma distributions derived from (93).
for additional shocks or time-varying parameters to be identifiable. Thus. as in (66). (96) Now imagine replacing the constant Frisch elasticity ν in (52) and (95) by a timevarying process νt .6. the preference shock appears in the labor supply function Ht = ν Wt − ν Ct + (1 + ν)Bt . in which we have replaced the constant parameter B. Thus. by a time-varying parameter Bt . 2010 5. In a log-linear approximation of the equilibrium conditions. we never mentioned time-varying parameters. then νt has no effects on the first-order dynamics. it is important that the log-linear approximation be replaced by a nonlinear solution technique. we simply referred to Bt as a labor supply or preference shock. the time-varying elasticity will appear as an additional additive shock in (96) and therefore be indistinguishable in its dynamic effects from Bt . the authors use a second-order perturbation method to solve the model and the particle filter to approximate its likelihood function. (95) We can interpret our original objective function (52) as a generalization of (95). Thus.1. the topic of DSGE models with time-varying autoregressive parameters has essentially been covered in Section 4. If H∗ /B∗ = 1.2 DSGE Models with Drifting Parameters 67 Recall the stochastic growth model introduced in Section 4. Suppose that one changes the objective function of the household to ∞ I t E s=0 β t+s ln Ct+s − (Ht+s /B)1+1/ν 1 + 1/ν . provided that the steady-state ratio H∗ /B∗ = 1. Fern´ndez-Villaverde and Rubio-Ram´ a ırez (2008) take a version of the constant-coefficient DSGE model estimated by Smets and Wouters (2003) and allow for time variation in the coefficients that determine the interest-rate policy of the central bank and the degree of price and wage stickiness in the economy.1.which affects the disutility associated with working. a time-varying parameter is essentially just another shock. For instance. . But in our discussion of the DSGE model in Section 4. then all structural shocks (or timevarying coefficients) appear additively in the equilibrium conditions. for instance. If the DSGE model is log-linearized.Del Negro. To capture the different effects of a typical monetary policy shock and a shock that changes the central bank’s reaction to deviations from the inflation target.1. Schorfheide – Bayesian Macroeconometrics: April 18.
respectively.2. We will begin by adding regime-switching to the coefficients of the reduced-form VAR specified in (1). . l. without any restrictions. For simplicity. 2010 68 5. . suppose that M = 2 and all elements of Φ(Kt ) and Σ(Kt ) switch simultaneously. Σ(Kt )) (97) using the same definitions of Φ and xt as in Section 2.2. Σ(l)) are MNIW and the priors for the regime-switching probabilities π11 and π22 are independent Beta distributions. MS models are able to capture sudden changes in time-series dynamics.1. . m ∈ {1.2 Models with Markov-Switching Parameters Markov-switching (MS) models represent an alternative to drifting autoregressive coefficients in time-series models with time-varying parameters. who used them to allow for different GDP-growth-rate dynamics in recession and expansion states. . Here. nsim : . M }.2). Recall the two different representations of a time-varying target inflation rate in Figure 7. . . ut ∼ iidN (0. 2.1 Markov-Switching VARs MS models have been popularized in economics by the work of Hamilton (1989). Unlike before. We denote the values of the VAR parameter matrices in state Kt = l by Φ(l) and Σ(l).2. Schorfheide – Bayesian Macroeconometrics: April 18.1) and then consider the estimation of DSGE models with MS parameters (section 5. the coefficient vector Φ is now a function of Kt . l = 1. We will begin with a discussion of MS coefficients in the context of a VAR (section 5.2: Gibbs Sampler for Unrestricted MS VARs For s = 1. Kt is a discrete M -state Markov process with time-invariant transition probabilities πlm = P [Kt = l | Kt−1 = m]. If the prior distributions of (Φ(l). which we write in terms of a multivariate linear regression model as yt = xt Φ(Kt ) + ut . 5. then posterior inference in this simple MS VAR model can be implemented with the following Gibbs sampler Algorithm 5. . The piecewise constant path of the target can be generated by a MS model but not by the driftingparameter model of the previous subsection. .Del Negro.
S. Y ) using a variant of the Carter and Kohn (1994) approach. Draw π11 and π22 conditional on (Φ(s) (s). described in detail in Giordani. If one ignores the relationship between the transition probabilities and the distribution of K1 . . Σ(s) (s). Draw (Φ(s) (l). Draw K1:T conditional on (Φ(s) (l). then model (97) becomes a change-point model in which state 2 is the final state. the unrestricted MS VAR in (97) with coefficient matrices that are a priori independent across states may involve a large number of 4 (s) (i−1) . π11 and Kohn (This Volume). If K1 is distributed according to the stationary distribution of the Markov chain. Pitt. l = 1. but the time of the break is unknown. Chopin and Pelgrin (2004) consider a setup that allows the joint estimation of the parameters and the number of regimes that have actually occurred in the sample period. Leon-Gonzalez. Let Tl be a set that contains the time periods when Kt = l. 2010 1. ut ∼ N (0. π11 (i−1) (i−1) 69 . Σ(s) (l). 2. (s) (s) (s) (s) (s) More generally. Koop and Potter (2007) and Koop and Potter (2009) explore posterior inference in change-point models under various types of prior distributions. Y ). By increasing the number of states and imposing the appropriate restrictions on the transition probabilities. and Strachan (2009) consider a modification of Primiceri (2005)’s framework where parameters evolve according to a change-point model and study the evolution over time of the monetary policy transmission mechanism in the United States. the posterior of Φ(l) and Σ(l) is MNIW. Σ(s) (l)) conditional on (K1:T . Koop. π22 (i−1) . t ∈ Tl . Under a conjugate prior. Schorfheide – Bayesian Macroeconometrics: April 18. 3. If one imposes the condition that π22 = 1 and π12 = 0.4 Alternatively.j + πjj = 1. one can generalize the change-point model to allow for several breaks. then the posteriors of π11 and π22 take the form of Beta distributions. 2. Σ(l)). GDP growth toward stabilization. obtained from the regression yt = xt Φ(l) + ut . for a process with M states one would impose the restrictions πM M = 1 and πj+1. In a multivariate setting. Y ). Kim and Nelson (1999a) use a changepoint model to study whether there has been a structural break in postwar U. such a model can be viewed as a structural-break model in which at most one break can occur. π22 (i−1) . then the Beta distributions can be used as proposal distributions in a Metropolis step. K1:T .Del Negro.
The Gibbs sampler for the parameters of (100) is obtained .S. (ii) only the coefficients of the private-sector equations switch.l correspond to the coefficient associated with lag l of variable i in equation j.l λi. For instance. ut ∼ iidN (0. if the prior for D(Kt ) is centered at zero.1. Sims and Zha (2006) impose constraints on the evolution of D(Kt ) across states. Thus far. This model captures growth-rate differentials between recessions and expansions and is used to capture the joint dynamics of U. To avoid a proliferation of parameters. (100) If D(Kt ) = 0. The authors impose the restriction that only the trend is affected by the MS process: ∗ yt = yt + Γ0 (Kt ) + yt . ¯ The authors reparameterize the k × n matrix A(Kt ) as D(Kt ) + GA0 (Kt ). the prior for the reduced-form VAR is centered at a random-walk representation.Del Negro. .j. and (iii) only coefficients that implicitly control innovation variances (heteroskedasticity) change.j. + Φp yt−p + ut . Sims and Zha (2006) extend the structural VAR given in (30) to a MS setting: yt A0 (Kt ) = xt A(Kt ) + t . and parameter restrictions can compensate for lack of sample information. as implied by the mean of the Minnesota prior (see Section 2. Thus. yt = Φ1 yt−1 + . I) (99) is a vector of orthogonal structural shocks and xt is defined as in Section 2. (98) where ∗ ∗ yt = yt−1 + Γ1 (Kt ). where t t ∼ iidN (0.3 that expresses yt as a deterministic trend and autoregressive deviations from this trend. Paap and van Dijk (2003) start from the VAR specification used in Section 2. The authors impose that di. aggregate output and consumption. . Schorfheide – Bayesian Macroeconometrics: April 18. yt A0 (Kt ) = xt (D(Kt ) + GA0 (Kt )) + t . Let di. we have focused on reduced-form VARs with MS parameters. then the reduced-form VAR coefficients are given by Φ = A(Kt )[A0 (Kt )]−1 = G and the elements of yt follow random-walk processes.j. Loosely speaking.j (Kt ). where S is a k × n with the n × n identity matrix in the first n rows and zeros elsewhere.l (Kt ) = δi. The authors use their setup to estimate MS VAR specifications in which (i) only the coefficients of the monetary policy rule change across Markov states. This specification allows for shifts in D(Kt ) to be equation or variable dependent but rules out lag dependency.2). 2010 70 coefficients. Σ).
In most applications. Consider the nonlinear equilibrium conditions of our stochastic growth model in (61).2 DSGE Models with Markov-Switching Coefficients A growing number of papers incorporates Markov-switching effects in DSGE models. Kt+1 . and solving the nonlinear model while accounting for the time variation in θ. it is straightforward. E E E The vector ηt comprises the following one-step-ahead rational expectations forecast errors: ηt = (Ct − I t−1 [Ct ]). and Zha (2008).2. Details are provided in Sims. albeit slightly tedious. 5. The most rigorous and general treatment of Markov-switching coefficients would involve replacing the vector θ with a function of the latent state Kt . Ht . I t [at+1 ]. Rt .t . one can define the vector xt such that the observables yt can. Waggoner. we write the linearized equilibrium conditions of the DSGE model in the following canonical form: Γ0 (θ)xt = C(θ) + Γ1 (θ)xt−1 + Ψ(θ) t + Π(θ)ηt . Schorfheide – Bayesian Macroeconometrics: April 18. Yt . θ(Kt ). which we denote by θ(Kt ). and the vector xt can be defined as follows: xt = Ct . the literature has focused on various short-cuts. Wt . .2. At . that is: yt = Ψ0 (θ) + Ψ1 (θ)t + Ψ2 (θ)xt .4 and 5.t ] . I t [Ct+1 ]. Bt .2. b. Following Sims (2002b). as in Section 4. which introduce Markov-switching in the coefficients of the linearized model given by (66). 2010 71 by merging and generalizing Algorithms 2. It .Del Negro. With these definitions. (at − I t−1 [at ]). including our stochastic growth model. to rewrite (66) in terms of the canonical form (101). be expressed simply as a linear function of xt . Since the implementation of the solution and the subsequent computation of the likelihood function are very challenging. at . (102) Markov-switching can be introduced into the linearized DSGE model by expressing the DSGE model parameters θ as a function of a hidden Markov process Kt . I t [Rt+1 ] . (Rt − I t−1 [Rt ]) E E E and t stacks the innovations of the exogenous shocks: t =[ a. θ is defined in (63). (101) For the stochastic growth model presented in Section 4.
For instance. but not the matrices Ψ0 . Schorfheide (2005) constructs an approximate likelihood that depends only on θ1 .1. Ψ2 . (104) where only Φ0 and µ depend on the Markov process Kt (indirectly through θ2 (Kt )). Ψ1 . discussed in Kim and Nelson (1999b). Φ1 . and Φ . Waggoner.1 to implement posterior inference. 2. Equation (104) defines a (linear) Markov-switching state-space model. Schorfheide – Bayesian Macroeconometrics: April 18. the resulting rational expectations system can be written as Γ0 (θ1 )xt = C(θ1 . and the state transition probabilities are denoted by πlm . which can be low or high. θ2 (1). To capture this explanation in a Markovswitching rational expectations model. Using the same notation as in Section 5. 2010 72 Schorfheide (2005) considers a special case of this Markov-switching linear rational expectations framework. and Zha (2009) is more ambitious in that it allows for switches in all the matrices of the canonical rational expectations model: Γ0 (θ(Kt ))xt = C(θ(Kt )) + Γ1 (θ(Kt ))xt−1 + Ψ(θ(Kt )) t + Π(θ(Kt ))ηt . A candidate explanation for the reduction of macroeconomic volatility in the 1980s is a more forceful reaction of central banks to inflation deviations. θ2 (Kt )) + Γ1 (θ1 )xt−1 + Ψ(θ1 ) t + Π(θ1 )ηt (103) and is solvable with the algorithm provided in Sims (2002b). . The analysis in Schorfheide (2005) is clearly restrictive. If we partition the parameter vector θ(Kt ) into a component θ1 that is unaffected by the hidden Markov process Kt and a component θ2 (Kt ) that varies with Kt and takes the values θ2 (l). This likelihood function is then used in Algorithm 4.2. because in his analysis the process Kt affects only the target inflation rate of the central bank. with the understanding that the system matrices are functions of the DSGE model parameters θ1 and θ2 (Kt ). it is necessary that not just the intercept in (101) but also the slope coefficients be affected by the regime shifts. xt = Φ1 xt−1 + Φ [µ(Kt ) + t ] + Φ0 (Kt ). there is a large debate in the literature about whether the central bank’s reaction to inflation and output deviations from target changed around 1980. Thus. Following a filtering approach that simultaneously integrates over xt and Kt .Del Negro. subsequent work by Davig and Leeper (2007) and Farmer. l = 1. θ2 (2) and the transition probabilities π11 and π22 . The solution takes the special form yt = Ψ0 + Ψ1 t + Ψ2 xt . the number of states is M = 2.
Sims (1993) and Cogley. Sims and Zha (2006) conduct inference with a MS VAR and find no support for the hypothesis that the parameters of the monetary policy rule differed pre. Cogley and Sargent (2005b) find that their earlier empirical results are robust to time-variation in the volatility of shocks and argue that changes in the monetary policy rule are partly responsible for the changes in inflation dynamics. Bayesian inference in a TVP VAR yields posterior estimates of the reduced-form coefficients φt in (90). whether monetary policy played a major role in affecting inflation dynamics. for example. they provide evidence that it was the behavior of the private sector that changed and that shock heteroskedasticity is important. that is. Conditioning on estimates of φt for various periods between 1960 and 2000. the debate over whether the dynamics of U. or other structural changes – it is likely that these same causes affected the dynamics of inflation. Cogley and Sargent (2002) compute the spectrum of inflation based on their VAR and use it as evidence that both inflation volatility and persistence have changed dramatically in the United States.and post-1980. To the contrary. to the extent that they have. Whatever the causes of the changes in output dynamics were – shocks. He claims that variation in the volatility of the shocks is the main cause for the lower volatility of both inflation and business cycles in the post-Volcker period. monetary policy. this debate evolved in parallel to the debate over the magnitude and causes of the Great Moderation. 2010 73 Characterizing the full set of solutions for this general MS linear rational expectations model and conditions under which a unique stable solution exists is the subject of ongoing research. Here. 5. including macroeconomic forecasting. Similarly.Del Negro.3 Applications of Bayesian TVP Models Bayesian TVP models have been applied to several issues of interest.S. Primiceri (2005) argues that monetary policy has indeed changed since the 1980s but that the impact of these changes on the rest of the economy has been small. using an AR time-varying coefficients VAR identified with sign restrictions Canova and Gambetti (2009) find little evidence that monetary policy has become more aggressive in . Schorfheide – Bayesian Macroeconometrics: April 18. Morozov. Naturally. we shall focus on one specific issue. inflation changed over the last quarter of the 20th century and. and Sargent (2005). namely. Based on an estimated structural TVP VAR. the decline in the volatility of business cycles around 1984 initially documented by Kim and Nelson (1999a) and McConnell and Perez-Quiros (2000).
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responding to inflation since the early 1980s. Cogley and Sbordone (2008) use a TVP VAR to assess the stability of the New Keynesian Phillips curve during the past four decades. Given the numerical difficulties of estimating nonlinear DSGE models, there currently exists less published empirical work based on DSGE models with timevarying coefficients. Two notable exceptions are the papers by Justiniano and Primiceri (2008) discussed in Section (4.5) and Fern´ndez-Villaverde and Rubio-Ram´ a ırez (2008). The latter paper provides evidence that after 1980 the U.S. central bank has changed interest rates more aggressively in response to deviations of inflation from the target rate. The authors also find that the estimated frequency of price changes has decreased over time. This frequency is taken as exogenous within the Calvo framework they adopt.
6
Models for Data-Rich Environments
We now turn to inference with models for data sets that have a large cross-sectional and time-series dimension. Consider the VAR(p) from Section 2: yt = Φ1 yt−1 + . . . + Φp yt−p + Φc + ut , ut ∼ iidN (0, Σ), t = 1, . . . , T
where yt is an n × 1 vector. Without mentioning it explicitly, our previous analysis was tailored to situations in which the time-series dimension T of the data set is much larger than the cross-sectional dimension n. For instance, in Illustration 2.1 the time-series dimension was approximately T = 160 and the cross-sectional dimension was n = 4. This section focuses on applications in which the ratio T /n is relatively small, possibly less than 5. High-dimensional VARs are useful for applications that involve large cross sections of macroeconomic indicators for a particular country – for example, GDP and its components, industrial production, measures of employment and compensation, housing starts and new orders of capital goods, price indices, interest rates, consumer confidence measures, et cetera. Examples of such data sets can be found in Stock and Watson (1999) and Stock and Watson (2002). Large-scale VARs are also frequently employed in the context of multicountry econometric modeling. For instance, to study international business cycles among OECD countries, yt might
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be composed of aggregate output, consumption, investment, and employment for a group of 20 to 30 countries, which leads to n > 80. In general, for the models considered in this section there will be a shortage of sample information to determine parameters, leading to imprecise inference and diffuse predictive distributions. Priors can be used to impose either hard or soft parameter restrictions and thereby to sharpen inference. Hard restrictions involve setting combinations of VAR coefficients equal to zero. For instance, Stock and Watson (2005), who study international business cycles using output data for the G7 countries, impose the restriction that in the equation for GDP growth in a given country enter only the trade-weighted averages of the other countries’ GDP growth rates. Second, one could use very informative, yet nondegenerate, prior distributions for the many VAR coefficients, which is what is meant by soft restrictions. Both types of restrictions are discussed in Section 6.1. Finally, one could express yt as a function of a lower-dimensional vector of variables called factors, possibly latent, that drive all the comovement among the elements of yt , plus a vector ζt of so-called idiosyncratic components, which evolve independently from one another. In such a setting, one needs only to parameterize the evolution of the factors, the impact of these on the observables yt , and the evolution of the univariate idiosyncratic components, rather than the dynamic interrelationships among all the elements of the yt vector. Factor models are explored in Section 6.2.
6.1
Restricted High-Dimensional VARs
We begin by directly imposing hard restrictions on the coefficients of the VAR. As before, define the k × 1 vector xt = [yt−1 , . . . , yt−p , 1] and the k × n matrix Φ = [Φ1 , . . . , Φp , Φc ] , where k = np + 1. Moreover, let Xt = In ⊗ xt and φ = vec(Φ) with dimensions kn × n and kn × 1, respectively. Then we can write the VAR as yt = X t φ + u t , ut ∼ iidN (0, Σ). (105)
To incorporate the restrictions on φ, we reparameterize the VAR as follows: φ = M θ. (106)
θ is a vector of size κ << nk, and the nk × κ matrix M induces the restrictions by linking the VAR coefficients φ to the lower-dimensional parameter vector θ. The elements of M are known. For instance, M could be specified such that the
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coefficient in Equation i, i = 1, .., n, associated with the l’th lag of variable j is the sum of an equation-specific, a variable-specific parameter, and a lag-specific parameter. Here, θ would comprise the set of all n + n + p equation/variable/lagspecific parameters, and M would be an indicator matrix of zeros and ones that selects the elements of θ associated with each element of φ. The matrix M could also be specified to set certain elements of φ equal to zero and thereby exclude regressors from each of the n equations of the VAR. Since the relationship between φ and θ is linear, Bayesian inference in this restricted VAR under a Gaussian prior for θ and an Inverted Wishart prior for Σ is straightforward. To turn the hard restrictions (106) into soft restrictions, one can construct a hierarchical model, in which the prior distribution for φ conditional on θ has a nonzero variance: φ = M θ + ν, ν ∼ N (0, V ), (107)
where ν is an nk ×1 vector with nk ×nk covariance matrix V . The joint distribution of parameters and data can be factorized as p(Y, φ, θ) = p(Y |φ)p(φ|θ)p(θ). (108)
A few remarks are in order. First, (108) has the same form as the DSGE-VAR discussed in Section 4.7.3, except that the conditional distribution of φ given θ is centered at the simple linear restriction M θ rather than the rather complicated VAR approximation of a DSGE model. Second, (108) also nests the Minnesota prior discussed in Section 2.2, which can be obtained by using a degenerate distribution for θ concentrated at θ with a suitable choice of M , θ, and V . Third, in practice the choice of the prior covariance matrix V is crucial for inference. In the context of the Minnesota prior and the DSGE-VAR, we expressed this covariance matrix in terms of a low-dimensional vector λ of hyperparameters such that V (λ) −→ 0 ( V (λ) −→ ∞) as λ −→ ∞ ( λ −→ 0) and recommended conditioning on a value of λ that maximizes the marginal likelihood function pλ (Y ) over a suitably chosen grid. Finally, since the discrepancy between the posterior mean estimate of φ and the restriction M θ can be reduced by increasing the hyperparameter λ, the resulting Bayes estimator of φ is often called a shrinkage estimator. De Mol, Giannone, and Reichlin (2008) consider a covariance matrix V that in our notation takes the form V = Σ ⊗ (Ik /λ2 ) and show that there is a tight connection between these shrinkage estimators and estimators of conditional mean functions obtained from factor
which we will discuss below.Del Negro. they allow for timevariation in φ and let φt = M θ + νt . The authors interpret the time-varying θt as a vector of latent factors. Inserting (109) into (105). (110) The n × κ matrix of regressors Xt M essentially contains weighted averages of the regressors. If one chooses a prior covariance matrix of the form V = Σ ⊗ (Ik /λ2 ). Schorfheide – Bayesian Macroeconometrics: April 18. then the covariance matrix of ζt reduces to (1 + (xt xt )/λ2 )Σ. we obtain the system yt = (Xt M )θ + ζt . They discuss in detail how to implement Bayesian inference in this more general environment. V ). Their setting is therefore related to that of the factor models described in the next subsection. Canova and Ciccarelli (2009) allow the deviations of φ from the restricted subspace characterized by M θ to differ in each period t. where the weights are given by the columns of M . which simplifies inference. The random vector ζt is given by ζt = Xt νt +ut and. Canova and Ciccarelli (2009) further generalize expression (109) by assuming that the vector θ is time-varying and follows a simple autoregressive law of motion. since xt contains lagged values of yt . νt ∼ iidN (0. λ) ∝ (1 + (xt xt )/λ2 )Σ T −1/2 (111) × t=1 exp − 1 (yt − Xt M θ) Σ−1 (yt − Xt M θ) . resulting in a model for which Bayesian inference is fairly straightforward to implement. 2010 77 models. (109) The deviations νt from the restriction M θ are assumed to be independent over time. forms a Martingale difference sequence with conditional covariance matrix Xt V Xt + Σ. 2(1 + (xt xt )/λ2 ) and Bayesian inference under a conjugate prior for θ and Σ is straightforward. M could be chosen such that yt is a . In fact. as is often done in the factor model literature. In multicountry VAR applications. the random deviations νt can be merged with the VAR innovations ut . They document empirically that with a suitably chosen shrinkage parameter the forecast performance of their Bayes predictor constructed from a large number of regressors is similar to the performance of a predictor obtained by regressing yt on the first few principal components of the regressors xt . The likelihood function (conditional on the initial observations Y−p+1:0 ) takes the convenient form p(Y1:T |θ. Formally.
T. n.t ∼ iidN (0. (112) Here.2 Dynamic Factor Models Factor models describe the dynamic behavior of a possibly large cross section of observations as the sum of a few common components.2. and of series-specific components. say. .4 surveys various extensions of the basic DFM. The factors follow a vector autoregressive processes of order q: ft = Φ0.Del Negro. (113) . Schorfheide – Bayesian Macroeconometrics: April 18.2. . ft is a κ × 1 vector of factors that are common to all observables.1. . then the business cycles in the various countries are highly synchronized. which capture idiosyncratic dynamics of each series.2. . ai is a constant. . Our baseline version of the DFM is introduced in Section 6.2. .t .1 ft−1 + . t = 1. .t = ai + λi ft + ξi.t to the factor ft . for example – the contribution of Stock and Watson (1989) generated renewed interest in this class of models among macroeconomists. and posterior inference is described in Section 6. Moreover. 6. While Stock and Watson (1989) employ maximum likelihood methods. average lagged output growth and unemployment across countries.t . Finally. Canova and Ciccarelli (2009) use their framework to study the convergence in business cycles among G7 countries. . If most of the variation in the elements of yt is due to the cross-sectional averages.t is an idiosyncratic process that is specific to each i. i = 1. Geweke and Zhou (1996) and Otrok and Whiteman (1998) conduct Bayesian inference with dynamic factor models. which explain comovements.q ft−q + u0. These authors use a factor model to exploit information from a large cross section of macroeconomic time series for forecasting. Section 6. 6. and λi is a 1 × κ vector of loadings that links yi. . Σ0 ). into the sum of two unobservable components: yi. u0. While factor models have been part of the econometricians’ toolbox for a long time – the unobservable index models by Sargent and Sims (1977) and Geweke (1977)). Some applications are discussed in Section 6. + Φ0. 2010 78 function of lagged country-specific variables and.2. .2.t . and ξi.1 Baseline Specification A DFM decomposes the dynamics of n observables yi.3.
One can premultiply ft and its lags in (112) and (113) as well as u0.Del Negro. and so forth. . We used 0-subscripts to denote parameter matrices that describe the law of motion of the factors. .t−1 + .t ∼ iidN (0.t = φi. and 0 denotes a zero restriction. Without further restrictions.pi ξi. X denotes an unrestricted element. σi ). However. without changing the distribution of the observables. These orthogonality assumptions are important to identifying the factor model.t and y2.t innovations are independent across i and independent of the innovations to the law of motion of the factors u0.κ = . . these zero restrictions alone are not sufficient for identification because the factors and hence the matrices Φ0. 2010 79 where Σ0 and the Φ0.t is a κ × 1 vector of innovations. . .t does not affect y1.t . Under this transformation. 2 ui.t by a κ × κ invertible matrix H and postmultiply the vectors λi and the matrices Φ0.t . The restrictions can be interpreted as follows. . λκ The loadings λi for i > κ are always left unrestricted.j matrices are of dimension κ × κ and u0.t does not affect y1. Schorfheide – Bayesian Macroeconometrics: April 18. . Example 6.and postmultiplication of an arbitrary invertible lower-triangular κ × κ matrix Htr without changing the distribution of the observables. Λ1. There are several approaches to restricting the parameters of the DFM to normalize the factors and achieve identification. X X ···X X Λ1.t . factor f3. the latent factors and the coefficient matrices of the DFM are not identifiable.κ to be lower-triangular: X 0···0 0 .t−pi + ui.j by H −1 . . According to (115). the factor innovations . .κ = Λtr 1. The idiosyncratic components follow autoregressive processes of order pi : ξi. the ui. (114) At all leads and lags. = .κ (115) Here. We will provide three specific examples in which we impose restrictions on Σ0 and the first κ loading vectors stacked in the matrix λ1 .t .. . factor f2.1: Geweke and Zhou (1996) restrict Λ1. as they imply that all comovements in the data arise from the factors. .j and Σ0 could still be transformed by pre.1 ξi. + φi.
i = 1.t . factor fi. Moreover. be the diagonal elements of Λ1.κ .κ is restricted to be the identity matrix and Σ0 is an unrestricted covariance matrix.t is uncorrelated with all other observables.t are factors that affect the Eastern and Western regions. i = 1.i ≥ 0. the one-entries on the diagonal of Λ1. (117) Thus. 3. For instance. the signs of the factors need to be normalized. In this case. imagine that the factor model is used to study comovements in output across U.κ take care of the sign normalization.Del Negro.t . . As in Example 6. .t correspond to output in state i in period t. . (116) Finally. where f1. . one can choose Htr = Σ−1 such 0. The one-entries on the diagonal of Λ1. .κ is restricted to be lower-triangular with ones on the diagonal and Σ0 is a diagonal matrix with nonnegative elements. Since under the normalization λi. .t is interpreted as a national business cycle and f2. Example 6. respectively.i . 2010 80 become Htr u0. . κ. The sign normalization can be achieved with a set of restrictions of the form λi. we simply let Σ0 = Iκ .S.tr and its transpose. Example 6.j = 0 if state i does not belong to region j = 2. Let λi. κ. This transformation leads to a normalization in which Λ1.2. To implement this normalization. This transformation leads to a normalization in which Λ1. Schorfheide – Bayesian Macroeconometrics: April 18. Imposing λ1. there exists a potential pitfall.1 = 1 may result in a misleading inference for the factor as well as for the other loadings. . For concreteness. suppose that the number of factors is κ = 3. .3: Suppose we start from the normalization in Example 6.i = 1. . . and let yi. .κ the loadings by H −1 . (115).tr that the factor innovations reduce to a vector of independent standard Normals.t and f3. one might find it attractive to impose overidentifying restrictions.κ by H −1 . . and (117) provide a set of identifying restrictions.1 and proceed with premultiplying the factors by the matrix H = Λtr in (115) and postmultiplying 1. states. (116). one could impose the condition that λi. i = 1. Since Σ0 can be expressed as the product of the unique lowertriangular Choleski factor Σ0. Finally. imagine that there is only one factor and that y1. κ.2: Suppose we start from the normalization in the previous example and proceed with premultiplying the factors by the diagonal matrix H that is composed of the diagonal elements of Λtr in (115) and postmultiplying the loadings 1.t is forced to have a unit impact on yi.κ also take care of the sign normalization.
which can be derived from the autoregressive law of motion (114) by assuming that ξi. . . the distribution of ft conditional on (Y1:t−1 . yi. T. . φi. we adopt the convention that Yt0 :t1 and Ft0 :t1 denote the sequences {yt0 . ft1 }.t−p − ai − λi ft−p ) + ui. . . θ0 ) n × i=1 p(Yi. . ... and latent factors can be written as p(Y1:T .t = ai + λi ft + φi. σi . (F0:p . As we did previously in this chapter. we exploited the fact that the conditional distribution of yi. To obtain the factorization on the right-hand side of (119). θi ) and p(ft |Ft−q:t−1 .p ] .1:p (θi ) . . F0:t−1 . .1 .t−p:t−1 . . . respectively. θi ) in (119) represents the distribution of the first p observations conditional on yi. . The joint distribution of data. θ0 ) can easily be derived from expressions (118) and (113).1:p |F0:p . . .t |Yi. which is given by ai + f1 .p (yi. .p ] be the parameters entering (118) and θ0 be the parameters pertaining to the law of motion of the factors (113). where L here denotes the lag operator. . To simplify the notation.t .2. Schorfheide – Bayesian Macroeconometrics: April 18. Σi.1:p (θi ) is the covariance matrix of [ξi.t |Yi.t is stationary for all θi in the . ξi. .1 (yi.−(τ +p) = 0 for some τ > 0.1 . Ft−p:t . Moreover. F0:T . The quasi-differenced measurement equation takes the form yi.p Lp . θi ) p(F0:p |θ0 ) i=1 p(θi ) p(θ0 ). parameters.. we will discuss the case in which the lag length in (114) is the same for all i (pi = p) and q ≤ p + 1.2 Priors and Posteriors 81 We now describe Bayesian inference for the DFM.t given (Y1:t−1 . . The distributions p(yi. (118) Let θi = [ai .. yt1 } and {ft0 . . .1 L · · · − φi. for t = p+1. θi ) p(ft |Ft−q:t−1 . +φi.p the factors. θi ) ∼ N . θ0 ) is a function only of Ft−q:t−1 .1 . . If the law of motion of ξi. Premultiply (112) by 1 − φi.t−1 − ai − λi ft−1 ) + .t−p:t−1 and on the factors only through Ft−p:t . Ft−p:t .−(τ +1) = .1:p |F0:p . θ0 ) i=1 T n (119) = t=p+1 n i=1 p(yi. λi . F0:t . θi ) depends on lagged observables only through Yi.t−p:t−1 . {θi }n . The term p(Yi. . 2010 6. ai + fp (120) The matrix Σi.Del Negro. φi. = ξi. respectively.
V φi ). Draws from the distribution associated with (121) can be obtained with the procedure of Chib and Greenberg (1994).. The autoregressive coefficients for the factors and the idiosyncratic shocks have a Normal prior. N (ai . represent the priors for θi and θ0 . p(θi ) and p(θ0 ). . in Otrok and Whiteman (1998). . Specifically..1 . If the prior for λi. Y1:T ) ∝ p(θi ) t=p+1 p(yi. θ0 . 2010 82 support of the prior. one can set τ = ∞. . and its log is not a quadratic function of θi . In some applications. vec(Φ0. namely... A Gibbs sampler can be used to generate draws from the posterior distribution. the prior for the idiosyncratic volatilities σi can be chosen to be of the Inverted Gamma form. then the density associated with the prior for λi needs to be multiplied by the indicator function I{λi. If . Detailed derivations can be found in Otrok and Whiteman (1998).i ≥ 0} to impose the constraint (117). . Otrok and Whiteman (1998)). Conditional on the factors. κ elements are restricted to be nonnegative to resolve the sign-indeterminacy of the factors as in Example 6. the first two terms on the right-hand side correspond to the density of a Normal-Inverted Gamma distribution. The last term reflects the effect of the initialization of the AR(p) error process.i < 0. V λi ).t lie outside the unit circle. the priors on the constant term ai and the loadings λi are normal. which are typically chosen to be conjugate (see.i . Ft−p:t . θi ). θi ) p(Yi. .q ) ] and assume that Σ0 is normalized to be equal to the identity matrix.i .1 ) . The posterior density takes the form T p(θi |F0:T . The prior for φ0 is N (φ0 . .1:p becomes the covariance matrix associated with the unconditional distribution of the idiosyncratic shocks. it may be desirable to truncate the prior for φ0 (φi ) to rule out parameters for which not all of the roots of the characteristic polynomial associated with the autoregressive laws of motion of ft and ξi. and Σi. Equation (112) is a linear Gaussian regression with AR(p) errors. (121) Under a conjugate prior. φi. If the λi. The initial distribution of the factors p(F0:p |θ0 ) can be obtained in a similar manner using (113). . .t |Yi.Del Negro. for instance. one can use an acceptance sampler that discards all draws of θi for which λi.i ≥ 0}.t−p:t−1 . Schorfheide – Bayesian Macroeconometrics: April 18. the prior for φi = [φi. Define φ0 = [vec(Φ0.1. i = 1.1:p |F0:p . i = 1. The remaining terms. Finally. V ai ) and N (λi . Likewise. . V φ0 ). The basic structure of the sampler is fairly straightforward though some of the details are tedious and can be found. .p ] is N (φi . κ includes the indicator function I{λi. for example.
fp . θ0 . {θi }n . the first two terms are proportional to the density of a MNIW distribution if Σ0 is unrestricted and corresponds to a multivariate normal density if the DFM is normalized such that Σ0 = I. Waggoner. which implies that computational cost is linear in the size of the cross section.i ≥ 0. As in the case of θi . . . . say. Otrok i=1 and Whiteman (1998) explicitly write out the joint Normal distribution of the observations Y1:T and the factors F0:T .n . F0:T ) i=1 such that λi. and 5 If X = [X1 .Del Negro. θ0 . then one can resolve the sign indeterminacy by postprocessing the output of the (unrestricted) Gibbs sampler: for each set of draws ({θi }n . Two approaches exist in the Bayesian DFM literature. . θ0 cannot be directly sampled from. the sampling can be implemented one i at a time. the posterior for the coefficients θ0 in (113) is obtained from a multivariate generalization of the preceding steps. Conditional on the factors. Σ11 − 22 ¡ Σ12 Σ−1 Σ21 . The last terms capture the probability density function of the initial factors f0 . κ. θ0 . one draws the factors F0:T conditional on ({θi }n . X2 ] is distributed N (µ. Since the errors ξi. In the third block of the Gibbs sampler. Schorfheide – Bayesian Macroeconometrics: April 18. Thus.t in equation (112) are independent across i. Σ) then X1 |X2 is distributed N µ1 +Σ12 Σ−1 (X2 −µ2 ). . F0:T |{θi }i=1. Its density can be written as p(θ0 |F0:T . An alternative is to cast the DFM into a linear state-space form and apply the algorithm of Carter and Kohn (1994) for sampling from the distribution of the latent states. described in Giordani. flip the sign of the i’th factor and the sign of the loadings of all n observables on the ith factor. Pitt. one can use a variant of the procedure proposed by Chib and Greenberg (1994). . Hamilton. If the prior for θ0 is conjugate.i < 0. p(Y1:T . . θ0 ) p(θ0 )p(F0:p |θ0 ). Y1:T ) using the formula for conditional means and covariance matrices of a multivariate normal distribution. 2010 83 the prior of the loadings does not restrict λi. Y1:T ) ∝ i=1 t=p+1 T p(ft |Ft−p:t−1 . 22 . θ0 ) and derive the posterior distribution p(F0:T |{θi }i=1.n . .5 Their approach involves inverting matrices of size T and hence becomes computationally expensive for data sets with a large time-series dimension. Y1:T ). but is symmetric around zero. and Zha (2007) discuss the sign normalization and related normalization issues in other models at length. i = 1. (122) The first term on the right-hand side corresponds to the conditional likelihood function of a VAR(q) and has been extensively analyzed in Section 2. where the partitions of µ and Σ conform with the partitions of X. a MNIW distribution.
t ] . The Gibbs sampler can be summarized as follows . To avoid the increase in the dimension of the state vector with the cross-sectional dimension n. We will now provide some more details on how to cast the DFM into state-space form with iid measurement errors and a VAR(1) state-transition equation. . The (p + 1) × 1 vector ft collects the latent states and is defined ˜ as ft = [ft . this conditional distrii=1 bution can be obtained from the joint distribution p(F0:p .t . As mentioned above. Stacking (118) for all i. .. ft−p ] . the Φj ’s are diagonal n × n matrices with elements φ1. we shall subsequently assume that the factor ft is scalar (κ = 1). φn. . Del Negro and Otrok (2008) provide formulas for the initialization. . .t . . Schorfheide – Bayesian Macroeconometrics: April 18.1 . (123) where L is the temporal lag operator. Φ0. .. 01×(p+1−q) ] Ip 0p×1 . .j . . 2010 84 Kohn (This Volume). . . . θ0 ). . λn −λn φn. (125) Since (123) starts from t = p + 1 as opposed to t = 1. .. θ0 ) by using i=1 the formula for conditional means and covariance matrices of a multivariate normal distribution. T. . 0. . un.t = [u0. . Y1:p |{θi }n . .1 . −λ1 φ1. . .j . . an ] . . 0] is an iid (p + 1) × 1 random vector and Φ0 is the (p + 1) × ˜ (p + 1) companion form matrix ˜ Φ0 = [Φ0. t = p + 1. ∗ . . ut = ˜ ˜ ˜ ˜ [u1. . . yn. . . .t ] .t . .. it is convenient to exclude the AR(p) processes ξi. For ease of notation. one needs to initialize the filtering step in the Carter and Kohn (1994) algorithm with the conditional distribution of p(F0:p |Y1:p . a = [a1 .t from the state vector and to use the quasi-differenced measurement equation (118) instead of (112).q .Del Negro.p . and λ1 −λ1 φ1..t . Λ = . . the random variables ut in the measurement equa˜ ˜ tion (123) are iid. ˜ (124) ˜ where u0.1 . . one obtains the measurement equation p p (In − j=1 ˜ Φj Lj )˜t = (In − y j=1 ˜ ˜ ˜ a Φj )˜ + Λ∗ ft + ut .p Due to the quasi-differencing. . The state-transition equation is obtained by expressing the law of motion of the factor (113) in companion form ˜ ˜ ˜ ft = Φ0 ft−1 + u0. . . . −λn φn. yt = [y1. . {θi }n .
Schorfheide – Bayesian Macroeconometrics: April 18.3 Applications of Dynamic Factor Models How integrated are international business cycles? Are countries more integrated in terms of business-cycle synchronization within a region (say. Otrok. Latin America). . {θi }n . . regional factors that capture region-specific cycles (say. and country-specific cycles. Y1:T ). which will be discussed in more detail in Section 7. Draw F0:T . i=1 (s) (s) 3. The model includes a world factor that captures the world business cycle. . . is numerically challenging. θ0 . .1: Sampling from the Posterior of the DFM For s = 1. The authors also consider a MCMC approach where the number of factors is treated as an unknown parameter and is drawn jointly with all the other parameters. investment. The authors estimate a DFM on a panel of annual data on output.2. 2. Lopes and West (2004) discuss the computation of marginal likelihoods for a static factor model in which the factors are iid. and consumption for 60 countries and about 30 years. which is precisely what Kose. 2010 Algorithm 6.Del Negro. In principle. for instance. Y1:T ) from (121). This can be done independently for each i = 1. in the . world cycles are on average as important as country-specific cycles. 6. and Whiteman (2003) do. Draw θ0 conditional on (F0:T (s) (s) (s−1) (s) . we have not discussed the issue of determining the number of factors κ. The exact distributions can be found in the references given in this section. . Draw θi (s) 85 conditional on (F0:T (s−1) . In practice. i=1 We have omitted the details of the conditional posterior distributions. Last. . within Europe) than across regions (say. θ0 (s−1) . conditional on ({θi }n . These factors are assumed to evolve independently from one another. the computation of marginal likelihoods for DFMs. In terms of the variance decomposition of output in the G7 countries. The authors find that international business-cycle comovement is significant. Y1:T ) from (122). one can regard DFMs with different κ’s as individual models and treat the determination of the number of factors as a model selection or a model averaging problem. n. . nsim : 1. which are needed for the evaluation of posterior model probabilities. France and the United States)? Has the degree of comovement changed significantly over time as trade and financial links have increased? These are all natural questions to address using a dynamic factor model.
. not surprisingly. Factor Augmented VARs: Bernanke.4 Extensions and Alternative Approaches We briefly discuss four extensions of the basic DFM presented above. stance of monetary policy and the national business cycle). . .t + λi ft + ξi. suggesting that integration is no higher within regions than across regions. we can conduct inference on the country factors even if the number of series per country is small. .2. t = 1. while the latter is associated with regional business cycles and other region-specific conditions (for example. In a Bayesian framework estimating models where regional or country-specific factors are identified by imposing the restriction that the respective factors have zero loadings on series that do not belong to that region or country is quite straightforward. for example. These extensions include Factor Augmented VARs. Models with such restrictions are harder to estimate using nonparametric methods such as principal components. First. House prices have both an important national and regional component.Del Negro. and Eliasz (2005) introduce Factor augmented VARs (or FAVARs). where the former is associated with nationwide conditions (for example. the FAVAR allows for additional observables y0. . DFMs with time-varying parameters. using Bayesian methods. Boivin. Moreover. The FAVAR approach introduces two changes to the standard factor model. Otrok. 6. which becomes yi. to enter the measurement equation. and Whiteman (2003). much more important than world cycles. while nonparametric methods have a harder time characterizing the uncertainty that results from having a small cross section. T. . Schorfheide – Bayesian Macroeconometrics: April 18. (126) . 2010 86 sense that world and country-specific cycles explain a similar share of the variance of output growth.t = ai + γi y0. as is the case in Kose. n. country-specific cycles are. migration and demographics). The study of house prices is another interesting application of factor models. i = 1. . Del Negro and Otrok (2007) apply dynamic factor models to study regional house prices in the US. For the entire world. Regional cycles are not particularly important at all. hierarchical DFMs.t . . and hybrid models that combine a DSGE model and a DFM.t . the federal funds rate.
The idiosyncratic components ξi. More- over. Second. Bernanke.t−q + u0.t .t evolve according to (114 ). and Ω0 is an arbitrary orthogonal matrix.3) and (ii) the κ × m matrix obtained by stacking the first κ γi ’s is composed of zeros. respectively. and Eliasz (2005) assume that (i) the κ × κ matrix obtained by stacking the first κ λi ’s equals the identity Iκ (as in Example 6. and the innovations to their law 2 of motion ui. Boivin.t = Φ0.t = Σ0.t−1 + . In contrast.4. with the difference that the variance-covariance matrix Σ0 is no longer restricted to be diagonal.t at all leads and lags. the observable vector y0. .t ∼ iidN (0.2. + Φ0. In particular. Bernanke.j matrices are now of size (κ + m) × (κ + m).t and γi are m × 1 and 1 × m vectors.t are subject to the distributional assumptions ui.t as in (21): u0. and Eliasz (2005) apply their model to study the effects of monetary policy shocks in the United States. 2010 87 where y0. Likewise.t is still assumed to be normally distributed with mean 0 and variance Σ0 . For given factors. u0. The appeal of the FAVAR is that it affords a combination of factor analysis with the structural VAR analysis described in Section 2. obtaining the posterior distribution for the parameters of (126) and (127) is straightforward.1 ft−1 y0. The Φ0.t ∼ N (0. Boivin. unanticipated changes in monetary policy only affect the factors with a one-period lag.tr Ω0 0. (127) which is the reason for the term factor augmented VAR. This identification implies that the central bank responds contemporaneously to the information contained in the factors.t relates to a vector of structural shocks 0. The innovation vector u0. At least in principle. conducting inference in a FAVAR is a straightforward application of the tools described in Section 6.t .2. one can assume that the vector of reduced-form shocks u0. In order to achieve identification.q ft−q y0.1. Schorfheide – Bayesian Macroeconometrics: April 18. They identify monetary policy shocks by imposing a short-run identification scheme where Ω0 is diagonal as in Example 2. Σ0 ).t and the unobservable factor ft are assumed to jointly follow a vector autoregressive process of order q: ft y0. the factors can be drawn using expressions (126) and the first κ equations of the VAR . σi ). we maintain the assumption that the innovations ui.t are independent across i and independent of u0.Del Negro. (128) where Σtr is the unique lower-triangular Cholesky factor of Σ0 with nonnegative 0 diagonal elements. .
Mumtaz and Surico (2008) introduce time-variation in the law of motion of the factors (but not in any of the other parameters) and use their model to study cross-country inflation data. and so forth). 2010 88 in (127). The second innovation amounts to introducing stochastic volatility in the law of motion of the factors and the idiosyncratic shocks. Otrok.2. Schorfheide – Bayesian Macroeconometrics: April 18. comovements across countries may have changed as a result of increased financial or trade integration. the regional factors evolve according to a factor model in which the common components are the the world factors. Del Negro and Otrok (2008) accomplish that by modifying the standard factor model in two ways. Del Negro and Otrok (2008) apply this model to study the time-varying nature of international business cycles. in the attempt to determine whether the Great Moderation has country-specific or international roots. switches from fixed to flexible exchange rates. or because of monetary arrangements (monetary unions. This approach is more parsimonious than the one used by Kose. in the study of international business cycles – the application discussed in the previous section – the three levels of aggregation are country. and Whiteman (2003). we may want to allow for timevariation in the parameters of a factor model. This feature allows for changes in the sensitivity of individual series to common factors. Their approach entails building a hierarchical set of factor models. For concreteness. This feature accounts for changes in the relative importance of common factors and of idiosyncratic shocks.Del Negro. Only the most disaggregated factors – the countrylevel factors – would appear in the measurement equation (112). For instance. and world. Moench. Time-Varying Parameters: For the same reasons that it may be useful to allow parameter variation in a VAR as we saw in Section 5. as the measurement and transition equations. the country factors evolve according to a factor model in which the common components are the factors at the next level of aggregation (the regional factors). Both loadings and volatilities evolve according to a random walk without drift as in Cogley and Sargent (2005b). Hierarchical factors: Ng. and Potter (2008) pursue a modeling strategy different from the one outlined in Section 6. where the hierarchy is determined by the level of aggregation. In turn. First. they make the loadings vary over time. regional. respectively.1. in a state-space representation. Combining DSGE Models and Factor Models: Boivin and Giannoni (2006a) estimate a DSGE-DFM that equates the latent factors with the state variables . Similarly.
φi. For instance. Y1:T ). Kryshko (2010) documents that the space spanned by the factors of a DSGE-DFM is very similar to the space spanned by factors extracted from an unrestricted DFM. . . Accordingly. that is. i = 1. . 2010 89 of a DSGE model. As before. λi . Details are provided in Boivin and Giannoni (2006a) and Kryshko (2010).p ] . investment. Using multiple (noisy) measures implicitly allows a researcher to obtain a more precise measure of DSGE model variables – provided the measurement errors are approximately independent – and thus sharpens inference about the DSGE model parameters and the economic state variables. whereas Step (iii) can be implemented with a modified version of the Random-Walk-Metropolis step described in Algorithm 4. Schorfheide – Bayesian Macroeconometrics: April 18. Since in the DSGE-DFM the latent factors have a clear economic interpretation. This relationship can be used to center a prior distribution for λi . Y1:T ). θDSGE . . i=1 (ii) the conditional distribution of F1:T given ({θi }n . hours worked. the factor dynamics are therefore subject to the restrictions implied by the DSGE model and take the form ft = Φ1 (θDSGE )ft−1 + Φ (θDSGE ) t . price inflation.t corresponds to log GDP. wages. wage rates. Equation (129) is then combined with measurement equations of the form (112). (129) where the vector ft now comprises the minimal set of state variables associated with the DSGE model and θDSGE is the vector of structural DSGE model parameters. . The solution of the stochastic growth model delivers a functional relationship between log GDP and the state variables of the DSGE model. and (iii) the i=1 distribution of θDSGE given ({θi }n . . inflation. Y1:T ). He then uses the DSGE-DFM to study the effect of unanticipated changes in technology . define θi = [ai . Steps (i) and (ii) resemble Steps 1 and 3 i=1 in Algorithm 6. Details of how to specify such a prior can be found in Kryshko (2010). .1. θDSGE . and so forth.Del Negro. consumption. σi . φi. In the context of the simple stochastic growth model analyzed in Section 4.1 . multiple measures of employment and labor usage.1. and interest rates to multiple observables. as well as the shocks that drive the economy. it is in principle much easier to elicit prior distributions for the loadings λi . this vector would contain the capital stock as well as the two exogenous processes. n. Inference in a DSGEDFM can be implemented with a Metropolis-within-Gibbs sampler that iterates over (i) the conditional posterior distributions of {θi }n given (F1:T . . suppose yi. Boivin and Giannoni (2006a) use their DSGE-DFM to relate DSGE model variables such as aggregate output.
More specifically. there is uncertainty about the importance of such features in empirical models. which are elements of the vector section of macroeconomic variables.1: Consider the two (nested) models: M1 : M2 : yt = u t . Thus. ut ∼ iidN (0. yt = θ(2) xt + ut . θ(0) ∼ 0 with prob. denoted by πi. informational frictions. In the context of a DSGE model. Example 7. wage stickiness. λ . Researchers working with dynamic factor models are typically uncertain about the number of factors necessary to capture the comovements in a cross section of macroeconomic or financial variables. combined with great variation in the implications for policy across models. which is illustrated in the following example. Bayesian analysis allows us to place probabilities on the two models. 1). Mi ) and the prior density p(θ(i) |Mi ) are part of the specification of a model Mi . 1) with prob. N (0. both the likelihood function p(Y |θ(i) . ut ∼ iidN (0. in the context of VARs there is uncertainty about the number of lags and cointegration relationships as well as appropriate restrictions for identifying policy rules or structural shocks. a researcher might be uncertain whether price stickiness. 1 − λ . In a Bayesian framework.Del Negro. Then the mixture of M1 and M2 is equivalent to a model M0 M0 : yt = θ(0) xt +ut . θ(2) ∼ N (0. Here M1 restricts the regression coefficient θ(2) in M2 to be equal to zero. Suppose we assign prior probability π1. on a large cross 7 Model Uncertainty The large number of vector autoregressive and dynamic stochastic general equilibrium models encountered thus far. Schorfheide – Bayesian Macroeconometrics: April 18. or monetary frictions are quantitatively important for the understanding of business-cycle fluctuations and should be accounted for when designing monetary and fiscal policies. 1). makes the problem of model uncertainty a compelling one in macroeconometrics. ut ∼ iidN (0.0 . Model uncertainty is conceptually not different from parameter uncertainty. In view of the proliferation of hard-to-measure coefficients in time-varying parameter models. a model is formally defined as a joint distribution of data and parameters.0 = λ to M1 . 90 t in (129). 1). 2010 and monetary policy. 1).
Mi )p(θ(i) |Mi )dθ(i) . which can all be nested in an unrestricted state-space model. . posterior model probabilities are often overly decisive. The remainder of this section is organized as follows.0 . (130) . in that one specification essentially attains posterior probability one and all other specifications receive probability zero. in particular those that are based on DSGE models. Section 7. which complicates the computation of the posterior distribution. M πj.0 p(Y1:T |Mi ) . Schorfheide – Bayesian Macroeconometrics: April 18.2. 2010 91 In principle.T = πi. The posterior model probabilities are given by πi. .3. a decision maker might be inclined to robustify her decisions. These issues are discussed in Section 7.1 Posterior Model Probabilities and Model Selection Suppose we have a collection of M models denoted by M1 through MM . as evident from the example. In view of potentially implausible posterior model probabilities. . for example VARs of lag length p = 1. However. . and it is useful to regard restricted versions of a large encompassing model as models themselves. . . and prior probability πi. 7. pmax and cointegration rank r = 1. Thus. this prior distribution would have to assign nonzero probability to certain lower-dimensional subspaces.1 discusses the computation of posterior model probabilities and their use in selecting among a collection of models. . We use a stylized optimal monetary policy example to highlight this point in Section 7. Rather than first selecting a model and then conditioning on the selected model in the subsequent analysis. Each model has a parameter vector θ(i) .0 p(Y1:T |Mj ) j=1 p(Y1:T |Mi ) = p(Y1:T |θ(i) . In many macroeconomic applications. n or a collection of linearized DSGE models. . it may be more desirable to average across models and to take model uncertainty explicitly into account when making decisions.Del Negro. in most of the applications considered in this chapter such an approach is impractical. a proper prior distribution p(θ(i) |Mi ) for the model parameters. one could try to construct a prior distribution on a sufficiently large parameter space such that model uncertainty can be represented as parameter uncertainty. These decisive probabilities found in individual studies are difficult to reconcile with the variation in results and model rankings found across different studies and therefore are in some sense implausible.
t−1 . a proper prior could be obtained by replacing the dummy observations Y ∗ and X ∗ with presample observations. We briefly mentioned in Sections 2. Mi ). In the context of a VAR. we could regard observations Y1:T ∗ as presample and p(θ|Y1:T ∗ ) as a prior for θ that incorporates this presample information. it is important that p(θ|Y1:T ∗ ) be a proper density. It is beyond the scope of this chapter to provide a general discussion of the use of posterior model probabilities or odds ratios for model comparison. As long as the likelihood functions p(Y1:T |θ(i) . provided the prior model probabilities are also adjusted to reflect the presample information Y1:T ∗ . In turn.2 (hyperparameter choice for Minnesota prior) and 4. θ)p(θ|Y1:T ∗ )dθ.t−1 . who uses them to evaluate lag length . (131) log marginal likelihoods can be interpreted as the sum of one-step-ahead predictive scores. Y1. A survey is provided by Kass and Raftery (1995). The predictive score is small whenever the predictive distribution assigns a low density to the observed yt . Mi ) and prior densities p(θ(i) |Mi ) are properly normalized for all models. we shall highlight a few issues that are important in the context of macroeconometric applications. As before. and Villani (2001). Conditional on Y1:T ∗ .t−1 . who computes posterior odds for a collection of VARs and DSGE models. when making the prediction for yt . (132) The density p(YT ∗ +1:T |Y1:T ∗ ) is often called predictive (marginal) likelihood and can replace the marginal likelihood in (130) in the construction of posterior model probabilities.Del Negro. Schorfheide – Bayesian Macroeconometrics: April 18. Mi )p(θ(i) |Y1. 2010 92 where p(Y1:T |Mi ) is the marginal likelihood or data density associated with model Mi . Since in time-series models observations have a natural ordering. the posterior model probabilities are well defined. Two examples of papers that use predictive marginal likelihoods to construct posterior model probabilities are Schorfheide (2000). The terms on the right-hand side of (131) provide a decomposition of the one-step-ahead predictive densities p(yt |Y1. Since for any model Mi T ln p(Y1:T |Mi ) = t=1 ln p(yt |θ(i) .3 (prior elicitation for DSGE models) that in practice priors are often based on presample (or training sample) information. Mi )dθ(i) . the marginal likelihood function for subsequent observations YT ∗ +1:T is given by p(YT ∗ +1:T |Y1:T ∗ ) = p(Y1:T ) = p(Y1:T ∗ ) p(YT ∗ +1:T |Y1:T ∗ . This decomposition highlights the fact that inference about the parameter θ(i) is based on time t − 1 information.
the use of numerical procedures to approximate marginal likelihood functions is generally preferable for two reasons. First. A more detailed discussion of numerical approximation techniques for marginal likelihoods is provided in Chib (This Volume). While the exact marginal likelihood was not available for the DSGE models. There are only a few instances.1 that for a DSGE model. posterior inference is typically based on simulation-based methods. it can be computationally challenging. and the marginal likelihood approximation can often be constructed from the output of the posterior simulator with very little additional effort. We also mentioned in Section 4. which approximates ln p(Y |θ) + ln p(θ) by a quadratic function centered at the posterior mode or the maximum of the likelihood function. such as the VAR model in (1) with conjugate MNIW prior. Schorfheide (2000) compares Laplace approximations of marginal likelihoods for two small-scale DSGE models and bivariate VARs with 2-4 lags to numerical approximations based on a modified harmonic mean estimator. the discrepancy between the modified harmonic mean estimator and the Laplace approximation was around 0. While the results reported in Schorfheide (2000) are model and data specific. A more detailed discussion of predictive likelihoods can be found in Geweke (2005).02 for log densities. In fact. Finally. for priors represented through dummy observations the formula is given in (15).1 on a log scale. marginal likelihoods can be approximated analytically using a so-called Laplace approximation. The VARs were specified such that the marginal likelihood could be computed exactly. Schorfheide – Bayesian Macroeconometrics: April 18. in which the marginal likelihood p(Y ) = p(Y |θ)p(θ)dθ can be computed analytically. The approximation error of the numerical procedure was at most 0. the approximation error can be reduced to a desired level by increasing . The most widely used Laplace approximation is the one due to Schwarz (1978). Second. numerical approximations to marginal likelihoods can be obtained using Geweke (1999)’s modified harmonic mean estimator or the method proposed by Chib and Jeliazkov (2001). 2010 93 and cointegration rank restrictions in vector autoregressive models. whereas the error of the Laplace approximation was around 0.7.Del Negro. While the calculation of posterior probabilities is conceptually straightforward. which is known as Schwarz Criterion or Bayesian Information Criterion (BIC).5. or other models for which posterior draws have been obtained using the RWM Algorithm. An application of predictive likelihoods to forecast combination and model averaging is provided by Eklund and Karlsson (2007). Phillips (1996) and Chao and Phillips (1999) provide extensions to nonstationary time-series models and reduced-rank VARs.
then under fairly general conditions the posterior probability assigned to that model will converge to one as T −→ ∞. An early version of this result for general linear regression models was proved by Halpern (1974). If one among the M models M1 . for instance. Moreover. In this sense. A rule for selecting one out of M models can be formally derived from the following decision problem. for instance. . A treatment of model selection problems under more general loss functions can be found. . 2010 the number of parameter draws upon which the approximation is based. the probabilities associated with all other specifications are very small. . Schwarz (1978) and Phillips and Ploberger (1996)). If the loss function is symmetric in the sense that αij = α for all i = j. Bayesian model selection procedures are consistent from a frequentist perspective.2 in Section 7. and the loss of making inference or decisions based on the highest posterior probability model is not too large if one of the low probability models is in fact correct. a model selection approach might provide a good approximation if the posterior probability of one model is very close to one. . in Bernardo and Smith (1994). 94 Posterior model probabilities are often used to select a model specification upon which any subsequent inference is conditioned. The consistency result remains valid if the marginal likelihoods that are used to compute posterior model probabilities are replaced by Laplace approximations (see. the consistency is preserved in nonstationary time-series models. Suppose that a researcher faces a loss of zero if she chooses the “correct” model and a loss of αij > 0 if she chooses model Mi although Mj is correct. We shall elaborate on this point in Example 7.Del Negro. then it is straightforward to verify that the posterior expected loss is minimized by selecting the model with the highest posterior probability. for example. These Laplace approximations highlight the fact that log marginal likelihoods can be decomposed into a goodness-of-fit term. MM is randomly selected to generate a sequence of observations Y1:T . Mi ) and a term that penalizes the dimensionality. .2. Chao and Phillips (1999). comprising the maximized log likelihood function maxθ(i) ∈Θ(i) ln p(Y1:T |θ(i) . While it is generally preferable to average across all model specifications with nonzero posterior probability. where ki is the dimension of the parameter vector θ(i) . which in case of Schwarz’s approximation takes the form of −(ki /2) ln T . Schorfheide – Bayesian Macroeconometrics: April 18. prove that the use of posterior probabilities leads to a consistent selection of cointegration rank and lag length in vector autoregressive models.
All variables in this model are meant to be in log deviations from some steady state. At a minimum. 2010 95 7.t s. This class of policies is evaluated under the loss function 2 2 Lt = (πt + yt ).t ∼ iidN (0. Finally.t . Schorfheide – Bayesian Macroeconometrics: April 18. (133) is a cost (supply) shock.2 Decision Making and Inference with Multiple Models Economic policy makers are often confronted with choosing policies under model uncertainty. the central bank is considering a class of new monetary policies. 1). In period T . 1). is correct. the utility of a representative agent in a DSGE model. . the variability of aggregate output and inflation – or micro-founded albeit model-specific – for instance. 6 (136) Chamberlain (This Volume) studies the decision problem of an individual who chooses between two treatments from a Bayesian perspective.t .t d. if in fact one of the other models Mj . d. (134) is a demand shock. assume that up until period T monetary policy was mt = 0. The optimal decision from a Bayesian perspective is obtained by minimizing the expected loss under a mixture of models. Conditioning on the highest posterior probability model can lead to suboptimal decisions.t +δ s.2: Suppose that output yt and inflation πt are related to each other according to one of the two Phillips curve relationships Mi : yt = θ(Mi )πt + where s. 2. Example 7. (135) δ controls the strength of the central bank’s reaction to supply shocks.6 Moreover.Del Negro. policy decisions are often made under a fairly specific loss function that is based on some measure of welfare.t ∼ iidN (0. j = i.t . s. The following example provides an illustration. Assume that the demand side of the economy leads to the following relationship between inflation and money mt : πt = mt + where d. the decision maker should account for the loss of a decision that is optimal under Mi . indexed by δ: mt = − d. i = 1. This welfare loss function might either be fairly ad-hoc – for example.
this model-selection-based procedure completely ignores the loss that occurs if in fact M2 is the correct model. π2. To provide a numerical illustration. πi. the best among the two decisions.T = 0. it is optimal to set δ ∗ (M1 ) = −0.Del Negro. we let θ(M1 ) = 1/10. In particular. We will derive the optimal decision and compare it with two suboptimal procedures that are based on a selection step. and. obtained by minimizing . taking into account the posterior model probabilities πi. δ ∗ (M2 ).T L(M1 . Schorfheide – Bayesian Macroeconometrics: April 18. suppose that the policy maker had proceeded in two steps: (i) select the highest posterior probability model. Second.T = 0. which minimizes the posterior risk if only model Mi is considered. δ). which is larger than R(δ ∗ ) and shows that it is suboptimal to condition the decision on the highest posterior probability model. If the policy maker implements the recommendation of advisor Ai . while choosing between δ ∗ (M1 ) and δ ∗ (M2 ) is preferable to conditioning on the highest posterior probability model. δ) + π2. Third. it is preferable to implement the recommendation of advisor A2 because R(δ ∗ (M2 )) < R(δ ∗ (M1 )). then Table 4 provides the matrix of relevant expected losses.39. θ(M2 ) = 1. conditional on M1 . The risk associated with this decision is R(δ ∗ (M1 )) = 0. is inferior to the optimal decision δ ∗ .85. and (ii) conditional on this model. even though the posterior odds favor the model entertained by A1 . (138) A straightforward calculation leads to δ ∗ = argminδ R(δ) = −0. determine the optimal choice of δ. First.32 and the posterior risk associated with this decision is R(δ ∗ ) = 0. The highest posterior probability model is M1 .T . which in this example is given by R(δ) = π1.T denotes the posterior probability of model Mi at the end of period T . suppose that the policy maker relies on two advisors A1 and A2 . δ) = (δθ(Mi ) + 1)2 + δ 2 .T L(M2 . π1.10. Notice that there is a large loss associated with δ ∗ (M2 ) if in fact M1 is the correct model. Thus. Advisor Ai recommends that the policy maker implement the decision δ ∗ (Mi ). (137) Here.92.61. the expected period loss associated with a particular policy δ under model Mi is L(Mi . 2010 96 If one averages with respect to the distribution of the supply shocks. from a Bayesian perspective it is optimal to minimize the posterior risk (expected loss). However.
conditioning on the highest posterior probability leads to approximately the same predictive density as model averaging.50 Risk R(δ) 0.5 the overall posterior expected loss. in fact.1 δ ∗ (M1 ) M1 1. Consider. In more realistic applications. For instance.82 0. According to Cogley and Sargent’s analysis. In this case.Del Negro. The authors consider a traditional Keynesian model with a strong output and inflation trade-off versus a model in which the Phillips curve is vertical in the long run.S. Mi ). In fact. These models would themselves involve unknown parameters. Often.92 0. the posterior probability of the Keynesian model was already very small by the mid-1970s. Cogley and Sargent (2005a) provide a nice macroeconomic illustration of the notion that one should not implement the decision of the highest posterior probability model if it has disastrous consequences in case one of the other models is correct.04 0. 2010 97 Table 4: Expected Losses Decision δ∗ = −0.99 1.T p(yT +h |Y1:T .90 δ ∗ (M2 ) = −0.32 = −0. (139) Thus. predictive distributions are important.56 0. and the natural rate model suggested implementing a disinflation policy. However. The authors conjecture that this consideration may have delayed the disinflation until about 1980. a prediction problem. Schorfheide – Bayesian Macroeconometrics: April 18.15 M2 0. for example. loss depends on future realizations of yt . Notice that only if the posterior probability of one of the models is essentially equal to one. the two simple models would be replaced by more sophisticated DSGE models. the costs associated with this disinflation were initially very high if. p(yT +h |Y1:T ) is the result of the Bayesian averaging of model-specific predictive densities p(yT +h |Y1:T ). economy. the Keynesian model provided a better description of the U.85 0. in this numerical illustration the gain from averaging over models is larger than the difference between R(δ ∗ (M1 )) and R(δ ∗ (M2 )). . The h-step-ahead predictive density is given by the mixture M p(yT +h |Y1:T ) = i=1 πi. There exists an extensive literature on applications of Bayesian model averaging.
Bayesian model averaging has also become popular in growth regressions following the work of Fernandez. Based on the exclusion of parameters. then the implementation of model averaging can be challenging. one can in principle generate 268 ≈ 3 · 1020 submodels. This is a special case of Bayesian forecast combination. Since there is uncertainty about exactly which explanatory variables to include in a growth regression. Ley. If the model space is very large. the number of restrictions actually visited by the MCMC simulation is only a small portion of all possible restrictions. and Masanjala and Papageorgiou (2008). the computation of posterior probabilities for all submodels can be a daunting task. Suppose one constructs submodels by restricting VAR coefficients to zero. Ni. which is discussed in more general terms in Geweke and Whiteman (2006). and Steel (2001). The recent empirical growth literature has identified a substantial number of variables that potentially explain the rate of economic growth in a cross section or panel of countries. Strachan and van Dijk (2006) average across VARs with different lag lengths and cointegration restrictions to study the dynamics of the Great Ratios. then it is optimal to average posterior mean forecasts from the M models. and Wright (2008) uses Bayesian model averaging to construct exchange rate forecasts. 2010 98 Min and Zellner (1993) use posterior model probabilities to combine forecasts. and Miller (2004) uses a simplified version of Bayesian model averag- . George. leading to a coefficient matrix Φ with 68 elements. Doppelhofer. In a nutshell. George. The authors also provide detailed references to the large literature on Bayesian variable selection in problems with large sets of potential regressors. However. Schorfheide – Bayesian Macroeconometrics: April 18.Del Negro. Doppelhofer. An MCMC algorithm then iterates over the conditional posterior distribution of model parameters and variable selection indicators. and Sun (2008) develop a stochastic search variable selection algorithm for a VAR that automatically averages over high posterior probability submodels. If the goal is to generate point predictions under a quadratic loss function. and Sun (2008) introduce binary indicators that determine whether a coefficient is restricted to be zero.1. Sala-i Martin. which involved a 4-variable VAR with 4 lags. Consider the empirical Illustration 2. as is typical of stochastic search applications. Even if one restricts the set of submodels by requiring that a subset of the VAR coefficients are never restricted to be zero and one specifies a conjugate prior that leads to an analytical formula for the marginal likelihoods of the submodels. The paper by Sala-i Martin. and Miller (2004). Ni. As an alternative. using the posterior model probabilities as weights. Bayesian model averaging is an appealing procedure.
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ing, in which marginal likelihoods are approximated by Schwarz (1978)’s Laplace approximation and posterior means and covariances are replaced by maxima and inverse Hessian matrices obtained from a Gaussian likelihood function.
7.3
Difficulties in Decision-Making with Multiple Models
While Bayesian model averaging is conceptually very attractive, it very much relies on the notion that the posterior model probabilities provide a plausible characterization of model uncertainty. Consider a central bank deciding on its monetary policy. Suppose that a priori the policy makers entertain the possibility that either wages or prices of intermediate goods producers are subject to nominal rigidities. Moreover, suppose that – as is the case in New Keynesian DSGE models – these rigidities have the effect that wage (or price) setters are not able to adjust their nominal wages (prices) optimally, which distorts relative wages (prices) and ultimately leads to the use of an inefficient mix of labor (intermediate goods). The central bank could use its monetary policy instrument to avoid the necessity of wage (price) adjustments and thereby nullify the effect of the nominal rigidity. Based on the tools and techniques in the preceding sections, one could now proceed by estimating two models, one in which prices are sticky and wages are flexible and one in which prices are flexible and wages are sticky. Results for such an estimation, based on a variant of the Smets and Wouters (2007) models, have been reported, for instance, in Table 5 of Del Negro and Schorfheide (2008). According to their estimation, conducted under various prior distributions, U.S. data favor the sticky price version of the DSGE model with odds that are greater than e40 . Such odds are not uncommon in the DSGE model literature. If these odds are taken literally, then under relevant loss functions we should completely disregard the possibility that wages are sticky. In a related study, Del Negro, Schorfheide, Smets, and Wouters (2007) compare versions of DSGE models with nominal rigidities in which those households (firms) that are unable to reoptimize their wages (prices) are indexing their past price either by the long-run inflation rate or by last period’s inflation rate (dynamic indexation). According to their Figure 4, the odds in favor of the dynamic indexation are greater than e20 , which again seems very decisive. Schorfheide (2008) surveys a large number of DSGE model-based estimates of price and wage stickiness and the degree of dynamic indexation. While the papers included in this survey build on the same theoretical framework, variations in some
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details of the model specification as well as in the choice of observables lead to a significant variation in parameter estimates and model rankings. Thus, posterior model odds from any individual study, even though formally correct, appear to be overly decisive and in this sense implausible from a meta perspective. The problem of implausible odds has essentially two dimensions. First, each DSGE model corresponds to a stylized representation of a particular economic mechanism, such as wage or price stickiness, augmented by auxiliary mechanisms that are designed to capture the salient features of the data. By looking across studies, one encounters several representations of essentially the same basic economic mechanism, but each representation attains a different time-series fit and makes posterior probabilities appear fragile across studies. Second, in practice macroeconometricians often work with incomplete model spaces. That is, in addition to the models that are being formally analyzed, researchers have in mind a more sophisticated structural model, which may be too complicated to formalize or too costly (in terms of intellectual and computational resources) to estimate. In some instances, a richly parameterized vector autoregression that is only loosely connected to economic theory serves as a stand-in. In view of these reference models, the simpler specifications are potentially misspecified. For illustrative purpose, we provide two stylized examples in which we explicitly specify the sophisticated reference model that in practice is often not spelled out. Example 7.3: Suppose that a macroeconomist assigns equal prior probabilities to
2 2 two stylized models Mi : yt ∼ iidN (µi , σi ), i = 1, 2, where µi and σi are fixed. In
addition, there is a third model M0 in the background, given by yt ∼ iidN (0, 1). For the sake of argument, suppose it is too costly to analyze M0 formally. If a sequence of T observations were generated from M0 , the expected log posterior odds of M1 versus M2 would be I 0 ln E π1,T π2,T = I 0 − E − − = − T 1 2 ln σ1 − 2 2 2σ1
T
(yt − µ1 )2
t=1 T
T 1 2 ln σ2 − 2 2 2σ2
(yt − µ2 )2
t=1
1 T 1 T 2 2 ln σ1 + 2 (1 + µ2 ) + ln σ2 + 2 (1 + µ2 ) , 1 2 2 2 σ1 σ2
where the expectation is taken with respect to y1 , . . . , yT under M0 . Suppose that the location parameters µ1 and µ2 capture the key economic concept, such as wage
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or price stickiness, and the scale parameters are generated through the various auxiliary assumptions that are made to obtain a fully specified DSGE model. If the
2 2 two models are based on similar auxiliary assumptions, that is, σ1 ≈ σ2 , then the
posterior odds are clearly driven by the key economic contents of the two models. If, however, the auxiliary assumptions made in the two models are very different, it is possible that the posterior odds and hence the ranking of models M1 and M2 are
2 2 dominated by the auxiliary assumptions, σ1 and σ2 , rather than by the economic
contents, µ1 and µ2 , of the models. Example 7.4: This example is adapted from Sims (2003). Suppose that a researcher considers the following two models. M1 implies yt ∼ iidN (−0.5, 0.01) and model M2 implies yt ∼ iidN (0.5, 0.01). There is a third model, M0 , given by yt ∼ iidN (0, 1), that is too costly to be analyzed formally. The sample size is T = 1. Based on equal prior probabilities, the posterior odds in favor of model M1 are π1,T 1 = exp − [(y1 + 1/2)2 − (y1 − 1/2)2 ] π2,T 2 · 0.01 = exp {−100y1 } .
Thus, for values of y1 less than -0.05 or greater than 0.05 the posterior odds are greater than e5 ≈ 150 in favor of one of the models, which we shall term decisive. The models M1 (M2 ) assign a probability of less than 10−6 outside the range [−0.55, −0.45] ([0.45, 0.55]). Using the terminology of the prior predictive checks described in Section 4.7.2, for observations outside these ranges one would conclude that the models have severe difficulties explaining the data. For any observation falling into the intervals (−∞, −0.55], [−0.45, −0.05], [0.05, 0.45], and [0.55, ∞), one would obtain decisive posterior odds and at the same time have to conclude that the empirical observation is difficult to reconcile with the models M1 and M2 . At the same time, the reference model M0 assigns a probability of almost 0.9 to these intervals. As illustrated through these two stylized examples, the problems in the use of posterior probabilities in the context of DSGE models are essentially twofold. First, DSGE models tend to capture one of many possible representations of a particular economic mechanism. Thus, one might be able to find versions of these models that preserve the basic mechanisms but deliver very different odds. Second, the models often suffer from misspecification, which manifests itself through low posterior probabilities in view of more richly parameterized vector autoregressive models that are less tightly linked to economic theory. Posterior odds exceeding e50 in a sample of
T ].T ) ln(1 − qπ1.T )L(M2 . Sims (2003) recommends introducing continuous parameters such that different sub-model specifications can be nested in a larger encompassing model. To ensure that the distorted probability of M1 lies in the unit interval. The second term in (140) penalizes the distortion as a function of the Kullback-Leibler divergence between the undistorted and distorted probabilities. a policy maker might find it attractive to robustify her decision. Hence. τ (140) Here. Schorfheide – Bayesian Macroeconometrics: April 18.T L(M1 . This concern can be represented through the following game between the policy maker and a fictitious adversary. If. then the penalty is infinite and nature will not distort π1. a proper characterization of posterior uncertainty about the strength of various competing decision-relevant economic mechanisms remains a challenge. This pooling amounts essentially to creating a convex combination of onestep-ahead predictive distributions. Underlying this robustness is often a static or dynamic two-person zero-sum game. Example 7. then conditional on a particular δ nature will set .2.Del Negro. δ) + (1 − qπ1. In view of these practical limitations associated with posterior model probabilities.T ] qπ1. Continued: Recall the monetary policy problem described at the beginning of this section. δ) + 1 π1.T . The time-invariant weights of this mixture of models is then estimated by maximizing the log predictive score for this mixture (see Expression (131)). the domain of q is restricted to [0. In fact. τ = ∞. 2010 102 120 observations are suspicious (to us) and often indicate that we should compare different models or consider a larger model space. Suppose scepticism about the posterior probabilities π1.T ) . The downside of creating these encompassing models is that it is potentially difficult to properly characterize multimodal posterior distributions in high-dimensional parameter spaces.T ln(qπ1.2. however.1/π1. If τ is equal to zero.T ) + (1 − π1. which we illustrate in the context of Example 7. called nature: min δ max q∈[0.T generates some concern about the robustness of the policy decision to perturbations of these model probabilities. which are derived from individual models. Geweke (2010) proposes to deal with incomplete model spaces by pooling models. nature uses q to distort the posterior model probability of model M1 . 1/π1. there is a growing literature in economics that studies the robustness of decision rules to model misspecification (see Hansen and Sargent (2008)).T and π2.
the Nash equilibrium is summarized in Table 5. Schorfheide – Bayesian Macroeconometrics: April 18.T if L(M1 . δ) in the relevant region for δ.30 10. These adjustments may reflect some scepticism about the correct formalization of the relevant economic mechanisms as well as the availability of information that is difficult to process in macroeconometric models such as VARs and DSGE models.00 -0.32 1.60 -0.19 100 1.00 1. δ) > L(M2 . L(M1 . and in response the policy maker reduces (in absolute terms) her response δ to a supply shock. Thus.0 1.10 -0. . For selected values of τ . 2010 103 Table 5: Nash Equilibrium as a Function of Risk Sensitivity τ τ q ∗ (τ ) δ ∗ (τ ) 0. The particular implementation of robust decision making in Example 7. In our numerical illustration. While it is our impression that in actual decision making a central bank is taking the output of formal Bayesian analysis more and more seriously.00 1. δ) and q = 0 otherwise. δ) > L(M2 .43 -0.Del Negro. the final decision about economic policies is influenced by concerns about robustness and involves adjustments of model outputs in several dimensions.12 q = 1/π1.2 is very stylized. nature has an incentive to increase the probability of M1 .
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” Journal of Monetary Economics. 54–81. (2006): “Were There Regime Switches in U. 4. 97(3). (1999): “Error Bands for Impulse Responses. MIT Press. (2001): “Vector Autoregressions.” Econometrica. Inflation Dynamics’ . 949–968. Schorfheide – Bayesian Macroeconometrics: April 18.. (2002b): “Solving Linear Rational Expectations Models. 67(5). 1123–1175. D. 96(1). A. F. 1–20. A. and T. MIT Press. Fischer. 44(2). vol. 15(4).” Journal of Econometrics.” in NBER Macroeconomics Annual 1989. 1113– 1155. pp. and T. 1591–1599. vol. C.S. and H. Uhlig (1991): “Understanding Unit Rooters: A Helicopter Tour. (2003): “Probability Models for Monetary Policy Decisions. J. 20(1-2). Princeton University. Stock. 351–394.S. Blanchard. 293–335..” Manuscript. (1999): “Forecasting Inflation. (2007): “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.” Econometrica. and M. W. and K. 255–274. Bernanke. 16. C. by O.” in NBER Macroeconomics Annual 2001. Watson (1989): “New Indices of Coincident and Leading Economic Indicators.. Smets. pp. 2010 116 (2002a): “Comment on Cogley and Sargent’s ‘Evolving post World War II U.” International Economic Review. Cambridge. 59(6). ed. Sims.Del Negro.. 39(4). 101–115. 146(2). Rogoff.” Journal of the European Economic Association. Wouters (2003): “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area.. Waggoner. Cambridge.” Journal of Economic Perspectives. S. Sims. by B. ed. A.” American Economic Review. 373–379. 1(5). Sims. and S. 586–606. Monetary Policy?. J. H. Zha (1998): “Bayesian Methods for Dynamic Multivariate Models. and R. C. Zha (2008): “Methods for Inference in Large Multiple-Equation Markov-Switching Models. .” Computational Economics.” American Economic Review.
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Inflation and interest rates are annualized (A%). . data from 1964:Q1 to 2006:Q4.Del Negro. Output is depicted in percentage deviations from a linear deterministic trend. and Interest Rates 20 16 12 8 4 0 -4 -8 1965 1970 1975 1980 1985 1990 1995 2000 2005 Output Deviations from Trend [%] Inflation [A%] Federal Funds Rate [A%] Notes: The figure depicts U. Schorfheide – Bayesian Macroeconometrics: April 18.S. 2010 118 Figure 1: Output. Inflation.
Schorfheide – Bayesian Macroeconometrics: April 18.Del Negro. 2010 119 Figure 2: Response to a Monetary Policy Shock Notes: The figure depicts 90% credible bands and posterior mean responses for a VAR(4) to a one-standard deviation monetary policy shock. .
6 7.7 8.0 4.8 6.8 8. 2010 120 Figure 3: Nominal Output and Investment 8.Del Negro.0 7.0 7.5 6.4 -1.0 -2. Right Axis) Notes: The figure depicts U. .0 6.5 5. Logs.5 65 70 75 80 85 90 95 00 05 9. Schorfheide – Bayesian Macroeconometrics: April 18.5 7. Left Axis) GDP (Nom.8 Log Nominal Investment-Output Ratio -1.6 9. Logs.5 8.2 8.9 6.S. data from 1964:Q1 to 2006:Q4.2 -1.6 -1.4 -2.0 5.1 65 70 75 80 85 90 95 00 05 Investment (Nom.
01).1). and B ∼ N (−1. 0. 1). 2010 121 Figure 4: Posterior Density of Cointegration Parameter Notes: The figure depicts Kernel density approximations of the posterior density for B in β = [1. . B ∼ N (−1. 0.Del Negro. B] based on three different priors: B ∼ N (−1. Schorfheide – Bayesian Macroeconometrics: April 18.
Schorfheide – Bayesian Macroeconometrics: April 18. The gray shaded bands indicate NBER recessions.Del Negro. . 2010 122 Figure 5: Trends and Fluctuations Notes: The figure depicts posterior medians and 90% credible intervals for the common trends in log investment and output as well as deviations around these trends.
. Sample period is 1955:Q1 to 2006:Q4. and Labor Productivity 12 8 4 0 -4 -8 -12 55 60 65 70 75 80 85 90 95 00 05 Log Labor Productivity Log Output Log Hours Notes: Output and labor productivity are depicted in percentage deviations from a deterministic trend. Hours. and hours are depicted in deviations from its mean. Schorfheide – Bayesian Macroeconometrics: April 18. 2010 123 Figure 6: Aggregate Output.Del Negro.
scaled by 400 to convert it into annualized percentages (A%). . Schorfheide – Bayesian Macroeconometrics: April 18.Del Negro. 2010 124 Figure 7: Inflation and Measures of Trend Inflation 14 12 10 8 6 4 2 0 60 65 70 75 80 85 90 95 00 05 Inflation Rate (A%) HP Trend Constant Mean Mean with Breaks Notes: Inflation is measured as quarter-to-quarter changes in the log GDP deflator. The sample ranges from 1960:Q1 to 2005:Q4. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8826776742935181, "perplexity": 3264.471695062893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109670.98/warc/CC-MAIN-20170821211752-20170821231752-00326.warc.gz"} |
http://www.aimsciences.org/article/doi/10.3934/cpaa.2007.6.453 | # American Institute of Mathematical Sciences
2007, 6(2): 453-464. doi: 10.3934/cpaa.2007.6.453
## The singularity analysis of solutions to some integral equations
1 Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0524 2 Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309-0526
Received January 2006 Revised October 2006 Published March 2007
We consider a system of Euler-Lagrange equations associated with the weighted Hardy-Littlewood-Sobolev inequality in $R^n$. We demonstrate that the positive solutions of the system of Euler-Lagrange equations are asymptotic to certain forms of limit around the center and near infinity, respectively. The results are proven using the optimal integrability conditions for the positive solutions of the system of equations.
Citation: Congming Li, Jisun Lim. The singularity analysis of solutions to some integral equations. Communications on Pure & Applied Analysis, 2007, 6 (2) : 453-464. doi: 10.3934/cpaa.2007.6.453
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2016 Impact Factor: 0.801 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8097891211509705, "perplexity": 3841.7634693637615}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864837.40/warc/CC-MAIN-20180522170703-20180522190703-00258.warc.gz"} |
https://brilliant.org/problems/merrily-swinging-around/ | # Merrily Swinging Around
When we swing a pendulum with a small angle, we can approximate its motion to be simple harmonic motion. For a pendulum whose length is $l$, the time period of the pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$. Note that the time period is independent of the amplitude of oscillation.
Does this result hold true for larger amplitudes as well? How does the time period depend on the amplitude $\theta_0$ as it goes from $0^\circ$ to $90^\circ?$
Note: Ignore air resistance
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9852872490882874, "perplexity": 192.03049824359408}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00369.warc.gz"} |
http://mathhelpforum.com/calculus/69404-compute-limit-3-n-2-n-1-a.html | # Math Help - Compute the limit (3^n)/(2^n)+1
1. ## Compute the limit (3^n)/(2^n)+1
Compute the limit of the sequence
(3^n)/ ((2^n)+1)
I have simplified a much harder problem to this limit and i am having a mind blank... helpplease? cheers
2. The $n$th term tends to $(3/2)^n$.
3. Originally Posted by sebjory
Compute the limit of the sequence
(3^n)/ ((2^n)+1)
I have simplified a much harder problem to this limit and i am having a mind blank... helpplease? cheers
$\frac{3^n}{2^n + 1} \geq \frac{3^n}{2^n + 2^n} = \tfrac{1}{2}\left( \tfrac{3}{2} \right)^n \to \infty$
4. Originally Posted by sebjory
Compute the limit of the sequence
(3^n)/ ((2^n)+1)
I have simplified a much harder problem to this limit and i am having a mind blank... helpplease? cheers
Could also use L'Hoptial's rule on
$\lim_{x \to \infty} \frac{3^x}{2^x+1} = \lim_{x \to \infty} \frac{3^x \ln 3}{2^x \ln 2} = \frac{\ln 3}{\ln 2} \lim_{x \to \infty} \left( \frac{3}{2} \right)^x \to \infty$ as seen in the ThePerfectHacker post.
5. Hello, sebjory!
Yet another approach . . .
$\lim_{n\to\infty} \frac{3^n}{2^n + 1}$
Divide top and bottom by $3^n\!:\;\;\frac{\frac{1}{3^n}\cdot3^n}{\frac{1}{3^ n}(2^n+1)} \;=\;\frac{1}{\frac{2^n}{3^n} + \frac{1}{3^n}}$
Therefore: . $\lim_{n\to\infty}\left[\frac{1}{\left(\frac{2}{3}\right)^n + \frac{1}{3^n}}\right] \;=\; \frac{1}{0+0} \;=\;\infty$
6. thanks a hell of a lot guys that was exactly what i was looking for. Think i might use Sorobans solution nice and elegant. cant believe i didnt see it
7. Originally Posted by Soroban
Hello, sebjory!
Yet another approach . . .
$\frac{1}{0+0} \;=\;\infty$
Soroban! Nooo! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9750115275382996, "perplexity": 2696.1747184601336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257825358.53/warc/CC-MAIN-20160723071025-00306-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://forum.azimuthproject.org/discussion/comment/18189/ | #### Howdy, Stranger!
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# Lecture 24 - Chapter 2: Pricing Resources
edited May 2018
Today's lecture will be very short, consisting solely of some puzzles about prices.
We often compare resources by comparing their prices. So, we have some set of things $$X$$ and a function $$f: X \to \mathbb{R}$$ that assigns to each thing a price. Given two things in the set $$X$$ we can then say which costs more... and this puts a preorder on the set $$X$$. Here's the math behind this:
Puzzle 75. Suppose $$(Y, \le_Y)$$ is a preorder, $$X$$ is a set and $$f : X \to Y$$ is any function. Define a relation $$\le_X$$ on $$X$$ by
$$x \le_X x' \textrm{ if and only if } f(x) \le_Y f(x') .$$ Show that $$(X, \le_X )$$ is a preorder.
Sometimes this trick gives a poset, sometimes not:
Puzzle 76. Now suppose $$(Y, \le_Y)$$ is a poset. Under what conditions on $$f$$ can we conclude that $$(X, \le_X )$$ defined as above is a poset?
We often have a way of combining things: for example, at a store, if you can buy milk and you can buy eggs, you can buy milk and eggs. Sometimes this makes our set of things into a monoidal preorder:
Puzzle 77. Now suppose that $$(Y, \le_Y, \otimes_Y, 1_Y)$$ is a monoidal preorder, and $$(X,\otimes_X,1_X )$$ is a monoid. Define $$\le_X$$ as above. Under what conditions on $$f$$ can we conclude that $$(X,\le_X\otimes_X,1_X)$$ is a monoidal preorder?
We will come back to these issues in a bit more depth when we discuss Section 2.2.5 of the book.
To read other lectures go here.
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1.
Maybe with the lack of a lecture today, people will post in the discussion groups. Maybe I'm being too optimistic.
Anyway, Puzzle 75 feels very weird, since $$X$$ could be a completely disjoint set.
Comment Source:Maybe with the lack of a lecture today, people will post in the discussion groups. Maybe I'm being too optimistic. Anyway, Puzzle 75 feels very weird, since \$$X \$$ could be a completely disjoint set.
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2.
edited May 2018
Puzzle 75 is about things like this "a dozen eggs costs more than a stick of butter". We have a set $$\mathbb{R}$$ whose elements are amounts of money, ordered in the usual way. We have a set $$X$$ whose elements are things you can buy in the grocery store. And we have a function $$f: X \to \mathbb{R}$$ mapping each thing you can buy in the grocery store to its price. Say
$$f(\text{a dozen eggs}) = 3.50$$ and
$$f(\text{a stick of butter}) = 0.75$$ Then we say
$$\text{a stick of butter} \le_X \text{a dozen eggs}$$ because
$$0.75 \le_{\mathbb{R}} 3.50 .$$ This is just a way of saying that a stick of butter is cheaper than a dozen eggs. It makes perfect sense. Please, someone do these puzzles!
By the way, Brandon passed his thesis defense, and all my students are happy. =D> =D> =D> =D> =D> =D>
Comment Source:Puzzle 75 is about things like this "a dozen eggs costs more than a stick of butter". We have a set \$$\mathbb{R}\$$ whose elements are _amounts of money_, ordered in the usual way. We have a set \$$X\$$ whose elements are _things you can buy in the grocery store_. And we have a function \$$f: X \to \mathbb{R}\$$ mapping each thing you can buy in the grocery store to its price. Say $f(\text{a dozen eggs}) = 3.50$ and $f(\text{a stick of butter}) = 0.75$ Then we say $\text{a stick of butter} \le_X \text{a dozen eggs}$ because $0.75 \le_{\mathbb{R}} 3.50 .$ This is just a way of saying that a stick of butter is cheaper than a dozen eggs. It makes perfect sense. Please, someone do these puzzles! By the way, Brandon passed his thesis defense, and all my students are happy. =D> =D> =D> =D> =D> =D>
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3.
Your commodity pricing example gives me a hunch, can I prove Puzzle 75 by pullback? That is to say, pullback the $$\le_Y$$ along $$f$$ to induce a relationship $$\le_X$$ on the set $$X$$.
Comment Source:Your commodity pricing example gives me a hunch, can I prove Puzzle 75 by pullback? That is to say, pullback the \$$\le_Y \$$ along \$$f \$$ to induce a relationship \$$\le_X \$$ on the set \$$X \$$.
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4.
edited May 2018
Marius worked on these these Puzzles in Lecture 23. Here is his comment. I thought I would copy them here so we can all talk in one place!
Puzzle 75.
Suppose $$(Y, \le_Y)$$ is a preorder, $$X$$ is a set and $$f : X \to Y$$ is any function. Define a relation $$\le_X$$ on $$X$$ by
$$x \le_X x' \textrm{ if and only if } f(x) \le_Y f(x') .$$ Show that $$(X, \le_X )$$ is a preorder.
Our relation turns $$f$$ into a monotone map. For all $$x \in X$$ we have $$f(x) \le_Y f(x)$$ and thus $$x \le_X x$$ satisfying reflexivity. Similarly, for all $$x,y,z \in X$$, $$f(x) \le_Y f(y)$$ and $$f(y) \le_Y f(z)$$ implies $$f(x) \le_Y f(z)$$ and thus $$x \le_X y$$ and $$y \le_X z$$ implies $$x \le_X z$$ satisfying transitivity. This gives us a preorder on X.
Puzzle 76.
Now suppose $$(Y, \le_Y)$$ is a poset. Under what conditions on $$f$$ can we conclude that $$(X, \le_X )$$ defined as above is a poset?
Since we don't want to induce any equivalent elements in $$X$$, $$f$$ must be injective.
Puzzle 77.
Now suppose that $$(Y, \le_Y, \otimes_Y, 1_Y)$$ is a monoidal preorder, and $$(X,\otimes_X,1_X )$$ is a monoid. Define $$\le_X$$ as above. Under what conditions on $$f$$ can we conclude that $$(X,\le_X\otimes_X,1_X)$$ is a monoidal preorder?
We need to assure that our induced preorder structure is compatible with our monoidal structure. To this end we require our monotone map $$f$$ to be a monoidal monotone for which $$1_Y \le_Y f(1_X)$$ and $$f(x) \otimes_Y f(y) \le_Y f(x \otimes_X y)$$
Regarding Puzzle 71, does this mean we simply need to find injective monoidal monotones to other commutative monoidal posets (e.g $$(\mathbb{R}, \le, +, 0 )$$) or do we need stricter requirements to preserve the commutative sturcture (e.g $$1_Y = f(1_X)$$ and $$f(x) \otimes_Y f(y) = f(x \otimes_X y)$$)?
I'm off to bed, so maybe someone else can continue my thought process...
Comment Source:Marius worked on these these Puzzles in Lecture 23. <a href = "https://forum.azimuthproject.org/discussion/comment/18135/#Comment_18135× ">Here is his comment.</a> I thought I would copy them here so we can all talk in one place! >**Puzzle 75.** >>Suppose \$$(Y, \le_Y) \$$ is a preorder, \$$X\$$ is a set and \$$f : X \to Y\$$ is any function. Define a relation \$$\le_X\$$ on \$$X\$$ by >>$x \le_X x' \textrm{ if and only if } f(x) \le_Y f(x') .$ >>Show that \$$(X, \le_X ) \$$ is a preorder. >Our relation turns \$$f \$$ into a *monotone map*. For all \$$x \in X \$$ we have \$$f(x) \le_Y f(x)\$$ and thus \$$x \le_X x\$$ satisfying reflexivity. Similarly, for all \$$x,y,z \in X \$$, \$$f(x) \le_Y f(y)\$$ and \$$f(y) \le_Y f(z)\$$ implies \$$f(x) \le_Y f(z)\$$ and thus \$$x \le_X y\$$ and \$$y \le_X z\$$ implies \$$x \le_X z\$$ satisfying transitivity. This gives us a preorder on X. >**Puzzle 76.** >>Now suppose \$$(Y, \le_Y) \$$ is a poset. Under what conditions on \$$f\$$ can we conclude that \$$(X, \le_X ) \$$ defined as above is a poset? >Since we don't want to induce any equivalent elements in \$$X\$$, \$$f \$$ must be injective. >**Puzzle 77.** >>Now suppose that \$$(Y, \le_Y, \otimes_Y, 1_Y) \$$ is a monoidal preorder, and \$$(X,\otimes_X,1_X ) \$$ is a monoid. Define \$$\le_X\$$ as above. Under what conditions on \$$f\$$ can we conclude that \$$(X,\le_X\otimes_X,1_X) \$$ is a monoidal preorder? >We need to assure that our induced preorder structure is compatible with our monoidal structure. To this end we require our *monotone map* \$$f \$$ to be a *monoidal monotone* for which \$$1_Y \le_Y f(1_X) \$$ and \$$f(x) \otimes_Y f(y) \le_Y f(x \otimes_X y) \$$ >Regarding Puzzle 71, does this mean we simply need to find injective *monoidal monotones* to other commutative monoidal posets (e.g \$$(\mathbb{R}, \le, +, 0 )\$$) or do we need stricter requirements to preserve the commutative sturcture (e.g \$$1_Y = f(1_X) \$$ and \$$f(x) \otimes_Y f(y) = f(x \otimes_X y) \$$)? > I'm off to bed, so maybe someone else can continue my thought process...
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5.
Puzzle 76. I agree with Marius that $$f$$ must be injective. In fact I think this is a necessary and sufficient condition! But before the proof, a small example.
In John's example where $$X$$ is a set of groceries and $$f$$ maps groceries to their cost, $$\text{grocery 1} \leq \text{grocery 2}$$ iff the cost of grocery 1 is less than or equal to the cost of grocery 2. If $$f$$ is not injective then there exist two different groceries (let's say apples and oranges) with the same cost (let's say $1). Since in the world of cost$1 $$\leq$$ $1 by reflexivity, in the world of groceries we have apples $$\leq$$ oranges and oranges $$\leq$$ apples. This means that apples and oranges are equivalent (which makes sense because they are equivalent in terms of cost). But of course apples $$\neq$$ oranges. So the groceries with the relation induced by $$f$$ does not form a poset! This argument works in general to show that if $$f$$ induces a poset relation $$(X, \leq_X)$$, then $$f$$ is injective. Proof by contradiction: Suppose that $$f$$ is not injective. Then there exists $$x,x' \in X$$ such that $$f(x) = f(x')$$ where $$x \neq x'$$. By reflexivity $f(x) \leq_Y f(x') \text{ and } f(x') \leq_Y f(x).$ By definition of $$\leq_X$$, this means that $$x \leq_X x' \text{ and } x' \leq_X x.$$ Since $$x \neq x'$$, this means that $$(X, \leq_X)$$ is not a poset. The converse is also true: If $$f$$ is injective, then it induces a poset relation $$(X, \leq_X)$$. Proof: Suppose that $$x \leq_X x' \text{ and } x' \leq_X x.$$ Then by the definition of $$\leq_X$$ $f(x) \leq_Y f(x') \text{ and } f(x') \leq_Y f(x).$ Since $$(Y, \leq_Y)$$ is a poset, this implies that $$f(x) = f(x')$$. And since $$f$$ is injective, this means that $$x = x'$$. Comment Source:**Puzzle 76.** I agree with Marius that \$$f\$$ must be injective. In fact I think this is a necessary and sufficient condition! But before the proof, a small example. In John's example where \$$X\$$ is a set of groceries and \$$f\$$ maps groceries to their cost, $$\text{grocery 1} \leq \text{grocery 2}$$ iff the cost of grocery 1 is less than or equal to the cost of grocery 2. If \$$f\$$ is not injective then there exist two different groceries (let's say apples and oranges) with the same cost (let's say \$1). Since in the world of cost \$1 \$$\leq\$$ \$1 by reflexivity, in the world of groceries we have apples \$$\leq\$$ oranges and oranges \$$\leq \$$ apples. This means that apples and oranges are equivalent (which makes sense because they are equivalent in terms of cost). But of course apples \$$\neq \$$ oranges. So the groceries with the relation induced by \$$f\$$ does not form a poset! This argument works in general to show that if \$$f\$$ induces a poset relation \$$(X, \leq_X) \$$, then \$$f\$$ is injective. *Proof by contradiction:* Suppose that \$$f\$$ is not injective. Then there exists \$$x,x' \in X\$$ such that \$$f(x) = f(x')\$$ where \$$x \neq x'\$$. By reflexivity \$f(x) \leq_Y f(x') \text{ and } f(x') \leq_Y f(x).\$ By definition of \$$\leq_X \$$, this means that $$x \leq_X x' \text{ and } x' \leq_X x.$$ Since \$$x \neq x' \$$, this means that \$$(X, \leq_X) \$$ is not a poset. The converse is also true: If \$$f\$$ is injective, then it induces a poset relation \$$(X, \leq_X) \$$. *Proof:* Suppose that $$x \leq_X x' \text{ and } x' \leq_X x.$$ Then by the definition of \$$\leq_X\$$ \$f(x) \leq_Y f(x') \text{ and } f(x') \leq_Y f(x).\$ Since \$$(Y, \leq_Y) \$$ is a poset, this implies that \$$f(x) = f(x')\$$. And since \$$f\$$ is injective, this means that \$$x = x'\$$.
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edited May 2018
Puzzle 77
Claim If $$f(x) \otimes_Y f(x') = f( x \otimes_X x')$$ then the relation $$\leq_X$$ induced by $$f$$ makes $$(X, \otimes_X, 1_X, \leq_X)$$ a monoidal preorder.
(In the second example below I show that this is actually too strong of a condition on $$f$$ but it's a starting place! )
Proof: Suppose that $$x \leq_X x'$$ and $$y \leq_X y'$$. Then $$f(x) \leq_Y f(x')$$ and $$f(y) \leq_Y f(y' )$$. Since $$(Y, \otimes_Y, 1_Y, \leq_Y)$$ is a monoidal preorder this means that $f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y').$ $$f$$ exactly preserves the tensor structure so, $f(x \otimes_X y) \leq_Y f(x' \otimes_X y')$ which implies that $$x \otimes_X y \leq_X x' \otimes_X y'$$ by the definition of $$\leq_X$$.
Example I started thinking about some examples inspired by John's grocery example and the H20 example from Lecture 22 .
Let $$X$$ represent collections of groceries that can be bought at the "Eggs and Milk" store. Since the "Eggs and Milk" store only sells eggs and milk, every element of $$X$$ can be represented by a pair $$(a,b) \in \mathbb N^2$$ where $$a$$ is the number of eggs bought and $$b$$ is the number of milks bought. $$X$$ can be turned into a monoid by defining $(a,b) \otimes_X (c,d) = (a + c, b + d)$ and where $$1_X = (0,0)$$. Suppose that eggs cost $1 and milk costs$2. This means we should define a cost map $$f: X \to \mathbb R$$ by (f ((a,b)) = a + 2b\). $$f$$ preserves the $$\otimes$$ structure because $f((a,b)) \otimes_{\mathbb R} f((c,d)) = (a + 2b) + (c + 2d) = (a + c) + 2(b + d) = f((a+c, b + d)) = f((a,b) \otimes_X (c,d)).$ Another way of saying this is "The cost of buying two sets of groceries separately is the same as the cost of buying them together". This means that we have turned the groceries into a monoidal preorder!
Example
Suppose that the "Eggs and Milk" store now charges $0.10 for a bag with each purchase. This means that the cost function now looks like $g((a,b)) = a + 2b + 0.10$ $$g$$ doesn't exactly preserve the $$\otimes$$ structure because now the bag charge means that: "the cost of buying two sets of groceries separately is more than the cost of buying them together". In math words, $g((a,b)) \otimes g((c,d)) \geq g((a \otimes c, b \otimes d)) .$ I was interested that this is the opposite condition from what Marius proposed. My next question was whether $$g$$ induced a monoidal preorder on the groceries anyway. It does, essentially because the bag charges cancel out. Here is the math: Suppose that $(a,b) \leq (c,d) \text{ and }(a',b') \leq (c',d')$ Therefore $g(a,b) \leq g(c,d) \text{ and }g(a',b') \leq g(c',d')$ $\implies a+ 2b + 0.10 \leq c + 2d + 0.10 \text{ and }a' + 2b' + 0.10 \leq c' + 2d' + 0.10$ $\implies a+ 2b \leq c + 2d \text{ and }a' + 2b' \leq c' + 2d'$ $\implies (a + a') + 2(b + b') \leq (c + c') + 2(d + d')$ $\implies (a + a') + 2(b + b') + 0.10 \leq (c + c') + 2(d + d') + 0.10$ $\implies g((a,b) \otimes (a', b')) \leq g((c,d) \otimes (c',d'))$ $\implies (a,b) \otimes (a', b') \leq (c,d) \otimes (c',d')$ This lead me to a new claim... New Claim If $$f(x) \otimes_Y f(x') \geq f( x \otimes_X x')$$ then the relation $$\leq_X$$ induced by $$f$$ makes $$(X, \otimes_X, 1_X, \leq_X)$$ a monoidal preorder. But I have yet to prove it! I'm also wondering about Marius's suggestion that $$f$$ should satisfy $$1_Y\leq_Y f(1_X)$$ This is true in both my examples, since buying zero items costs more than or equal to$0.
Phew that was a lot! Interested to hear what others think!
Comment Source:**Puzzle 77** **Claim** If \$$f(x) \otimes_Y f(x') = f( x \otimes_X x')\$$ then the relation \$$\leq_X\$$ induced by \$$f\$$ makes \$$(X, \otimes_X, 1_X, \leq_X) \$$ a monoidal preorder. (In the second example below I show that this is actually too strong of a condition on \$$f\$$ but it's a starting place! ) *Proof:* Suppose that \$$x \leq_X x'\$$ and \$$y \leq_X y' \$$. Then \$$f(x) \leq_Y f(x')\$$ and \$$f(y) \leq_Y f(y' )\$$. Since \$$(Y, \otimes_Y, 1_Y, \leq_Y)\$$ is a monoidal preorder this means that \$f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y'). \$ \$$f\$$ exactly preserves the tensor structure so, \$f(x \otimes_X y) \leq_Y f(x' \otimes_X y') \$ which implies that \$$x \otimes_X y \leq_X x' \otimes_X y'\$$ by the definition of \$$\leq_X\$$. **Example** I started thinking about some examples inspired by John's grocery example and the H20 example from <a href = "https://forum.azimuthproject.org/discussion/2084/lecture-22-chapter-2-symmetric-monoidal-preorders#latest"> Lecture 22 </a>. Let \$$X\$$ represent collections of groceries that can be bought at the "Eggs and Milk" store. Since the "Eggs and Milk" store only sells eggs and milk, every element of \$$X\$$ can be represented by a pair \$$(a,b) \in \mathbb N^2\$$ where \$$a\$$ is the number of eggs bought and \$$b\$$ is the number of milks bought. \$$X\$$ can be turned into a monoid by defining \$(a,b) \otimes_X (c,d) = (a + c, b + d) \$ and where \$$1_X = (0,0) \$$. Suppose that eggs cost \$1 and milk costs \$2. This means we should define a cost map \$$f: X \to \mathbb R\$$ by $$f ((a,b)) = a + 2b\$$. \$$f\$$ preserves the \$$\otimes\$$ structure because \$f((a,b)) \otimes_{\mathbb R} f((c,d)) = (a + 2b) + (c + 2d) = (a + c) + 2(b + d) = f((a+c, b + d)) = f((a,b) \otimes_X (c,d)).\$ Another way of saying this is "The cost of buying two sets of groceries separately is the same as the cost of buying them together". This means that we have turned the groceries into a monoidal preorder! **Example** Suppose that the "Eggs and Milk" store now charges \$0.10 for a bag with each purchase. This means that the cost function now looks like \$g((a,b)) = a + 2b + 0.10\$ \$$g\$$ doesn't exactly preserve the \$$\otimes\$$ structure because now the bag charge means that: "the cost of buying two sets of groceries separately is *more* than the cost of buying them together". In math words, \$g((a,b)) \otimes g((c,d)) \geq g((a \otimes c, b \otimes d)) .\$ I was interested that this is the opposite condition from what Marius proposed. My next question was whether \$$g\$$ induced a monoidal preorder on the groceries anyway. It does, essentially because the bag charges cancel out. Here is the math: Suppose that \$(a,b) \leq (c,d) \text{ and }(a',b') \leq (c',d')\$ Therefore \$g(a,b) \leq g(c,d) \text{ and }g(a',b') \leq g(c',d')\$ \$\implies a+ 2b + 0.10 \leq c + 2d + 0.10 \text{ and }a' + 2b' + 0.10 \leq c' + 2d' + 0.10\$ \$\implies a+ 2b \leq c + 2d \text{ and }a' + 2b' \leq c' + 2d'\$ \$\implies (a + a') + 2(b + b') \leq (c + c') + 2(d + d') \$ \$\implies (a + a') + 2(b + b') + 0.10 \leq (c + c') + 2(d + d') + 0.10 \$ \$\implies g((a,b) \otimes (a', b')) \leq g((c,d) \otimes (c',d')) \$ \$\implies (a,b) \otimes (a', b') \leq (c,d) \otimes (c',d') \$ This lead me to a new claim... **New Claim** If \$$f(x) \otimes_Y f(x') \geq f( x \otimes_X x')\$$ then the relation \$$\leq_X\$$ induced by \$$f\$$ makes \$$(X, \otimes_X, 1_X, \leq_X) \$$ a monoidal preorder. But I have yet to prove it! I'm also wondering about Marius's suggestion that \$$f\$$ should satisfy > \$$1_Y\leq_Y f(1_X)\$$ This is true in both my examples, since buying zero items costs more than or equal to \$0. Phew that was a lot! Interested to hear what others think!
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7.
edited May 2018
Thanks Sophie for re-posting my comment in the right place and for your nice proof that $$f$$ must be injective! Regarding:
I was interested that this is the opposite condition from what Marius proposed.
I just took the definition for a monoidal monotone from 7 sketches p.46 without thinking it through all that much. Given your example in comment 6, I see that in our interpretation of grocery shopping and resource theories your condition seems to make more sense. Batching processes usually results in lower costs and/or more products. My condition could also be the case in grocery shopping, however.
Example Consider that you have a bunch of coupons for the grocery store giving you a flat 0.50$discount. However, you may only use one coupon per visit to the store. This means that "the cost of buying two sets of groceries separately is less than the cost of buying them together". I think we need to also reverse the inequality in the second condition if we stick to your condition. It might be instructive to consider monoidal monotone maps between monoidal preorders with different units to think about this. For example $$f: (\mathbb{N},\le, +, 0) \hookrightarrow (\mathbb{N},\le, *, 1)$$ or $$g: (\mathbb{N},\le, *, 1) \hookrightarrow (\mathbb{N},\le, +, 0)$$, where $$f$$ and $$g$$ are the inclusions. For $$f$$ it is the case that $$f(x) \otimes_Y f(y) \ge_Y f(x \otimes_X y)$$ and $$1_Y \ge_Y f(1_X)$$. For $$g$$ it is the case that $$g(x) \otimes_Y g(y) \le_Y g(x \otimes_X y)$$ and $$1_Y \le_Y g(1_X)$$. So based on this one example it seems that either condition works as long as one is consistent. This means that for $$1_Y = f(1_X)$$ we could use either inequality. Edit: Just realized we probably only need one version of the conditions since we can formally take the function to the opposite preorder to get the other. Comment Source:Thanks Sophie for re-posting my comment in the right place and for your nice proof that \$$f\$$ must be injective! Regarding: > I was interested that this is the opposite condition from what Marius proposed. I just took the definition for a monoidal monotone from 7 sketches p.46 without thinking it through all that much. Given your example in comment 6, I see that in our interpretation of grocery shopping and resource theories your condition seems to make more sense. Batching processes usually results in lower costs and/or more products. My condition could also be the case in grocery shopping, however. **Example** Consider that you have a bunch of coupons for the grocery store giving you a flat 0.50$ discount. However, you may only use one coupon per visit to the store. This means that "the cost of buying two sets of groceries separately is *less* than the cost of buying them together". I think we need to also reverse the inequality in the second condition if we stick to your condition. It might be instructive to consider monoidal monotone maps between monoidal preorders with different units to think about this. For example \$$f: (\mathbb{N},\le, +, 0) \hookrightarrow (\mathbb{N},\le, *, 1) \$$ or \$$g: (\mathbb{N},\le, *, 1) \hookrightarrow (\mathbb{N},\le, +, 0) \$$, where \$$f \$$ and \$$g \$$ are the inclusions. For \$$f\$$ it is the case that \$$f(x) \otimes_Y f(y) \ge_Y f(x \otimes_X y) \$$ and \$$1_Y \ge_Y f(1_X)\$$. For \$$g\$$ it is the case that \$$g(x) \otimes_Y g(y) \le_Y g(x \otimes_X y) \$$ and \$$1_Y \le_Y g(1_X)\$$. So based on this one example it seems that either condition works as long as one is consistent. This means that for \$$1_Y = f(1_X)\$$ we could use either inequality. *Edit:* Just realized we probably only need one version of the conditions since we can formally take the function to the opposite preorder to get the other.
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8.
@Marius, Sophie: that's very interesting!
It may be worth pointing out that your result
Claim If $$f(x) \otimes_Y f(x') = f( x \otimes_X x')$$ then the relation $$\leq_X$$ induced by $$f$$ makes $$(X, \otimes_X, 1_X, \leq_X)$$ a monoidal preorder.
generalizes Matthew's proposed solution to Puzzle 71, which turns the complex numbers into a commutative monoidal preorder. Do you see how?
Comment Source:@Marius, Sophie: that's very interesting! It may be worth pointing out that your result > **Claim** If \$$f(x) \otimes_Y f(x') = f( x \otimes_X x')\$$ then the relation \$$\leq_X\$$ induced by \$$f\$$ makes \$$(X, \otimes_X, 1_X, \leq_X) \$$ a monoidal preorder. generalizes [Matthew's proposed solution to Puzzle 71](https://forum.azimuthproject.org/discussion/comment/18065/#Comment_18065×), which turns the complex numbers into a commutative monoidal preorder. Do you see how?
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9.
edited May 2018
If you mean:
$$x \preceq_p y \iff p \cdot x \leq p \cdot y$$
then $$f(x) = p \cdot x$$ and we see that $$f(x) \otimes_Y f(x') = p \cdot x + p \cdot x' = p \cdot (x+x') = f( x \otimes_Y x')$$ since multiplication distributes over addition.
Comment Source:If you mean: > $$x \preceq_p y \iff p \cdot x \leq p \cdot y$$ then \$$f(x) = p \cdot x \$$ and we see that \$$f(x) \otimes_Y f(x') = p \cdot x + p \cdot x' = p \cdot (x+x') = f( x \otimes_Y x')\$$ since multiplication distributes over addition.
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edited May 2018
Regarding this puzzle:
Puzzle 76. Now suppose $$(Y, \le_Y)$$ is a poset. Under what conditions on $$f$$ can we conclude that $$(X, \le_X )$$ defined as above is a poset?
Sophie wrote:
Puzzle 76. I agree with Marius that $$f$$ must be injective. In fact I think this is a necessary and sufficient condition!
That's right! But you don't need me to tell you this, since you proved it, so you know it's right.
(Of course sometimes we screw up when proving things, but writing down a proof and carefully checking the logic can reduce the chance of error quite dramatically.)
Comment Source:Regarding this puzzle: > **Puzzle 76.** Now suppose \$$(Y, \le_Y) \$$ is a poset. Under what conditions on \$$f\$$ can we conclude that \$$(X, \le_X ) \$$ defined as above is a poset? Sophie wrote: > **Puzzle 76**. I agree with Marius that \$$f\$$ must be injective. In fact I think this is a necessary and sufficient condition! That's right! But you don't need me to tell you this, since you proved it, so you _know_ it's right. (Of course sometimes we screw up when proving things, but writing down a proof and carefully checking the logic can reduce the chance of error quite dramatically.)
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11.
edited May 2018
And regarding this one:
Puzzle 77. Now suppose that $$(Y, \le_Y, \otimes_Y, 1_Y)$$ is a monoidal preorder, and $$(X,\otimes_X,1_X )$$ is a monoid. Define $$\le_X$$ as above. Under what conditions on $$f$$ can we conclude that $$(X,\le_X\otimes_X,1_X)$$ is a monoidal preorder?
Sophie wrote:
Claim If $$f(x) \otimes_Y f(x') = f( x \otimes_X x')$$ then the relation $$\leq_X$$ induced by $$f$$ makes $$(X, \otimes_X, 1_X, \leq_X)$$ a monoidal preorder.
Yes, that's right! So this is a sufficient condition, and this is the answer I had in mind.
You suggest that a weaker condition may be enough:
$$f( x \otimes_X x') \le f(x) \otimes_Y f(x') \qquad \star$$ for all $$x,x' \in X$$.
Let's see. To prove $$\leq_X$$ is a monoidal preorder, we need to prove
$$x_1 \le_X x_1' \textrm{ and } x_2 \le_X x_2' \textrm{ imply } x_1 \otimes_X x_2 \le_X x_1' \otimes_X x_2'$$ for all $$x_1,x_1',x_2,x_2' \in X$$. In other words, we need
$$f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$$ On the other hand, since $$(Y, \le_Y, \otimes_Y, 1_Y)$$ is a monoidal preorder, we know that
$$f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') .$$ If we assume condition $$\star$$, we also know
$$f(x_1 \otimes_X x_2) \le_Y f(x_1)\otimes_Y f(x_2) .$$ Combining this with what we know, we get
$$f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1') \otimes_Y f(x_2') .$$ But this does not yet get us what we need! Remember, we need
$$f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$$ The obvious way to get this is to also assume
$$f(x) \otimes_Y f(x') \le f(x \otimes_X x') \qquad \star\star$$ for all $$x,x' \in X$$. But $$\star$$ together with $$\star\star$$ is just your earlier condition
$$f(x) \otimes_Y f(x') = f(x \otimes_X x')$$ I don't see how either $$\star$$ or $$\star\star$$ is enough for this problem. I don't think either one by itself will do the job.
Comment Source:And regarding this one: > **Puzzle 77.** Now suppose that \$$(Y, \le_Y, \otimes_Y, 1_Y) \$$ is a monoidal preorder, and \$$(X,\otimes_X,1_X ) \$$ is a monoid. Define \$$\le_X\$$ as above. Under what conditions on \$$f\$$ can we conclude that \$$(X,\le_X\otimes_X,1_X) \$$ is a monoidal preorder? Sophie wrote: > **Claim** If \$$f(x) \otimes_Y f(x') = f( x \otimes_X x')\$$ then the relation \$$\leq_X\$$ induced by \$$f\$$ makes \$$(X, \otimes_X, 1_X, \leq_X) \$$ a monoidal preorder. Yes, that's right! So this is a sufficient condition, and this is the answer I had in mind. You suggest that a weaker condition may be enough: $f( x \otimes_X x') \le f(x) \otimes_Y f(x') \qquad \star$ for all \$$x,x' \in X\$$. Let's see. To prove \$$\leq_X\$$ is a monoidal preorder, we need to prove $x_1 \le_X x_1' \textrm{ and } x_2 \le_X x_2' \textrm{ imply } x_1 \otimes_X x_2 \le_X x_1' \otimes_X x_2'$ for all \$$x_1,x_1',x_2,x_2' \in X\$$. In other words, we need $f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$ On the other hand, since \$$(Y, \le_Y, \otimes_Y, 1_Y) \$$ is a monoidal preorder, we know that $f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') .$ If we assume condition \$$\star\$$, we also know $f(x_1 \otimes_X x_2) \le_Y f(x_1)\otimes_Y f(x_2) .$ Combining this with what we know, we get $f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1') \otimes_Y f(x_2') .$ But this does not yet get us what we need! Remember, we need $f(x_1) \le_Y f(x_1') \textrm{ and } f(x_2) \le_Y f(x_2') \textrm{ imply } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$ The obvious way to get this is to also assume $f(x) \otimes_Y f(x') \le f(x \otimes_X x') \qquad \star\star$ for all \$$x,x' \in X\$$. But \$$\star\$$ together with \$$\star\star\$$ is just your earlier condition $f(x) \otimes_Y f(x') = f(x \otimes_X x')$ I don't see how either \$$\star\$$ or \$$\star\star\$$ is enough for this problem. I don't think either one by itself will do the job.
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12.
edited May 2018
Sophie wrote:
I'm also wondering about Marius's suggestion that $$f$$ should satisfy $$1_Y\leq_Y f(1_X)$$
I don't think this condition plays any role in Puzzle 77. There's an interesting asymmetry in the definition of "monoidal preorder": the operation $$\otimes$$ needs to get along with relation $$\le$$, but the unit $$1$$ does not.
Later we will meet various kinds of maps between monoidal preorders: see Section 2.2.5. These should remind you of Puzzle 77, and they involve conditions on the unit. They are definitely relevant to your "pricing of groceries" examples... but nonetheless, I don't think any conditions on the unit are relevant to Puzzle 77.
I could be wrong.
Comment Source:Sophie wrote: > I'm also wondering about Marius's suggestion that \$$f\$$ should satisfy > \$$1_Y\leq_Y f(1_X)\$$ I don't think this condition plays any role in Puzzle 77. There's an interesting asymmetry in the definition of "monoidal preorder": the operation \$$\otimes\$$ needs to get along with relation \$$\le\$$, but the unit \$$1\$$ does not. Later we will meet various kinds of _maps_ between monoidal preorders: see Section 2.2.5. These should remind you of Puzzle 77, and they involve conditions on the unit. They are definitely relevant to your "pricing of groceries" examples... but nonetheless, I don't think any conditions on the unit are relevant to Puzzle 77. I could be wrong.
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13.
I've decided to make these puzzles into a mini-lecture, just because they fit pretty well into the overall flow of what we're doing: learning about monoidal preorder and their role in economics.
Comment Source:I've decided to make these puzzles into a mini-lecture, just because they fit pretty well into the overall flow of what we're doing: learning about monoidal preorder and their role in economics.
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14.
Thanks Marius, Tobias, and John for the responses! I had a lot of fun working on these problems.
Marius, I really like the example of getting a discount instead of a bag charge! Your comment about opposite categories also made me think that given a function $$f: X \to Y$$ we can define a relation on $$X$$ in an opposite way by $x \leq_X x' \iff f(x) \geq_Y f(x').$
I also wanted to check my thinking about Puzzle 77 again.
I showed that the property $$f(x) \otimes_Y f(x') = f(x \otimes_X x')$$ is sufficient for making $$(X, \leq_X, \otimes_X, 1_x)$$ a monoidal pre-order. But the examples of a bag cost and coupon discount that Marius and I suggested, show that this is not a necessary condition, since in both of those cases we only have $$f(x) \otimes_Y f(x') \leq f(x \otimes_X x')$$ and $$f(x) \otimes_Y f(x') \geq f(x \otimes_X x')$$ respectively. So as of yet, we don't have a nice necessary and sufficient condition on $$f$$ for making $$(X, \leq_X, \otimes_X, 1_x)$$ a monoidal pre-order. Is that correct?
Comment Source:Thanks Marius, Tobias, and John for the responses! I had a lot of fun working on these problems. Marius, I really like the example of getting a discount instead of a bag charge! Your comment about opposite categories also made me think that given a function \$$f: X \to Y\$$ we can define a relation on \$$X\$$ in an opposite way by \$x \leq_X x' \iff f(x) \geq_Y f(x').\$ I also wanted to check my thinking about Puzzle 77 again. I showed that the property \$$f(x) \otimes_Y f(x') = f(x \otimes_X x') \$$ is sufficient for making \$$(X, \leq_X, \otimes_X, 1_x) \$$ a monoidal pre-order. But the examples of a bag cost and coupon discount that Marius and I suggested, show that this is not a necessary condition, since in both of those cases we only have \$$f(x) \otimes_Y f(x') \leq f(x \otimes_X x') \$$ and \$$f(x) \otimes_Y f(x') \geq f(x \otimes_X x') \$$ respectively. So as of yet, we don't have a nice necessary <b>and</b> sufficient condition on \$$f\$$ for making \$$(X, \leq_X, \otimes_X, 1_x) \$$ a monoidal pre-order. Is that correct?
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15.
edited May 2018
Sophie: I haven't carefully checked those bag cost and coupon discount examples, so I can't promise that $$f(x) \otimes_Y f(x') = f(x \otimes_X x')$$ is not necessary. But I'm willing to believe you.
Re-examining what I wrote, it seems that a necessary and sufficient condition is
$$f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') \textrm{ implies } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$$ It's late, so I'll have to check this when I'm more awake. Does this condition hold in your examples?
Comment Source:Sophie: I haven't carefully checked those bag cost and coupon discount examples, so I can't promise that \$$f(x) \otimes_Y f(x') = f(x \otimes_X x') \$$ is not necessary. But I'm willing to believe you. Re-examining what I wrote, it seems that a necessary and sufficient condition is $f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') \textrm{ implies } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2') .$ It's late, so I'll have to check this when I'm more awake. Does this condition hold in your examples?
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16.
John: Yes your condition hold for both the bag cost and coupon examples. Also I can see how it slides right into the proof I gave in Comment 6. I wrote,
$f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y').$ $$f$$ exactly preserves the tensor structure so, $f(x \otimes_X y) \leq_Y f(x' \otimes_X y')$
Just replace "$$f$$ exactly preserves the tensor structure" with "by hypothesis"!
Comment Source:John: Yes your condition hold for both the bag cost and coupon examples. Also I can see how it slides right into the proof I gave in Comment 6. I wrote, > \$f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y'). \$ \$$f\$$ exactly preserves the tensor structure so, \$f(x \otimes_X y) \leq_Y f(x' \otimes_X y') \$ Just replace "\$$f\$$ exactly preserves the tensor structure" with "by hypothesis"!
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17.
Great, so this rather complicated condition is exactly the necessary and sufficient one!
By the way, there's more about grocery store prices in Lecture 27. I hadn't realized until teaching this course how much category theory, or at least poset theory, is lurking in the humble corner grocery store.
Comment Source:Great, so this rather complicated condition is exactly the necessary and sufficient one! By the way, there's more about grocery store prices in [Lecture 27](https://forum.azimuthproject.org/discussion/2098/lecture-27-chapter-2-adjoints-of-monoidal-monotones/p1). I hadn't realized until teaching this course how much category theory, or at least poset theory, is lurking in the humble corner grocery store.
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18.
edited May 2018
You can also solve these sorts of problems with 'calculus of variations' so you have a a budget, some choices about how to allocate it if you are shopping, and a budget constraint . Usually written as a Lagrangian. The more complex cases basically involve tensor products. Category theory I think includes calculus of variations (or multiobjective optimization) as a special case. But it's a different more general dialect.
Comment Source:You can also solve these sorts of problems with 'calculus of variations' so you have a a budget, some choices about how to allocate it if you are shopping, and a budget constraint . Usually written as a Lagrangian. The more complex cases basically involve tensor products. Category theory I think includes calculus of variations (or multiobjective optimization) as a special case. But it's a different more general dialect.
• Options
19.
edited June 2018
Is the condition: $$f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') \textrm{ implies } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2')$$ really necessary? I'm having a hard time trying to prove it. What I mean in detail is: Assuming that $$(X,\le_X,\otimes_X,1_X)$$ is a monoidal preorder, prove that the condition must hold.
Comment Source:Is the condition: $f(x_1)\otimes_Y f(x_2) \le_Y f(x_1') \otimes_Y f(x_2') \textrm{ implies } f(x_1 \otimes_X x_2) \le_Y f(x_1' \otimes_X x_2')$ really necessary? I'm having a hard time trying to prove it. What I mean in detail is: Assuming that \$$(X,\le_X,\otimes_X,1_X) \$$ is a monoidal preorder, prove that the condition must hold. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9107794165611267, "perplexity": 1318.8055607422239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00092.warc.gz"} |
https://www.physicsforums.com/threads/electric-field-help.85860/ | # Electric field help
1. Aug 21, 2005
### arutha
I have these questions on electric fields that I'm a bit confused on..
A flat circle of radius 8 cm is placed in a uniform electric field of 8.5 × 10^2 N/C. What is the electric flux (in Nm^2/C) through the circle when its face is at 51° to the field lines?
I just use EAcos(theta) don't I? Where A is 2*pi*r, but that angle do I use 51 or 90-51 since it is the angle is meant to be between the normal and the object not the object and the surface right?
A metallic sphere of radius 22 cm is negatively charged. The magnitude of the resulting electric field, close to the outside surface of the sphere, is 1.8 × 10^2 N/C. Calculate the net electric flux (in Nm^2/C) outward through a spherical surface surrounding, and just beyond, the metallic sphere's surface.
I'm thinking just E*A*cos(theta) again.. Would the answer be negative because it is negatively charged?
Two concentric spherical shells of radii R1=1 m and R2=2 m, contain charge Q1=0.005 C and Q2=0.0065 C respectively.
Calculate the Electric field at a distance r=1.79 m from the centerpoint of the spheres
I have absolutely no idea on this one.. How does it work with the two charges? And what if I was calculating the field outside the two spheres, would that be any different?
A very long solid nonconducting cylinder of radius 18.3 cm possesses a uniform volume charge density of 1.68 μC/m^3. Determine the magnitude of the electric field (in N/C) inside the cylinder at a radial distance of 8.8 cm from the cylinder's central axis
Heres what I've thought of, multiply the volume charge density by the volume of the cylindar to get the charge in μC, then use E=kQ/r^2 to get the magnitude of the electric field. Is that right? Edit: That won't work because I don't have a length of the cylindar to get the volume... Woops.
Thanks for any help, btw I don't want numbers or any answers I'd rather hear the process then get the numbers myself so I can figure out other problems of similar nature..
Last edited: Aug 21, 2005
2. Aug 21, 2005
### mukundpa
oooooooooooo
what is the area of a circle 2*pi*r ???? Check it.
3. Aug 21, 2005
### arutha
Oh yeah I forgot the square after the r... I wrote it down on the sheet, just missed typing it.
4. Aug 21, 2005
### mukundpa
A = (Pi)*r^2
5. Aug 21, 2005
### mukundpa
For the rest problems go through Guass's Theorem
6. Aug 22, 2005
### arutha
Well, I got them all except the last one now. Still have absolutely no idea how to do it, I've gone through my text book, lecture notes and everythnig but can't find anything on it.
7. Aug 22, 2005
### mukundpa
The distance of the point at which the field magnitude is required is 8.8 cm which is less then the radius of cylinder 18.3 cm.
Consider a coaxial cylindrical Gaussian surface of radius 8.8 cm and apply the Gauss’s theorem. Remember the charge to be taken within the Gaussian surface. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9424264430999756, "perplexity": 867.6273014003327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719155.26/warc/CC-MAIN-20161020183839-00560-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://mathstrek.blog/2013/11/28/elementary-module-theory-iv-linear-algebra/ | ## Elementary Module Theory (IV): Linear Algebra
Throughout this article, a general ring is denoted R while a division ring is denoted D.
## Dimension of a Vector Space
First, let’s consider the dimension of a vector space V over D, denoted dim(V). If W is a subspace of V, we proved earlier that any basis of W can be extended to give a basis of V, thus dim(W) ≤ dim(V).
Furthermore, we claim that if $\{v_i + W\}$ is a basis of the quotient space V/W, then the vi‘s, together with a basis $\{w_j\}$ of W, form a basis of V:
• If $\sum_i r_i v_i + \sum_j r_j' w_j = 0$ for some $r_i, r_j' \in D$, its image in V/W gives $\sum_i r_i (v_i + W) = 0$ and thus each $r_i$ is zero. This gives $\sum_j r_j' w_j = 0$; since $\{w_j\}$ forms a basis of W, each $r_j' = 0.$ This proves that $\{v_i\} \cup \{w_j\}$ is linearly independent.
• Let $v\in V$. Its image v+W in V/W can be written as a linear combination $\sum_i r_i (v_i + W) = v+W$ for some $r_i \in R.$ Hence $v - \sum_i r_i v_i \in W$ and can be written as a linear combination of $\{w_j\}.$ So v can be written as a linear combination of $\{v_i\} \cup \{w_j\}.$
Conclusion: dim(W) + dim(V/W) = dim(V). Now if fV → W is any homomorphism of vector spaces, the first isomorphism theorem tells us that V/ker(f) is isomorphic to im(f). Hence, dim(V) = dim(ker(f)) + dim(im(f)).
If V is finite-dimensional and dim(V) = dim(W), then:
• (f is injective) iff (ker(f) = 0) iff (dim(ker(f)) = 0) iff (dim(im(f)) = dim(V)) iff (dim(im(f)) = dim(W)) iff (im(f) = W) iff (f is surjective).
Thus, (f is injective) iff (f is surjective) iff (f is an isomorphism).
For infinite-dimensional V and W, take the free vector spaces $V = W = D^{(\mathbf{N})}$ and let fV → W take the tuple $(r_1, r_2, \ldots) \mapsto (0, r_1, r_2, \ldots).$ Then f is injective but not surjective.
Over a general ring, even if M and N are free modules, the kernel and image of fM → N may not be free. This follows from the fact that a submodule of a free module is not free in general, as we saw earlier. Hence it doesn’t make sense to talk about dim(ker(f)) and dim(im(f)) for such cases.
In a Nutshell. The main results are:
• for a D-linear map f : V → W, dim(V) = dim(ker(f)) + dim(im(f));
• if dim(V) = dim(W), then f is injective iff it is surjective.
## Matrix Algebra
Recall that an R-module M is free if and only if it has a basis $\{m_i\}_{i\in I}$, in which case we can identify $R^{(I)} \cong M$ via $(r_i)_{i\in I}\mapsto \sum_{i\in I} r_i m_i.$ Let’s restrict ourselves to the case of finite free modules, i.e. modules with finite bases. If $M\cong R^a$ and $N\cong R^b,$ the group of homomorphisms is identified with $\text{Hom}(M, N)\cong R^{ab}$ in terms of b × a matrices in R.
Let’s make this identification a bit more explicit. Pick a basis $\{m_1, \ldots, m_a\}$ of M and $\{n_1, \ldots, n_b\}$ of N. We have:
$R^a \cong M, \ (r_1, \ldots, r_a) \mapsto \sum_{i=1}^a r_i m_i\$ and $\ R^b \cong N, (r_1, \ldots, r_b)\mapsto \sum_{j=1}^b r_j n_j.$
A module homomorphism fM → N is expressed as a matrix as follows:
Example 1
Take RR, the field of real numbers and $M = \{a + bx + cx^2 : a, b, c\in\mathbf{R}\}$ and $N = \{a + bx : a, b\in \mathbf{R}\}$ where x is an indeterminate here. The map fM → N given by f(p(x)) = dp/dx is easily checked to be R-linear.
Pick basis {1, x x2} of M and {1, x} of N. Since f(1) = 0, f(x) = 1 and f(x2) = 2x, the resulting f takes $m_1 \mapsto 0, m_2\mapsto n_1, m_3 \mapsto 2n_2.$ Hence, the matrix corresponding to these bases is $\begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 2\end{pmatrix}.$
On the other hand, if we pick basis {1+x, –x, 1+x2} of M and basis {1+x, 1+2x} of N, then
• $f(m_1) = f(1+x) = 1 = 2n_1 - n_2$;
• $f(m_2) = -1 = -2n_1 + n_2$;
• $f(m_3) = 2x = -2n_1 + 2n_2$
which gives the matrix representation $\begin{pmatrix} 2 & -2 & -2 \\ -1 & 1 & 2\end{pmatrix}.$
Example 2
Let M = {ab√2 : ab integers} which is a Z-module. Take fM → M which takes z to (3-√2)z. It’s clear that f is a homomorphism of additive groups and hence Z-linear. Since the domain and codomain modules are identical (M), let’s pick a single basis.
If we pick {1, √2}, then
• $f(m_1) = f(1) = 3-\sqrt 2 = 3m_1 - m_2$;
• $f(m_2) = f(\sqrt 2) = -2 + 3\sqrt 2 = -2m_1 + 3m_2$
thus giving the matrix representation $\begin{pmatrix} 3 & -2 \\ -1 & 3\end{pmatrix}.$ Replacing the basis by {-1, 1+√2} would give us: $\begin{pmatrix} -4 & -1 \\ 1 & 2\end{pmatrix}.$
Thus, the matrix representation for fV → W depends on our choice of bases for V and W. If VW, then it’s often convenient to pick the same basis.
## Dual Module
We saw earlier that $\text{Hom}(R, M) \cong M$ as an R-module isomorphism. What about Hom(MR) then?
Definition. The dual module of left-module M is defined to be $M^* := \text{Hom}(M, R).$ This is a right R-module, via the following right action:
• if $r\in R$ and $f:M\to R$, then the resulting $f\cdot r$ takes $m\mapsto f(m)r$.
From the universal property of direct sums and products, we see that:
$(\oplus_{i\in I} M_i)^* \cong \prod_{i\in I} M_i^*.$
Let’s check that we get a right-module structure on M*: indeed, $(f\cdot r_1)\cdot r_2$ takes m to $(f\cdot r_1)(m)r_2 = (f(m)r_1)r_2$ which is the image of $f\cdot (r_1 r_2)$ acting on m.
The module $M^*$ is called the dual because it’s a right module instead of a left one. Note that if N were a right-module, the resulting space Hom(NR) of all right-module homomorphisms would give us a left module $N^*.$ It’s not true in general that $M^{**} \cong M$ but it holds for finite-dimensional vector spaces over a division ring.
Theorem. If V is a finite-dimensional vector space over division ring D, then $V^{**} \cong V.$
Proof.
Consider the map $V^* \times V\to D$ which takes (fv) to f(v). Fixing f, we get a map $v\mapsto f(v)$ which is a left-module homomorphism. Fixing v, we get a right-module homomorphism $f\mapsto f(v)$ since (f·r) corresponds to the map $v\mapsto f(v)r$ by definition. This gives a left-module homomorphism $\phi:V\to V^{**}.$
Since V is finite dimensional, it suffices to show $\text{ker}\phi = 0$. But if $v\in V-\{0\}$, we can extend {v} to a basis of V. Define a linear map fV → D which takes v to 1 and all other basis elements to 0. Then $(\phi(v))(f) = f(v) \ne 0$ so $\phi(v) \ne 0.$ This shows that $\phi$ is injective and thus an isomorphism. ♦
One way to visualise the duality is via this diagram:
Exercise
It’s tempting to define a module structure on Hom(MR) via $(f\cdot r)(m) = f(rm).$ What’s wrong with this definition? [ Answer: the resulting f·r : MR is not a left-module homomorphism. ]
## Dual Basis
Suppose $\{ v_1, v_2, \ldots, v_n\}$ is a basis of V. Let $f_i : V\to D$ (i = 1, …, n) be linear maps defined as follows:
$f_i(v_j) = \begin{cases} 1, \quad &\text{ if } j = i, \\ 0, \quad &\text{ if } j\ne i.\end{cases}$
Each $f_i$ is well-defined by the universal property of the free module V. Using the Kronecker delta function, we can just write $f_i(v_j) = \delta_{ij}.$ This is called the dual basis for $\{v_1, \ldots, v_n\}.$
[ Why is this a basis, you might ask? We know that dim(V*) = dim(V) = n, so it suffices to check that $f_1, \ldots, f_n$ is linearly independent. For that, we write $\sum_i f_i\cdot r_i=0$ for some $r_1, \ldots, r_n \in D$ (recall that V* is a right module). Then for each j = 1, …, n, we have
$0 = \sum_i (f_i\cdot r_i)(v_j) = \sum_i f_i(v_j)r_i = \sum_i \delta_{ij}r_i = r_j$
and we’re done. ]
Now if $f\in V^*$ and $v\in V,$ we can write $f = \sum_{i=1}^n f_i c_i$ and $v = \sum_{j=1}^n d_j v_j$ for some $c_i, d_j \in D.$ Then
\begin{aligned}f(v) &= \left(\sum_{i=1}^n f_i c_i\right)\left(\sum_{j=1}^n d_j v_j\right) = \sum_{i=1}^n f_i\left(\sum_{j=1}^n d_j v_j\right)c_i \\ &= \sum_{i=1}^n \sum_{j=1}^n d_j\delta_{ij}c_i = \sum_{i=1}^n d_i c_i\end{aligned}
which is the product between a row vector & a column vector.
One thus gets a natural inner product between a vector space and its dual. Recall that in an Euclidean vector space $V = \mathbf{R}^3$, there’s a natural inner product given by the usual dot product which is inherent in the geometry of the space. However, for generic vector spaces, it’s hard to find a natural inner product. E.g. what would one be for the space of all polynomials of degree at most 2? Thus, the dual space provides a “cheap” and natural way to get an inner product.
## Example
Consider the space $V = \{a + bx + cx^2 : a, b, c\in \mathbf{R}\}$ over the reals R=R. Examples of elements of V* are:
• $f\mapsto f(1)$ which takes $(a+bx+cx^2)\mapsto a+b+c$;
• $f\mapsto \left.\frac {df}{dx}\right|_{x=-1}$ which takes $(a+bx+cx^2) \mapsto -b+2c$;
• $f\mapsto \int_0^1 (a+bx+cx^2) dx$ which takes $(a+bx+cx^2) \mapsto a + \frac b 2 + \frac c 3$.
It’s easy to check that these three elements of V* are linearly independent and hence form a basis. Note: in this case, the base ring is a field so right modules are also left, i.e. V* and V are isomorphic as abstract vector spaces! However, there’s no “natural” isomorphism between them since in order to establish an isomorphism, one needs to pick a basis of V, a basis of V* and map the corresponding elements to each other. On the other hand, the isomorphism between V** and V is completely natural.
Exercise.
[ All vector spaces in this exercise are of finite dimension. ]
Let $\{v_1, \ldots, v_n\}$ be a basis of V and $\{f_1, \ldots, f_n\}$ be its dual basis for V*. Denote the dual basis of $\{f_1, \ldots, f_n\}$ by $\{\alpha_1, \ldots, \alpha_n\}$ in V**. Prove that under the isomorphism $V\cong V^{**}$, we have $v_i = \alpha_i.$
Let $\{v_i\}$ be a basis of V and $\{w_j\}$ be a basis of W. If TV → W is a linear map, then the matrix representation of T with respect to bases $\{v_i\}, \{w_j\}$ is denoted M.
• Prove that the map T* : W* → V* which takes W → D to the composition º T : V → D is a linear map of right modules.
• Let $\{f_i\}$ be the dual basis of $\{v_i\}$ for V* and $\{g_j\}$ be the dual basis of $\{w_j\}$ for W*. Prove that the matrix representation of T* with respect to bases $\{f_i\}, \{g_j\}$ is the transpose of M.
## More on Duality
Let V be a finite-dimensional vector space over D and V* be its dual. We claim that there’s a 1-1 correspondence between subspaces of V and those of V*, which is inclusion-reversing. Let’s describe this:
• if $W\subseteq V$ is a subspace, define $W^\perp := \{ f\in V^* : f(w) = 0 \text{ for all } w\in W\};$
• if $X\subseteq V^*$ is a subspace, define $X^\perp := \{v\in V : f(v) = 0 \text{ for all } f\in X\}.$
The following preliminary results are easy to prove.
Proposition.
• $W^\perp$ is a subspace of V*;
• $X^\perp$ is a subspace of V;
• if $W_1\subseteq W_2\subseteq V$, then $W_1^\perp \supseteq W_2^\perp$;
• if $X_1\subseteq X_2 \subseteq V^*$, then $X_1^\perp \supseteq X_2^\perp$;
• $W\subseteq W^{\perp\perp}$ and $X\subseteq X^{\perp\perp}$.
We’ll skip the proof, though we’ll note that the above result in fact holds for any subsets $W\subseteq V$ and $X\subseteq V^*$. This observation also helps us to remember the direction of inclusion for $W\subseteq W^{\perp\perp}$ since in this general case, $W^{\perp\perp}$ is the subspace of V generated by W.
The main thing we want to prove is the following:
Theorem. If $W\subseteq V$ is a subspace, then $W^{\perp\perp} = W$. Likewise if $X\subseteq V^*$ is a subspace, then $X^{\perp\perp} = X.$
Proof.
Pick a basis $\{v_1, \ldots, v_k\}$ of W and extend it to a basis $\{v_1, \ldots, v_n\}$ of V, where dim(W) = k and dim(V) = n. Let $\{f_1, \ldots, f_n\} \subset V^*$ be the dual basis.
If $v\in V-W,$ write $v = \sum_{i=1}^n r_i v_i$ where each $r_i\in D.$ Since v is outside W, $r_j\ne 0$ for some j>k. This gives $f_j(v) = f_j(\sum_i r_i v_i) = r_j \ne 0$ and $f_j\in W^\perp$ since j>k. Hence $v\not\in W^{\perp\perp}$ and we have $W^{\perp\perp} \subseteq W.$
The case for X is obtained by replacing V with V* and identifying $V^{**} \cong V$. ♦
Thus we get the following correspondence:
Furthermore, the dimensions “match”. E.g. suppose dim(V) = n, so dim(V*) = n. Then we claim that for any subspace W of V of dimension k,
• $\dim(W^{\perp}) = n-k$;
• $V^* / W^\perp \cong W^*$ naturally.
Since dim(W*) = dim(W) = k, the first statement follows from the second. From results above, the inclusion map W → V induces a map of the dual spaces V* → W*. The kernel of this map is precisely the set of all $f\in V^*$ such that f(w) = 0 for all w in W, which is exactly $W^\perp.$ This proves our claim. ♦
This entry was posted in Notes and tagged , , , , . Bookmark the permalink. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 139, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9887526035308838, "perplexity": 476.496093092914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00140.warc.gz"} |
https://stat.mit.edu/events/ankur-moitra-mit/ | # Stochastics and Statistics Seminar
## Robust Statistics, Revisited
Speaker Name: Ankur Moitra (MIT)
Date: March 10, 2017
Time: 11:00am
Location: E18-304
Abstract:
Starting from the seminal works of Tukey (1960) and Huber (1964), the field of robust statistics asks: Are there estimators that provable work in the presence of noise? The trouble is that all known provably robust estimators are also hard to compute in high-dimensions.
Here, we study a basic problem in robust statistics, posed in various forms in the above works. Given corrupted samples from a high-dimensional Gaussian, are there efficient algorithms to accurately estimate its parameters? We give the first algorithms that are able to tolerate a constant fraction of corruptions that is independent of the dimension. Additionally, we give several more applications of our techniques to product distributions and various mixture models.
This is based on joint work with Ilias Diakonikolas, Jerry Li, Gautam Kamath, Daniel Kane and Alistair Stewart.
Speaker Bio:
Ankur Moitra is the Rockwell International Assistant Professor in the Department of Mathematics at MIT. The aim of his work is to bridge the gap between theoretical computer science and machine learning by developing algorithms with provable guarantees and foundations for reasoning about their behavior. He is a recipient of a Packard Fellowship, a Sloan Fellowship, an NSF CAREER Award, an NSF Computing and Innovation Fellowship and a Hertz Fellowship. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8212506771087646, "perplexity": 746.7197575058822}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122739.53/warc/CC-MAIN-20170423031202-00507-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://webwork.maa.org/moodle/mod/forum/discuss.php?d=2835 | ## WeBWorK Main Forum
### Why scientific notation requires "X" instead of "*" for multiplication? Aren't students conditioned to use "*" everywhere?
by Christian Seberino -
Number of replies: 1
I noticed you can't create a problem that requires scientific notation nor
enter an answer in scientific notation without using "X" instead of "*"
for multiplication.
Why? Aren't students expecting to use "*" since that is what they use
everywhere else for multiplication?
cs
DOCUMENT();
"PGstandard.pl",
"PGML.pl",
"MathObjects.pl",
"PGcourse.pl",
"parserNumberWithUnits.pl",
"contextArbitraryString.pl",
"parserPopUp.pl",
"contextInequalities.pl",
"contextScientificNotation.pl",
);
TEXT(beginproblem());
######################################################################
Context("ScientificNotation");
BEGIN_PGML
See if you can enter 1230 in scientific notation.
[____________]{Compute("1.23 x 10**3")}
END_PGML
######################################################################
ENDDOCUMENT();
### Re: Why scientific notation requires "X" instead of "*" for multiplication? Aren't students conditioned to use "*" everywhere?
by Davide Cervone -
It's because that's what the person who requested this context required. It was designed for use in a high-school course where the notational requirements were very strict.
If you want to use * for the multiplication, you can add it into the context as follows:
Context("ScientificNotation"); | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9359574913978577, "perplexity": 4217.866891444035}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710712.51/warc/CC-MAIN-20221129232448-20221130022448-00411.warc.gz"} |
https://math.stackexchange.com/questions/1997523/why-can-the-row-reduced-echelon-matrix-r-only-be-identity-matrix | # Why can the row-reduced echelon matrix $R$ only be identity matrix?
I'm reading Linear Algebra by Hoffman, Kunze where the authors explained that a $n\times n$ matrix $A$ being invertible is equivalent to the fact that $A$ is row-equivalent to $n\times n$ matrix $R$ which is an identity matrix.
In the proof of the theorem, they wrote:
$$R= E_k\ldots E_2E_1 A$$ where $E_1,\ldots,E_k$ are elementary matrices. Each $E_j$ is invertible, and so $$A = E_1^{-1}\ldots E_k^{-1}~R\,.$$ ... Since, $R$ is a (square) row-reduced echelon matrix, $R$ is invertible if and only if $R=I\,.$ [...]
I couldn't get the conclusion, since any row of $R$ can't be zero, it has to be identity matrix $I\,.$ Why is it so?
Isn't there any other row-reduced echelon matrix other than the identity matrix having no zero row and invertible? Why is it so?
Suppose that $R$ is a matrix in row-reduced echelon form, and that $R$ has no zero-rows. That means that $R$ has a pivot (leading $1$) in every row.
This means that we have $n$ pivots in an $n \times n$ matrix. However, since no column of a row-reduced matrix can have two pivots, it must be that every single column has a pivot. In other words, every column has a leading $1$ in some entry, and the other entries of that column of zero.
In other words, the columns of $R$ must be the columns of the identity. The only order we can put those columns in and have $R$ in row-echelon form is the order in which $R = I$.
• I do not understand your answer. You say that "every column has a leading $1$ in some entry, and the other entries of that column of zero.". But why can't the row reduced echelon form have a zero row? – ab123 Sep 3 '18 at 11:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9325418472290039, "perplexity": 178.75382093602246}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00485.warc.gz"} |
http://physics.stackexchange.com/questions/68852/autocorrelation-and-power-density-spectrum-continuous-markov-process | # Autocorrelation and Power density spectrum : Continuous Markov Process
I've been reading through the paper from Gillespie on Brownian motion and Johnson Noise (DOI, PDF).
He considers $X_s(t)$, a zero-mean stochastic variable, that is stationary in the sense that all of its moments $\langle X_s(t)^k\rangle$ are time independent. He further defines the autocorrelation function (2.39)
$$\langle X_s(t)X_s(t+t')\rangle \equiv C_X(t')$$ which is independent of time since all the moments are time independent. The mean is over all possible values of X.
I cannot interpret this autocorrelation. I have been told that it measures how much the random variable fluctuates but I cannot convince myself of that.
I think this is the relevant question in order to answer my dilemma : on the same page of the definition of the autocorrelation, he goes on showing that its frequency fourrier transform
$$C_X(t) = \int \limits_{0}^\infty S_x(\nu) cos(2\pi \nu t)$$ can be related to the variance of $X_s(t)$ as $$\langle X_s(t)^2 \rangle = \int \limits_0^\infty S_x(\nu)d\nu$$
Now in the Ornstein Uhlenbeck process, $X_s(t)$ is to be interpreted as the speed of particle, subject to a drag force and a white-noise random force ($\Gamma$) $$\frac{dX_s(t)}{dt} = -\gamma X_s(t) + \sqrt{c}\Gamma(t)$$ One can then compute the dissipated power spectrum which originates from the drag force. Since power is force times speed, one gets
$$\langle P_{diss} \rangle = \gamma\langle X_s(t)^2\rangle \quad \to \quad P_{diss}(\nu) = \gamma S_X(\nu) = \gamma \frac{2c}{\gamma^2+(2\pi\nu)^2}$$ Where the last equality holds for the process at study. Gillespie simply says that this means that only the low frequency regime contributes to the dissipated power, and the high frequency regime doesn't. But frequency of what ?
My interpretation would be this : the frequency argument ammounts to saying that if the variable is auto-correlated also for long times (low frequency in fourier), then you will have significant dissipated power. Coming back to my original question: do long autocorrelation times mean that the particle fluctuates a lot, and if so, why ?
-
The $C_X(t')= \langle X_s(t)X_s(t+t')\rangle$ should be compared with the statistical correlation (Wikipedia: http://en.wikipedia.org/wiki/Correlation_and_dependence). With the statistical correlation one measures the dependency between two veriables. If two variables are independent they will have a correlation equal to zero. If two variables tend to have the same value, the correlation is positive and if two varibles tend to have opposite values the correlation is negative.
For the case of Brownian motian, I guess that $X_s(t)$ is the velocity-distribution considering that the VACF (velocity autocorrelationfunction) is mostly used in the theory of Brownian motion. Then $C_X(t')$ tells you what the correlation is between the velocity at time $t$ and at time $t+t'$. For Continuous Markovchains this should drop exponentially, which is also the case for the Brownian motion. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9275797009468079, "perplexity": 347.169055842708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663372.35/warc/CC-MAIN-20140930004103-00001-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://aas.org/archives/BAAS/v27n2/aas186/abs/S5006.html | Deep $JHK$ Photometry and the Infrared Luminosity Function of the Galactic Bulge
Session 50 -- The Milky Way
Display presentation, Thursday, June 15, 1995, 9:20am - 4:00pm
## [50.06] Deep $JHK$ Photometry and the Infrared Luminosity Function of the Galactic Bulge
Glenn P. Tiede, Jay A. Frogel, and D.M. Terndrup (OSU)
We derive the deepest, most complete near-IR luminosity function for Galactic bulge stars yet obtained based on new $JHK$ photometry for stars in two fields of Baade's Window. When combined with previously published data, we are able to construct a luminosity function over the range $5.5 \leq K_0 \leq 16.5$. The slope of the luminosity function as well as the top of the first ascent giant branch are consistent with expectations based on the Revised Yale Isochrones. Unfortunately, this consistency only sets weak constraints on the range in age and [Fe/H] for the Baade's Window stars.
A blue sequence of foreground stars is clearly visible on the $J-K, K$ color-magnitude diagrams we have derived.
We use the relationship between [Fe/H] and the giant branch slope derived from near-IR observations of metal rich globular clusters by (Kuchinski, L.E., Frogel, J.A., Terndrup, D.M., \& Persson, S.E. 1995, AJ, 109, 1131) to calculate the metallicity for several bulge fields along the minor axis. For Baade's Window we calculate that [Fe/H] $= -0.28 \pm 0.16$, consistent with the recent estimate of (McWilliam, A., \& Rich, R.M. 1994, ApJS, 91, 749), but somewhat lower than previous estimates based on CO and TiO absorption bands and the $JHK$ colors of the M giants by (Frogel, J. A., Terndrup, D.M., Blanco, V.M., \& Whitford, A.E. 1990, ApJ, 353, 494). Between b $= -3$ and -12 we find a gradient in [Fe/H] of $-0.06 \pm 0.03$ dex/degree, consistent with other, independent derivations.
We derive a helium abundance for Baade's Window with the $R$ and $R^\prime$ methods and find that Y $= 0.27 \pm 0.03$.
Finally, we find that the bolometric corrections for bulge K giants ($V - K \geq 2$) are in excellent agreement with empirical derivations based on observations of globular cluster and local field stars. However, for the redder M giants we find, as did Frogel and Whitford 1987, that the bolometric corrections differ by several tenths of a magnitude from those derived for field giants and adopted in the Revised Yale Isochrones. This difference most likely arises from the excess molecular blanketing in the V and I bands of the bulge giants relative to that seen in field stars. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8872423768043518, "perplexity": 4009.5294963090932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257827080.38/warc/CC-MAIN-20160723071027-00325-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/64856/defining-computability-for-functionals-of-partial-oracles | Defining computability for functionals of partial oracles
I believe a recursive (partial) functional $F:\mathbb{N}^\mathbb{N}\to\mathbb{N}$ is ordinarily defined as one for which the "graph" relation $F(\alpha)=n$ is recursively enumerable, which means it can be expressed in the form $$F(\alpha)=n \iff \exists x.Q(\overline{\alpha}(x), n, x)$$ for some (primitive?) recursive total predicate $Q$. Here $\overline{\alpha}(x) = \langle \alpha(0), \ldots, \alpha(x-1)\rangle$, i. e., the $x$-tuple of all the values of $\alpha(t)$ for $t\lt x$ encoded as a single natural number (it's not important how). This definition of recursiveness intuitively coincides with computability if we think of $\alpha$ as being given by an oracle (exercise, or see Shoenfield, Mathematical Logic.)
Unfortunately, I'm actually interested in the generalization where $\alpha$ may be a partial function itself and we don't know for which $t$ $\alpha(t)$ is undefined. If we try to evaluate $\alpha(t)$ and it happens to be undefined, then we simply wait forever for the answer which never comes. We can't cancel the request, either: once we ask the oracle for $\alpha(t)$, we're committed. Also, the oracle can only entertain one query at a time. (This is very important! For example, the functional that returns 0 if the domain of $\alpha$ is not empty and is undefined otherwise is not computable here, but it is computable if the oracle can entertain an arbitrary number of simultaneous queries. Similarly, allowing $n$ simultaneous queries yields a different class of computable functionals for each $n$.) The definition of recursiveness for partial functionals in the first paragraph fails in this generalization, since it could happen that our computation of $F(\alpha)$ queries a finite set of values of $\alpha(t)$ all with $t\lt x$, but $\alpha$ is undefined for some other $t\lt x$, so $\overline\alpha(x)$ is already undefined but our computation is fine.
In summary, I'm asking for a generalization of "recursive partial functional" for this situation.
-
I like your concept, but do you have a specific question about it? – Joel David Hamkins May 13 '11 at 0:37
A thorough answer to this question will be quite long. In the meantime, may suggest section 4 of John R. Longley's survey, Notions of Computability at Higher Types I, [homepages.inf.ed.ac.uk/jrl/Research/notions1.pdf] ? – Ulrik Buchholtz May 13 '11 at 4:00
@Ulrik: It is long, but it seems completely relevant to my question. Besides, I've been curious about this subject for a while, so I don't mind a bit of reading. Thanks! – Darsh Ranjan May 14 '11 at 1:59
This sounds like Jaap van Oosten's partial combinatory algebra $\mathcal{B}$, or its effective version, to be precise. You can read about it in John Longley's survey paper, as mentioned by Ulrik in the comments, or specifically in John's "Sequentially realizable functionals". | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8674883842468262, "perplexity": 454.8367417888793}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096686.2/warc/CC-MAIN-20150627031816-00289-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.bartleby.com/solution-answer/chapter-144-problem-148cyu-chemistry-and-chemical-reactivity-10th-edition/9781337399074/the-catalyzed-decomposition-of-hydrogen-peroxide-is-first-order-in-h2o2-it-was-found-that-the/18de5bbc-7309-11e9-8385-02ee952b546e | # The catalyzed decomposition of hydrogen peroxide is first-order in [H 2 O 2 ]. It was found that the concentration of H 2 O 2 decreased from 0.24 M to 0.060 M over a period of 282 minutes. What is the half-life of H 2 O 2 ? What is the rate constant for this reaction? What is the initial rate of decomposition at the beginning of this experiment (when [H 2 O 2 ] = 0.24 M)?
### Chemistry & Chemical Reactivity
10th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781337399074
### Chemistry & Chemical Reactivity
10th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781337399074
#### Solutions
Chapter
Section
Chapter 14.4, Problem 14.8CYU
Textbook Problem
## Expert Solution
### Want to see the full answer?
Check out a sample textbook solution.See solution
### Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
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*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8323324918746948, "perplexity": 3677.3888147998514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141197278.54/warc/CC-MAIN-20201129063812-20201129093812-00214.warc.gz"} |
http://physionet.cps.unizar.es/physiotools/plt/plt/html/node49.html | Next: Preparing Plots for the Web Up: Preparing Printed Output Previous: Processing, previewing and printing
# Using plt with pdfLATEX
Most of the techniques described in this chapter for preparing PostScript output from LATEX documents and .eps format plt figures will work without changes if you use pdfLATEX to prepare PDF output from LATEX documents and .pdf format plt figures. If you are creating figures specifically for inclusion in a PDF document, use a command of the form
```plt -T lw ... | lwcat -pdf >fig.pdf
```
to make a PDF figure. If you have already generated a PostScript figure, use a command such as
```epstopdf fig.ps
```
to make fig.pdf from an existing fig.ps. (epstopdf is freely available from CTAN, http://www.ctan.org/.) It is usually not necessary to make any changes to an existing LATEX source document in order to format it using pdfLATEX; thus, for example, your document should still use the epsfig package, even though your included figures will be in PDF rather than EPS format. When you specify the names of the figure files, always use the form
```\epsfig{file=fig}
```
If you avoid writing file=fig.ps or file=fig.pdf, then the correct version of your figure will be chosen automatically when formatting your document with latex and dvips or with pdflatex.
The only feature of epsfig described in this appendix that is not currently supported by pdfLATEX is the clip= option, which is ignored. If you are reading the PDF version of this book, the figure in section B.3 illustrates the results; you should avoid using the clip= option if you anticipate using pdfLATEX.
Using pdfLATEX to format myfile.tex is a one-step process:
```pdflatex myfile
```
Unless there are errors, this command should produce myfile.pdf, which can be viewed using gv, xpdf, Acrobat, or any other PDF reader.
Next: Preparing Plots for the Web Up: Preparing Printed Output Previous: Processing, previewing and printing
George B. Moody ([email protected])
2005-04-26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.964835524559021, "perplexity": 4243.118174290171}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688158.27/warc/CC-MAIN-20170922022225-20170922042225-00296.warc.gz"} |
https://math.hecker.org/2017/12/27/linear-algebra-and-its-applications-exercise-3-4-14/ | ## Linear Algebra and Its Applications, Exercise 3.4.14
Exercise 3.4.14. Given the vectors
$a = \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} \quad b = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} \quad c = \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}$
find the corresponding orthonormal vectors $q_1$, $q_2$, and $q_3$.
Answer: We first choose $a' = a$. We then have
$b' = b - \frac{(a')^Tb}{(a')^Ta'}a' = b - \frac{1 \cdot 1 + 1 \cdot 0 + 0 \cdot 1}{1^2 + 1^2 + 0^2}a' = b - \frac{1}{2}a'$
$= \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} - \frac{1}{2} \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 1 \end{bmatrix}$
We then have
$c' = c - \frac{(a')^Tc}{(a')^Ta'}a' - \frac{(b')^Tc}{(b')^Tb'}b' = c - \frac{1 \cdot 0 + 1 \cdot 1 + 0 \cdot 1}{1^2 + 1^2 + 0^2}a' - \frac{\frac{1}{2} \cdot 0 + (-\frac{1}{2}) \cdot 1 + 1 \cdot 1}{(\frac{1}{2})^2 + (-\frac{1}{2})^2+ 1^2}b'$
$= c' - \frac{1}{2}a' - \frac{\frac{1}{2}}{\frac{3}{2}}b' = c - \frac{1}{2}a' - \frac{1}{3}b'$
$= \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} - \frac{1}{2} \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} - \frac{1}{3} \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} - \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ 0 \end{bmatrix} - \begin{bmatrix} \frac{1}{6} \\ -\frac{1}{6} \\ \frac{1}{3} \end{bmatrix}$
$= \begin{bmatrix} -\frac{2}{3} \\ \frac{2}{3} \\ \frac{2}{3} \end{bmatrix}$
Now that we have calculated the orthogonal vectors $a'$, $b'$, and $c'$, we can normalize them to create the orthonormal vectors $q_1$, $q_2$, and $q_3$. We have
$\|a'\| = \sqrt{1^2+1^2 + 0^2} = \sqrt{2}$
$\|b'\| = \sqrt{(\frac{1}{2})^2 + (-\frac{1}{2})^2 + 1^2} = \sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}$
$\|c'\| = \sqrt{(-\frac{2}{3})^2 + (\frac{2}{3})^2 + (\frac{2}{3})^2} = \sqrt{\frac{12}{9}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$
so that
$q_1 = a' / \|a'\| = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{bmatrix}$
$q_2 = b' / \|b'\| = \frac{\sqrt{2}}{\sqrt{3}} \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 1 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}\sqrt{3}} \\ -\frac{1}{\sqrt{2}\sqrt{3}} \\ \frac{2}{\sqrt{2}\sqrt{3}} \end{bmatrix}$
$q_3 = c' / \|c'\| = \frac{\sqrt{3}}{2} \begin{bmatrix} -\frac{2}{3} \\ \frac{2}{3} \\ \frac{2}{3} \end{bmatrix} = \begin{bmatrix} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}$
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
This entry was posted in linear algebra and tagged , . Bookmark the permalink. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 23, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9189487099647522, "perplexity": 956.6910572171587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000044.37/warc/CC-MAIN-20190626013357-20190626035357-00028.warc.gz"} |
http://mathhelpforum.com/math-topics/4581-complex-number-finding-roots-print.html | # Complex number-finding roots
• July 31st 2006, 01:32 AM
kingkaisai2
Complex number-finding roots
Find the roots of the equation z^2=21-20i
• July 31st 2006, 04:30 AM
Soroban
Hello, kingkaisai2!
Edit: I corrected my wrong sign below ... Sorry for any confusion it caused.
I don't know what methods you've been taught . . .
Quote:
Find the roots of the equation $z^2 \:=\:21-20i$
Let $z = a + bi$, where $a$ and $b$ are real.
We have: . $(a + bi) \:= \:21 - 20i$
Then: . $a^2 + 2abi$+ $b^2i^2\:=\:$ $21 - 20i\quad\Rightarrow\quad (a^2 - b^2) + 2abi \:=\:21 - 20i$
Equate real and imaginary components: . $\begin{array}{cc}a^2 - b^2 \:= \:21\\ 2ab \:= \:-20\end{array}$ $\begin{array}{cc}(1)\\(2)\end{array}$
From (2), we have: . $b = -\frac{10}{a}$
Substitute into (1): . $a^2 - \left(-\frac{10}{a}\right)^2\:=\:21\quad\Rightarrow\quad a^2 - \frac{100}{a^2}\:=\:21$
Multiply by $a^2:\;\;a^4 - 100\:=\:21a^2\quad\Rightarrow\quad a^4 - 21a^2 - 100\:=\:0$
Factor: . $(a^2 + 4)(a^2 - 25)\:=\:0$
We have two equations to solve:
. . $a^2 + 4\:=\:0\quad\Rightarrow\quad a^2\,=\,-4\;\cdots \text{ but }a\text{ must be }real.$
. . $a^2 - 25\:=\:0\quad\Rightarrow\quad a^2\,=$ $\,25\quad\Rightarrow\quad a\,=\,\pm5$
Substitute into (2): . $b \:= \:-\frac{10}{\pm5} \:=\:\mp2$
Therefore: . $\boxed{z\;=\;\{5 - 2i,\;-5 + 2i\}}$
• July 31st 2006, 11:02 AM
Quick
Quote:
Originally Posted by Soroban
Hello, kingkaisai2!
I don't know what methods you've been taught . . .
Let $z = a + bi$, where $a$ and $b$ are real.
We have: . $(a + bi) \:= \:21 - 20i$
Then: . $a^2 + 2abi - b^2i^2\:=\:$ $21 - 20i\quad\Rightarrow\quad (a^2 - b^2) + 2abi \:=\:21 - 20i$
shouldn't it be $(a^2+b^2)+2abi=21-20i$? because i^2 equals -1 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9882603883743286, "perplexity": 4247.262601359869}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982292181.27/warc/CC-MAIN-20160823195812-00173-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://converths.com/1500-meters-to-miles-online-calculator-for-units/ | How do you usually convert between different units of conversion, like 1500 meters to miles? How many miles is 1500 meters?
## 1500 meters is equal to 0.9320565 miles.
Online Unit Numerator: 1500 meters in miles
## What is 1500 meters in miles?
We usually use different units for length in different countries. There are several internationally agreed systems of measurements.
For example, the metric system, Imperial units (also known as British Imperial), and the Chinese system of weights and measures. Each and every system of unit and conversion is common in various countries and regions.
## How long is 1500 meters in miles?
But, 1500 meters is equal to how many miles? To get result, we need to refer to the basic formulas, that 1 meter is 0.000621371 miles, and 1 mile is 1609.3 meters. We can multiply or divide them when we want to convert meters to miles, that is 1 meter multiply by 0.000621371 miles, or 1 mile is divided by 1609.3 meters.
Also check out the video below for details about the conversion, and you can always round up decimals to their nearest whole number, for instance, 0.000621371 miles can be rounded up to 0.000621 miles. Anyway, 1500 meters how many miles?
So,
# Method No. 1:
. 1 meter = 0.000621371 miles
. 1 m = 0.000621371 ml
1500 meters = 1500 x1 m = 1500 x 0.000621371 m = 0.9320565 miles
1500 meters ≈ 0.932 miles
(PS: m = meter (plural: meters), mi or ml = mile (plural: miles))
# Method No. 2:
. 1 mile = 1609.3 meters
. 1 ml = 1609.3 m
1500 meters = 1500 ÷ 1 ml = 1500 ÷ 1609.3 m = 4.971105 miles
1500 meters 0.932 miles
# Method No. 3:
. 1 kilometer = 1000 meters
. 1 km = 1000 m
1500 meters = 1500 ÷ 1 km = 1500 ÷ 1000 m = 1.5 kilometers
. 1 mile = 1.609 kilometers
. 1 mi = 1.609 km
1.5 kilometers = 1.5 ÷ 1 ml = 1.5 ÷ 1.609 = 0.932 miles
1500 meters =1.5 kilometers 0.932 miles
## 1500 Meters is How Many Mile – Video
Got a different answer? Which unit system do you use or prefer?
Leave your comment below, share with a friend and never stop wondering.❤️ | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8417573571205139, "perplexity": 3065.660973303598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711016.32/warc/CC-MAIN-20221205100449-20221205130449-00782.warc.gz"} |
https://www.computer.org/csdl/trans/tp/2008/12/ttp2008122098-abs.html | The Community for Technology Leaders
Issue No. 12 - December (2008 vol. 30)
ISSN: 0162-8828
pp: 2098-2108
ABSTRACT
Image registration consists in estimating geometric and photometric transformations that align two images as best as possible. The direct approach consists in minimizing the discrepancy in the intensity or color of the pixels. The inverse compositional algorithm has been recently proposed by Baker et al. for the direct estimation of groupwise geometric transformations. It is efficient in that it performs several computationally expensive calculations at a pre-computation phase. Photometric transformations act on the value of the pixels. They account for effects such as lighting change. Jointly estimating geometric and photometric transformations is thus important for many tasks such as image mosaicing. We propose an algorithm to jointly estimate groupwise geometric and photometric transformations while preserving the efficient pre-computation based design of the original inverse compositional algorithm. It is called the dual inverse compositional algorithm. It uses different approximations than the simultaneous inverse compositional algorithm and handles groupwise geometric and global photometric transformations. Its name stems from the fact that it uses an inverse compositional update rule for both the geometric and the photometric transformations. We demonstrate the proposed algorithm and compare it to previous ones on simulated and real data. This shows clear improvements in computational efficiency and in terms of convergence.
INDEX TERMS
Computer vision, Intensity, color, photometry, and thresholding
CITATION
Adrien Bartoli, "Groupwise Geometric and Photometric Direct Image Registration", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 2098-2108, December 2008, doi:10.1109/TPAMI.2008.22 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9138222336769104, "perplexity": 1331.5266539467646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542009.32/warc/CC-MAIN-20161202170902-00465-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://discuss.tlapl.us/msg03314.html | # Re: [tlaplus] Re: How to understand the concept "step simulation"
hi Stephan, thanks for the informative example. I am familiar with inductive invariants, my sticking point is that the formula in question does not require Inv to be initially true. Here's how it appears
So as it stands, it seems to me we can establish the 2nd conjunct by setting Inv to False. Or am I still missing something?
thanks
On Thursday, December 5, 2019 at 1:44:46 AM UTC-8, Stephan Merz wrote:
Let me try another attempt for explaining the issue. To make things simpler, let's leave aside the issue of refinement mapping, that is, consider just the identity refinement mapping. We want to prove
(0) InitL /\ [][NextL]_varsL => InitH /\ [][NextH]_varsH
Obviously, this can be reduced to proving
(1) InitL => InitH
(2) NextL \/ varsL' = varsL => NextH \/ varsH' = varsH
However, the obligation (2) is very likely going to be unprovable because really, we only have to prove that implication for all reachable states (i.e., reachable in runs of the low-level spec) rather than for completely arbitrary states, and that's where the invariant comes in.
Let's look at a stupid example: our high-level specification has one variable initialized to zero and that keeps growing while remaining an even number:
Even == {n \in Int : n % 2 = 0}
InitH == x = 0
NextH == x' > x /\ x' \in Even
Our low-level specification has two variables x and y that evolve as follows:
InitL == x = 0 /\ y = 0
NextL == x' = x+y /\ y' = y+2
Condition (2) now requires us to show
(x' = x+y /\ y'=y+2) \/ (x'=x /\ y'=y)
=> (x' > x /\ x' \in Even) \/ x' = x
but this implication is not true and therefore cannot be proved: we have no information about the "types" of x and y, so they could be strings for example. Even if they are integers, we could have x=42 and y=7, x' = 49 and y'=9, and the right-hand side will be false. And indeed, such a state cannot be reached because the low-level spec ensures that x and y are always even. Therefore we define
Inv == x \in Even /\ y \in Even
and relax our proof obligations to be
(1') InitL => InitH /\ Inv
(2') Inv /\ (NextL \/ varsL' = varsL) => Inv' /\ (NextH \/ varsH' = varsH)
which still implies our high-level goal (0). I leave proving (1') and (2') for our example as an exercise to you.
Indeed, Inv can be an arbitrary state predicate and has to be "invented" by the system designer / verifier. But it must be an invariant of the low-level specification, and FALSE is unlikely to be one.
You may also want to read section 6.8 of the Hyperbook.
Hope this helps,
Stephan
On 5 Dec 2019, at 09:58, ss.ne...@xxxxxxxxx wrote:
I have to admit I'm a bit confused by the explanation in the text too and don't quite see what Inv is representing. For example, can I set Inv to anything that allows me to prove the formula, what if I set it to False?
Thanks
On Sunday, March 10, 2019 at 12:52:43 PM UTC-7, Leslie Lamport wrote:
(1) If we remove the Inv from the formula Inv /\ Next => ..., it would assert
that a step starting in any state that satisfies Next satisfies "..." --
for example a state in which memQ is a sequence of imaginary numbers.
I have no idea if that assertion is true for such a starting state.
However, it suffices to prove the assertion for steps starting in a
reachable state. Conjoining the invariant Inv allows you to prove
the assertion only for reachable states. You have to choose Inv so
it asserts what is true about reachable states that makes the
implication true. To do this, you have to understand why the theorem
you're trying to prove is true.
(2) That mapping isn't derived; you have to invent it. The sentence
beginning "Intuitively" that starts on line 9 of page 63 tells you
what condition that substitution must satisfy. To be able to choose
the necessary mapping, y
ou need to understand why the theorem you're
trying to prove is true .
Leslie
On Wednesday, March 6, 2019 at 10:53:35 PM UTC-8, Oliver Yang wrote:
Hi All,
In Section 5.8 of book "Specifying Systems", the "Proving Impl" is introduced. I have a rough understanding of refinement mapping, which
essentially maps states of Spec A to the states of Spec B. However, I have a hard time understanding "step simulation".
1) What's the purpose of introducing the invariant Inv in Formula 5.3? What are we trying to achieve here?
2) How do we derive the mapping: omem = vmem, octl = ..., obuf = buf? It looks like we jumped to the conclusion without showing any proof?
Thanks,
Oliver
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https://mikepawliuk.ca/2017/05/23/euclidean-ramsey-theory-2-ramsey-doccourse-prague-2016/ | # Euclidean Ramsey Theory 2 – Ramsey DocCourse Prague 2016
The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.
Title: Euclidean Ramsey Theory 2 (of 3).
Lecturer: David Conlon.
Date: November 25, 2016.
Main Topics: Ramsey implies spherical, an algebraic condition for spherical, partition regular equations, an analogous result for edge Ramsey.
Definitions: Spherical, partition regular.
Lecture 1 – Lecture 2 – Lecture 3
Ramsey DocCourse Prague 2016 Index of lectures.
## Introduction
In the first lecture we defined the relevant terms and then established that all (non-degenerate) triangles are Ramsey. In this lecture we will compare the property of being spherical with being Ramsey. In this lecture we will show that Ramsey implies spherical (or more precisely, that non spherical sets cannot be Ramsey).
Definition. A set $X$ is spherical if there is an $n$ such that $X \subseteq S^n$.
Typically $S$ will be finite, but this is not formally required.
The proofs are those of Erdos et Al, and go by establishing a tight algebraic condition for a set being spherical.
1. Show that three points in a line are not Ramsey.
2. Define a partition regular equation.
3. Prove two colouring lemmas about partition regular equations.
4. Relate spherical sets to a tight algebraic condition.
5. Put everything together to prove that Ramsey implies spherical.
## (Evenly spaced) lines aren’t Ramsey
Let $L = \{x,y,z\}$ where $d(x,y) = d(y,z) = 1$ and $d(x,z) = 2$; it is a line segment with three points equally spaced.
Theorem. The line segment $L$ is not Ramsey.
“The reason is you can take a spherical shell’ colouring.” These shell colourings are very important.
This doesn’t work for cube colourings’ (i.e. using a different norm) since by Dvoretsky’s Theorem, hyperplane slices of cubes basically look spherical.
Proof. Fix $n$. Define the colouring $\chi : \mathbb{R}^n \rightarrow \{0,1,2,3\}$ by $\chi(x) = \lfloor x \cdot x \rfloor$. (You’re taking spherical shells of radii $\sqrt{n}$.)
[Picture]
By the Cosine rule we get $a^2 = b^2 + 1 - 2b\cos(\theta)$ and $c^2 = b^2 + 1 + 2b\cos(\theta)$. So we get $a^2 + c^2 = 2b^2 +2$.
Suppose that $x,y,z$ have the same colour. This means that there is an $i \in \{0,1,2,3\}$ such that $a^2 = 4k_1 + i + \epsilon_1$ and $b^2 = 4k_2 + i + \epsilon_2$ and $c^2 = 4k_3 + i + \epsilon_3$, where each $0 \leq \epsilon_j < 1$.
Putting this into our cosine law info gives
$\displaystyle 4(k_1 + k_3 - 2k_2) -2 = 2\epsilon_2 - \epsilon_1 - \epsilon_3,$
which is a contradiction since the left is $2 \mod 4$ but the right is strictly between $-2$ and $2$.
## Partition regular equations
Eventually we will relate the condition of a set being spherical with a tight algebraic condition. With this in mind, we examine when algebraic conditions can yield Ramsey witnesses. We start with a general discussion of partition regular equations.
Definition. An equation is partition regular if every finite colouring of $\mathbb{R}^n$ contains a monochromatic solution to the equation.
For example,
1. Schur. $x + y = z$.
2. Van der Waerden. $x + y = 2z$.
3. Rado. A simple equation $\sum_{i=1}^k c_i x_i = 0$ is partition regular if and only if there is a non empty $I$ such that $\sum_{i \in I} c_i = 0$.
Exercise. If the equation is translation invariant then you get a corresponding density result.
Use this to show that you always get a non-trivial solution.
## Are there inhomogeneous equations that are partition regular? Two lemmas.
First an example.
Example. $x + y = z + 1$.
We can homogenize this equation by replacing the variables. Use $x = x^\prime+1, y = y^\prime +1$ and $z = z^\prime+1$. This gives the equation $x^\prime + y^\prime = z^\prime$.
Basically, these are the only types of partition regular equations.
Lemma 1. There is a $2n$ colouring $\chi$ of $\mathbb{R}$ with no solution of
$\displaystyle \sum_{i=1}^n (x_i - x^\prime_i) = 1$
with $\chi(x_i) = \chi(x^\prime_i)$ for all $i$.
The number of colours is equal to the number of variables.
This is a strong result of the equation not being partition regular. You can’t have a monochromatic solution, you can’t even have all the paired variables agree!
The idea is to colour whether you are in a certain interval.
Proof. Fix $n$. Colour $x \in \mathbb{R}$ with $j$ if $x \in [2m + \frac{j}{n}, 2m + \frac{j+1}{n}]$ for some integer $m$.
If $\chi(x_i) = \chi(x^\prime_i)$, then $x_i - x^\prime_i = 2m_i + \epsilon_i$ where $\vert \epsilon_i \vert < \frac{1}{n}$.
So
$\displaystyle 1 = \sum_{i=1}^n (x_i - x^\prime_i) = \sum_{i=1}^n 2m_i + \sum_{i=1}^n \epsilon_i.$
Here the first sum is an even number, and the second is $< 1$, a contradiction.
Now we increase the number of colours to deal with a more general equation.
Lemma 2. There is a $(2n)^n$ colouring $\chi$ of $\mathbb{R}$ with no solution of
$\displaystyle \sum_{i=1}^n c_i (x_i - x^\prime_i) = b \neq 0$
with $\chi(x_i) = \chi(x^\prime_i)$ for all $i$.
Proof. Fix $n$. By dividing by $b$ it suffices to consider $b = 1$.
Let $\chi$ be the ($2n$) colouring from Lemma 1.
Define $\chi^\prime(x) = (\chi(c_1 x), \chi(c_2 x), \ldots, \chi(c_n x))$.
Now if $\chi^\prime(x_i) = \chi^\prime(x^\prime_i)$, then $\chi(c_i x_i) = \chi(c_i x^\prime_i)$.
So $c_i(x_i - x_i^\prime) = 2m_i + \epsilon_i$ where $\vert \epsilon_i \vert < \frac{1}{n}$.
If this happens for all $i$, then we have a contradiction identical to the one in Lemma 1.
In the original paper there was a similar lemma but it had a worse bound on the number of colours. This improvement was observed by Strauss a little later.
Note that these equations are not susceptible to the “translation trick” since $(y_i + 1) - (y_i^\prime + 1) = y_i - y_i^\prime$.
## Characterizing spherical in terms of an algebraic condition
The following is the main technical lemma. The proof is purely algebraic.
Theorem. A set $X = \{\vec{x}_0, \ldots, \vec{x}_t\} \subset \mathbb{R}^n$ is not spherical if and only if there are constants $c_i$, not all $0$, such that
$\displaystyle \sum_{i=1}^t c_i (\vec{x}_i - \vec{x}_0) = 0$
and
$\displaystyle \sum_{i=1}^t c_i (\vec{x}_i^2 - \vec{x}_0^2) = \vec{b}.$
For readability, we will write $x$ instead of $\vec{x}$. We will make use of the following useful fact:
Useful identity.
$\displaystyle a^2 - b^2 = (a - c)^2 - (b - c)^2 + 2a \cdot c - 2 b \cdot c.$
Using $c=b$ yields
$\displaystyle a^2 - b^2 = (a - b)^2 + 2b(a - b).$
Proof of $\Leftarrow$. Assume that $X$ is spherical and satisfies the first equation. We will show the second equality fails.
Say $X$ has centre $w (\in \mathbb{R}^n)$ and radius $r$.
For each $i$ we have:
$r^2$
• $= (x_i - w) \cdot (x_i - w)$
• $= ((x_i -x_0) + (x_0 - w)) \cdot ((x_i -x_0) + (x_0 - w))$
• $= (x_i -x_0)^2 + (x_0 - w)^2 + 2(x_i - x_0)(x_0-w)$. Here the second term is $r^2$.
So we must have $(x_i -x_0)^2 = -2(x_i - x_0)(x_0-w)$ for each $i$. So by multiplying by $c_i$ and adding up we get
$\displaystyle \sum_{i=1}^t c_i (x_i - x_0)^2 = -2(x_0-w)\sum_{i=1}^t c_i (x_i-x_0) = 0.$
By using the special case of the useful identity, we get:
$\displaystyle \sum_{i=1}^t c_i (x_i^2 - x_0^2) = \sum_{i=1}^t(x_i-x_0)^2 - 2x_0 \sum_{i=1}^t c_i (x_0 - x_i).$
We know the first sum is $0$ by our above calculations, and by assumption we know
$\displaystyle 2x_0 \cdot \sum_{i=1}^t c_i (x_i - x_0) = 0,$
Proof of $\Rightarrow$. Assume $X$ is not spherical, and moreover that it is minimal (in the sense that removing any one point makes it spherical). In particular, $X$ is not a non-degenerate simplex. So there is a linear relation
$\displaystyle \sum_{i=1}^t c_i (x_i - x_0).$
Assume that $c_t \neq 0$. By minimality, $\{x_0, \ldots, x_{t-1}\}$ is spherical, and is on a sphere with centre $w$ and radius $r$.
Thus
$\displaystyle x_i^2 - x_0^2 = (x_i - w)^2 - (x_0 - w)^2 + 2x_i \cdot w - 2 x_0 \cdot w.$
So
$\displaystyle \sum c_i (x_i^2 - x_0^2) = \sum c_i ((x_i - w)^2 - (x_0 - w)^2) + 2w \cdot \sum c_i (x_i - x_0),$
here the second sum is $0$, and the first, by minimality, is
$\displaystyle c_t ((x_t - w)^2 - (x_0 - w)^2) \neq 0,$
which isn’t $0$ since the distances of $x_t$ and $x_0$ to $w$ are different.
## Ramsey implies spherical
We are now in a position to put everything together.
Theorem. All Ramsey sets are spherical.
Proof. Assume $X$ is not spherical. So there are constants $c_1, \ldots, c_t$ and a vector $\vec{b} \neq \vec{0}$ such that
$\displaystyle \sum c_i (\vec{x}_i - \vec{x}_0) = 0$
and
$\displaystyle \sum c_i (\vec{x}_i^2 - \vec{x}_0^2) = \vec{b}.$
Technical exercise. Any congruent copy of $X$ satisfies the same equations.
(Use the fact that congruence is formed by rotations and translations. The translations will spit out terms like $\star$.)
In every non-zero coordinate of $\vec{b}$ use the colouring $\chi$ from Lemma 2, and set $\chi^\prime(x) = \chi(x^2)$. This will give no monochromatic solution to
$\displaystyle \sum c_i (\vec{x}_i^2 - \vec{x}_0^2) = \vec{b}.$
This is the end of this lecture’s material on point-Ramsey. We shift gears a little now.
## Edge Ramsey
Instead of colouring points, we can colour pairs of points. This leads to the notion of edge Ramsey. We mention two results in this area.
Theorem. If the edge set $X$ is not vertex spherical and not bipartite, it is not edge Ramsey.
Proof. Suppose the vertex set is not spherical. Colour the points, using $\chi$, so that no copy of $X$ has a monochromatic vertex set.
Now colour the edge $(x,y)$ with $\chi^\prime (x,y) = (\chi(x), \chi(y))$.
Each edge has the same colour and must contain two distinct vertex colours. So the edge set is bi-partite.
This gives us an analogous theorem to the theorem that Ramsey implies spherical.
Theorem. If $X$ is edge Ramsey then the points lie on two concentric spheres.
The proof is a variation on what we’ve seen.
## References
See lecture 1 for references. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 130, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9576830863952637, "perplexity": 423.19012158347357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141164142.1/warc/CC-MAIN-20201123182720-20201123212720-00462.warc.gz"} |
https://www.physicsforums.com/threads/positronium-from-vacuum-fluctuations.750170/ | # Positronium from vacuum fluctuations ?
1. Apr 22, 2014
### xortdsc
Hi,
I wondered if it is theoretically possible that the vacuum energy produces an electron/positron pair which then bonds into positronium instead of directly annihilating again. And if it is theoretically possible has this ever been observed ?
Thanks and cheers.
2. Apr 22, 2014
### The_Duck
No. This would violate energy conservation.
3. Apr 23, 2014
### xortdsc
I see. So how could I visualize this ? The electron/positron pair which can be spontanously produced by vacuum fluctuations (which should be possible, causing the casimir effect) do not separate far enough to escape each other (to produce a "real" electron/positron pair) nor to separate enough to create a positronium system ? Is that right ?
4. Apr 23, 2014
### craigi
It's a really new paper.
http://arxiv.org/pdf/1404.5243v1.pdf
Submitted on 21 Apr 2014
Abstract:
Positron scattering and annihilation on noble gas atoms below the positronium formation threshold is studied ab initio using many-body theory methods. The many-body theory provides a near-complete understanding of the positron-noble-gas-atom system at these energies and yields accurate numerical results. It accounts for positron-atom and electron-positron correlations, e.g., polarization of the atom by the incident positron and the non-perturbative process of virtual positronium formation. These correlations have a large effect on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter Zeff (effective number of electrons participating in annihilation) rise steeply along the sequence of noble gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.
Last edited: Apr 23, 2014
5. Apr 28, 2014
### xortdsc
ah thank you. so if i understand it correctly this article seems to suggest that spontaneous creation of virtual positronium is indeed a possibility.
Similar Discussions: Positronium from vacuum fluctuations ? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8567666411399841, "perplexity": 1778.8783685352562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804666.54/warc/CC-MAIN-20171118055757-20171118075757-00671.warc.gz"} |
https://www.varsitytutors.com/psat_math-help/how-to-multiply-square-roots | # PSAT Math : How to multiply square roots
## Example Questions
### Example Question #11 : Square Roots And Operations
Multiply and simplify. Assuming all integers are positive real numbers.
Explanation:
Multiply the coefficents outside of the radicals.
Then multiply the radicans. Simplify by checking for a perfect square.
### Example Question #1 : How To Multiply Square Roots
Mulitply and simplify. Assume all integers are positive real numbers.
Explanation:
Order of operations, first distributing the to all terms inside the parentheses.
### Example Question #1 : How To Multiply Square Roots
The square root(s) of 36 is/are ________.
6 and -6
None of these answers are correct.
6
-6
6, -6, and 0
6 and -6
Explanation:
To square a number is to multiply that number by itself. Because 6 x 6 = 36 AND -6 x -6 = 36, both 6 and -6 are square roots of 36.
### Example Question #12 : Basic Squaring / Square Roots
Simplify:
Explanation:
Multiplication of square roots is easy! You just have to multiply their contents by each other. Just don't forget to put the result "under" a square root! Therefore:
becomes
Now, you need to simplify this:
You can "pull out" two s. (Note, that it would be even easier to do this problem if you factor immediately instead of finding out that .)
After pulling out the s, you get: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9634414315223694, "perplexity": 1595.4040377215767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590901.10/warc/CC-MAIN-20180719125339-20180719145339-00323.warc.gz"} |
http://mathoverflow.net/questions/122605/do-the-solutions-of-the-maurer-cartan-equation-form-a-simplicial-set/123128 | # Do the solutions of the Maurer--Cartan equation form a simplicial set?
The Maurer--Cartan equation is the equation: $$d\gamma+\frac 12[\gamma,\gamma]=0$$ where $\gamma$ represents a degree one element in a differential graded Lie algebra $\mathfrak g^\ast$. Let's denote the set of solutions by $MC(\mathfrak g^\ast)$. I need to have some notion of (higher) homotopies between elements of the set $MC(\mathfrak g^\ast)$. One way of doing this would be to define a simplicial set $\mathsf{MC}(\mathfrak g^\ast)$ whose zero simplices are the set $MC(\mathfrak g^\ast)$. I have indeed seen the phrase "simplicial set of solutions to the Maurer--Cartan equation" in papers. Is there a standard construction of this simplicial set? If so, how should I think about it, and what are some good references?
In fact, it seems that the $n$-simplices in $\mathsf{MC}(\mathfrak g^\ast)$ should be $MC(\mathfrak g^\ast\otimes\Omega^\ast(\Delta^n))$ where $\Omega^\ast(\Delta^n)$ is the differential graded algebra of differential forms on the standard simplex $\Delta^n$. Can I use something smaller (hopefully finite dimensional) instead of $\Omega^\ast(\Delta^n)$? Perhaps just the simplicial cochain complex $C^\ast(\Delta^n)$?
-
I think there's an Annals paper by Getzler on this topic. – Fernando Muro Feb 22 '13 at 7:10
By the way, one cannot use simplicial cochains (at least in an obvious way) since that algebra is not commutative, but you can work with polynomial differential forms. – Fernando Muro Feb 22 '13 at 10:46
I wrote a paper on that: arxiv.org/abs/math.AT/0603563 – André Henriques Mar 10 '13 at 13:47
I thought I'd expand on Fernando's comments and add a little bit. Your instincts are correct, there is in fact a finite dimensional model of $\Omega^{\ast}( \Delta_{n} )$, which are called the polynomial differential forms: $$k[ \Delta_{n} ] = k [ t_0, \ldots , t_n, dt_0, \ldots, dt_n ] / \left( (\sum t_i) - 1, \sum dt_i \right)$$ where $|t_i| = 0, d(t_i) = dt_i.$ Note that we take the free graded commutative algebra, so $dt_i^{2} = 0$ for degree reasons.
Each $k[\Delta_n]$ is a differential graded commutative algebra, and the assignment $$n \mapsto k[\Delta_n]$$ is a simplicial object in the category of differential graded commutative algebras.
In their book "On PL DeRham Theory and Rational Homotopy Type" (Memoirs of the AMS, Number 179), Bousfield and Gugenheim demonstrate that the simplicial sets $cdgA(R, L \otimes k[\Delta_{\bullet}] )$ give a simplicial enrichment of the model category structure on commutative differential graded algebras which behave like a simplicial model category. In "Homological Algebra of Homotopy Algebras," Hinich shows that over a field of characteristic zero, this is true for the model category structure on $O$-algebras for any operad $O$, ie, $dgOA(R, L \otimes k[\Delta_{\bullet}])$ is a simplicial enrichment of the category $dgOA$ which behaves like a simplicial model category.
Now, I don't know how to answer your question for the set $MC(\mathfrak{g}^{\ast})$. However, when you consider $MC(\mathfrak{g}^{\ast} \otimes R)$ for some finite dimensional, nilpotent commutative dgA $R$, we have the identification: $$MC( \mathfrak{g} \otimes R ) = dgLie ( \Omega(R^{\vee}), \mathfrak{g}^{\ast}).$$ where $R^{\vee}$ is the hom-dual commutative differential graded coalgebra to $R$, and $\Omega$ is the cobar construction which carries commutative differential graded coalgebra to quasifree dg Lie algebras. In particular, the right-hand side is precisely the points in the simplicial set $$dgLie(\Omega(R^{\vee}), \mathfrak{g}^{\ast} \otimes k[\Delta^{\bullet}]),$$ and the simplicial set is a Kan-complex because every dg Lie algebra is fibrant, and $\Omega$ takes values in cofibrant dg-Lie algebras. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9400426745414734, "perplexity": 199.86756848436605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737940789.96/warc/CC-MAIN-20151001221900-00086-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/28332/is-lagranges-theorem-the-most-basic-result-in-finite-group-theory | # Is Lagrange's theorem the most basic result in finite group theory?
Motivated by this question, can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group is an exponent for every element in the group?)
The simplest proof I can think of uses the coset proof of Lagrange's theorem in disguise and goes like this: take $a \in G$ and consider the map $f\colon G \to G$ given by $f(x)=ax$. Consider now the orbits of $f$, that is, the sets $\mathcal{O}(x)=\{ x, f(x), f(f(x)), \dots \}$. Now all orbits have the same number of elements and $|\mathcal{O}(e)| = o(a)$. Hence $o(a)$ divides $|G|$.
This proof has perhaps some pedagogical value in introductory courses because it can be generalized in a natural way to non-cyclic subgroups by introducing cosets, leading to the canonical proof of Lagrange's theorem.
Has anyone seen a different approach to this result that avoids using Lagrange's theorem? Or is Lagrange's theorem really the most basic result in finite group theory?
• How do you define "the most basic result"? Certainly, uniqueness of inverses (et cetera) is a basic result, even though it is a triviality. Anyhow - your question is a good one: I am surprised how often I apply Lagrange's theorem. (even though I hardly think of it under that name. It's just a fact of life) – Fredrik Meyer Mar 25 '11 at 6:19
• @Fredrik: I mean, non-trivial result. – lhf Mar 25 '11 at 11:34
• For abelian groups the proof is pretty simple, just multiply all the elements in the group and in the image of $f$. – N. S. Apr 9 '11 at 20:04
• @lhf: I just saw elsewhere the link you provided to a paper of Pengelley which reproduces Cayley's first paper on group theory with insightful footnotes. In particular (as you know...) Cayley states the theorem in question and says only "it can be shown": neither cosets nor Lagrange's Theorem are anywhere in sight. I think this link would make a nice addition to your question. – Pete L. Clark Aug 6 '11 at 22:39
• @lhf: Also, I like the proof you give above using orbits. – Pete L. Clark Aug 6 '11 at 23:00
Consider the representation of $\langle a \rangle$ on the free vector space on $G$ induced by left multiplication. Its character is $|G|$ at the identity and $0$ everywhere else. Thus it contains $|G|/|\langle a \rangle|$ copies of the trivial representation. Since this must be an integer, $|\langle a \rangle|$ divides $|G|$. Developing character theory without using Lagrange's theorem is left as an exercise to the reader.
• Wasn't there a book that said "... is left as an exercise for the masochistic reader"? – Arturo Magidin May 10 '11 at 20:42
• thanks, though it's hardly in the elementary nature I'm looking for. – lhf May 10 '11 at 21:03
• Hmm -- I'm wondering whether the humourous aspect of this answer was apparent enough -- perhaps the last sentence should have been followed by a smiley :-) – joriki May 11 '11 at 7:23
• I wonder what Linderholm would say (Mathematics made difficult) – Bill Dubuque May 12 '11 at 3:44
• While I am aware this remark comes many years later - Spivak in his Comprehensive Introduction to Differential Geometry vol 1 makes this remark in an appendix to the chapter on tangent bundles where he is proving their uniqueness. The argument proceeds in two main steps, and after carrying out the first, and many pages of diagram chasing, he makes the remark Arturo mentions. – Alfred Yerger Jan 3 '18 at 1:52
I am late... Here is a proposal, probably not far from Ihf's answer.
For $$a \in G$$ of order $$p$$, define the binary relation $$x\cal Ry$$ : $$\exists k\in \mathbb{N} ; k such that $$y=a^kx$$
$$\cal R$$ is an equivalence relation on $$G$$ and sets up a partition of $$G$$.
A class is defined by $$C_x=\left\{a^kx|k=0,1,\ldots,p-1 \right\}$$
All the classes have $$p$$ elements, then $$n=|G|$$ is a multiple of $$p$$ ; $$(n=pm)$$ and $$a^n=a^{pm}=e$$
• This is exactly the coset proof for the cyclic group generated by $a$. – lhf Aug 2 '19 at 10:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 14, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8451353907585144, "perplexity": 449.125803895452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107896778.71/warc/CC-MAIN-20201028044037-20201028074037-00377.warc.gz"} |
https://www.lmfdb.org/L/rational/12/405%5E6/1.1/c3e6-0 | Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
12-405e6-1.1-c3e6-0-0 $4.88$ $1.86\times 10^{8}$ $12$ $3^{24} \cdot 5^{6}$ 1.1 $$[3.0]^{6} 3 1 0 0.0789296 Modular form 405.4.e.u 12-405e6-1.1-c3e6-0-1 4.88 1.86\times 10^{8} 12 3^{24} \cdot 5^{6} 1.1$$ $[3.0]^{6}$ $3$ $1$ $0$ $0.136424$ Modular form 405.4.e.q
12-405e6-1.1-c3e6-0-2 $4.88$ $1.86\times 10^{8}$ $12$ $3^{24} \cdot 5^{6}$ 1.1 $$[3.0]^{6} 3 1 0 0.202865 Modular form 405.4.e.v 12-405e6-1.1-c3e6-0-3 4.88 1.86\times 10^{8} 12 3^{24} \cdot 5^{6} 1.1$$ $[3.0]^{6}$ $3$ $1$ $0$ $0.209179$ Modular form 405.4.e.t
12-405e6-1.1-c3e6-0-4 $4.88$ $1.86\times 10^{8}$ $12$ $3^{24} \cdot 5^{6}$ 1.1 $$[3.0]^{6} 3 1 0 0.210937 Modular form 405.4.e.s 12-405e6-1.1-c3e6-0-5 4.88 1.86\times 10^{8} 12 3^{24} \cdot 5^{6} 1.1$$ $[3.0]^{6}$ $3$ $1$ $0$ $0.216864$ Modular form 405.4.e.r
12-405e6-1.1-c3e6-0-6 $4.88$ $1.86\times 10^{8}$ $12$ $3^{24} \cdot 5^{6}$ 1.1 $$[3.0]^{6} 3 1 0 0.675198 Modular form 405.4.a.l 12-405e6-1.1-c3e6-0-7 4.88 1.86\times 10^{8} 12 3^{24} \cdot 5^{6} 1.1$$ $[3.0]^{6}$ $3$ $1$ $6$ $1.31545$ Modular form 405.4.a.k | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9884182810783386, "perplexity": 307.73828600681327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00513.warc.gz"} |
http://mathhelpforum.com/calculus/16842-help-w-trig-integrals-print.html | # Help w/ Trig Integrals
Show 40 post(s) from this thread on one page
Page 1 of 2 12 Last
• July 14th 2007, 02:03 AM
Help w/ Trig Integrals
$\int(\sin{x})^3(\cos{x})^3dx$
am i going to use trigonometric or int by parts?
help
• July 14th 2007, 04:34 AM
Soroban
I have to ask . . .
Are those really $x^3$ ?
We can integrate: $\sin^3\!x\cos^3\!x$ . . . but not $\sin(x^3)\cos(x^3)$
• July 14th 2007, 04:35 AM
oopss
its $(\sin{x})^3 (\cos{x})^3$
• July 14th 2007, 04:40 AM
topsquark
$\int sin^3(x) cos^3(x) dx$
Let $y = sin(x)$, then $dy = cos(x) dx$
$\int sin^3(x) cos^3(x) dx = \int sin^3(x) cos^2(x) cos(x) dx$
$= \int sin^3(x) (1 - sin^2(x)) cos(x) dx = \int y^3 (1 - y^2) dy$
$= \int (y^3 - y^5)$
I'm sure you can take it from here.
-Dan
• July 14th 2007, 04:47 AM
im sure that either sin(x) or cos(x) is integrable
but the integrator has a different answer
maybe use integration by parts?
• July 14th 2007, 06:37 AM
Jhevon
Quote:
Originally Posted by Soroban
We can integrate: $\sin^3\!x\cos^3\!x$ . . . but not $\sin(x^3)\cos(x^3)$
Can someone tell me once and for all how can you tell if you can't integrate something, or something is not integrable analytically using elementary functions or whatever...wait, did i ask this question before?
I know we can't integrate $e^{x^2}$ and according to Soroban, we can't integrate $\sin \left( x^3 \right) \cos \left( x^3 \right)$, but how do we know that for sure? What's the proof that we can't integrate those functions by hand?
• July 14th 2007, 07:13 AM
Plato
This totally my own opinion: Your confusion is understandable and it comes from the very sad conflating of the words integral and antiderivative. They are not the same. An integral is a number, quite often gotten by way of an antiderivative using the fundamental theorem of integral calculus. An antiderivative is just what is says it is.
Of the antiderivative of $\sin(x^3)$ does exits but we would the series representation for $\sin(x)$ to get it. Therefore, it is proper to say that no elementary representation of the antiderivative of $\sin(x^3)$ exist in the Calculus II sense of the term.
• July 14th 2007, 07:23 AM
topsquark
Quote:
Originally Posted by topsquark
$\int sin^3(x) cos^3(x) dx$
Let $y = sin(x)$, then $dy = cos(x) dx$
$\int sin^3(x) cos^3(x) dx = \int sin^3(x) cos^2(x) cos(x) dx$
$= \int sin^3(x) (1 - sin^2(x)) cos(x) dx = \int y^3 (1 - y^2) dy$
Now,
$= \int (y^3 - y^5)$
I'm sure you can take it from here.
-Dan
To continue
$= \frac{1}{4}y^4 - \frac{1}{6}y^6 + C$
$= \frac{1}{4}sin^4(x) - \frac{1}{6}sin^6(x) + C$
Now, my TI-92 comes up with:
$-\frac{sin^2(x) cos^4(x)}{6} - \frac{cos^4(x)}{12}$
and the Integrator comes up with
$\frac{1}{192} ( cos(6x) - 9 cos(2x))$
All of these solutions are correct, despite how it might look. The point is that we are doing indefinite integration, so any solution that differs from another by only a constant are all correct. If you spend the time (or just plug it through on your calculator) you will find that all three solutions differ from each other by some constant. (Neither the TI-92 nor the Integrator remind you to add the arbitrary constant on the end.)
-Dan
• July 14th 2007, 07:27 AM
thanks topsquark
ohh ok
• July 14th 2007, 07:43 AM
Krizalid
You can use the fact
$\int\sin^mx\cos^nx~dx={\color{blue}\frac{\sin^{m+1 }(x)\cos^{n-1}(x)}{m+n}+\frac{n-1}{m+n}\int\sin^mx\cos^{n-2}(x)~dx},~m\ne-n$
:D:D
• July 14th 2007, 09:12 AM
galactus
Quote:
Originally Posted by Jhevon
Can someone tell me once and for all how can you tell if you can't integrate something, or something is not integrable analytically using elementary functions or whatever...wait, did i ask this question before?
I know we can't integrate $e^{x^2}$ and according to Soroban, we can't integrate $\sin \left( x^3 \right) \cos \left( x^3 \right)$, but how do we know that for sure? What's the proof that we can't integrate those functions by hand?
I believe sin(x^3) is done using what is known as a Lommel integral. Don't know much about it though. Just as sin(x^2) is a Fresnel.
I couldn't find reference to Lommel in wiki. Perhaps, that would be a good MathHelpWiki for someone to take on?.
One should be able to use topics from advanced calc to prove sin(x^3) in not integrable by elementary means. Maybe Dirichlet test or something.
It is continuous and differentiable.
I may have to delve into it some more.
• July 14th 2007, 10:13 AM
DivideBy0
As far as I know,
$
\int {\sin x^3 ~dx} = - \frac{1}
{2}i\left( {\frac{{x\Gamma\left( {\displaystyle\frac{1}
{3},ix^3 } \right)}}
{{3\sqrt[3]{{ix^3 }}}} - \frac{{x\Gamma\left( {\displaystyle\frac{1}
{3}, - ix^3 } \right)}}
{{3\sqrt[3]{{ - ix^3 }}}}} \right) + k$
• July 14th 2007, 02:46 PM
galactus
Yeah. I ran it through Maple and it gave me a horrendous result with LommelSi. It may be equivalent to your result, though. Just a different animal.
• July 14th 2007, 04:03 PM
Krizalid
Quote:
Originally Posted by DivideBy0
As far as I know,
$
\int {\sin x^3 ~dx} = - \frac{1}
{2}i\left( {\frac{{x\Gamma\left( {\displaystyle\frac{1}
{3},ix^3 } \right)}}
{{3\sqrt[3]{{ix^3 }}}} - \frac{{x\Gamma\left( {\displaystyle\frac{1}
{3}, - ix^3 } \right)}}
{{3\sqrt[3]{{ - ix^3 }}}}} \right) + k$
I know the forum where you got that :D:D
• July 14th 2007, 05:42 PM
ThePerfectHacker
I can find,
$\int_0^{\infty} \sin x^3 \cos x^3 dx$ :cool:
And,
$\int_0^{\infty} \sin x^3 dx$
And,
$\int_0^{\infty} \cos x^3 dx$
Eventhough these functions are not elementary.
(I sometimes love Complex Analysis).
Show 40 post(s) from this thread on one page
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https://www.math10.com/forum/viewtopic.php?f=42&t=8289& | # Find all 6-digit multiples of 22 of the form 5d5,22e
### Find all 6-digit multiples of 22 of the form 5d5,22e
Find all 6-digit multiples of 22 of the form 5d5,22e where d and e are digits. What is the maximum value of d?
CORBELLA
Posts: 1
Joined: Tue Apr 16, 2019 11:54 pm
Reputation: 0 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.970186173915863, "perplexity": 1056.301396034046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998581.65/warc/CC-MAIN-20190617223249-20190618005249-00316.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/44236-another-algebra-question.html | # Math Help - Another Algebra Question
1. ## Another Algebra Question
For n ≥ 5 A_n alternating groups which is the
group of permutation . Is it a simple group?
2. Originally Posted by mathemanyak
For n ≥ 5 A_n alternating groups which is the
group of permutation . Is it a simple group?
Yes it is a simple group. This is related | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9758514165878296, "perplexity": 1775.3420259215416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00415-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://se.mathworks.com/help/stats/classificationpartitionedlinearecoc.kfoldmargin.html | Main Content
# kfoldMargin
Classification margins for observations not used in training
## Syntax
``m = kfoldMargin(CVMdl)``
``m = kfoldMargin(CVMdl,Name,Value)``
## Description
example
````m = kfoldMargin(CVMdl)` returns the cross-validated classification margins obtained by `CVMdl`, which is a cross-validated, error-correcting output codes (ECOC) model composed of linear classification models. That is, for every fold, `kfoldMargin` estimates the classification margins for observations that it holds out when it trains using all other observations.`m` contains classification margins for each regularization strength in the linear classification models that comprise `CVMdl`.```
example
````m = kfoldMargin(CVMdl,Name,Value)` uses additional options specified by one or more `Name,Value` pair arguments. For example, specify a decoding scheme or verbosity level.```
## Input Arguments
expand all
Cross-validated, ECOC model composed of linear classification models, specified as a `ClassificationPartitionedLinearECOC` model object. You can create a `ClassificationPartitionedLinearECOC` model using `fitcecoc` and by:
1. Specifying any one of the cross-validation, name-value pair arguments, for example, `CrossVal`
2. Setting the name-value pair argument `Learners` to `'linear'` or a linear classification model template returned by `templateLinear`
To obtain estimates, kfoldMargin applies the same data used to cross-validate the ECOC model (`X` and `Y`).
### Name-Value Arguments
Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.
Binary learner loss function, specified as the comma-separated pair consisting of `'BinaryLoss'` and a built-in, loss-function name or function handle.
• This table contains names and descriptions of the built-in functions, where yj is a class label for a particular binary learner (in the set {-1,1,0}), sj is the score for observation j, and g(yj,sj) is the binary loss formula.
ValueDescriptionScore Domaing(yj,sj)
`'binodeviance'`Binomial deviance(–∞,∞)log[1 + exp(–2yjsj)]/[2log(2)]
`'exponential'`Exponential(–∞,∞)exp(–yjsj)/2
`'hamming'`Hamming[0,1] or (–∞,∞)[1 – sign(yjsj)]/2
`'hinge'`Hinge(–∞,∞)max(0,1 – yjsj)/2
`'linear'`Linear(–∞,∞)(1 – yjsj)/2
`'logit'`Logistic(–∞,∞)log[1 + exp(–yjsj)]/[2log(2)]
`'quadratic'`Quadratic[0,1][1 – yj(2sj – 1)]2/2
The software normalizes the binary losses such that the loss is 0.5 when yj = 0. Also, the software calculates the mean binary loss for each class.
• For a custom binary loss function, e.g., `customFunction`, specify its function handle `'BinaryLoss',@customFunction`.
`customFunction` should have this form
`bLoss = customFunction(M,s)`
where:
• `M` is the K-by-L coding matrix stored in `Mdl.CodingMatrix`.
• `s` is the 1-by-L row vector of classification scores.
• `bLoss` is the classification loss. This scalar aggregates the binary losses for every learner in a particular class. For example, you can use the mean binary loss to aggregate the loss over the learners for each class.
• K is the number of classes.
• L is the number of binary learners.
For an example of passing a custom binary loss function, see Predict Test-Sample Labels of ECOC Model Using Custom Binary Loss Function.
By default, if all binary learners are linear classification models using:
• SVM, then `BinaryLoss` is `'hinge'`
• Logistic regression, then `BinaryLoss` is `'quadratic'`
Example: `'BinaryLoss','binodeviance'`
Data Types: `char` | `string` | `function_handle`
Decoding scheme that aggregates the binary losses, specified as the comma-separated pair consisting of `'Decoding'` and `'lossweighted'` or `'lossbased'`. For more information, see Binary Loss.
Example: `'Decoding','lossbased'`
Estimation options, specified as the comma-separated pair consisting of `'Options'` and a structure array returned by `statset`.
To invoke parallel computing:
• You need a Parallel Computing Toolbox™ license.
• Specify `'Options',statset('UseParallel',true)`.
Verbosity level, specified as the comma-separated pair consisting of `'Verbose'` and `0` or `1`. `Verbose` controls the number of diagnostic messages that the software displays in the Command Window.
If `Verbose` is `0`, then the software does not display diagnostic messages. Otherwise, the software displays diagnostic messages.
Example: `'Verbose',1`
Data Types: `single` | `double`
## Output Arguments
expand all
Cross-validated classification margins, returned as a numeric vector or matrix.
`m` is n-by-L, where n is the number of observations in `X` and L is the number of regularization strengths in `Mdl` (that is, `numel(Mdl.Lambda)`).
`m(i,j)` is the cross-validated classification margin of observation i using the ECOC model, composed of linear classification models, that has regularization strength `Mdl.Lambda(j)`.
## Examples
expand all
Load the NLP data set.
`load nlpdata`
`X` is a sparse matrix of predictor data, and `Y` is a categorical vector of class labels.
For simplicity, use the label 'others' for all observations in `Y` that are not `'simulink'`, `'dsp'`, or `'comm'`.
`Y(~(ismember(Y,{'simulink','dsp','comm'}))) = 'others';`
Cross-validate a multiclass, linear classification model.
```rng(1); % For reproducibility CVMdl = fitcecoc(X,Y,'Learner','linear','CrossVal','on');```
`CVMdl` is a `ClassificationPartitionedLinearECOC` model. By default, the software implements 10-fold cross validation. You can alter the number of folds using the `'KFold'` name-value pair argument.
Estimate the k-fold margins.
```m = kfoldMargin(CVMdl); size(m)```
```ans = 1×2 31572 1 ```
`m` is a 31572-by-1 vector. `m(j)` is the average of the out-of-fold margins for observation `j`.
Plot the k-fold margins using box plots.
```figure; boxplot(m); h = gca; h.YLim = [-5 5]; title('Distribution of Cross-Validated Margins')```
One way to perform feature selection is to compare k-fold margins from multiple models. Based solely on this criterion, the classifier with the larger margins is the better classifier.
Load the NLP data set. Preprocess the data as in Estimate k-Fold Cross-Validation Margins, and orient the predictor data so that observations correspond to columns.
```load nlpdata Y(~(ismember(Y,{'simulink','dsp','comm'}))) = 'others'; X = X';```
Create these two data sets:
• `fullX` contains all predictors.
• `partX` contains 1/2 of the predictors chosen at random.
```rng(1); % For reproducibility p = size(X,1); % Number of predictors halfPredIdx = randsample(p,ceil(0.5*p)); fullX = X; partX = X(halfPredIdx,:);```
Create a linear classification model template that specifies optimizing the objective function using SpaRSA.
`t = templateLinear('Solver','sparsa');`
Cross-validate two ECOC models composed of binary, linear classification models: one that uses the all of the predictors and one that uses half of the predictors. Indicate that observations correspond to columns.
```CVMdl = fitcecoc(fullX,Y,'Learners',t,'CrossVal','on',... 'ObservationsIn','columns'); PCVMdl = fitcecoc(partX,Y,'Learners',t,'CrossVal','on',... 'ObservationsIn','columns');```
`CVMdl` and `PCVMdl` are `ClassificationPartitionedLinearECOC` models.
Estimate the k-fold margins for each classifier. Plot the distribution of the k-fold margins sets using box plots.
```fullMargins = kfoldMargin(CVMdl); partMargins = kfoldMargin(PCVMdl); figure; boxplot([fullMargins partMargins],'Labels',... {'All Predictors','Half of the Predictors'}); h = gca; h.YLim = [-1 1]; title('Distribution of Cross-Validated Margins')```
The distributions of the k-fold margins of the two classifiers are similar.
To determine a good lasso-penalty strength for a linear classification model that uses a logistic regression learner, compare distributions of k-fold margins.
Load the NLP data set. Preprocess the data as in Feature Selection Using k-fold Margins.
```load nlpdata Y(~(ismember(Y,{'simulink','dsp','comm'}))) = 'others'; X = X';```
Create a set of 11 logarithmically-spaced regularization strengths from $1{0}^{-8}$ through $1{0}^{1}$.
`Lambda = logspace(-8,1,11);`
Create a linear classification model template that specifies using logistic regression with a lasso penalty, using each of the regularization strengths, optimizing the objective function using SpaRSA, and reducing the tolerance on the gradient of the objective function to `1e-8`.
```t = templateLinear('Learner','logistic','Solver','sparsa',... 'Regularization','lasso','Lambda',Lambda,'GradientTolerance',1e-8);```
Cross-validate an ECOC model composed of binary, linear classification models using 5-fold cross-validation and that
```rng(10); % For reproducibility CVMdl = fitcecoc(X,Y,'Learners',t,'ObservationsIn','columns','KFold',5)```
```CVMdl = ClassificationPartitionedLinearECOC CrossValidatedModel: 'LinearECOC' ResponseName: 'Y' NumObservations: 31572 KFold: 5 Partition: [1x1 cvpartition] ClassNames: [comm dsp simulink others] ScoreTransform: 'none' Properties, Methods ```
`CVMdl` is a `ClassificationPartitionedLinearECOC` model.
Estimate the k-fold margins for each regularization strength. The scores for logistic regression are in [0,1]. Apply the quadratic binary loss.
```m = kfoldMargin(CVMdl,'BinaryLoss','quadratic'); size(m)```
```ans = 1×2 31572 11 ```
`m` is a 31572-by-11 matrix of cross-validated margins for each observation. The columns correspond to the regularization strengths.
Plot the k-fold margins for each regularization strength.
```figure; boxplot(m) ylabel('Cross-validated margins') xlabel('Lambda indices')```
Several values of `Lambda` yield similarly high margin distribution centers with low spreads. Higher values of `Lambda` lead to predictor variable sparsity, which is a good quality of a classifier.
Choose the regularization strength that occurs just before the margin distribution center starts decreasing and spread starts increasing.
`LambdaFinal = Lambda(5);`
Train an ECOC model composed of linear classification model using the entire data set and specify the regularization strength `LambdaFinal`.
```t = templateLinear('Learner','logistic','Solver','sparsa',... 'Regularization','lasso','Lambda',Lambda(5),'GradientTolerance',1e-8); MdlFinal = fitcecoc(X,Y,'Learners',t,'ObservationsIn','columns');```
To estimate labels for new observations, pass `MdlFinal` and the new data to `predict`.
expand all
## References
[1] Allwein, E., R. Schapire, and Y. Singer. “Reducing multiclass to binary: A unifying approach for margin classifiers.” Journal of Machine Learning Research. Vol. 1, 2000, pp. 113–141.
[2] Escalera, S., O. Pujol, and P. Radeva. “On the decoding process in ternary error-correcting output codes.” IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 32, Issue 7, 2010, pp. 120–134.
[3] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of error-correcting output codes.” Pattern Recogn. Vol. 30, Issue 3, 2009, pp. 285–297.
## Extended Capabilities
Introduced in R2016a
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https://www.physicsforums.com/threads/magnetic-flux-emf.228967/ | # Magnetic Flux/EMF.
1. Apr 14, 2008
### jcpwn2004
1. The problem statement, all variables and given/known data
A patient's breathing is monitored by wrapping a 200 turn flexible metal belt around the patient's chest. When the patient inhales, the area encircled by the coil increases by .0039m^2. The magnitude of the Earth's magnetic field is 50x10^-6 T and it makes an angle of 50 degrees with the direction perpendicular to the coil. If the patient requires 1.5s to inhale, find the average emf induced in the coil.
2. Relevant equations
Magnetic flux=BA. EMF= N x change in(MagFlux)/change in time.
3. The attempt at a solution
I don't understand why i'm not gettting this problem it seems pretty straight forward. I do Magnetic Flux = BA so (50x10^-6)(.0039)(cos40) which equals 1.5x10^-7. Then I use the 2nd equation and emf = 200(1.5x10^-7)/1.5 and I get 2x10^-5 V. The answer is supposed to be 16.7x10^-6 V though.
2. Apr 14, 2008
### mysqlpress
I think it is the problem with "makes an angle of 50 degrees with the direction perpendicular to the coil"
and magnetic flux is defined as BA not B delta A.
The equation should be
e.m.f = -N dBA/dt = -NBdA/dt where dA is the area changed.
3. Apr 15, 2008
### jcpwn2004
i don't see how that makes a difference? don't you get the same thing?
4. Apr 15, 2008
### alphysicist
Hi jcpwn2004
If the magnetic field is constant, the magnetic flux through a loop is
B A cos(theta)
where theta is the angle between the direction of the field and the perpendicular to the loop. So that angle in your calculation needs to be 50 degrees, not 40 degrees.
5. Apr 15, 2008
### mysqlpress
perpendicular to the coil area. I would say
and
you don't actually know the magnetic flux since the area is not given, but a change in area is given.
6. Apr 15, 2008
### alphysicist
Hi mysqlpress,
Would you say there is a difference between perpendicular to the coil area and perpendicular to the loop? I chose those words because that was the wording in the original problem and I don't think there is any ambiguity. But I've been wrong before.
In your first post, remember that the process of breathing will not lead to a uniform rate of change for the flux, and so we do not want to use the instantaneous emf equation with the derivative (we don't know enough to find the derivative), but the average emf equation with the differences.
I know in this problem it's rather straightforward to see that you use the difference form (all they give you is the changes) but in certain problems it could be vital to keep the definitions of each in mind. If a problem was
A single loop of wire has a magnetic flux of $\Phi = \sin(t)$ for the times from $t=0\to \pi$. What is the instantaneous induced emf magnitude in the loop during this time?
then the result would be
$${\cal E}(t)=\cos(t)$$
but if the question had been What is the average induced emf magnitude during this time? the result would be ${\cal E}=0$
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https://www.physics-in-a-nutshell.com/article/47/polar-representation-and-eulers-formula | Physics in a nutshell
$\renewcommand{\D}[2][]{\,\text{d}^{#1} {#2}}$ $\DeclareMathOperator{\Tr}{Tr}$
Polar Representation and Euler's Formula
As was seen before, one can represent any complex number as a vector in a two-dimensional plane - the so-called Argand diagram. Commonly, complex numbers are written in terms of rectangular coordinates with the $x$-coordinate being given by the real part and the $y$-coordinate by the imaginary part of the complex number.
Polar Representation
An equivalent way to represent complex numbers is provided by the polar representation. Here each corresponding vector is characterised by its length $|z|=\sqrt{z \bar{z}} \in [0,\infty)$ and the angle $\varphi \in [0,2\pi)$ between the real axis and this vector.[1]
The domains of the coordinates $|z|\in [0,\infty)$ and $\varphi\in [0,2\pi)$ are limited in order to ensure a unique assignment between the complex numbers and the points in space. For instance, raising the angle by $2\pi$ or $360^\circ$ reproduces the same point in space and hence the same complex number. Equivalently, raising the angle by $\pi$ or $180^\circ$ corresponds to a simple multiplication by -1 of the whole number.
One can easily see that the rectangular coordinates $x$ and $y$ are related to the polar coordinates $|z|$ and $\varphi$ by basic trigonometric relationships:[2] \begin{align} x &= \Re{z} = |z| \cos (\varphi) \\ y &= \Im{z} = |z| \sin (\varphi) \\[1ex] \Rightarrow \quad z &= x+iy = |z| \left[ \cos (\varphi) + i \sin (\varphi) \right] \label{eq:square-brackets} \end{align} Accordingly, the polar coordinates can be expressed in terms of the rectangular ones as well: \begin{align} |z| &= \sqrt{z\bar{z}} = \sqrt{x^2+y^2} \\ \tan (\varphi) &=\frac{\sin (\varphi)}{\cos (\varphi)} = \frac{y}{x} \end{align} Since $\tan$ is periodic, one needs to be careful with its inverse function (which is not unique). A given ratio of $y$ and $x$ can correspond to different values of $\varphi$. Thus, one needs to pay special attention when calculating $\varphi$. The correct way of doing that is provided by the so-called atan2 function.
If one now goes ahead and tries to simplify the expression in square brackets in eq. \eqref{eq:square-brackets}, one obtains a result which is quite remarkable:
Euler's Formula
The expression $\cos (\varphi) + i \sin (\varphi)$ can be simplified by replacing the trigonometric functions $\cos$ and $\sin$ with their power series representations and by using the relation $i^2=-1$:[3] \begin{align} \cos (\varphi) + i \sin (\varphi) &= \sum_{i=0}^{\infty} (-1)^n \frac{\varphi^{2n}}{(2n)!} + i \sum_{i=0}^{\infty} (-1)^n \frac{\varphi^{2n+1}}{(2n+1)!} \nonumber \\ &= \underbrace{ \sum_{i=0}^{\infty} i^{2n} \frac{\varphi^{2n}}{(2n)!}}_\text{even terms} + \underbrace{ \sum_{i=0}^{\infty} i^{2n+1} \frac{\varphi^{2n+1}}{(2n+1)!} }_\text{odd terms} \nonumber \\ &= \sum_{n=0}^{\infty} \frac{(i\varphi)^n}{n!} = e^{i\varphi} \end{align}
The result of this short calculation is referred to as Euler's formula:[4][5] \begin{align} e^{i\varphi} = \cos (\varphi) + i \sin (\varphi) \end{align}
The importance of the Euler formula can hardly be overemphasised for multiple reasons:
• It indicates that the exponential and the trigonometric functions are closely related to each other for complex arguments even though they exhibit a completely different behaviour for real arguments. In particular, one can express the trigonometric functions in terms of complex exponentials by using the definitions of the real and imaginary part of a complex number:[6][7] \begin{align} \cos(\varphi) &= \Re{e^{i\varphi}} = \frac{e^{i\varphi} + e^{-i\varphi}}{2} \\ \sin(\varphi) &= \Im{e^{i\varphi}} = \frac{e^{i\varphi} - e^{-i\varphi}}{2i} \end{align} In general it is much easier to evaluate expressions that are given in terms of exponentials as compared to trigonometric ones - some examples/applications are given here.
• Evaluating the Euler formula for $\varphi=\pi$ yields a result which is considered as one of the most beautiful mathematical expressions that were ever found: \begin{align} e^{i\pi} + 1 = 0 \end{align} This expression unifies the three very fundamental numbers $e$, $\pi$ and $i$ as well as 0 and 1 within a single and even very simple equation.
• Furthermore, products of complex numbers can be rather unpleasant to evaluate if the numbers are given in rectangular representation. However, such products can be handled very easily when being given in polar form as will be demonstrated below.
Multiplication of Complex Numbers
Let $z_1 = |z_1| e^{i\varphi_1}$ and $z_2 = |z_2| e^{i\varphi_2}$ be two complex numbers in polar representation. Their product is given by:[8][9] \begin{align} z_1 z_2 = |z_1||z_2| e^{i(\varphi_1+\varphi_2)} \end{align} Hence, its absolute value $|z_1 z_2 | = |z_1| |z_2|$ is the product of the individual absolute values $|z_1|$ and $|z_2|$ and its angle is equal to the sum of the individual angles $\varphi_1$ and $\varphi_2$.
Have a look at the following example \begin{align} z_1 = \frac{3}{2} e^{i\frac{\pi}{6}}& \quad\text{and}\quad z_2 = 2 e^{i \frac{3\pi}{4}} \\ \Leftrightarrow \quad &z_1 z_2 = 3 e^{i\frac{11\pi}{12}} \end{align} which is a straight forward calculation. The result is visualised in figure 2:
The same calculation could be done in rectangular coordinates just as well, but it would definitely be less fun as you can convince yourself: \begin{align} z_1 = \sqrt{\frac{3}{4}} + i \frac{1}{2} \quad\text{and}\quad z_2 = -\sqrt{\frac{1}{2}} + i \sqrt{\frac{1}{2}} \end{align} Therefore it is reasonable to use the polar representation when dealing with products of complex numbers.
References
[1] Christian B. Lang, Norbert Pucker Mathematische Methoden in der Physik Springer Spektrum 2016 (ch. 2.1) [2] Christian B. Lang, Norbert Pucker Mathematische Methoden in der Physik Springer Spektrum 2016 (ch. 2.1) [3] Wolfgang Nolting Grundkurs Theoretische Physik 1 Springer 2012 (ch. 2.3) [4] Wolfgang Nolting Grundkurs Theoretische Physik 1 Springer 2012 (ch. 2.3) [5] Christian B. Lang, Norbert Pucker Mathematische Methoden in der Physik Springer Spektrum 2016 (ch. 2.3.1) [6] Wolfgang Nolting Grundkurs Theoretische Physik 1 Springer 2012 (ch. 2.3) [7] Christian B. Lang, Norbert Pucker Mathematische Methoden in der Physik Springer Spektrum 2016 (ch. 2.3.1) [8] Wolfgang Nolting Grundkurs Theoretische Physik 1 Springer 2012 (ch. 2.3) [9] Christian B. Lang, Norbert Pucker Mathematische Methoden in der Physik Springer Spektrum 2016 (ch. 2.3.1)
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https://awwalker.com/2017/09/01/the-philosophy-of-square-root-cancellation/ | # The Philosophy of Square-Root Cancellation
Partial sums of the Möbius function appear to grow no faster than a square-root.
A great many problems in analytic number theory concern bounds for finite sums in which some amount of cancellation is to be expected. For example, one might study the partial sums of the Möbius function,
$\displaystyle M(x) = \sum_{n \leq x} \mu(n),$
which satisfies the trivial bound $M(x) = O(x)$. As the Möbius function changes sign infinitely often, we expect some amount of cancellation in $M(x)$, but such progress is hard won. Indeed, the unspecified improvement $M(x)=o(x)$ is already equivalent to the famous Prime Number Theorem (PNT).
Just how much cancellation do we expect in the sum $M(x)$? Replacing the PNT with the Riemann hypothesis, we could show $M(x) = O(x^{1/2+\epsilon})$ for all $\epsilon > 0$. (In fact, these two statements are equivalent.) Conversely, $\Omega_\pm$-results (due to Kotnik and te Riele, e.g.) imply that the exponent 1/2 is essentially optimal. We might say that $M(x)$ is suspected to demonstrate square-root cancellation, since $M(x)$ is (conjecturally) no larger than the square-root of the length of its defining sum.
A second example concerns bounds for the Kloosterman sums
$\displaystyle S(m,n;x) = \sum_{u (x)^\times} e\!\left(\frac{m u + n u^{-1}}{x} \right),$
in which $e(z) = e^{2\pi i z}$. Here, the trivial bound $\vert S(m,n;x) \vert \leq \varphi(x) \leq x$ was famously improved upon by Weil’s oh-so-non-trivial estimate
$\displaystyle \vert S(m,n;x) \vert \leq d(x) \sqrt{\gcd(m,n,x)}\sqrt{x},$
which is $O(x^{1/2+\epsilon})$ for fixed $m$ and $n$. In other words, Kloosterman sums demonstrate square-root cancellation.
In this note, I’ll discuss why square-root cancellation is so typical in problems in number theory, and give a quick survey of important sums known or widely conjectured to satisfy bounds of this form.
— RANDOM WALKS —
It is widely speculated that the values of the Möbius function behave like a random variable $\{\pm 1\}$ on the square-free integers. Given this, what might we expect out of $M(x)$?
Let $\widetilde{\mu}: [1,x] \to \{\pm 1\}$ be a “random” function (ie. chosen uniformly at random from the $2^x$ functions of this form). These are called random walks, and in this particular case, often lumped together as the simple random walk on $\mathbb{Z}$. The number of random walks that would give $\widetilde{M}(x) = k$ is
$\displaystyle \binom{x}{(x-k)/2},$
provided of course that $x$ and $k$ have the same parity. From here, various estimates can give bounds on the probability that $\widetilde{M}(x)$ exceeds $O(x^\alpha)$. To spare you a slog, we might cite Hoeffding’s inequality, which here provides
$\displaystyle \mathbb{P}\big(\vert \widetilde{M}(x) \vert \geq t \big) \leq 2 \exp\left( - \frac{x t^2}{2} \right).$
Note that this probability becomes vanishingly small as $t$ exceeds $O(\sqrt{x})$, so we conclude that “most” random walks exhibit a form of square-root cancellation. Considering the partial sums of arithmetic functions as walks leads to the following moral principle, which I’ll call The Philosophy of Square-Root Cancellation:
The Philosophy of Square-Root Cancellation:
We should expect square root cancellation in the partial sum of any arithmetic function that behaves “randomly”.
Returning to the Möbius function, we note that the Riemann hypothesis follows from the conjecture that $\mu$ behaves like a random variable. (This is the probabilistic evidence towards the Riemann hypothesis.)
— A SURVEY OF SQUARE-ROOT CANCELLATION IN NUMBER THEORY —
We have already seen two cases (Kloosterman sums and $M(x)$) in which square-root cancellation is proven or widely conjectured. In this section, I’d like to fill out the picture with a great many more examples.
I: The Pólya–Vinogradov Inequality. In 1918 Pólya and Vinagrodov (independently) showed that
$\displaystyle \bigg\vert \sum_{n \in [A,B]} \chi(n) \bigg\vert = O\big(\sqrt{q} \log q\big),$
in which $\chi$ is any non-prinicipal Dirichlet character of modulus $q$ and $A are integers. Since the sum of $\chi$ over all of the residues mod $q$ is $0$ (by orthogonality), we may assume that the sum above is no longer than $q$ in length, so Pólya–Vinagradov represents square-root cancellation.
Under the assumption of GRH, Montgomery and Vaughn (1977) have given the slight improvement $O(\sqrt{q}\log\log q)$. On the other hand, it is known (Paley, 1932) that these character sums are infinitely often $\gg \sqrt{q}\log \log q$, so square-root cancellation is the best one can expect.
II: Classical Gauss Sums. The Gauss sum of a Dirichlet character $\chi$ of modulus $q$ is the finite sum
$\displaystyle G(\chi) = \sum_{u=1}^q \chi(u) e^{2\pi i u/q}.$
These sums were first considered by Gauss under the assumption that $\chi$ was the Legendre symbol. Here, Gauss proved that $G(\chi)= i \sqrt{q}$ or $\sqrt{q}$ depending on the residue of $q$ mod $4$, and the generalization $\vert G(\chi) \vert = \sqrt{q}$ holds for any primitive character.
This cancellation is most easily seen as a consequence of the Plancherel formula with respect to Fourier inversion on $\mathbb{Z}/q\mathbb{Z}$.
III: Counting Points on Elliptic Curves. Fix $a,b \in \mathbb{Z}$ and consider the elliptic curve
$\displaystyle E: \quad y^2 =x^3 +ax +b$
over the finite field $\mathbb{F}_p$, with $p$ prime. The number of points $(x,y)$ on the reduction of $E$, which we write as $N_p$, can be written in terms of the Legendre symbol:
$\displaystyle N_p = p+ \sum_{x=0}^{p-1} \binom{x^3+ax+b}{p}.$
Square-root cancellation suggests that $\vert N_p - p \vert = O(\sqrt{p})$ may hold. This (proven) result is known as Hasse’s theorem, and essentially follows from a bound on the magnitude of the roots of the local zeta function of $E$. (That is, Hasse’s theorem represents the analogue of the Riemann hypothesis for the local zeta function of $E$.)
IV: The Gauss Circle Problem. The Gauss circle problem concerns estimates for the number $S_2(R)$ of integer lattice points bounded by the circle of radius $\sqrt{R}$. One expects (and Gauss showed) that $S_2(R) \sim \pi R$. More precisely, Gauss proved that
$S_2(R) = \pi R + P_2(R),$
in which $P_2(R)$ is an error term satisfying $P_2(R) = O(\sqrt{R})$. To see this another way, let $r_2(n)$ denote the number of representations of $n$ as a sum of two squares. Then, since
$\displaystyle P_2(R) = \sum_{m \leq R} \left(r_2(m)-\pi\right),$
we recognize Gauss’ bound as a form of square-root cancellation after accounting for a main term. Surprisingly, greater-than-squareroot cancellation is conjectured to occur within $P_2(R)$, and we expect $P_2(R) = O(R^{1/4+\epsilon})$.
This deviation from “random'” behavior can be explained in practice by shortening the sum of length $R$ via Poisson summation. It may also be possible to recognize the additional cancellation as a consequence of the Hecke relations. (Indeed, a general greater-than-squareroot cancellation is known for sums of coefficients of other modular forms.)
— EXERCISES —
Exercise 1. Let $\widetilde{\mu}: [1,x] \to \{\pm 1\}$ be a random function as before, with random walk $\widetilde{M}(x)$. Use Stirling’s approximation to prove that
$\displaystyle \mathbb{P}(\vert \widetilde{M}(x) \vert \leq x^\alpha) = \sqrt{\frac{2}{\pi}} \cdot x^{\alpha-\frac{1}{2}}+O\big(x^{3\alpha-\frac{3}{2}}\big).$
Conclude that “most” random functions $\widetilde{\mu}$ are $\Omega(x^{1/2-\epsilon})$ for all $\epsilon > 0$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 82, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.987760603427887, "perplexity": 756.5129154786126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506959.34/warc/CC-MAIN-20200402111815-20200402141815-00504.warc.gz"} |
https://mathoverflow.net/questions/321071/is-there-a-theorem-showing-that-de-rham-homology-is-isomorphic-to-singular-homol | # Is there a theorem showing that de Rham homology is isomorphic to singular homology?
The only exposition of de Rham homology I've found is an appendix to Uranga and Ibanezs book on String Phenomenology. It was brief and gave only basic outline of how to construct this homology.
Now de Rhams theorem asserts that there is an isomorphism between de Rham cohomology of smooth manifolds and that of singular cohomology; and so what appears to be an invariant of smooth structure, is actually an invariant of topological structure.
Is there a similar theorem showing an isomorphism between de Rham homology and singular homology?
• What is deRham homology? – Praphulla Koushik Jan 17 '19 at 4:02
• I think one uses currents instead of differential forms... – Francesco Polizzi Jan 17 '19 at 8:58
• See Chapter IV of De Rham's book Differentiable manifolds. The result you want follows from Thm.16 in Sec. 21. – Liviu Nicolaescu Jan 17 '19 at 9:28
• I think the book of Breadon, Geometry and topology contains a proof (for cohomology) – Ali Taghavi Jan 17 '19 at 10:42
• @FrancescoPolizzi: There is a description using currents; but the book I've alluded to above uses submanifolds. I appreciate currents are more general, and subsume submanifolds by way of Stokes theorem; however, I find the description of homology via submanifolds more intuitive than the simplicial approach in Hatcher. To my mind it makes a better beginning. Though of course one needs to know what a manifold is - but intuitively we know what this is. – Mozibur Ullah Jan 17 '19 at 17:20
I guess that by de Rham homology you mean the homology groups $$H_{k, \, \mathrm{dR}}(X)$$ constructed on a closed manifold $$X$$ by using the complex of currents.
In that case, [1, Theorem 2 page 582] shows that there is an isomorphism between $$H^{n-k}_{\mathrm{dR}}(X)$$ and $$H_{k, \, \mathrm{dR}}(X)$$, where the cohomology is the usual one (constructed by using the complex of differential forms) and $$n = \dim X$$.
Now, using the standard De Rham isomorphism between $$H^{n-k}_{\mathrm{dR}}(X)$$ and the singular cohomology group $$H^{n-k}_{\mathrm{sing}}(X, \, \mathbb{R})$$, together with the Poincaré duality $$H^{n-k}_{\mathrm{sing}}(X, \, \mathbb{R}) \simeq H_{k, \,\mathrm{sing}}(X, \, \mathbb{R})$$, we deduce the desired isomorphism $$H_{k, \, \mathrm{dR}}(X) \simeq H_{k, \,\mathrm{sing}}(X, \, \mathbb{R}).$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9056735634803772, "perplexity": 343.38287437414937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107905965.68/warc/CC-MAIN-20201029214439-20201030004439-00358.warc.gz"} |
https://math.stackexchange.com/questions/778287/number-of-lattice-points-in-an-n-ball | # number of lattice points in an n-ball
I have faced a problem in my work and I will appreciate any hint/reference as I am not much into the lattice problems.
Assume an n-dimensional lattice $\Lambda_n$ with generator matrix $G$. Note that lattice points are not necessarily integer, i.e., $x\in \mathbb{R}$ where $x$ is a lattice point. Is there a way to count/estimate/bound the number of lattice points inside and on an n-ball?
any hint or reference to appropriate literature is appreciated
• You mean to say that the lattice points are the images of some integer lattice under a linear transformation, and therefore $x\in\mathbb R^n$? So you might as well ask for integer lattice points in some $n$-dimensional paraboloid. Not that I think that formulation is any easier, mind, just thinking out loud. What kind of performance are you looking for? Would a scan conversion which gives an exact answer $m$ (i.e. there are $m$ points inside the ball) in time $O\left(m^{(n-1)/n}\right)$ be preferable to one which uses the bounding box for a very loose bound in $O(1)$? – MvG May 2 '14 at 13:05
• I was googling about the lattice points in an n-ball and found some papers about integer lattices (Gauss' circle problem) but in my problem the lattice is not integer. With $x\in \mathbb{R}$ I mean that the entries of the lattice point (vector $x$) are real numbers. I am not sure if the exact number of the lattice points inside an n-ball is solved but even a bound can be enough to proceed with my problem. – M.X May 2 '14 at 13:38
• What do you mean by “solved”? Sure you can compute that number, a brute force enumeration will yield the count eventually. On the other hand, a closed formula might be unrealistic. – MvG May 2 '14 at 14:08
The $n$-volume of the fundamental parallelotope is the absolute value of the determinant of $G.$
The $n$-volume of the ball of radius $1$ is, in shorthand, $\pi^{n/2}/ (n/2)!,$ or $$\omega_n = \frac{\pi^{n/2}}{\Gamma \left( 1 + \frac{ n}{2} \right)}.$$ The volume of the ball of radius $R$ is $\omega_n R^n.$
So, there is your estimate of the count, $\omega_n R^n / |G|.$
• @jvnv looked at your posts, not sure what part of this could be a problem for you. The volume of the ball should be in any mathematical statistics book; the easiest method is induction by 2, even/odd dimension, using polar coordinates for the integral. Note that I am assuming $G$ expresses a basis of the lattice as its rows, so the Gram matrix is actually $G G^T.$ For anything in that area, try SPLAG by Conway and Sloane. Sphere Packing Lattices and Groups – Will Jagy Sep 25 '17 at 17:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8235827684402466, "perplexity": 215.7180539440173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319470.94/warc/CC-MAIN-20190824020840-20190824042840-00506.warc.gz"} |
https://pos.sissa.it/374/054/ | Volume 374 - Light Cone 2019 - QCD on the light cone: from hadrons to heavy ions (LC2019) - Contributed
Boson Stars and QCD Boson Stars
U. Kulshreshtha,* S. Kumar", D.S. Kulshreshtha", J. Kunz"
*corresponding author
Full text: pdf
Pre-published on: May 06, 2020
Published on: May 26, 2020
Abstract
In this talk, we present a review of our work on boson stars in a theory of a massless complex scalar field in the presence of a $U(1)$ gauge field and gravity. A sequence of bifurcation points obtained in the phase diagrams of the theory is presented and the plots of the mass $~M~$ versus charge $~Q~$ as well as plots of the mass per unit charge $~M/Q~$ versus the charge $~Q~$ of the boson stars are presented along with a discussion of the results. We also present some ideas on the possibilities of QCD boson stars.
DOI: https://doi.org/10.22323/1.374.0054
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8848193287849426, "perplexity": 1360.3474519449649}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00278.warc.gz"} |
http://www.sciforums.com/threads/do-heavier-objects-fall-faster.39234/page-2 | Do heavier objects fall faster?
Discussion in 'Physics & Math' started by mountainhare, Aug 2, 2004.
1. Brandon9000Registered Senior Member
Messages:
172
Aside from air resistance, all objects near the surface of the earth fall at an acceleration of:
GM/r^2
Where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the falling object and the center of the Earth.
This is approximately 9.8 meters per second squared, and it is the same for all objects, regardless of their mass.
3. J_WilsonRegistered Member
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4
That is not right Brandon. There is an equation that looks something like that to give you force. f=ma so the acceleration is f/m. We've already established this.
5. Brandon9000Registered Senior Member
Messages:
172
A = F/m where F, m, and A refer to the falling object.
F = (GMm)/r^2 where M = mass of Earth and m = mass of the falling object.
Plugging the 2nd equation into the first, which is equivalent to dividing the 2nd by m, gives, A = GM/r^2, as in my original post, regardless of the mass of the falling object. This particular acceleration is called "the acceleration due to gravity." Note that the only mass which appears in this equation is the mass of the Earth.
Incidentally, you can find this material in virtually every high school Physics book in the world.
7. Blue_UKDrifting MindValued Senior Member
Messages:
1,446
Brandon, check one of my above posts (lots of colour) - we all agree that objects accel towards earth at the same rate, it's the earth's accel towards the object that changes!
8. Brandon9000Registered Senior Member
Messages:
172
This is so, but the acceleration of the Earth toward the object is infinitessimal. Someone may find this interesting theoretically, but the Earth's acceleration is so tiny as to be of no practical significance. The force exerted on the Earth by the object is identical to the force exerted on the object by the Earth, but the Earth has incomparably greater mass.
9. Blue_UKDrifting MindValued Senior Member
Messages:
1,446
I agree.
Needless to say I am more interested in the actual physics than the practical observation.
10. newbie56kRegistered Member
Messages:
25
What r u guys doing, the ratio of force to mass is the same for large and small objects.
Force = mass x acceleration (force is equal to acceleration, w=ma [same thing])
98N Force
--------- = 9.8m/s/s
10kg Mass
4900N Force
----------- =9.8m/s/s
500Kg Mass
See the acceleration is the same, for large and small. I got most of this from my midterm exam notes for physics and i got a 103% in it.
People think that heavier objects fall faster because it hurts much more when it lands on their foot.
11. curioucityUnbelievable and oddRegistered Senior Member
Messages:
2,429
The problem of roughly mixing force and pressure, and density too, maybe...
12. MacMRegistered Senior Member
Messages:
10,104
You need to be careful in what you stipulate. Falling faster meaning F=ma of a free falling object, it is correct to say they all fall at the same rate.
However, even getting that 103% on your mid-term fails to acknowledge that the earth indeed also moves toward the object and does so to a greater extent for a more massive object such that the closure rate and contact with the earth from an initial height (in theory) actually contacts earth sooner because the earth moved more toward the heavier object.
I refer you to "Blue UK's" post on 8/3/04 at 6:58 AM above. He shows you mathematically why this is the reality (even though it is immeasureable).
13. vslayerRegistered Senior Member
Messages:
4,969
the objects are both being pulled by the same amount of force(gravity) so the only factor to slow them down is wind resistance, if you dropped a ten ton weight and a parachute in a vacuum they would land at the same time.
tho only extro factor is the force on imparct, in which case you would multiply the mass by the amount of gravity.
in coclusion:
during a freefall with no resistance, the force of all objects are equal, it is only when they land that their mass or surface area becomes a factor
14. MacMRegistered Senior Member
Messages:
10,104
I normally tend to agree with you on things but here you have made some errors.
1 - Free falling objects do NOT all have the same force. i.e. - a 1 gram ball falls under a 1 gram force. A 10 kg ball falls under a 10 kg force. That is the meaning of the equivelence principle between inertia and gravity. Since objects acclerate by amounts of force which are always equal to the mass the rate of acceleration is the same but not the accelerating force.
2 - However it can be seen that objects only contact the earth at the same time in such tests if the test is conducted simultaneously. And in that case both objects contact the earth sooner than if either had been tested independantly.
3 - Since the force on the object is 1 gram or 10 kg causing their acceleration, the complimentary force on earth must be equal. It is obvious that if you apply a series of forces to earth with a 10,000/1 ratio of magnitude you are going to get an acceleration of the earth toward the objects which have a 10,000/1 magnitude. That is to say the earth moves 10,000 times as far toward the free-falling object which has the 10 kg mass.
Since the earths motion in response to free-falling objects is different in each case the closure rate and contact of the free falling object with earth MUST change and the time is not the same.
15. vslayerRegistered Senior Member
Messages:
4,969
but lets say the earths gravity has a power of 10
the earth can only pull things at a speed of 10 because that is all its power allows
no matter how much an object weighs it can only ever go as fast as 10
the only thing to make a light object fall slower is the fact that it cannot displace as much air as a heavier object
in a vacuum both objects would be pulled at a speed of 10, and since they do not need to displace any other particles there is nothing to give the heavier one an advantage
16. MacMRegistered Senior Member
Messages:
10,104
What you are missing is this: (Air resistance ignored).
If filmed against a scaled backdrop (i.e. - a tape measure and a clock) where the tape hangs from a point in space above earth (not attached to earth) and a light and heavy object are dropped individually, you could then see that each crossed markings of the tape at identical times.
But what you miss is that while these objects are in free-fall the earth is either moving (F=ma) toward theses objects with a force that is either heavy or light. Clearly the earth during such free-fall time will move more under the influence of the force from the heavy object. Hence the heavy object ultimately travels less distance before contacting the earth because the earth move closure to it that it did when the lighter oject was free-falling.
Because the havy object must travel less distance (at the same speeds and acceleration) as the lighter object it requires less time for free-fall to contact with earth.
Now if we make the scale a solid ruler mounted to earth one would see the collective closure rate between earth and the free-falling objects and low and behold we would see that heavy objects were falling faster in such a test.
17. Paul TRegistered Senior Member
Messages:
460
MacM, I would say those are BS. Say those two objects were let to fall at the same time. Let ignore other falling objects, consider just those two objects and also, of course, assume that earth movement toward those objects is signaficant at all. Shouldn't the earth accelerate toward the falling object at one certain rate (not difference rate for each falling object)? Force resultant to earth is due to both of the falling object. You can't expect earth to move at one accelleration rate to object A and another to object B, while A and B move side by side at the same acceleration.
18. PeteIt's not rocket surgeryRegistered Senior Member
Messages:
10,166
Hi Paul,
A larger mass requires greater force than a smaller mass to accelerate at the same rate.
If A and B are of different masses, but experience the same acceleration, then they must be subject to different forces.
This means that the Earth also experiences greater force when the larger mass object is falling.
A few notes:
Objects falling side-by-side is a different problem. Since they are falling together, the Earth is moving toward both. You also need to consider the attraction between the objects...
The problem changes again depending on exactly how far away from each other are the two objects falling at the same time...
The problem changes again if you consider the direction of separation between the objects, as any North-South separation will involve Coriolis forces, and attraction between the objects will have curious effects on East-West separation...
When considering the objects' effect on the Earth, you should also consider tidal effects. The near part of the Earth is attracted much more strongly than the far part, so the Earth will be stretched. This means that the Earth's material properties (bulk modulus etc) will need to be considered...
Further complicated by differences in material properties throughout the Earth...
Of course, all these problems are insignificant beside local variations in gravity. For reasonably sized objects, such things as random air mass movements (ie weather) will have more effect on the fall rate than any of the above mentioned issues.
19. Paul TRegistered Senior Member
Messages:
460
Hi Pete
This is certainly okay to me.
This was exactly the case mentioned by MacM. Therefore, earth should accelerate to both object at one rate only.
Even if the film was taken one at a time for object A and B, which has different mass, there is one thing remain the same...the system center of mass. If we don't consider the variation of gravitational acceleration due to the change of distance, the acceleration of object A and B relative to the system center of mass is not affected by the rate of earth acceleration toward the object (or the system center of mass). Therefore, I didn't see MacM's idea indicating that somehow heavier object fall faster. He just picked the wrong reference point.
I think we can put a side all those issues for the time being.
20. MacMRegistered Senior Member
Messages:
10,104
1 - First you must understand that the affect only occurs if the objects are dropped independantly at different times.
2 - The mass of Earth is 5.9742E24Kg
3 - If dropped independantly a 1 gram mass places a 1 gram force on earth during free-fall. F = ma, a = F/m:
a = 0.001kg/5.9742kg = 1.6738E-28
4 - If you now drop a 10kg mass during free fall it generates a force on Earth of 10kg:
a = 10kg/5.9742E24kg = 1.6738E-24
The acceleration by the earth (however miniscule) during a free-fall period of a mass is 10,000 times greater for a mass 10,000 times as large. The acceleration of the free-falling masses is always the same because the accelerating force equals the inertial mass.
5 - Dropped simultaneously the collective mass in free-fall is 10.001kg and induces a force of 10.001kg on the Earth :
a = F/m = 10.001kg/5.9742E24kg = 1.6740E-24
In this case both objects contact the earth at the same time but the total time is less than if either are dropped independantly.
The point that people seem to be missing is that this is "Closure Rate" from point of free-fall to contact. The velocity of free-falling objects relative to the point of initial release is always the same but the velocity relative to earth varies because earth also moves (at differnt rates) towards the free-falling objects. The magnitude of motion during free-fall is inversly proportional to the masses involved. That is the total distance moved is divided between the Earth and the object in proportion to their masses.
If a 10kg object is placed 16 feet (using rounded generic numbers here) above earth, due to the formula used we expect it to travel 16 feet in one second and make contact but the reality is that it only free-falls for 1 second minus the 1.6738E-24 acceleration time reduced because Earth moved in response to the 10kg force.
For the 1 gm object it free-falls for 1 second minus 1.6738E-28 acceleration time. You can see that the reality is that the closure rate is less for heavier objects, even though it is true that the acceleration of the object and its terminal velocity relative to its free-fall origin are the same for either mass. The impact velocity with Earth however is greater and the time period of the free-fall is less because Earth acclerates, hence moves greater distance towqrd heavier objects and attains a greater velocity during the free-fall.
21. MacMRegistered Senior Member
Messages:
10,104
You have clearly mis-read my post. I stated objects falling simultaneously will contact Earth at the same time but that that time will be less than if they were dropped indenpendantly at different times.
Not at all. You are picking a different reference point than is used in the F = G * m1 * m2 / r^2 and F = ma formulas. See my previous response to your post to me above. The "Closure Rate" (time of free-fall) is less for heavier objects.
22. Paul TRegistered Senior Member
Messages:
460
Okay. Let's go with that situation.
This is a meaningless argument with respect to "Do heavier object fall faster?" Your argument doesn't prove anything. It's like:
At one time, you walk slowly toward a car accelerating toward you at rate 9.81m/s<sup>2</sup>, then at other time you run toward that car and you argued that when you run, the car closure rate is higher -- equivalent to having higher acceleration. This argument has not much value as it prove nothing about whether the car acceleration increase because you are running (the car acceleration, of course, not affected by your running!). You just picked an incorrect reference point to assess the problem.
Your argument, as I said tell us nothing about whether heavier object fall faster or not...hence, it's a pointless argument.
23. MacMRegistered Senior Member
Messages:
10,104
Not at all. I clearly pointed out the arguement; including the fact that from the reference point of the start of free fall the acceleration and velocity of all objects are the same.
I also pointed out the FACT that the time to impact with the earth IS NOT THE SAME. Should you actually set up a test capable of measuring this insignifigant difference you will find that due to the variable closure rate your test will yield results which show that the heavier objects impact the earth sooner.
I didn't pick an incorrect reference point I am simply showing that it is only one view and that a timed free-fall over an equal distance is less for the heavier object.
Your test being referenced from earth will result in a velocity calculation which is higher. The momentum of impact if you measure it at the earth's surface will be greater.
Remember, all velocity is relative. If earth is the rest reference for the test (which it generally and normally is), then you stand corrected.
Last edited: Aug 15, 2004 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8029397130012512, "perplexity": 800.2018919486575}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578517558.8/warc/CC-MAIN-20190418101243-20190418123243-00478.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=288696 | ## Adding salt to ice question
When salt is added to a ice water solution it makes the ice melt at a colder temperture than zero degrees C. I'm told because it weakens the bonds that hold the ice together. Is the latent heat asorbed by the melting ice at the new lower temperture the same as if the salt was not added and melted at 0 degrees C? Is there the same amount of joules absorbed from the surroundings of the solution to melt the ice if the surroundings are above 0 degrees C?
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Recognitions: Science Advisor The main effect here is on the entropy of the liquid phase. Most phase transitions are due to what are known as order-disorder transitions. In such cases, there is a competition between the two phases. In the solid phase, the molecules are well ordered such that the interactions between molecules are optimized. This gives the system a low potential energy (enthalpy) at the cost of having low entropy (low disorder). In the liquid phase, the molecules have more disorder (higher entropy) at the cost of losing some of the optimal interactions (higher enthalpy). Remember from thermodynamics that molecular systems would like to minimize their potential energy (like a ball wants to roll down a hill) and increase their entropy (like how it's easy for your room to go from an ordered state to a messy, disordered state but not the other way around). Thus, we have a problem with the solid-liquid transition. Going from solid to liquid raises the entropy (good) but also raises the enthalpy (bad). Conversely, going from liquid to solid lowers the enthalpy (good) at the cost of lowering entropy (bad). So, whether something is solid or liquid depends on whether lowering enthalpy or raising entropy is more important. For reasons that are too complicated to explain succinctly now, temperature determines the relative importance of entropy and enthalpy. At high temperatures, systems would like to raise their entropy more than they would like to lower their enthalpy, and the opposite is true of lower temperatures. So, how does salt play into this? Salt is largely excluded from the crystal lattice of ice so it does not significantly affect the enthalpy or entropy of the ice. However, salt dissolves in water, so it affects both the entropy and enthalpy of the liquid phase. The dominant contribution of the salt is to raise the entropy of the liquid phase. Since the entropy of the liquid phase is larger in the presence of salt, water pays a larger entropic penalty when going from liquid to solid. Therefore at zero degrees Celsius, where the contributions from enthalpy and entropy were previously equal, the balance gets tipped toward the liquid form. This explains why salt can melt ice on roads. To regain the balance between the changes in entropy and enthalpy, one must go to lower temperatures since lower temperatures put less emphasis on the entropic penalty.
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## Adding salt to ice question
Quote by philrainey Is the latent heat asorbed by the melting ice at the new lower temperture the same as if the salt was not added and melted at 0 degrees C? Is there the same amount of joules absorbed from the surroundings of the solution to melt the ice if the surroundings are above 0 degrees C?
I believe the amount of energy going into the melting ice from the surroundings would be slightly larger due to the addition of salt, as the dissolution of NaCl in water is slightly endothermic. However, this effect isn't connected to the freezing point depression, which occurs as Ygggdrasil described it. Salts that dissolve exothermally also lead to freezing point depression; it's a colligative effect.
why I asked this is because I was thinking if one can get the cooling at a lower temperture(-21) from ice frozen at 0 and put in a salt surray, one perhaps could get colder cooling for less energy (refrigeration energy)input as it takes less energy to cool from zero than minus 21. Perhaps adding a contaminate to another fluild (say CO2 ice in a liquid CO2 surray with contaminate).
if one trys to separate the water from salt solution by sucking (evapourating off) the water vapour with a compressor does it take more energy to do so than just evapourating pure water? the entropy of the solution is higher than if it were pure water so would there be a lower entropy difference between the salt solution to water vapour than to pure water to water vapour?( I'm thinking the vapour has a higher entropy than a liquid) Would this mean a higher boiling temperture to offset the smaller entropy gain?Or less heat asorbed in the latent heat of the water turning to vapour?
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Homework Help | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8184788823127747, "perplexity": 916.4546289398164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698090094/warc/CC-MAIN-20130516095450-00021-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.randform.org/blog/?p=2167 | on amounts
The area of the above squares shall visualize a certain amount of money.
A little puzzle for randform visitors:
The upper outer square visualizes an amount which is … times bigger as the amount of the upper inner square.
The lower outer square visualizes an amount which is … times bigger as the amount of the lower inner square.
solution:
If inkscape doesnt have a bug then the amount which is visualized by the area of the outer square should be in both cases twice as big as the amount visualized by the inner square. I.e. if the inner square visualizes 300 billion $then the outer square visualizes 600 billion$.
more precise: the upper inner square has an area of 4*4 units and thus the upper outer square has an area of 4*4*2 units, the lower inner square an area of 1*1 units.
comments in german, french and russian will be translated into english.
you can use LaTeX in your math comments, by using the $shortcode: [latex] E = m c^2$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8778160214424133, "perplexity": 1083.1074898437698}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864624.7/warc/CC-MAIN-20180522034402-20180522054402-00487.warc.gz"} |
https://asmedigitalcollection.asme.org/MNHT/proceedings-abstract/MNHT2008/42924/453/330608 | This paper quantifies the influence of copper (II) oxide (CuO) nanoparticle concentration on the boiling performance of R134a/polyolester mixtures on a roughened, horizontal flat surface. Nanofluids are liquids that contain dispersed nanosize particles. Two lubricant based nanofluids (nanolubricants) were made with a synthetic polyolester and 30 nm diameter CuO particles to a 4% and a 2% volume fraction, respectively. As reported in a previous study for the 4% volume fraction nanolubricant, a 0.5% nanolubricant mass fraction with R134a resulted in a heat transfer enhancement relative to the heat transfer of pure R134a/polyolester (99.5/0.5) of between 50% and 275%. The same study had shown that increasing the mass fraction of the 4% volume fraction nanolubricant resulted in smaller, but significant, boiling heat transfer enhancements. The present study shows that use of a nanolubricant with half the concentration of CuO nanoparticles (2% by volume) resulted in either no improvement or boiling heat transfer degradations with respect to the R134a/polyolester mixtures without nanoparticles. Consequently, significant refrigerant/lubricant boiling heat transfer enhancements are possible with nanoparticles; however, the nanoparticle concentration is an important determining factor. Further research with nanolubricants and refrigerants are required to establish a fundamental understanding of the mechanisms that control nanofluid heat transfer.
This content is only available via PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8926423788070679, "perplexity": 4004.556219051134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300616.11/warc/CC-MAIN-20220117182124-20220117212124-00111.warc.gz"} |
http://clay6.com/qa/553/choose-the-correct-answer-the-probability-of-obtaining-an-even-prime-number | Browse Questions
# Choose the correct answer: The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
$\begin{array} ((A) 0 \quad & (B) \frac{1}{3} \quad & (C) \frac{1}{12} \quad & (D) \frac{1}{36} \end{array}$
Can you answer this question?
When a pair of die is rolled once, the sample space consists of 6 $\times$ 6 = 36 elements.
Of the possible outcomes, the only even prime number is 2, and getting a 2 on each die can occur only once.
Therefore the P (obtaining an even prime number on each die, when a pair of dice is rolled ) = $\large\frac{1}{36}$
answered Jun 19, 2013 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.84903883934021, "perplexity": 308.858583794472}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279915.8/warc/CC-MAIN-20170116095119-00275-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/85607-advanced-statistics-questions.html | # Math Help - Advanced Statistics Questions
I have two questions:
1) Let X_1, X_2, ..., X_n be i.i.d. from a distribution with pdf:
I am supposed to find the MLE (maxmium likelihood estimator) for theda. However, if I take the derivative of the likelihood function (Likelihood function given below) and set it equal to zero, it doesn't work.
I must maximize the likelihood function a different way then. I argue that in order for the likelihood function to be maximized,
(which is the first order statistic; thus "theda hat" equals the minimum).
Is my logic correct?
2) Let X_1, X_2, ..., X_n be i.i.d. with distribution Laplace(u,1). Find the Fisher information for u.
Here's the pdf:
When I solve the Fisher information, I_n (u), I get zero... is this right? If not, what is another way to solve it?
Thanks for the help!
2. nope, the largest the joint density can be is when theta is as small as possible.
You have $I(0\le X_{(n)}\le \theta)$.
Hence the LARGEST order stat not the smallest is the MLE.
It's sufficient too.
3. Thanks, matheagle! Considering I did that one wrong, check my work on the following (which I thought I did correctly):
Let X_1, X_2, ... , X_n be i.i.d. from a distribution with a pdf:
FYI: I noticed that this a:
.
Find the MLE for sigma. Again, like the previous problem, the derivative of the likelihood function won't help me, so I look the at likelihood function:
I argue that the likelihood function is maximized when sigma is minimized. However, sigma can only be as small as the largest order statistic because of the bounds of X. So,
Am I right? I am a little hesitant of my answer because mu is also in the bounds of X, so I don't know if I have to include mu somehow in there as well.
Thanks again!
4. Sorry. I'm no longer answering questions here. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9825426340103149, "perplexity": 623.8486792375822}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678697363/warc/CC-MAIN-20140313024457-00082-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://sourceforge.net/p/texniccenter/bugs/340/ | ## #340 In outline pane remove tex formatting from section headings
open
nobody
5
2012-12-05
2012-11-22
Mario Valle
No
Writing for a journal I'm forced to use section headings like the following:
\section*{\sffamily \Large Seeing and Understanding}
\subsubsection*{\sffamily \normalsize Colors}
Is it possible to remove the latex formatting commands before outputting the section title? I know this is not a general solution, things like \textbf{Interactivity} needs more work.
This is a low priority enhancement request. I hope the journal latex knowledge will improve in the future...
Thanks!
mario
## Discussion
• Tino Weinkauf - 2012-12-05
So sorry that you have to write for such a journal! ;-)
Anyway, I will add this as a bug report. I am surprised that we did not do this yet.
• Tino Weinkauf - 2012-12-05
The described error has been added to the official bug list. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9759001135826111, "perplexity": 3745.420527021825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948551162.54/warc/CC-MAIN-20171214222204-20171215002204-00090.warc.gz"} |
http://peeterjoot.com/tag/charge-distribution/ | [Click here for a PDF of this post with nicer formatting]
When computing the most general solution of the electrostatic potential in a plane, Jackson [1] mentions that $$-2 \lambda_0 \ln \rho$$ is the well known potential for an infinite line charge (up to the unit specific factor). Checking that statement, since I didn’t recall what that potential was offhand, I encountered some inconsistencies and non-convergent integrals, and thought it was worthwhile to explore those a bit more carefully. This will be done here.
### Using Gauss’s law.
For an infinite length line charge, we can find the radial field contribution using Gauss’s law, imagining a cylinder of length $$\Delta l$$ of radius $$\rho$$ surrounding this charge with the midpoint at the origin. Ignoring any non-radial field contribution, we have
\label{eqn:lineCharge:20}
\int_{-\Delta l/2}^{\Delta l/2} \ncap \cdot \BE (2 \pi \rho) dl = \frac{\lambda_0}{\epsilon_0} \Delta l,
or
\label{eqn:lineCharge:40}
\BE = \frac{\lambda_0}{2 \pi \epsilon_0} \frac{\rhocap}{\rho}.
Since
\label{eqn:lineCharge:60}
\frac{\rhocap}{\rho} = \spacegrad \ln \rho,
this means that the potential is
\label{eqn:lineCharge:80}
\phi = -\frac{2 \lambda_0}{4 \pi \epsilon_0} \ln \rho.
### Finite line charge potential.
Let’s try both these calculations for a finite charge distribution. Gauss’s law looses its usefulness, but we can evaluate the integrals directly. For the electric field
\label{eqn:lineCharge:100}
\BE
= \frac{\lambda_0}{4 \pi \epsilon_0} \int \frac{(\Bx – \Bx’)}{\Abs{\Bx – \Bx’}^3} dl’.
Using cylindrical coordinates with the field point $$\Bx = \rho \rhocap$$ for convience, the charge point $$\Bx’ = z’ \zcap$$, and a the charge distributed over $$[a,b]$$ this is
\label{eqn:lineCharge:120}
\BE
= \frac{\lambda_0}{4 \pi \epsilon_0} \int_a^b \frac{(\rho \rhocap – z’ \zcap)}{\lr{\rho^2 + (z’)^2}^{3/2}} dz’.
When the charge is uniformly distributed around the origin $$[a,b] = b[-1,1]$$ the $$\zcap$$ component of this field is killed because the integrand is odd. This justifies ignoring such contributions in the Gaussing cylinder analysis above. The general solution to this integral is found to be
\label{eqn:lineCharge:140}
\BE
=
\frac{\lambda_0}{4 \pi \epsilon_0}
\evalrange{
\lr{
\frac{z’ \rhocap }{\rho \sqrt{ \rho^2 + (z’)^2 } }
+\frac{\zcap}{ \sqrt{ \rho^2 + (z’)^2 } }
}
}{a}{b},
or
\label{eqn:lineCharge:240}
\boxed{
\BE
=
\frac{\lambda_0}{4 \pi \epsilon_0}
\lr{
\frac{\rhocap }{\rho}
\lr{
\frac{b}{\sqrt{ \rho^2 + b^2 } }
-\frac{a}{\sqrt{ \rho^2 + a^2 } }
}
+ \zcap
\lr{
\frac{1}{ \sqrt{ \rho^2 + b^2 } }
-\frac{1}{ \sqrt{ \rho^2 + a^2 } }
}
}.
}
When $$b = -a = \Delta l/2$$, this reduces to
\label{eqn:lineCharge:160}
\BE
=
\frac{\lambda_0}{4 \pi \epsilon_0}
\frac{\rhocap }{\rho}
\frac{\Delta l}{\sqrt{ \rho^2 + (\Delta l/2)^2 } },
which further reduces to \ref{eqn:lineCharge:40} when $$\Delta l \gg \rho$$.
### Finite line charge potential. Wrong but illuminating.
Again, putting the field point at $$z’ = 0$$, we have
\label{eqn:lineCharge:180}
\phi(\rho)
= \frac{\lambda_0}{4 \pi \epsilon_0} \int_a^b \frac{dz’}{\lr{\rho^2 + (z’)^2}^{1/2}},
which integrates to
\label{eqn:lineCharge:260}
\phi(\rho)
= \frac{\lambda_0}{4 \pi \epsilon_0 }
\ln \frac{ b + \sqrt{ \rho^2 + b^2 }}{ a + \sqrt{\rho^2 + a^2}}.
With $$b = -a = \Delta l/2$$, this approaches
\label{eqn:lineCharge:200}
\phi
\approx
\frac{\lambda_0}{4 \pi \epsilon_0 }
\ln \frac{ (\Delta l/2) }{ \rho^2/2\Abs{\Delta l/2}}
=
\frac{-2 \lambda_0}{4 \pi \epsilon_0 } \ln \rho
+
\frac{\lambda_0}{4 \pi \epsilon_0 }
\ln \lr{ (\Delta l)^2/2 }.
Before $$\Delta l$$ is allowed to tend to infinity, this is identical (up to a difference in the reference potential) to \ref{eqn:lineCharge:80} found using Gauss’s law. It is, strictly speaking, singular when $$\Delta l \rightarrow \infty$$, so it does not seem right to infinity as a reference point for the potential.
There’s another weird thing about this result. Since this has no $$z$$ dependence, it is not obvious how we would recover the non-radial portion of the electric field from this potential using $$\BE = -\spacegrad \phi$$? Let’s calculate the elecric field from \ref{eqn:lineCharge:180} explicitly
\label{eqn:lineCharge:220}
\begin{aligned}
\BE
&=
-\frac{\lambda_0}{4 \pi \epsilon_0}
\spacegrad
\ln \frac{ b + \sqrt{ \rho^2 + b^2 }}{ a + \sqrt{\rho^2 + a^2}} \\
&=
-\frac{\lambda_0 \rhocap}{4 \pi \epsilon_0 }
\PD{\rho}{}
\ln \frac{ b + \sqrt{ \rho^2 + b^2 }}{ a + \sqrt{\rho^2 + a^2}} \\
&=
-\frac{\lambda_0 \rhocap}{4 \pi \epsilon_0}
\lr{
\inv{ b + \sqrt{ \rho^2 + b^2 }} \frac{ \rho }{\sqrt{ \rho^2 + b^2 }}
-\inv{ a + \sqrt{ \rho^2 + a^2 }} \frac{ \rho }{\sqrt{ \rho^2 + a^2 }}
} \\
&=
-\frac{\lambda_0 \rhocap}{4 \pi \epsilon_0 \rho}
\lr{
\frac{ -b + \sqrt{ \rho^2 + b^2 }}{\sqrt{ \rho^2 + b^2 }}
-\frac{ -a + \sqrt{ \rho^2 + a^2 }}{\sqrt{ \rho^2 + a^2 }}
} \\
&=
\frac{\lambda_0 \rhocap}{4 \pi \epsilon_0 \rho}
\lr{
\frac{ b }{\sqrt{ \rho^2 + b^2 }}
-\frac{ a }{\sqrt{ \rho^2 + a^2 }}
}.
\end{aligned}
This recovers the radial component of the field from \ref{eqn:lineCharge:240}, but where did the $$\zcap$$ component go? The required potential appears to be
\label{eqn:lineCharge:340}
\phi(\rho, z)
=
\frac{\lambda_0}{4 \pi \epsilon_0 }
\ln \frac{ b + \sqrt{ \rho^2 + b^2 }}{ a + \sqrt{\rho^2 + a^2}}
\frac{z \lambda_0}{4 \pi \epsilon_0 }
\lr{ \frac{1}{\sqrt{\rho^2 + b^2}}
-\frac{1}{\sqrt{\rho^2 + a^2}}
}.
When computing the electric field $$\BE(\rho, \theta, z)$$, it was convienent to pick the coordinate system so that $$z = 0$$. Doing this with the potential gives the wrong answers. The reason for this appears to be that this kills the potential term that is linear in $$z$$ before taking its gradient, and we need that term to have the $$\zcap$$ field component that is expected for a charge distribution that is non-symmetric about the origin on the z-axis!
### Finite line charge potential. Take II.
Let the point at which the potential is evaluated be
\label{eqn:lineCharge:360}
\Bx = \rho \rhocap + z \zcap,
and the charge point be
\label{eqn:lineCharge:380}
\Bx’ = z’ \zcap.
This gives
\label{eqn:lineCharge:400}
\begin{aligned}
\phi(\rho, z)
&= \frac{\lambda_0}{4\pi \epsilon_0} \int_a^b \frac{dz’}{\Abs{\rho^2 + (z – z’)^2 }} \\
&= \frac{\lambda_0}{4\pi \epsilon_0} \int_{a-z}^{b-z} \frac{du}{ \Abs{\rho^2 + u^2} } \\
&= \frac{\lambda_0}{4\pi \epsilon_0}
\evalrange{\ln \lr{ u + \sqrt{ \rho^2 + u^2 }}}{b-z}{a-z} \\
&=
\frac{\lambda_0}{4\pi \epsilon_0}
\ln \frac
{ b-z + \sqrt{ \rho^2 + (b-z)^2 }}
{ a-z + \sqrt{ \rho^2 + (a-z)^2 }}.
\end{aligned}
The limit of this potential $$a = -\Delta/2 \rightarrow -\infty, b = \Delta/2 \rightarrow \infty$$ doesn’t exist in any strict sense. If we are cavilier about the limits, as in \ref{eqn:lineCharge:200}, this can be evaluated as
\label{eqn:lineCharge:n}
\phi \approx
\frac{\lambda_0}{4\pi \epsilon_0} \lr{ -2 \ln \rho + \textrm{constant} }.
however, the constant ($$\ln \Delta^2/2$$) is infinite, so there isn’t really a good justification for using that constant as the potential reference point directly.
It seems that the “right” way to calculate the potential for the infinite distribution, is to
• Calculate the field from the potential.
• Take the PV limit of that field with the charge distribution extending to infinity.
• Compute the corresponding potential from this limiting value of the field.
Doing that doesn’t blow up. That field calculation, for the finite case, should include a $$\zcap$$ component. To verify, let’s take the respective derivatives
\label{eqn:lineCharge:420}
\begin{aligned}
-\PD{z}{} \phi
&=
-\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\frac{ -1 + \frac{z – b}{\sqrt{ \rho^2 + (b-z)^2 }} }{
b-z + \sqrt{ \rho^2 + (b-z)^2 }
}
\frac{ -1 + \frac{z – a}{\sqrt{ \rho^2 + (a-z)^2 }} }{
a-z + \sqrt{ \rho^2 + (a-z)^2 }
}
} \\
&=
\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\frac{ 1 + \frac{b – z}{\sqrt{ \rho^2 + (b-z)^2 }} }{
b-z + \sqrt{ \rho^2 + (b-z)^2 }
}
\frac{ 1 + \frac{a – z}{\sqrt{ \rho^2 + (a-z)^2 }} }{
a-z + \sqrt{ \rho^2 + (a-z)^2 }
}
} \\
&=
\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\inv{\sqrt{ \rho^2 + (b-z)^2 }}
-\inv{\sqrt{ \rho^2 + (a-z)^2 }}
},
\end{aligned}
and
\label{eqn:lineCharge:440}
\begin{aligned}
-\PD{\rho}{} \phi
&=
-\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\frac{ \frac{\rho}{\sqrt{ \rho^2 + (b-z)^2 }} }{
b-z + \sqrt{ \rho^2 + (b-z)^2 }
}
\frac{ \frac{\rho}{\sqrt{ \rho^2 + (a-z)^2 }} }{
a-z + \sqrt{ \rho^2 + (a-z)^2 }
}
} \\
&=
-\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\frac{\rho \lr{
-(b-z) + \sqrt{ \rho^2 + (b-z)^2 }
}}{ \rho^2 \sqrt{ \rho^2 + (b-z)^2 } }
\frac{\rho \lr{
-(a-z) + \sqrt{ \rho^2 + (a-z)^2 }
}}{ \rho^2 \sqrt{ \rho^2 + (a-z)^2 } }
} \\
&=
\frac{\lambda_0}{4\pi \epsilon_0 \rho}
\lr{
\frac{b-z}{\sqrt{ \rho^2 + (b-z)^2 }}
-\frac{a-z}{\sqrt{ \rho^2 + (a-z)^2 }}
}
.
\end{aligned}
Putting the pieces together, the electric field is
\label{eqn:lineCharge:460}
\BE =
\frac{\lambda_0}{4\pi \epsilon_0}
\lr{
\frac{\rhocap}{\rho} \lr{
\frac{b-z}{\sqrt{ \rho^2 + (b-z)^2 }}
-\frac{a-z}{\sqrt{ \rho^2 + (a-z)^2 }}
}
+
\zcap \lr{
\inv{\sqrt{ \rho^2 + (b-z)^2 }}
-\inv{\sqrt{ \rho^2 + (a-z)^2 }}
}
}.
For has a PV limit of \ref{eqn:lineCharge:40} at $$z = 0$$, and also for the finite case, has the $$\zcap$$ field component that was obtained when the field was obtained by direct integration.
### Conclusions
• We have to evaluate the potential at all points in space, not just on the axis that we evaluate the field on (should we choose to do so).
• In this case, we found that it was not directly meaningful to take the limit of a potential distribution. We can, however, compute the field from a potential for a finite charge distribution,
take the limit of that field, and then calculate the corresponding potential for the infinite distribution.
Is there a more robust mechanism that can be used to directly calculate the potential for an infinite charge distribution, instead of calculating the potential from the field of such an infinite distribution?
I think that were things go wrong is that the integral of \ref{eqn:lineCharge:180} does not apply to charge distributions that are not finite on the infinite range $$z \in [-\infty, \infty]$$. That solution was obtained by utilizing an all-space Green’s function, and the boundary term in that Green’s analysis was assumed to tend to zero. That isn’t the case when the charge distribution is $$\lambda_0 \delta( z )$$.
# References
[1] JD Jackson. Classical Electrodynamics. John Wiley and Sons, 2nd edition, 1975. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9842408299446106, "perplexity": 3421.3600847929515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514162.67/warc/CC-MAIN-20181021161035-20181021182535-00183.warc.gz"} |
https://physics.stackexchange.com/questions/321764/scalar-field-theories | # Scalar Field Theories
The Lagrangian density for a single real scalar field theory is $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-V(\phi)$$ I have often seen this written $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-V(\phi)$$ which appears to differ in the kinetic term.
Specifically $$(\partial_{\mu}\phi)^{2}=(\partial_{\mu}\phi)(\partial^{\mu}\phi)\neq\partial_{\mu}\phi\partial^{\mu}\phi=(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\phi\partial_{\mu}\partial^{\mu}\phi$$ where the product rule has been used in the last equality. Is this just sloppy notation (which is acceptable because only first derivatives in the field are considered anyway), or is my maths very bad?
• $\partial_\mu \phi \partial^\mu \phi$ always means $(\partial_{\mu}\phi)(\partial^{\mu}\phi)$. I have never seen it mean $\partial_\mu ( \phi \partial^\mu \phi )$ – Prahar Mar 27 '17 at 17:57
• You seem to think the implicit bracketing in $\partial_\mu \phi \partial^\mu \phi$ is $\partial_\mu (\phi\partial^\mu \phi)$. Why? – ACuriousMind Mar 27 '17 at 17:57
• @ACuriousMind If I had $x(t)$, $y(t)$ and $z(t)$ then given $\frac{d}{dt}xyz$ I would assume it meant $\frac{d}{dt}(xyz)$ and not $(\frac{d}{dt}x)(yz)$, so I've used that logic here... – Watw Mar 27 '17 at 18:00
## 1 Answer
1. The notations $(\partial\phi)^{2}$ and $(\partial_{\mu}\phi)^{2}$ are shorthands for $(\partial_{\mu}\phi)g^{\mu\nu}(\partial_{\nu}\phi)$, where $g^{\mu\nu}$ is the inverse metric tensor.
2. Generally speaking, different authors use different notation concerning how far derivatives act to the right. When in doubt, it is a good idea to insert extra parentheses or spaces in the notation. See also this related Phys.SE post.
3. However, in the specific context of OP's kinetic term $\partial_{\mu}\phi\partial^{\mu}\phi$, it seems universally accepted that it is supposed to mean $(\partial_{\mu}\phi)\partial^{\mu}\phi$ as opposed to $\partial_{\mu}(\phi\partial^{\mu}\phi)$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.9862728118896484, "perplexity": 268.42130009848313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145676.44/warc/CC-MAIN-20200222115524-20200222145524-00469.warc.gz"} |
https://worldwidescience.org/topicpages/n/net+charge+transfer.html | #### Sample records for net charge transfer
1. Net charge fluctuations and local charge compensation
International Nuclear Information System (INIS)
Fu Jinghua
2006-01-01
We propose net charge fluctuation as a measure of local charge correlation length. It is demonstrated that, in terms of a schematic multiperipheral model, net charge fluctuation satisfies the same Quigg-Thomas relation as satisfied by charge transfer fluctuation. Net charge fluctuations measured in finite rapidity windows depend on both the local charge correlation length and the size of the observation window. When the observation window is larger than the local charge correlation length, the net charge fluctuation only depends on the local charge correlation length, while forward-backward charge fluctuations always have strong dependence on the observation window size. Net charge fluctuations and forward-backward charge fluctuations measured in the present heavy ion experiments show characteristic features similar to those from multiperipheral models. But the data cannot all be understood within this simple model
2. The net charge at interfaces between insulators
International Nuclear Information System (INIS)
Bristowe, N C; Littlewood, P B; Artacho, Emilio
2011-01-01
The issue of the net charge at insulating oxide interfaces is briefly reviewed with the ambition of dispelling myths of such charges being affected by covalency and related charge density effects. For electrostatic analysis purposes, the net charge at such interfaces is defined by the counting of discrete electrons and core ion charges, and by the definition of the reference polarization of the separate, unperturbed bulk materials. The arguments are illustrated for the case of a thin film of LaAlO 3 over SrTiO 3 in the absence of free carriers, for which the net charge is exactly 0.5e per interface formula unit, if the polarization response in both materials is referred to zero bulk values. Further consequences of the argument are extracted for structural and chemical alterations of such interfaces, in which internal rearrangements are distinguished from extrinsic alterations (changes of stoichiometry, redox processes), only the latter affecting the interfacial net charge. The arguments are reviewed alongside the proposal of Stengel and Vanderbilt (2009 Phys. Rev. B 80 241103) of using formal polarization values instead of net interfacial charges, based on the interface theorem of Vanderbilt and King-Smith (1993 Phys. Rev. B 48 4442-55). Implications for non-centrosymmetric materials are discussed, as well as for interfaces for which the charge mismatch is an integer number of polarization quanta. (viewpoint)
3. Charge transfer in astrophysical nebulae
International Nuclear Information System (INIS)
Shields, G.A.
1990-01-01
Charge transfer has become a standard ingredient in models of ionized nebulae, supernovae remnants and active galactic nuclei. Charge transfer rate coefficients and the physics of ionized nebulae are considered. Charge transfer is applied to the ionization structure and line emission of ionized nebulae. Photoionized nebulae observations are used to test theoretical predictions of charge transfer rates. (author)
4. Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond
Ultrafast Dynamics of Chemical Reactions in Condensed Phase: Intramolecular Energy Transfer, Charge Transfer & Hydrogen Bond · PowerPoint Presentation · Slide 3 · Slide 4 · Slide 5 · Slide 6 · Slide 7 · Slide 8 · Slide 9 · Slide 10 · Slide 11 · Slide 12 · Slide 13 · Slide 14 · Slide 15 · Slide 16 · Slide 17 · Slide 18 · Slide 19.
5. Charge Transfer into Aqueous Droplets via Kilovolt Potentials
Science.gov (United States)
Hamlin, B. S.; Rosenberg, E. R.; Ristenpart, W. D.
2012-11-01
When an aqueous droplet immersed in an insulating oil contacts an electrified surface, the droplet acquires net charge. For sufficiently large field strengths, the charged droplet is driven back and forth electrophoretically between the electrodes, in essence bouncing'' between them. Although it is clear that the droplet acquires charge, the underlying mechanism controlling the charge transfer process has been unclear. Here we demonstrate that the chemical species present in the droplet strongly affect the charge transfer process into the drop. Using two independent charge measurement techniques, high speed video velocimetry and direct current measurement, we show that the charge acquired during contact is strongly influenced by the droplet pH. We also provide physical evidence that the electrodes undergo electroplating or corrosion for droplets with appropriate chemical species present. Together, the observations strongly suggest that electrochemical reactions govern the charge transfer process into the droplet.
6. Higher-moment measurements of net-kaon, net-charge and net-proton multiplicity distributions at STAR
International Nuclear Information System (INIS)
Sarkar, Amal
2014-01-01
In this paper, we report the measurements of the various moments, such as mean, standard deviation (σ), skewness (S) and kurtosis (κ) of the net-kaon, net-charge and net-proton multiplicity distributions at mid-rapidity in Au + Au collisions from √(s NN )=7.7 to 200 GeV with the STAR experiment at RHIC. This work has been done with the aim to locate the critical point on the QCD phase diagram. These moments and their products are related to the thermodynamic susceptibilities of conserved quantities such as net baryon number, net charge, and net strangeness as well as to the correlation length of the system which diverges in an ideal infinite thermodynamic system at the critical point. For a finite system, existing for a finite time, a non-monotonic behavior of these variables would indicate the presence of the critical point. Furthermore, we also present the moment products Sσ, κσ 2 of net-kaon, net-charge and net-proton multiplicity distributions as a function of collision centrality and energy. The energy and the centrality dependence of higher moments and their products have been compared with different models
7. Net charge of quark jets in (anti)neutrino interactions
International Nuclear Information System (INIS)
Teper, M.
1981-01-01
We analyse recent measurements of the net charges of quark jets in neutrino and antineutrino interactions. The data indicates that (i) the two quarks in the nucleon fragmentation region prefer to behave as a diquark rather than as a pair of independent quarks, and (ii) the struck quark does not appear to suffer any soft charge exchange of the kind that occurs when a valence quark inside a nucleon is slowed to x approx. O. (orig.)
8. Charge migration and charge transfer in molecular systems
Directory of Open Access Journals (Sweden)
Hans Jakob Wörner
2017-11-01
Full Text Available The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.
9. Spontaneous charged lipid transfer between lipid vesicles.
Science.gov (United States)
Richens, Joanna L; Tyler, Arwen I I; Barriga, Hanna M G; Bramble, Jonathan P; Law, Robert V; Brooks, Nicholas J; Seddon, John M; Ces, Oscar; O'Shea, Paul
2017-10-03
An assay to study the spontaneous charged lipid transfer between lipid vesicles is described. A donor/acceptor vesicle system is employed, where neutrally charged acceptor vesicles are fluorescently labelled with the electrostatic membrane probe Fluoresceinphosphatidylethanolamine (FPE). Upon addition of charged donor vesicles, transfer of negatively charged lipid occurs, resulting in a fluorescently detectable change in the membrane potential of the acceptor vesicles. Using this approach we have studied the transfer properties of a range of lipids, varying both the headgroup and the chain length. At the low vesicle concentrations chosen, the transfer follows a first-order process where lipid monomers are transferred presumably through the aqueous solution phase from donor to acceptor vesicle. The rate of transfer decreases with increasing chain length which is consistent with energy models previously reported for lipid monomer vesicle interactions. Our assay improves on existing methods allowing the study of a range of unmodified lipids, continuous monitoring of transfer and simplified experimental procedures.
10. Charge transfer in ionic systems
International Nuclear Information System (INIS)
Bacchus-Montabonel, M.C.; Tergiman, Y.S.; Vaeck, N.; Baloitcha, E.; Desouter-Lecomte, M.
2002-01-01
Charge transfer involving multiply charged ions in collision with atomic or molecular targets are determinant processes in controlled thermonuclear fusion research and astrophysical plasma. In such processes, an electron is generally captured in a excited state of the ion, followed by line emission. The observation of line intensities provides important information on the electron temperature, density and spacial distributions in the emitting region of the plasma. From a theoretical point of view, different approaches may be used with regard to the collisional energy range of the process. A semi-classical method is currently used at keV energies, but the description of very low-velocity processes requires a complete quantum mechanical treatment of the dynamics of both electrons and nuclei. The first approach extensively used is the resolution of the stationary close-coupling equations, but we have analyzed recently the efficiency of a time-dependent wave packet method which provides a clear and physical insight into the dynamics of the processes and may be particularly interesting for polyatomic systems since it allows the possibility of developing a fully quantal mechanical treatment for some degrees of freedom, the other ones being treated classically. The keV energy range treatment is presented on two examples pointing out the case of complex ion-atom collision systems, as well as the differences between ion-atom and ion-molecule mechanisms. In connection with translation energy spectroscopy experiments of McLaughlin et al in the 4-28 keV impact energy range, we present a complete ab-initio theoretical approach of the N 4+ (2s) 2 S + He system taking into account both single and double electron capture channels. This is an extremely complex collisional system which involves numerous channels with short range interactions and a very intricate interaction region may be observed for interatomic distances around R = 3.5 a.u.. In agreement with experimental data, the
11. Possible charge analogues of spin transfer torques in bulk superconductors
Science.gov (United States)
Garate, Ion
2014-03-01
Spin transfer torques (STT) occur when electric currents travel through inhomogeneously magnetized systems and are important for the motion of magnetic textures such as domain walls. Since superconductors are easy-plane ferromagnets in particle-hole (charge) space, it is natural to ask whether any charge duals of STT phenomena exist therein. We find that the superconducting analogue of the adiabatic STT vanishes in a bulk superconductor with a momentum-independent order parameter, while the superconducting counterpart of the nonadiabatic STT does not vanish. This nonvanishing superconducting torque is induced by heat (rather than charge) currents and acts on the charge (rather than spin) degree of freedom. It can become significant in the vicinity of the superconducting transition temperature, where it generates a net quasiparticle charge and alters the dispersion and linewidth of low-frequency collective modes. This work has been financially supported by Canada's NSERC.
12. Charge orders in organic charge-transfer salts
International Nuclear Information System (INIS)
Kaneko, Ryui; Valentí, Roser; Tocchio, Luca F; Becca, Federico
2017-01-01
Motivated by recent experimental suggestions of charge-order-driven ferroelectricity in organic charge-transfer salts, such as κ -(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl, we investigate magnetic and charge-ordered phases that emerge in an extended two-orbital Hubbard model on the anisotropic triangular lattice at 3/4 filling. This model takes into account the presence of two organic BEDT-TTF molecules, which form a dimer on each site of the lattice, and includes short-range intramolecular and intermolecular interactions and hoppings. By using variational wave functions and quantum Monte Carlo techniques, we find two polar states with charge disproportionation inside the dimer, hinting to ferroelectricity. These charge-ordered insulating phases are stabilized in the strongly correlated limit and their actual charge pattern is determined by the relative strength of intradimer to interdimer couplings. Our results suggest that ferroelectricity is not driven by magnetism, since these polar phases can be stabilized also without antiferromagnetic order and provide a possible microscopic explanation of the experimental observations. In addition, a conventional dimer-Mott state (with uniform density and antiferromagnetic order) and a nonpolar charge-ordered state (with charge-rich and charge-poor dimers forming a checkerboard pattern) can be stabilized in the strong-coupling regime. Finally, when electron–electron interactions are weak, metallic states appear, with either uniform charge distribution or a peculiar 12-site periodicity that generates honeycomb-like charge order. (paper)
13. Graphene Charge Transfer, Spectroscopy, and Photochemical Reactions
Energy Technology Data Exchange (ETDEWEB)
Brus, Louis [Columbia Univ., New York, NY (United States)
2017-01-31
This project focused on the special electronic and optical properties of graphene and adsorbed molecular species. Graphene makes an excellent substrate for current collection in nanostructured photovoltaic designs. Graphene is almost transparent, and can be used as a solar cell window. It also has no surface states, and thus current is efficiently transported over long distances. Progress in graphene synthesis indicates that there will soon be practical methods for making large pieces of graphene for devices. We now need to understand exactly what happens to both ground state and electronically excited molecules and Qdots near graphene, if we are going to use them to absorb light in a nano-structured photovoltaic device using graphene to collect photocurrent. We also need to understand how to shift the graphene Fermi level, to optimize the kinetics of electron transfer to graphene. And we need to learn how to convert local graphene areas to semiconductor structure, to make useful spatially patterned graphenes. In this final report, we describe how we addressed these goals. We explored the question of possible Surface Enhanced Raman spectroscopy from molecular Charge Transfer onto Graphene substrates. We observed strong hole doping of graphene by adsorbed halogens as indicated by the shift of the graphene G Raman band. In the case of iodine adsorption, we also observed the anionic species made by hole doping. At low frequency in the Raman spectrum, we saw quite intense lines from I3- and I5- , suggesting possible SERS. We reported on Fresnel calculations on this thin film system, which did not show any net electromagnetic field enhancement.
14. Symmetric charge transfer cross section of uranium
International Nuclear Information System (INIS)
Shibata, Takemasa; Ogura, Koichi
1995-03-01
Symmetric charge transfer cross section of uranium was calculated under consideration of reaction paths. In the charge transfer reaction a d 3/2 electron in the U atom transfers into the d-electron site of U + ( 4 I 9/2 ) ion. The J value of the U atom produced after the reaction is 6, 5, 4 or 3, at impact energy below several tens eV, only resonant charge transfer in which the product atom is ground state (J=6) takes place. Therefore, the cross section is very small (4-5 x 10 -15 cm 2 ) compared with that considered so far. In the energy range of 100-1000eV the cross section increases with the impact energy because near resonant charge transfer in which an s-electron in the U atom transfers into the d-electron site of U + ion. Charge transfer cross section between U + in the first excited state (289 cm -1 ) and U in the ground state was also obtained. (author)
15. Influence of kinematic cuts on the net charge distribution
Energy Technology Data Exchange (ETDEWEB)
Petersen, Hannah [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt (Germany); Oliinychenko, Dmytro [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine); Steinheimer, Jan [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)
2016-12-15
The higher moments of the net charge distributions, e.g. the skewness and kurtosis, are studied within an infinite hadronic matter calculation in a transport approach. By dividing the box into several parts, the volume dependence of the fluctuations is investigated. After confirming that the initial distributions follow the expectations from a binomial distribution, the influence of quantum number conservation in this case the net charge in the system on the higher moments is evaluated. For this purpose, the composition of the hadron gas is adjusted and only pions and ρ mesons are simulated to investigate the charge conservation effect. In addition, the effect of imposing kinematic cuts in momentum space is analysed. The role of resonance excitations and decays on the higher moments can also be studied within this model. This work is highly relevant to understand the experimental measurements of higher moments obtained in the RHIC beam energy scan and their comparison to lattice results and other theoretical calculations assuming infinite matter.
16. First result of net-charge jet-correlations from STAR
International Nuclear Information System (INIS)
Wang, Q.
2011-01-01
We presented results on azimuthal correlation of net-charge with high ρ T trigger particles. It is found that the net-charge correlation shape is similar to that of total-charge. On the near-side, the net-charge and total-charge ρ T spectra have similar shape and both are harder than the inclusives. On the away-side, the correlated spectra are not much harder than the inclusives, and the net-charge/total-charge ratio increases with ρ T and is similar to the inclusive ratio. (author)
17. Bond charges and electronic charge transfer in ternary semiconductors
International Nuclear Information System (INIS)
Pietsch, U.
1986-01-01
By means of a simple molecule-theoretic model of 'linear superposition of two-electron molecules' the bond charges between nearest neighbours and the effective charges of ions are calculated for ternary zinc-blende structure alloys as well as chalcopyrite semiconductors. Taking into account both, the charge transfer among the ions caused by the differences of electronegativities of atoms used and between the bonds created by the internal stress of the lattice a nearly unvaried averaged bond charge amount of the alloy is found, but rather dramatically changed local bond charge parameters in comparison with the respective values of binary compounds used. This fact should influence the noncentral force interaction in such semiconductors. (author)
18. Charge transfer reactions in Xe plasma expansion
International Nuclear Information System (INIS)
Jiao, C. Q.; Garscadden, A.; Ganguly, B. N.
2007-01-01
Charge transfer reactions of fast Xe ions with hydrocarbons including methane (CH 4 ), ethene (C 2 H 4 ), and propane (C 3 H 8 ) are studied by adding these hydrocarbon gases into a cross flowing Xe plasma expansion. Branching ratios and relative reaction rates for the charge transfers of fast Xe + with each of the three hydrocarbon gases are measured under different rf powers of the inductively coupled Xe discharge. For CH 4 /Xe system, we find that fast Xe + reacts readily with CH 4 generating CH 4 + and CH 3 + in a ratio of 1:0.56, with an estimated rate coefficient of (2.3±0.3)x10 -10 cm 3 /s at 75 W rf power which slowly increases to (2.9±0.3)x10 -10 cm 3 /s at 250 W (error bars reflect only the uncertainties due to the unknown extent of the ion recombination that follows the charge transfer reaction). These observed charge transfer reactions are made possible by the kinetically excited Xe ions produced by free expansion of the plasma. For the C 2 H 4 /Xe system product ions C 2 H 4 + and C 2 H 2 + are observed, and for C 3 H 8 /Xe, C 2 H 4 + and C 2 H 5 + and minor product ions including C 2 H 2 + and C 3 H 7 + are observed
19. NET: an inter-computer file transfer command
International Nuclear Information System (INIS)
Burris, R.D.
1978-05-01
The NET command was defined and supported in order to facilitate file transfer between computers. Among the goals of the implementation were greatest possible ease of use, maximum power (i.e., support of a diversity of equipment and operations), and protection of the operating system
20. Net-baryon-, net-proton-, and net-charge kurtosis in heavy-ion collisions within a relativistic transport approach
International Nuclear Information System (INIS)
Nahrgang, Marlene; Schuster, Tim; Stock, Reinhard; Mitrovski, Michael; Bleicher, Marcus
2012-01-01
We explore the potential of net-baryon, net-proton and net-charge kurtosis measurements to investigate the properties of hot and dense matter created in relativistic heavy-ion collisions. Contrary to calculations in a grand-canonical ensemble we explicitly take into account exact electric and baryon charge conservation on an event-by-event basis. This drastically limits the width of baryon fluctuations. A simple model to account for this is to assume a grand-canonical distribution with a sharp cut-off at the tails. We present baseline predictions of the energy dependence of the net-baryon, net-proton and net-charge kurtosis for central (b≤2.75 fm) Pb+Pb/Au+Au collisions from E lab =2A GeV to √(s NN )=200 GeV from the UrQMD model. While the net-charge kurtosis is compatible with values around zero, the net-baryon number decreases to large negative values with decreasing beam energy. The net-proton kurtosis becomes only slightly negative for low √(s NN ). (orig.)
1. Does charge transfer correlate with ignition probability?
International Nuclear Information System (INIS)
Holdstock, Paul
2008-01-01
Flammable or explosive atmospheres exist in many industrial environments. The risk of ignition caused by electrostatic discharges is very real and there has been extensive study of the incendiary nature of sparks and brush discharges. It is clear that in order to ignite a gas, an amount of energy needs to be delivered to a certain volume of gas within a comparatively short time. It is difficult to measure the energy released in an electrostatic discharge directly, but it is possible to approximate the energy in a spark generated from a well defined electrical circuit. The spark energy required to ignite a gas, vapour or dust cloud can be determined by passing such sparks through them. There is a relationship between energy and charge in a capacitive circuit and so it is possible to predict whether or not a spark discharge will cause an ignition by measuring the charge transferred in the spark. Brush discharges are in many ways less well defined than sparks. Nevertheless, some work has been done that has established a relationship between charge transferred in brush discharges and the probability of igniting a flammable atmosphere. The question posed by this paper concerns whether such a relationship holds true in all circumstances and if there is a universal correlation between charge transfer and ignition probability. Data is presented on discharges from textile materials that go some way to answering this question.
2. Computational Approach to Electron Charge Transfer Reactions
DEFF Research Database (Denmark)
Jónsson, Elvar Örn
-molecular mechanics scheme, and tools to analyse statistical data and generate relative free energies and free energy surfaces. The methodology is applied to several charge transfer species and reactions in chemical environments - chemical in the sense that solvent, counter ions and substrate surfaces are taken...... in to account - which directly influence the reactants and resulting reaction through both physical and chemical interactions. All methods are though general and can be applied to different types of chemistry. First, the basis of the various theoretical tools is presented and applied to several test systems...... and asymmetric charge transfer reactions between several first-row transition metals in water. The results are compared to experiments and rationalised with classical analytic expressions. Shortcomings of the methods are accounted for with clear steps towards improved accuracy. Later the analysis is extended...
3. Impact of charge-transfer excitons in regioregular polythiophene on the charge separation at polythiophene-fullerene heterojunctions
Science.gov (United States)
Polkehn, M.; Tamura, H.; Burghardt, I.
2018-01-01
This study addresses the mechanism of ultrafast charge separation in regioregular oligothiophene-fullerene assemblies representative of poly-3-hexylthiophene (P3HT)-[6,6]-phenyl-C61 butyric acid methyl ester (PCBM) heterojunctions, with special emphasis on the inclusion of charge transfer excitons in the oligothiophene phase. The formation of polaronic inter-chain charge separated species in highly ordered oligothiophene has been demonstrated in recent experiments and could have a significant impact on the net charge transfer to the fullerene acceptor. The present approach combines a first-principles parametrized multi-site Hamiltonian, based on time-dependent density functional theory calculations, with accurate quantum dynamics simulations using the multi-layer multi-configuration time-dependent Hartree method. Quantum dynamical studies are carried out for up to 182 electronic states and 112 phonon modes. The present analysis follows up on our previous study of (Huix-Rotllant et al 2015 J. Phys. Chem. Lett. 6 1702) and significantly expands the scope of this analysis by including the dynamical role of charge transfer excitons. Our investigation highlights the pronounced mixing of photogenerated Frenkel excitons with charge transfer excitons in the oligothiophene domain, and the opening of new transfer channels due the creation of such charge-separated species. As a result, it turns out that the interfacial donor/acceptor charge transfer state can be largely circumvented due to the presence of charge transfer excitons. However, the latter states in turn act as a trap, such that the free carrier yield observed on ultrafast time scales is tangibly reduced. The present analysis underscores the complexity of the transfer pathways at P3HT-PCBM type junctions.
4. Effect of net surface charge on particle sizing and material recognition by using phase Doppler anemometry
International Nuclear Information System (INIS)
Zhou Jun; Xie Li
2011-01-01
By taking net surface charge into consideration, the scattering field of particles illuminated by dual laser beams of phase Doppler anemometry (PDA) is computed based on Mie's theory, and the effect of net surface charge on the phase-diameter relationship and the phase ratio is studied. It is found that the phase-diameter relationship and the relationship between the phase ratio and the refractive index of charged particles could be significantly different from those of uncharged particles, which would lead to errors in particle sizing and the measurement of refractive indices. A method of recognizing charged particles and determining the value of their surface conductivity, which is related to net surface charge, is proposed by utilizing the effect of net surface charge on the measurement of refractive indices using PDA.
5. Effect of net surface charge on particle sizing and material recognition by using phase Doppler anemometry
Energy Technology Data Exchange (ETDEWEB)
Zhou Jun; Xie Li
2011-01-20
By taking net surface charge into consideration, the scattering field of particles illuminated by dual laser beams of phase Doppler anemometry (PDA) is computed based on Mie's theory, and the effect of net surface charge on the phase-diameter relationship and the phase ratio is studied. It is found that the phase-diameter relationship and the relationship between the phase ratio and the refractive index of charged particles could be significantly different from those of uncharged particles, which would lead to errors in particle sizing and the measurement of refractive indices. A method of recognizing charged particles and determining the value of their surface conductivity, which is related to net surface charge, is proposed by utilizing the effect of net surface charge on the measurement of refractive indices using PDA.
6. Charge transfer in gas electron multipliers
Energy Technology Data Exchange (ETDEWEB)
Ottnad, Jonathan; Ball, Markus; Ketzer, Bernhard; Ratza, Viktor; Razzaghi, Cina [HISKP, Bonn University, Nussallee 14-16, D-53115 Bonn (Germany)
2015-07-01
In order to efficiently employ a Time Projection Chamber (TPC) at interaction rates higher than ∝1 kHz, as foreseen e.g. in the ALICE experiment (CERN) and at CB-ELSA (Bonn), a continuous operation and readout mode is required. A necessary prerequisite is to minimize the space charge coming from the amplification system and to maintain an excellent spatial and energy resolution. Unfortunately these two goals can be in conflict to each other. Gas Electron Multipliers (GEM) are one candidate to fulfill these requirements. It is necessary to understand the processes within the amplification structure to find optimal operation conditions. To do so, we measure the charge transfer processes in and between GEM foils with different geometries and field configurations, and use an analytical model to describe the results. This model can then be used to predict and optimize the performance. The talk gives the present status of the measurements and describes the model.
7. Ultrafast Charge Photogeneration in MEH-PPV Charge-Transfer Complexes
NARCIS (Netherlands)
Bakulin, Artem A.; Paraschuk, Dmitry Yu; Pshenichnikov, Maxim S.; van Loosdrecht, Paul H. M.; Corkum, P; DeSilvestri, S; Nelson, KA; Riedle, E; Schoenlein, RW
2009-01-01
Visible-pump - IR-probe spectroscopy is used to study the ultrafast charge dynamics in MEH-PPV based charge-transfer complexes and donor-acceptor blends. Transient anisotropy of the polymer polaron band provides invaluable insights into excitation localisation and charge-transfer pathways.
8. Charge-transfer spectra of tetravalent lanthanide ions in oxides
NARCIS (Netherlands)
The charge-transfer spectra of Ce4+, Pr4+ and Tb4+ in a number of oxides are reported. It is noted that the position of the first charge-transfer band is fixed for the metal ion in an oxygen coordination of VI, but varies in VIII coordination as a function of the host lattice. It is argued that this
9. Characterisation of a CMOS charge transfer device for TDI imaging
International Nuclear Information System (INIS)
Rushton, J.; Holland, A.; Stefanov, K.; Mayer, F.
2015-01-01
The performance of a prototype true charge transfer imaging sensor in CMOS is investigated. The finished device is destined for use in TDI applications, especially Earth-observation, and to this end radiation tolerance must be investigated. Before this, complete characterisation is required. This work starts by looking at charge transfer inefficiency and then investigates responsivity using mean-variance techniques
10. Determination of net atomic charges in anthraquinone by means of 5-h X-ray diffraction experiment
Czech Academy of Sciences Publication Activity Database
Šlouf, Miroslav
2002-01-01
Roč. 611, 1-3 (2002), s. 139-146 ISSN 0022-2860 R&D Projects: GA ČR GA203/99/M037 Institutional research plan: CEZ:AV0Z4050913 Keywords : net charges * net atomic charges * charge density analysis Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.122, year: 2002
11. Charge Transfer and Catalysis at the Metal Support Interface
Energy Technology Data Exchange (ETDEWEB)
Baker, Lawrence Robert [Univ. of California, Berkeley, CA (United States)
2012-07-31
Kinetic, electronic, and spectroscopic characterization of model Pt–support systems are used to demonstrate the relationship between charge transfer and catalytic activity and selectivity. The results show that charge flow controls the activity and selectivity of supported metal catalysts. This dissertation builds on extensive existing knowledge of metal–support interactions in heterogeneous catalysis. The results show the prominent role of charge transfer at catalytic interfaces to determine catalytic activity and selectivity. Further, this research demonstrates the possibility of selectively driving catalytic chemistry by controlling charge flow and presents solid-state devices and doped supports as novel methods for obtaining electronic control over catalytic reaction kinetics.
12. Transfer Pricing; Charging of head office costs
Energy Technology Data Exchange (ETDEWEB)
Andersen, Joergen
1998-07-01
The key issues discussed in this presentation are (1) What are head office costs?, (2) Why is the charging an area of concern for international companies?, (3) Which part of head office costs should be charged?, (4) OECD guidelines on charging. Head office costs are classified as Shareholder costs, Stewardship costs, Costs related to a specific subsidiary or group of subsidiaries (on call), and Costs related to operational activities in the parent company. The OECD reports of 1984 and 1996 are discussed. In Norsk Hydro's experience, the practising of the OECD guidelines by national authorities are confusing and not consistent over time or across borders. To get a better understanding of how charging of corporate head office costs are dealt with on an international level, Norsk Hydro asked Deloitte and Touche in London to carry out a study on international companies' behaviour. Their conclusions are included.
13. Effects of acid concentration on intramolecular charge transfer ...
rate. Time-dependent density functional theory calculations have been performed to understand the observed spectroscopic results. Keywords. Intramolecular charge transfer; absorption and fluorescence; time resolved fluorescence measurements; acid concentration dependence; time-dependent density functional theory.
14. Charge-transfer collisions for polarized ion sources
International Nuclear Information System (INIS)
Schlachter, A.S.
1983-06-01
Charge-transfer processes relevant to polarized ion sources are discussed and results are summarized. The primary atom discussed is hydrogen, with particulr emphasis on H - formation. Heavier negative ions are briefly discussed
15. First study of the negative binomial distribution applied to higher moments of net-charge and net-proton multiplicity distributions
International Nuclear Information System (INIS)
Tarnowsky, Terence J.; Westfall, Gary D.
2013-01-01
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products (κσ 2 and Sσ) of the net-charge and net-proton distributions in Au + Au collisions at √(s NN )=7.7–200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products κσ 2 and Sσ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between κσ 2 and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus–nucleus collisions
16. Charge transfers in complex transition metal alloys (Ti2Fe)
International Nuclear Information System (INIS)
Abramovici, G.
1998-01-01
We introduce a new non-orthogonal tight-binding model, for complex alloys, in which electronic structure is characterized by charge transfers. We give the analytic calculation of a charge transfer, in which overlapping two-center terms are rigorously taken into account. Then, we apply numerically this result to an approximant phase of a quasicrystal of Ti 2 Fe alloy. This model is more particularly adapted to transition metals, and gives realistic densities of states. (orig.)
17. Charge transfer induced activity of graphene for oxygen reduction
International Nuclear Information System (INIS)
Shen, Anli; Xia, Weijun; Dou, Shuo; Wang, Shuangyin; Zhang, Lipeng; Xia, Zhenhai
2016-01-01
Tetracyanoethylene (TCNE), with its strong electron-accepting ability, was used to dope graphene as a metal-free electrocatalyst for the oxygen reduction reaction (ORR). The charge transfer process was observed from graphene to TCNE by x-ray photoelectron spectroscopy and Raman characterizations. Our density functional theory calculations found that the charge transfer behavior led to an enhancement of the electrocatalytic activity for the ORR. (paper)
18. Controlling the net charge on a nanoparticle optically levitated in vacuum
Science.gov (United States)
Frimmer, Martin; Luszcz, Karol; Ferreiro, Sandra; Jain, Vijay; Hebestreit, Erik; Novotny, Lukas
2017-06-01
Optically levitated nanoparticles in vacuum are a promising model system to test physics beyond our current understanding of quantum mechanics. Such experimental tests require extreme control over the dephasing of the levitated particle's motion. If the nanoparticle carries a finite net charge, it experiences a random Coulomb force due to fluctuating electric fields. This dephasing mechanism can be fully excluded by discharging the levitated particle. Here, we present a simple and reliable technique to control the charge on an optically levitated nanoparticle in vacuum. Our method is based on the generation of charges in an electric discharge and does not require additional optics or mechanics close to the optical trap.
19. Phonons and charge-transfer excitations in HTS superconductors
International Nuclear Information System (INIS)
Bishop, A.R.
1989-01-01
Some of the experimental and theoretical evidence implicating phonons and charge-transfer excitations in HTS superconductors is reviewed. It is suggested that superconductivity may be driven by a synergistic interplay of (anharmonic) phonons and electronic degrees of freedom (e.g., charge fluctuations, excitons). 47 refs., 5 figs
20. Theoretical treatment of charge transfer processes of relevance to astrophysics
Energy Technology Data Exchange (ETDEWEB)
Krstic, P.S.; Stancil, P.C.; Schultz, D.R.
1997-12-01
Charge transfer is an important process in many astrophysical and atmospheric environments. While numerous experimental and theoretical studies exist for H and He targets, data on other targets, particularly metals and molecules, are sparse. Using a variety of theoretical methods and computational techniques the authors are developing methods to estimate the cross sections for electron capture (charge transfer) in slow collisions of low charge state ions with heavy (Mg, Ca, Fe, Co, Ni and Zn) neutrals. In this ongoing work particular attention is paid to ascertaining the importance of double electron capture.
1. Theoretical treatment of charge transfer processes of relevance to astrophysics
International Nuclear Information System (INIS)
Krstic, P.S.; Stancil, P.C.; Schultz, D.R.
1997-12-01
Charge transfer is an important process in many astrophysical and atmospheric environments. While numerous experimental and theoretical studies exist for H and He targets, data on other targets, particularly metals and molecules, are sparse. Using a variety of theoretical methods and computational techniques the authors are developing methods to estimate the cross sections for electron capture (charge transfer) in slow collisions of low charge state ions with heavy (Mg, Ca, Fe, Co, Ni and Zn) neutrals. In this ongoing work particular attention is paid to ascertaining the importance of double electron capture
2. Collisional charging of individual submillimeter particles: Using ultrasonic levitation to initiate and track charge transfer
Science.gov (United States)
Lee, Victor; James, Nicole M.; Waitukaitis, Scott R.; Jaeger, Heinrich M.
2018-03-01
Electrostatic charging of insulating fine particles can be responsible for numerous phenomena ranging from lightning in volcanic plumes to dust explosions. However, even basic aspects of how fine particles become charged are still unclear. Studying particle charging is challenging because it usually involves the complexities associated with many-particle collisions. To address these issues, we introduce a method based on acoustic levitation, which makes it possible to initiate sequences of repeated collisions of a single submillimeter particle with a flat plate, and to precisely measure the particle charge in situ after each collision. We show that collisional charge transfer between insulators is dependent on the hydrophobicity of the contacting surfaces. We use glass, which we modify by attaching nonpolar molecules to the particle, the plate, or both. We find that hydrophilic surfaces develop significant positive charges after contacting hydrophobic surfaces. Moreover, we demonstrate that charging between a hydrophilic and a hydrophobic surface is suppressed in an acidic environment and enhanced in a basic one. Application of an electric field during each collision is found to modify the charge transfer, again depending on surface hydrophobicity. We discuss these results within the context of contact charging due to ion transfer, and we show that they lend strong support to O H- ions as the charge carriers.
3. Collisions of highly stripped ions at MeV energies in gas targets: charge transfer and ionization
International Nuclear Information System (INIS)
Schlachter, A.S.
1980-01-01
Cross sections have been measured for charge transfer and ionization in H 2 and rare-gas targets by fast, highly ionized carbon, iron, niobium, and lead ions in charge states +3 to +59, with energies in the range 0.1 to 4.8 MeV/amu. Experimental results are compared with classical-trajectory calculations; agreement is generally good. For a given target, the cross sections for net ionization reduce to a common curve when plotted as cross section divided by charge state versus energy per nucleon divided by charge state
4. The Properties of the Space-Charge and Net Current Density in Magnetized Plasmas
International Nuclear Information System (INIS)
Hatami, M. M.
2013-01-01
A hydrodynamic model is used to investigate the properties of positive space-charge and net current density in the sheath region of magnetized, collisional plasmas with warm positive ions. It is shown that an increase in the ion-neutral collision frequency, as well as the magnitude of the external magnetic field, leads to an increase in the net current density across the sheath region. The results also show that the accumulation of positive ions in the sheath region increases by increasing the ion-neutral collision frequency and the magnitude of the magnetic field. In addition, it is seen that an increase in the positive ion temperatures causes a decrease in the accumulation of positive ions and the net current density in the sheath region. (basic plasma phenomena)
5. Chemical sensors based on surface charge transfer
Science.gov (United States)
Mohtasebi, Amirmasoud; Kruse, Peter
2018-02-01
The focus of this review is an introduction to chemiresistive chemical sensors. The general concept of chemical sensors is briefly introduced, followed by different architectures of chemiresistive sensors and relevant materials. For several of the most common systems, the fabrication of the active materials used in such sensors and their properties are discussed. Furthermore, the sensing mechanism, advantages, and limitations of each group of chemiresistive sensors are briefly elaborated. Compared to electrochemical sensors, chemiresistive sensors have the key advantage of a simpler geometry, eliminating the need for a reference electrode. The performance of bulk chemiresistors can be improved upon by using freestanding ultra-thin films (nanomaterials) or field effect geometries. Both of those concepts have also been combined in a gateless geometry, where charge transport though a percolation network of nanomaterials is modulated via adsorbate doping.
6. Beam-energy and system-size dependence of dynamical net charge fluctuations
Czech Academy of Sciences Publication Activity Database
Abelev, B. I.; Aggarwal, M. M.; Ahammed, Z.; Anderson, B. D.; Arkhipkin, D.; Averichev, G. S.; Balewski, J.; Barannikova, O.; Barnby, L. S.; Baudot, J.; Baumgart, S.; Beavis, D.R.; Bellwied, R.; Benedosso, F.; Betancourt, M.J.; Betts, R. R.; Bhasin, A.; Bhati, A.K.; Bichsel, H.; Bielčík, Jaroslav; Bielčíková, Jana; Biritz, B.; Bland, L.C.; Bombara, M.; Bonner, B. E.; Botje, M.; Bouchet, J.; Braidot, E.; Brandin, A. V.; Bruna, E.; Bueltmann, S.; Burton, T. P.; Bysterský, Michal; Cai, X.Z.; Caines, H.; Sanchez, M.C.D.; Catu, O.; Cebra, D.; Cendejas, R.; Cervantes, M.C.; Chajecki, Z.; Chaloupka, Petr; Chattopadhyay, S.; Chen, H.F.; Chen, J.H.; Cheng, J.; Cherney, M.; Chikanian, A.; Choi, K.E.; Christie, W.; Clarke, R.F.; Codrington, M.J.M.; Corliss, R.; Cormier, T.M.; Coserea, R. M.; Cramer, J. G.; Crawford, H. J.; Das, D.; Dash, S.; Daugherity, M.; De Silva, L.C.; Dedovich, T. G.; DePhillips, M.; Derevschikov, A.A.; de Souza, R.D.; Didenko, L.; Djawotho, P.; Dunlop, J.C.; Mazumdar, M.R.D.; Edwards, W.R.; Efimov, L.G.; Elhalhuli, E.; Elnimr, M.; Emelianov, V.; Engelage, J.; Eppley, G.; Erazmus, B.; Estienne, M.; Eun, L.; Fachini, P.; Fatemi, R.; Fedorisin, J.; Feng, A.; Filip, P.; Finch, E.; Fine, V.; Fisyak, Y.; Gagliardi, C. A.; Gaillard, L.; Ganti, M. S.; Gangaharan, D.R.; Garcia-Solis, E.J.; Geromitsos, A.; Geurts, F.; Ghazikhanian, V.; Ghosh, P.; Gorbunov, Y.N.; Gordon, A.; Grebenyuk, O.; Grosnick, D.; Grube, B.; Guertin, S.M.; Guimaraes, K.S.F.F.; Gupta, A.; Gupta, N.; Guryn, W.; Haag, B.; Hallman, T.J.; Hamed, A.; Harris, J.W.; He, W.; Heinz, M.; Heppelmann, S.; Hippolyte, B.; Hirsch, A.; Hjort, E.; Hoffman, A.M.; Hoffmann, G.W.; Hofman, D.J.; Hollis, R.S.; Huang, H.Z.; Humanic, T.J.; Igo, G.; Iordanova, A.; Jacobs, P.; Jacobs, W.W.; Jakl, Pavel; Jena, C.; Jin, F.; Jones, C.L.; Jones, P.G.; Joseph, J.; Judd, E.G.; Kabana, S.; Kajimoto, K.; Kang, K.; Kapitán, Jan; Keane, D.; Kechechyan, A.; Kettler, D.; Khodyrev, V.Yu.; Kikola, D.P.; Kiryluk, J.; Kisiel, A.; Klein, S.R.; Knospe, A.G.; Kocoloski, A.; Koetke, D.D.; Kopytine, M.; Korsch, W.; Kotchenda, L.; Kushpil, Vasilij; Kravtsov, P.; Kravtsov, V.I.; Krueger, K.; Krus, M.; Kuhn, C.; Kumar, L.; Kurnadi, P.; Lamont, M.A.C.; Landgraf, J.M.; LaPointe, S.; Lauret, J.; Lebedev, A.; Lednický, Richard; Lee, Ch.; Lee, J.H.; Leight, W.; LeVine, M.J.; Li, N.; Li, C.; Li, Y.; Lin, G.; Lindenbaum, S.J.; Lisa, M.A.; Liu, F.; Liu, J.; Liu, L.; Ljubicic, T.; Llope, W.J.; Longacre, R.S.; Love, W.A.; Lu, Y.; Ludlam, T.; Ma, G.L.; Ma, Y.G.; Mahapatra, D.P.; Majka, R.; Mall, O.I.; Mangotra, L.K.; Manweiler, R.; Margetis, S.; Markert, C.; Matis, H.S.; Matulenko, Yu.A.; McShane, T.S.; Meschanin, A.; Milner, R.; Minaev, N.G.; Mioduszewski, S.; Mischke, A.; Mitchell, J.; Mohanty, B.; Morozov, D.A.; Munhoz, M. G.; Nandi, B.K.; Nattrass, C.; Nayak, T. K.; Nelson, J.M.; Netrakanti, P.K.; Ng, M.J.; Nogach, L.V.; Nurushev, S.B.; Odyniec, G.; Ogawa, A.; Okada, H.; Okorokov, V.; Olson, D.; Pachr, M.; Page, B.S.; Pal, S.K.; Pandit, Y.; Panebratsev, Y.; Panitkin, S.Y.; Pawlak, T.; Peitzmann, T.; Perevoztchikov, V.; Perkins, C.; Peryt, W.; Phatak, S.C.; Poljak, N.; Poskanzer, A.M.; Potukuchi, B.V.K.S.; Prindle, D.; Pruneau, C.; Pruthi, N.K.; Putschke, J.; Raniwala, R.; Raniwala, S.; Ray, R.L.; Redwine, R.; Reed, R.; Ridiger, A.; Ritter, H.G.; Roberts, J.B.; Rogachevskiy, O.V.; Romero, J.L.; Rose, A.; Roy, C.; Ruan, L.; Russcher, M.J.; Sahoo, R.; Sakrejda, I.; Sakuma, T.; Salur, S.; Sandweiss, J.; Sarsour, M.; Schambach, J.; Scharenberg, R.P.; Schmitz, N.; Seger, J.; Selyuzhenkov, I.; Seyboth, P.; Shabetai, A.; Shahaliev, E.; Shao, M.; Sharma, M.; Shi, S.S.; Shi, X.H.; Sichtermann, E.P.; Simon, F.; Singaraju, R.N.; Skoby, M.J.; Smirnov, N.; Snellings, R.; Sorensen, P.; Sowinski, J.; Spinka, H.M.; Srivastava, B.; Stadnik, A.; Stanislaus, T.D.S.; Staszak, D.; Strikhanov, M.; Stringfellow, B.; Suaide, A.A.P.; Suarez, M.C.; Subba, N.L.; Šumbera, Michal; Sun, X.M.; Sun, Y.; Sun, Z.; Surrow, B.; Symons, T.J.M.; de Toledo, A. S.; Takahashi, J.; Tang, A.H.; Tang, Z.; Tarnowsky, T.; Thein, D.; Thomas, J.H.; Tian, J.; Timmins, A.R.; Timoshenko, S.; Tokarev, M. V.; Trainor, T.A.; Tram, V.N.; Trattner, A.L.; Trentalange, S.; Tribble, R. E.; Tsai, O.D.; Ulery, J.; Ullrich, T.; Underwood, D.G.; Van Buren, G.; van Leeuwen, M.; Vander Molen, A.M.; Vanfossen, J.A.; Varma, R.; Vasconcelos, G.S.M.; Vasilevski, I.M.; Vasiliev, A. N.; Videbaek, F.; Vigdor, S.E.; Viyogi, Y. P.; Vokal, S.; Voloshin, S.A.; Wada, M.; Walker, M.; Wang, F.; Wang, G.; Wang, J.S.; Wang, Q.; Wang, X.; Wang, X.L.; Wang, Y.; Webb, G.; Webb, J.C.; Westfall, G.D.; Whitten, C.; Wieman, H.; Wissink, S.W.; Witt, R.; Wu, Y.; Tlustý, David; Xie, W.; Xu, N.; Xu, Q.H.; Xu, Y.; Xu, Z.; Yang, P.; Yepes, P.; Yip, K.; Yoo, I.K.; Yue, Q.; Zawisza, M.; Zbroszczyk, H.; Zhan, W.; Zhang, S.; Zhang, W.M.; Zhang, X.P.; Zhang, Y.; Zhang, Z.; Zhao, Y.; Zhong, C.; Zhou, J.; Zoulkarneev, R.; Zoulkarneeva, Y.; Zuo, J.X.
2009-01-01
Roč. 79, č. 2 (2009), 024906/1-024906/14 ISSN 0556-2813 R&D Projects: GA ČR GA202/07/0079; GA MŠk LC07048 Institutional research plan: CEZ:AV0Z10480505; CEZ:AV0Z10100502 Keywords : NET CHARGE * DYNAMICAL FLUCTUATIONS * HEAVY-ION COLLISIONS Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.477, year: 2009
7. Charge transfer cross sections for dysprosium and cerium
Energy Technology Data Exchange (ETDEWEB)
Adachi, Hajime; Tamura, Koji; Okazaki, Tetsuji; Shibata, Takemasa [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-06-01
Symmetric resonant charge transfer cross sections between singly ionized ions and the parent atoms were measured for dysprosium and cerium in the impact energy of 200-2000eV. The cross sections were determined from the ratio between the number of ions produced by charge transfer and those in primary ion beam. The primary ion beam was produced by a laser ion source in which their atoms were ionized by laser resonant photo-ionization. The slow ions produced by charge transfer and fast primary ions were detected with Faraday cups. The obtained cross sections were (1.82{+-}0.14) x 10{sup -14} cm{sup 2} for dysprosium and (0.88{+-}0.12) x 10{sup -14} cm{sup 2} for cerium in the above energy range. The difference of these values can mostly be explained by considering the electron configurations of these atoms and ions. (author)
8. Charge transfer properties of pentacene adsorbed on silver: DFT study
Energy Technology Data Exchange (ETDEWEB)
N, Rekha T.; Rajkumar, Beulah J. M., E-mail: [email protected] [PG & Research Department of Physics, Lady Doak College, Madurai 625002 (India)
2015-06-24
Charge transfer properties of pentacene adsorbed on silver is investigated using DFT methods. Optimized geometry of pentacene after adsorption on silver indicates distortion in hexagonal structure of the ring close to the silver cluster and deviations in co-planarity of carbon atoms due to the variations in bond angles and dihedral angles. Theoretically simulated absorption spectrum has a symmetric surface plasmon resonance peak around 486nm corresponding to the transfer of charge from HOMO-2 to LUMO. Theoretical SERS confirms the process of adsorption, tilted orientation of pentacene on silver surface and the charge transfers reported. Localization of electron density arising from redistribution of electrostatic potential together with a reduced bandgap of pentacene after adsorption on silver suggests its utility in the design of electro active organic semiconducting devices.
9. Charge transfer cross sections for dysprosium and cerium
International Nuclear Information System (INIS)
Adachi, Hajime; Tamura, Koji; Okazaki, Tetsuji; Shibata, Takemasa
1998-06-01
Symmetric resonant charge transfer cross sections between singly ionized ions and the parent atoms were measured for dysprosium and cerium in the impact energy of 200-2000eV. The cross sections were determined from the ratio between the number of ions produced by charge transfer and those in primary ion beam. The primary ion beam was produced by a laser ion source in which their atoms were ionized by laser resonant photo-ionization. The slow ions produced by charge transfer and fast primary ions were detected with Faraday cups. The obtained cross sections were (1.82±0.14) x 10 -14 cm 2 for dysprosium and (0.88±0.12) x 10 -14 cm 2 for cerium in the above energy range. The difference of these values can mostly be explained by considering the electron configurations of these atoms and ions. (author)
10. Mass and charge transfer within a floating water bridge
Science.gov (United States)
Fuchs, Elmar C.; Agostinho, Luewton L. F.; Eisenhut, Mathias; Woisetschläger, Jakob
2010-11-01
When high voltage is applied to pure water filled into two beakers close to each other, a connection forms spontaneously, giving the impression of a floating water bridge 1-8. This phenomenon is of special interest, since it comprises a number of phenomena currently tackled in modern water science. In this work, the charge and mass transfer through the water bridge are investigated with schlieren visualization and laser interferometry. It can be shown that the addition of a pH dye increases the H+ and OH- production with subsequent electrolysis, whereas schlieren and interferometric methods reveal another mechanism where charge and mass transfer appear to be coupled. Whereas this mechanism seems to be responsible for the electrolysis-less charge and mass transfer in the water bridge, it is increasingly superseded by the electrochemical mechanism with rising conductivity. Thus it can be shown that a pH dye does only indirectly visualize the charge transfer in the water bridge since it is dragged along with the water flow like any other dye, and additionally promotes conventional electrochemical conduction mechanisms, thereby enhancing electrolysis and reducing the masscoupled charge transport and thus destabilizing the bridge.
11. Charge-transfer properties in the gas electron multiplier
International Nuclear Information System (INIS)
Han, Sanghyo; Kim, Yongkyun; Cho, Hyosung
2004-01-01
The charge transfer properties of a gas electron multiplier (GEM) were systematically investigated over a broad range of electric field configurations. The electron collection efficiency and the charge sharing were found to depend on the external fields, as well as on the GEM voltage. The electron collection efficiency increased with the collection field up to 90%, but was essentially independent of the drift field strength. A double conical GEM has a 10% gain increase with time due to surface charging by avalanche ions whereas this effect was eliminated with the cylindrical GEM. The positive-ion feedback is also estimated. (author)
12. Scheduling of Crude Oil Operations in Refinery without Sufficient Charging Tanks Using Petri Nets
Directory of Open Access Journals (Sweden)
Yan An
2017-05-01
Full Text Available A short-term schedule for crude oil operations in a refinery should define and sequence the activities in detail. Each activity involves both discrete-event and continuous variables. The combinatorial nature of the scheduling problem makes it difficult to solve. For such a scheduling problem, charging tanks are a type of critical resources. If the number of charging tanks is not sufficient, the scheduling problem is further complicated. This work conducts a study on the scheduling problem of crude oil operations without sufficient charging tanks. In this case, to make a refinery able to operate, a charging tank has to be in simultaneous charging and feeding to a distiller for some time, called simultaneously-charging-and-feeding (SCF mode, leading to disturbance to the oil distillation in distillers. A hybrid Petri net model is developed to describe the behavior of the system. Then, a scheduling method is proposed to find a schedule such that the SCF mode is minimally used. It is computationally efficient. An industrial case study is given to demonstrate the obtained results.
13. Evaluation of intramolecular charge transfer state of 4-N, N ...
Abstract. Intramolecular charge transfer of 4-N,N-dimethylamino cinnamaldehyde (DMACA) in vacuum and in five different aprotic solvents has been studied by using time-dependent density functional theory. (TDDFT). Polarizable continuum model (PCM) was employed to consider solvent–solute interactions. The potential ...
14. Two-Centre Close-Coupling method in charge transfer
Directory of Open Access Journals (Sweden)
Reza Bagheri
2017-09-01
Full Text Available In the present work, the transition matrix elements as well as differential and total scattering cross-sections for positronium formation in Positron-Hydrogen atom collision and hydrogen formation in Positronium-Hydrogen ion collision, through the charge transfer channel by Two-Centre Close-Coupling method up to a first order approximation have been calculated. The charge transfer collision is assumed to be a three-body reaction, while the projectile is a plane wave. Additionally, the hydrogen and positronium atoms are assumed, initially, to be in their ground states. For the case of charge transfer in the scattering of positron by hydrogen atoms, the differential cross sections are plotted for the energy range of 50eV to 10keV, where the Thomas peak is clearly observable. Finally, the total scattering cross-section for the charge transfer in the collision of Positron-Hydrogen and Positronium-Hydrogen ion are plotted as a function of projectile energies and compared with other methods in the literature.
15. Charge transfer in chromium-transition metal alloys
International Nuclear Information System (INIS)
Kulakowski, K.; Maksymowicz, A.
1984-07-01
The average T-matrix approximation is applied for calculations of charge transfer of 3d-electrons in transition metal alloys. The role of concentration, long-range and short-range atomic order is investigated. The results are in reasonable agreement with experimental data. (author)
16. Charge-Transfer Complexes Studied by Dynamic Force Spectroscopy
Directory of Open Access Journals (Sweden)
Jurriaan Huskens
2013-03-01
Full Text Available In this paper, the strength and kinetics of two charge-transfer complexes, naphthol-methylviologen and pyrene-methylviologen, are studied using dynamic force spectroscopy. The dissociation rates indicate an enhanced stability of the pyrene-methylviologen complex, which agrees with its higher thermodynamic stability compared to naphthol-methylviologen complex.
17. Positron Annihilation in Solid Charge-Transfer Complexes
DEFF Research Database (Denmark)
Lévay, B.; Jansen, P.
1979-01-01
Positron lifetime and angular correlation measurements have been carried out on 1:1 charge-transfer complexes, on their pure donor and acceptor components and on the 1:1 M mechanical mixtures of these components. Complex formation reduced the intensity of the long-lifetime component of the donor...
18. Modeling charge transfer at organic donor-acceptor semiconductor interfaces
NARCIS (Netherlands)
Cakir, Deniz; Bokdam, Menno; de Jong, Machiel Pieter; Fahlman, M.; Brocks, G.
2012-01-01
We develop an integer charge transfer model for the potential steps observed at interfaces between donor and acceptor molecular semiconductors. The potential step can be expressed as the difference between the Fermi energy pinning levels of electrons on the acceptor material and holes on the donor
19. Enhancing SERS by Means of Supramolecular Charge Transfer
Science.gov (United States)
Wong, Eric; Flood, Amar; Morales, Alfredo
2009-01-01
In a proposed method of sensing small quantities of molecules of interest, surface enhanced Raman scattering (SERS) spectroscopy would be further enhanced by means of intermolecular or supramolecular charge transfer. There is a very large potential market for sensors based on this method for rapid detection of chemical and biological hazards. In SERS, the Raman signals (vibrational spectra) of target molecules become enhanced by factors of the order of 108 when those molecules are in the vicinities of nanostructured substrate surfaces that have been engineered to have plasmon resonances that enhance local electric fields. SERS, as reported in several prior NASA Tech Briefs articles and elsewhere, has remained a research tool and has not yet been developed into a practical technique for sensing of target molecules: this is because the short range (5 to 20 nm) of the field enhancement necessitates engineering of receptor molecules to attract target molecules to the nanostructured substrate surfaces and to enable reliable identification of the target molecules in the presence of interferants. Intermolecular charge-transfer complexes have been used in fluorescence-, photoluminescence-, and electrochemistry-based techniques for sensing target molecules, but, until now, have not been considered for use in SERS-based sensing. The basic idea of the proposed method is to engineer receptor molecules that would be attached to nanostructured SERS substrates and that would interact with the target molecules to form receptor-target supramolecular charge-transfer complexes wherein the charge transfer could be photoexcited.
20. Charge transfer devices and their application in physics
Energy Technology Data Exchange (ETDEWEB)
Soroko, L M [Joint Inst. for Nuclear Research, Dubna (USSR)
1979-01-01
Physical properties and technical specifications of charge transfer devices (CTD) are reviewed. The CTD are semiconductor devices based on silicon single crystals. The limiting charge density of the CTD, their efficiency of charge transfer, the background noise and radiation effects are considered. Fast response and low energy consumption are characteristic features of the devices. The application of the CTD in storage devices, real time spectral data processing systems and in streamer chambers is described. The algorithms of topological transformations in the stage of scanning particle track images, which can be realized with the help of the CTD are shortly considered. It is pointed out that applications of the CTD in different fields of science and technology are numerous and expanding.
1. Theory and simulation of charge transfer through DNA - nanotube contacts
International Nuclear Information System (INIS)
Rink, Gunda; Kong Yong; Koslowski, Thorsten
2006-01-01
We address the problem of charge transfer between a single-stranded adenine oligomer and semiconducting boron nitride nanotubes from a theoretical and numerical perspective. The model structures have been motivated by computer simulations; sample geometries are used as the input of an electronic structure theory that is based upon an extended Su-Schrieffer-Heeger Hamiltonian. By analyzing the emerging potential energy surfaces, we obtain hole transfer rates via Marcus' theory of charge transfer. In the presence of nanotubes, these rates exceed those of isolated DNA single strands by a factor of up to 10 4 . This enhancement can be rationalized and quantified as a combination of a template effect and the participation of the tube within a superexchange mechanism
2. Active pixel sensor with intra-pixel charge transfer
Science.gov (United States)
Fossum, Eric R. (Inventor); Mendis, Sunetra (Inventor); Kemeny, Sabrina E. (Inventor)
2004-01-01
An imaging device formed as a monolithic complementary metal oxide semiconductor integrated circuit in an industry standard complementary metal oxide semiconductor process, the integrated circuit including a focal plane array of pixel cells, each one of the cells including a photogate overlying the substrate for accumulating photo-generated charge in an underlying portion of the substrate, a readout circuit including at least an output field effect transistor formed in the substrate, and a charge coupled device section formed on the substrate adjacent the photogate having a sensing node connected to the output transistor and at least one charge coupled device stage for transferring charge from the underlying portion of the substrate to the sensing node.
3. Charge-transfer modified embedded atom method dynamic charge potential for Li-Co-O system.
Science.gov (United States)
Kong, Fantai; Longo, Roberto C; Liang, Chaoping; Nie, Yifan; Zheng, Yongping; Zhang, Chenxi; Cho, Kyeongjae
2017-11-29
To overcome the limitation of conventional fixed charge potential methods for the study of Li-ion battery cathode materials, a dynamic charge potential method, charge-transfer modified embedded atom method (CT-MEAM), has been developed and applied to the Li-Co-O ternary system. The accuracy of the potential has been tested and validated by reproducing a variety of structural and electrochemical properties of LiCoO 2 . A detailed analysis on the local charge distribution confirmed the capability of this potential for dynamic charge modeling. The transferability of the potential is also demonstrated by its reliability in describing Li-rich Li 2 CoO 2 and Li-deficient LiCo 2 O 4 compounds, including their phase stability, equilibrium volume, charge states and cathode voltages. These results demonstrate that the CT-MEAM dynamic charge potential could help to overcome the challenge of modeling complex ternary transition metal oxides. This work can promote molecular dynamics studies of Li ion cathode materials and other important transition metal oxides systems that involve complex electrochemical and catalytic reactions.
4. The charge transfer structure and effective energy transfer in multiplayer assembly film
International Nuclear Information System (INIS)
Li Mingqiang; Jian Xigao
2005-01-01
Charge transfer multiplayer films have been prepared by layer-by-layer self-assembly technique. The films incorporate the rare-earth-containing polyoxometalate K 11 [Eu{PW 11 O 39 } 2 ].nH 2 O and the rich electron polyelectrolyte poly(3-viny-1-methyl-pyridine) quaternary ammonium and display a linear increase in the absorption and film thickness with the number of deposition cycles. Ultraviolet and visible absorption spectra, atomic force micrographs, small-angle X-ray reflectivity measurements, and photoluminescence spectra were used to determine the structure of films. Linear and regular multilayer growth was observed. We can observe the formation of charge transfer complex compound in multiplayer by layer-by-layer assembly method. Most importantly, the luminescence spectra show the charge transfer band in assembly films, which suggest that energy could be effectively transferred to rare earth ions in assembly multiplayer films
5. Measurement of net electric charge and dipole moment of dust aggregates in a complex plasma.
Science.gov (United States)
Yousefi, Razieh; Davis, Allen B; Carmona-Reyes, Jorge; Matthews, Lorin S; Hyde, Truell W
2014-09-01
Understanding the agglomeration of dust particles in complex plasmas requires knowledge of basic properties such as the net electrostatic charge and dipole moment of the dust. In this study, dust aggregates are formed from gold-coated mono-disperse spherical melamine-formaldehyde monomers in a radiofrequency (rf) argon discharge plasma. The behavior of observed dust aggregates is analyzed both by studying the particle trajectories and by employing computer models examining three-dimensional structures of aggregates and their interactions and rotations as induced by torques arising from their dipole moments. These allow the basic characteristics of the dust aggregates, such as the electrostatic charge and dipole moment, as well as the external electric field, to be determined. It is shown that the experimental results support the predicted values from computer models for aggregates in these environments.
6. Study of charge transfer reactions in a microbial fuel cell
Energy Technology Data Exchange (ETDEWEB)
Martin, E.; Savadogo, O. [Ecole Polytechnique, Montreal, PQ (Canada). Dept. de Genie Chimique; National Research Council of Canada, Montreal, PQ (Canada). Biotechnology Research Inst.; Tartakovsky, B. [National Research Council of Canada, Montreal, PQ (Canada). Biotechnology Research Inst.
2008-07-01
Electron transfer reactions in a microbial fuel cell (MFC) were evaluated. The MFC was inoculated with anaerobic mesophilic sludge and operated with carbon felt, carbon cloth, and platinum (Pt) coated carbon cloth. The MFC was then fed with either acetate or glucose as a source of fuel and operated at a temperature of 25 degrees C and a pH of 7. Scanning electron microscopy (SEM) micrographs demonstrated that the micro-organisms colonized the anodes. Cyclic voltammetry and polarization tests were conducted using different fractions of the anodophilic biofilm in order to determine charge transfer routes. The study characterized the electron transfer mechanisms used by the exoelectrogenic micro-organisms to produce electricity. It was concluded that further research is needed to characterize reaction transfer routes. 2 refs., 1 fig.
7. Charge transfer in pi-stacked systems including DNA
International Nuclear Information System (INIS)
Siebbeles, L.D.A.
2003-01-01
Charge migration in DNA is a subject of intense current study motivated by long-range detection of DNA damage and the potential application of DNA as a molecular wire in nanoscale electronic devices. A key structural element, which makes DNA a medium for long-range charge transfer, is the array of stacked base pairs in the interior of the double helix. The overlapping pi-orbitals of the nucleobases provide a pathway for motion of charge carriers generated on the stack. This 'pi-pathway' resembles the columnarly stacked macrocyclic cores in discotic materials such as triphenylenes. The structure of these pi-stacked systems is highly disordered with dynamic fluctuations occurring on picosecond to nanosecond time scales. Theoretical calculations, concerning the effects of structural disorder and nucleobase sequence in DNA, on the dynamics of charge carriers are presented. Electronic couplings and localization energies of charge carriers were calculated using density functional theory (DFT). Results for columnarly stacked triphenylenes and DNA nucleobases are compared. The results are used to provide insight into the factors that control the mobility of charge carriers. Further, experimental results on the site-selective oxidation of guanine nucleobases in DNA (hot spots for DNA damage) are analyzed on basis of the theoretical results
8. Charge transfer in conjugated oligomers encapsulated into carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Almadori, Y.; Alvarez, L.; Michel, T.; Le Parc, R.; Bantignies, J.L.; Hermet, P.; Sauvajol, J.L. [Laboratoire Charles Coulomb UMR 5521, Universite Montpellier 2, 34095 Montpellier (France); Laboratoire Charles Coulomb UMR 5521, CNRS, 34095 Montpellier (France); Arenal, R. [Laboratoire d' Etude des Microstructures, CNRS-ONERA, 92322 Chatillon (France); Laboratorio de Microscopias Avanzadas, Instituto de Nanociencia de Aragon, U. Zaragoza, 50018 Zaragoza (Spain); Babaa, R. [Laboratoire de Chimie des Surfaces et Interfaces, CEA, IRAMIS, SPCSI, 91191 Gif-sur-Yvette Cedex (France); Chemical Engineering Department, University of Technology PETRONAS, UTP, Ipoh-Perak (Malaysia); Jouselme, B.; Palacin, S. [Laboratoire de Chimie des Surfaces et Interfaces, CEA, IRAMIS, SPCSI, 91191 Gif-sur-Yvette Cedex (France)
2011-11-15
This study deals with a hybrid system consisting in quaterthiophene derivative encapsulated inside single-walled and multi-walled carbon nanotubes. Investigations of the encapsulation step are performed by transmission electron microscopy. Raman spectroscopy data point out different behaviors depending on the laser excitation energy with respect to the optical absorption of quaterthiophene. At low excitation energy (far from the oligomer resonance window) there is no significant modification of the Raman spectra before and after encapsulation. By contrast, at high excitation energy (close to the oligomer resonance window), Raman spectra exhibit a G-band shift together with an important RBM intensity loss, suggesting a significant charge transfer between the inserted molecule and the host nanotubes. Those results suggest a photo induced process leading to a significant charge transfer. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
9. Barrier discharge. The transferred charge and ozone synthesis
International Nuclear Information System (INIS)
Gibalov, V.I.; Samoilovich, V.G.
1991-01-01
We have undertaken an experimental investigation of the influence of the conditions of barrier discharge implementation such as: the discharge gap value, the type of gas, and the polarity and dielectric permittivity of the dielectric electrode on the value of charge transferred in a micro-discharge. It is shown that the increase in the specific capacitance of the electrodes leads to proportional increase in the transferred charge value, reaching 100-200 nC in a discharge gap 1 mm, in air. In this case the amplitude and duration of a current pulse in the microdischarge reach, respectively, 10 to 15 A and 40 ns. It is also demonstrated that in air with increase in the discharge gap value one can observe a decrease in the efficiency of the ozone synthesis whereas in oxygen there exists a more complicated dependence: the maximum of efficiency is observed at a discharge gap value of 0.7 to 1.0 mm. (orig.)
10. Quasi-resonant K-K charge transfer
International Nuclear Information System (INIS)
Hagmann, S.; Cocke, C.L.; Richard, P.; Skutlartz, A.; Kelbch, S.; Schmidt-Boecking, H.; Schuch, R.
1983-01-01
The impact parameter dependence, P(b), of single and double K to K charge transfer have been deduced from the coincidences between K-Auger electrons and scattered particles for F 9+ + Ne and F 9+ + Ne collisions at 10 MeV and 4.4 MeV. The 4.4 MeV single K-K transfer probability exhibits oscillations with b. The P(b) for delta-electron emission is also reported. To obtain more details on the mechanism, K-Auger electron-Ne recoil ion coincidences are measured for both F 8+ and F 9+ projectiles. The relative amounts of recoil ions and of satellite and hypersatellite Auger transitions vary substantially with projectile charge state. 11 references, 11 figures
11. Transfer of momentum, mass and charge in heavy ion collisions
International Nuclear Information System (INIS)
Beck, F.; Feldmeier, H.; Dworzecka, M.
1979-01-01
A model for the first two phases of heavy ion collisions based on the transport of single nucleons through the window between the two scattering nuclei is described in some detail. It is pointed out that the model can account simultaneously for a large portion of the energy transfer from relative to intrinsic motion and for the observed variances in mass and charge numbers for reaction times up to the order of 10 -21 s. (P.L.)
12. Superconductivity and charge transfer excitations in high Tc superconductors
International Nuclear Information System (INIS)
Balseiro, C.A.; Alascio, B.; Gagliano, E.; Rojo, A.
1988-01-01
We present some numerical results to show that in a simple model which includes Cu 3d and O 2p orbitals together with inter and intra atomic correlations pairing between holes can occur due to charge transfer excitations. We present also a simple approximation to derive an effective Hamiltonian containing an interaction between particles which is attractive for some values of the different microscopic parameters
13. Momentum transfer in relativistic heavy ion charge-exchange reactions
Science.gov (United States)
Townsend, L. W.; Wilson, J. W.; Khan, F.; Khandelwal, G. S.
1991-01-01
Relativistic heavy ion charge-exchange reactions yield fragments (Delta-Z = + 1) whose longitudinal momentum distributions are downshifted by larger values than those associated with the remaining fragments (Delta-Z = 1, -2,...). Kinematics alone cannot account for the observed downshifts; therefore, an additional contribution from collision dynamics must be included. In this work, an optical model description of collision momentum transfer is used to estimate the additional dynamical momentum downshift. Good agreement between theoretical estimates and experimental data is obtained.
14. "Inverted" Solvent Effect on Charge Transfer in the Excited State.
Science.gov (United States)
Nau; Pischel
1999-10-04
Faster in cyclohexane than in acetonitrile is the fluorescence quenching of the azoalkane 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) by amines and sulfides. Although this photoreaction is induced by charge transfer (CT; see picture) and exciplexes are formed, the increase in the dipole moment of the exciplex is not large enough to offset the solvent stabilization of the excited reactants, and an "inverted" solvent effect results.
15. Interfacial Charge Transfer States in Condensed Phase Systems
Science.gov (United States)
Vandewal, Koen
2016-05-01
Intermolecular charge transfer (CT) states at the interface between electron-donating (D) and electron-accepting (A) materials in organic thin films are characterized by absorption and emission bands within the optical gap of the interfacing materials. CT states efficiently generate charge carriers for some D-A combinations, and others show high fluorescence quantum efficiencies. These properties are exploited in organic solar cells, photodetectors, and light-emitting diodes. This review summarizes experimental and theoretical work on the electronic structure and interfacial energy landscape at condensed matter D-A interfaces. Recent findings on photogeneration and recombination of free charge carriers via CT states are discussed, and relations between CT state properties and optoelectronic device parameters are clarified.
16. Plasma effect on tunnelling, charge transfer and transient quasimolecular states
International Nuclear Information System (INIS)
Fisher, D V
2003-01-01
The influence of a dense plasma environment on electron tunnelling between two ion potential wells in collectivized states and in charge-transfer collisions is studied. We show that the tunnelling probabilities in dilute plasma (in a close ion-ion collision) and in dense plasma differ strongly. The difference is due to the mixing between Stark components of donor-ion energy levels, caused by the field of spectator ions in a dense plasma. The mixing is determined by an angle α between the nearest-neighbour ion field and the total electric field acting on the donor ion. In close ion-ion binary collisions the mixing may be considered weak. However, for most plasma ions charge transfer, electron state collectivization and transient quasimolecule formation are strongly affected by the field of spectator ions. We derive approximate analytical expressions for the distribution function of α in an ideal plasma and perform molecular dynamics simulations to find the distribution function of α in both ideal and nonideal plasmas. Both α-dependent and average mixing coefficients are determined. We have found that the mixing is strong, even in ideal plasmas, and increases further with an increase in plasma nonideality. It is shown that there is no resonant charge transfer in dense plasmas. The applicability of a transient 'dicenter' quasimolecule model for dense plasmas is discussed
17. Surface Charge Transfer Doping of Monolayer Phosphorene via Molecular Adsorption.
Science.gov (United States)
He, Yuanyuan; Xia, Feifei; Shao, Zhibin; Zhao, Jianwei; Jie, Jiansheng
2015-12-03
Monolayer phosphorene has attracted much attention owing to its extraordinary electronic, optical, and structural properties. Rationally tuning the electrical transport characteristics of monolayer phosphorene is essential to its applications in electronic and optoelectronic devices. Herein, we study the electronic transport behaviors of monolayer phosphorene with surface charge transfer doping of electrophilic molecules, including 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ), NO2, and MoO3, using density functional theory combined with the nonequilibrium Green's function formalism. F4TCNQ shows optimal performance in enhancing the p-type conductance of monolayer phosphorene. Static electronic properties indicate that the enhancement is originated from the charge transfer between adsorbed molecule and phosphorene layer. Dynamic transport behaviors demonstrate that additional channels for hole transport in host monolayer phosphorene were generated upon the adsorption of molecule. Our work unveils the great potential of surface charge transfer doping in tuning the electronic properties of monolayer phosphorene and is of significance to its application in high-performance devices.
18. Doping Phosphorene with Holes and Electrons through Molecular Charge Transfer.
Science.gov (United States)
Vishnoi, Pratap; Rajesh, S; Manjunatha, S; Bandyopadhyay, Arkamita; Barua, Manaswee; Pati, Swapan K; Rao, C N R
2017-11-03
An important aspect of phosphorene, the novel two-dimensional semiconductor, is whether holes and electrons can both be doped in this material. Some reports found that only electrons can be preferentially doped into phosphorene. There are some theoretical calculations showing charge-transfer interaction with both tetrathiafulvalene (TTF) and tetracyanoethylene (TCNE). We have carried out an investigation of chemical doping of phosphorene by a variety of electron donor and acceptor molecules, employing both experiment and theory, Raman scattering being a crucial aspect of the study. We find that both electron acceptors and donors interact with phosphorene by charge-transfer, with the acceptors having more marked effects. All the three Raman bands of phosphorene soften and exhibit band broadening on interaction with both donor and acceptor molecules. First-principles calculations establish the occurrence of charge-transfer between phosphorene with donors as well as acceptors. The absence of electron-hole asymmetry is noteworthy. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
19. Energy and charge transfer in ionized argon coated water clusters
International Nuclear Information System (INIS)
Kočišek, J.; Lengyel, J.; Fárník, M.; Slavíček, P.
2013-01-01
We investigate the electron ionization of clusters generated in mixed Ar-water expansions. The electron energy dependent ion yields reveal the neutral cluster composition and structure: water clusters fully covered with the Ar solvation shell are formed under certain expansion conditions. The argon atoms shield the embedded (H 2 O) n clusters resulting in the ionization threshold above ≈15 eV for all fragments. The argon atoms also mediate more complex reactions in the clusters: e.g., the charge transfer between Ar + and water occurs above the threshold; at higher electron energies above ∼28 eV, an excitonic transfer process between Ar + * and water opens leading to new products Ar n H + and (H 2 O) n H + . On the other hand, the excitonic transfer from the neutral Ar* state at lower energies is not observed although this resonant process was demonstrated previously in a photoionization experiment. Doubly charged fragments (H 2 O) n H 2 2+ and (H 2 O) n 2+ ions are observed and Intermolecular Coulomb decay (ICD) processes are invoked to explain their thresholds. The Coulomb explosion of the doubly charged cluster formed within the ICD process is prevented by the stabilization effect of the argon solvent
20. Efficient charge generation by relaxed charge-transfer states at organic interfaces
KAUST Repository
Vandewal, Koen
2013-11-17
Interfaces between organic electron-donating (D) and electron-accepting (A) materials have the ability to generate charge carriers on illumination. Efficient organic solar cells require a high yield for this process, combined with a minimum of energy losses. Here, we investigate the role of the lowest energy emissive interfacial charge-transfer state (CT1) in the charge generation process. We measure the quantum yield and the electric field dependence of charge generation on excitation of the charge-transfer (CT) state manifold via weakly allowed, low-energy optical transitions. For a wide range of photovoltaic devices based on polymer:fullerene, small-molecule:C60 and polymer:polymer blends, our study reveals that the internal quantum efficiency (IQE) is essentially independent of whether or not D, A or CT states with an energy higher than that of CT1 are excited. The best materials systems show an IQE higher than 90% without the need for excess electronic or vibrational energy. © 2014 Macmillan Publishers Limited.
1. A new technique for the study of charge transfer in multiply charged ion-ion collisions
International Nuclear Information System (INIS)
Shinpaugh, J.L.; Meyer, F.W.; Datz, S.
1994-01-01
While large cross sections (>10 -16 cm 2 ) have been predicted for resonant charge transfer in ion-ion collisions, no experimental data exist for multiply charged systems. A novel technique is being developed at the ORNL ECR facility to allow study of symmetric charge exchange in multiply charged ion-ion collisions using a single ion source. Specific intra-beam charge transfer collisions occurring in a well-defined interaction region labeled by negative high voltage are identified and analyzed by electrostatic analysis in combination with ion time-of-flight coincidence detection of the collision products. Center-of-mass collision energies from 400 to 1000 eV are obtained by varying source and labeling-cell voltages. In addition, by the introduction of a target gas into the high-voltage cell, this labeling-voltage method allows measurement of electron-capture and -loss cross sections for ion-atom collisions. Consequently, higher collision energies can be investigated without the requirement of placing the ECR source on a high-voltage platform
2. Efficient charge generation by relaxed charge-transfer states at organic interfaces
KAUST Repository
Vandewal, Koen; Albrecht, Steve N.; Hoke, Eric T.; Graham, Kenneth; Widmer, Johannes; Douglas, Jessica D.; Schubert, Marcel; Mateker, William R.; Bloking, Jason T.; Burkhard, George F.; Sellinger, Alan; Frechet, Jean; Amassian, Aram; Riede, Moritz Kilian; McGehee, Michael D.; Neher, Dieter; Salleo, Alberto
2013-01-01
Interfaces between organic electron-donating (D) and electron-accepting (A) materials have the ability to generate charge carriers on illumination. Efficient organic solar cells require a high yield for this process, combined with a minimum of energy losses. Here, we investigate the role of the lowest energy emissive interfacial charge-transfer state (CT1) in the charge generation process. We measure the quantum yield and the electric field dependence of charge generation on excitation of the charge-transfer (CT) state manifold via weakly allowed, low-energy optical transitions. For a wide range of photovoltaic devices based on polymer:fullerene, small-molecule:C60 and polymer:polymer blends, our study reveals that the internal quantum efficiency (IQE) is essentially independent of whether or not D, A or CT states with an energy higher than that of CT1 are excited. The best materials systems show an IQE higher than 90% without the need for excess electronic or vibrational energy. © 2014 Macmillan Publishers Limited.
3. Dissociative electron attachment and charge transfer in condensed matter
International Nuclear Information System (INIS)
Bass, A.D.; Sanche, L.
2003-01-01
Experiments using energy-selected beams of electrons incident from vacuum upon thin vapour deposited solids show that, as in the gas-phase, scattering cross sections at low energies are dominated by the formation of temporary negative ions (or resonances) and that molecular damage may be effected via dissociative electron attachment (DEA). Recent results also show that charge transfer between anionic states of target molecules and their environment is often crucial in determining cross sections for electron driven processes. Here, we review recent work from our laboratory, in which charge transfer is observed. For rare gas solids, electron exchange between the electron-exciton complex and either a metal substrate or co-adsorbed molecule enhances the desorption of metastable atoms and/or molecular dissociation. We discuss how transient electron capture by surface electron states of a substrate and subsequent electron transfer to a molecular adsorbate enhances the effective cross sections for DEA. We also consider the case of DEA to CF 2 Cl 2 condensed on water and ammonia ices, where electron exchange between pre-solvated electron states of ice and transient molecular anions can also increase DEA cross sections. Electron transfer from molecular resonances into pre-solvated electron states of ice is also discussed
4. Charge Transfer Channels in Formation of Exciplex in Polymer Blends
Science.gov (United States)
Dou, Fei; Zhang, Xin-Ping
2011-09-01
The strong dependence of photoluminescence of charge transfer excited states or exciplex in a blend film of poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9'-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4- phenylenediamine) (PFB) on the excitation wavelengths and morphology is investigated. The experimental results reveal that electron transfer in the LUMOs from PFB to F8BT is more efficient than hole transfer in the HOMOs from PFB to F8BT for the formation of exciplex at the interfacial junctions between these two types of molecules in the blend film. Furthermore, energy transfer from the blue-emitting PFB to the green-emitting F8BT at the interfaces introduces an additional two-step channel and thus enhances the formation of an exciplex. This is important for understanding of charge generation and separation in organic bulk heterojunctions and for design of optoelectronic devices.
5. Charge Transfer Channels in Formation of Exciplex in Polymer Blends
International Nuclear Information System (INIS)
Dou Fei; Zhang Xin-Ping
2011-01-01
The strong dependence of photoluminescence of charge transfer excited states or exciplex in a blend film of poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9'-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4- phenylenediamine) (PFB) on the excitation wavelengths and morphology is investigated. The experimental results reveal that electron transfer in the LUMOs from PFB to F8BT is more efficient than hole transfer in the HOMOs from PFB to F8BT for the formation of exciplex at the interfacial junctions between these two types of molecules in the blend film. Furthermore, energy transfer from the blue-emitting PFB to the green-emitting F8BT at the interfaces introduces an additional two-step channel and thus enhances the formation of an exciplex. This is important for understanding of charge generation and separation in organic bulk heterojunctions and for design of optoelectronic devices. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
6. Quantum information transfer between topological and conventional charge qubits
International Nuclear Information System (INIS)
Li Jun; Zou Yan
2016-01-01
We propose a scheme to realize coherent quantum information transfer between topological and conventional charge qubits. We first consider a hybrid system where a quantum dot (QD) is tunnel-coupled to a semiconductor Majorana-hosted nanowire (MNW) via using gated control as a switch, the information encoded in the superposition state of electron empty and occupied state can be transferred to each other through choosing the proper interaction time to make measurements. Then we consider another system including a double QDs and a pair of parallel MNWs, it is shown that the entanglement information transfer can be realized between the two kinds of systems. We also realize long distance quantum information transfer between two quantum dots separated by an MNW, by making use of the nonlocal fermionic level formed with the pared Majorana feimions (MFs) emerging at the two ends of the MNW. Furthermore, we analyze the teleportationlike electron transfer phenomenon predicted by Tewari et al. [Phys. Rev. Lett. 100, 027001 (2008)] in our considered system. Interestingly, we find that this phenomenon exactly corresponds to the case that the information encoded in one QD just returns back to its original place during the dynamical evolution of the combined system from the perspective of quantum state transfer. (paper)
7. Charge transfer between O6+ and atomic hydrogen
Science.gov (United States)
Wu, Y.; Stancil, P. C.; Liebermann, H. P.; Buenker, R. J.; Schultz, D. R.; Hui, Y.
2011-05-01
The charge exchange process has been found to play a dominant role in the production of X-rays and/or EUV photons observed in cometary and planetary atmospheres and from the heliosphere. Charge transfer cross sections, especially state-selective cross sections, are necessary parameters in simulations of X-ray emission. In the present work, charge transfer due to collisions of ground state O6+(1s2 1 S) with atomic hydrogen has been investigated theoretically using the quantum-mechanical molecular-orbital close-coupling method (QMOCC). The multi-reference single- and double-excitation configuration interaction approach (MRDCI) has been applied to compute the adiabatic potential and nonadiabatic couplings, and the atomic basis sets used have been optimized with the method proposed previously to obtain precise potential data. Total and state-selective cross sections are calculated for energies between 10 meV/u and 10 keV/u. The QMOCC results are compared to available experimental and theoretical data as well as to new atomic-orbital close-coupling (AOCC) and classical trajectory Monte Carlo (CTMC) calculations. A recommended set of cross sections, based on the MOCC, AOCC, and CTMC calculations, is deduced which should aid in X-ray modeling studies.
8. Super-iron Nanoparticles with Facile Cathodic Charge Transfer
Energy Technology Data Exchange (ETDEWEB)
M Farmand; D Jiang; B Wang; S Ghosh; D Ramaker; S Licht
2011-12-31
Super-irons contain the + 6 valence state of iron. One advantage of this is that it provides a multiple electron opportunity to store additional battery charge. A decrease of particle size from the micrometer to the nanometer domain provides a higher surface area to volume ratio, and opportunity to facilitate charge transfer, and improve the power, voltage and depth of discharge of cathodes made from such salts. However, super-iron salts are fragile, readily reduced to the ferric state, with both heat and contact with water, and little is known of the resultant passivating and non-passivating ferric oxide products. A pathway to decrease the super-iron particle size to the nano-domain is introduced, which overcomes this fragility, and retains the battery capacity advantage of their Fe(VI) valence state. Time and power controlled mechanosynthesis, through less aggressive, dry ball milling, leads to facile charge transfer of super-iron nanoparticles. Ex-situ X-ray Absorption Spectroscopy is used to explore the oxidation state and structure of these iron oxides during discharge and shows the significant change in stability of the ferrate structure to lower oxidation state when the particle size is in the nano-domain.
9. StorNet: Integrated Dynamic Storage and Network Resource Provisioning and Management for Automated Data Transfers
International Nuclear Information System (INIS)
Gu Junmin; Natarajan, Vijaya; Shoshani, Arie; Sim, Alex; Katramatos, Dimitrios; Liu Xin; Yu Dantong; Bradley, Scott; McKee, Shawn
2011-01-01
StorNet is a joint project of Brookhaven National Laboratory (BNL) and Lawrence Berkeley National Laboratory (LBNL) to research, design, and develop an integrated end-to-end resource provisioning and management framework for high-performance data transfers. The StorNet framework leverages heterogeneous network protocols and storage types in a federated computing environment to provide the capability of predictable, efficient delivery of high-bandwidth data transfers for data intensive applications. The framework incorporates functional modules to perform such data transfers through storage and network bandwidth co-scheduling, storage and network resource provisioning, and performance monitoring, and is based on LBNL's BeStMan/SRM, BNL's TeraPaths, and ESNet's OSCARS systems.
10. Collective charge and mass transfer in heavy ion reactions
International Nuclear Information System (INIS)
Hahn, J.
1982-01-01
In this thesis the dynamics of the charge and mass asymmetry degree of freedom was studied in the framework of the fragmentation theory by means of a time-dependent Schroedinger equation. New is the introduction of a friction potential which describes the coupling of these collective degrees of freedom to the not explicitely treated other collective respectively internal degrees of freedom. Thereby it was shown that the measured widths of the isobaric charge distributions in the 86 Kr+sup(92,98)Mo reaction can be explained mainly by the quantum mechanical uncertainty in the charge asymmetry degree of freedom. The charge equilibration occurring at the begin of a deep inelastic collision can therefore by considered as a quantum mechanical, collective, damped motion which is connected with the excitation of the isovector giant dipole resonance of the nucleus-nucleus system. The study of the mass transfer in the reactions 132 Xe+ 120 Sn and 86 Kr+ 166 Er shows, how important at the begin of a deep inelastic collision shell structures and their conservation are for a large part of the reaction, even if the elemental distribution show no maxima in the region of magic shell closures. The experimental width are up to 10 MeV/A well described under conservation of the shell structure. (orig./HSI) [de
11. Charge Transfer in Collisions of S^4+ with H.
Science.gov (United States)
Stancil, P. C.; Turner, A. R.; Cooper, D. L.; Schultz, D. R.; Rakovic, M. J.; Fritsch, W.; Zygelman, B.
2001-05-01
Charge transfer processes due to collisions of ground state S^4+ ions with atomic hydrogen were investigated for energies between 1 meV/u and 10 MeV/u using the quantum-mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling, classical trajectory Monte Carlo (CTMC), and continuum distorted wave methods. The MOCC calculations utilized ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. A number of variants of the CTMC approach were explored, including different momentum and radial distributions for the initial state, as well as effective charge and quantum-defect models to determine the corresponding quantum state after capture into final partially-stripped S^3+ excited classical states. Hydrogen target isotope effects were explored and rate coefficients for temperatures between 100 and 10^6 K will be presented
12. Charge transfer in proton-hydrogen collisions under Debye plasma
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Arka [Department of Mathematics, Burdwan University, Golapbag, Burdwan 713 104, West Bengal (India); Kamali, M. Z. M. [Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur (Malaysia); Ghoshal, Arijit, E-mail: [email protected] [Department of Mathematics, Burdwan University, Golapbag, Burdwan 713 104, West Bengal (India); Department of Mathematics, Kazi Nazrul University, B.C.W. Campus, Asansol 713 304, West Bengal (India); Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur (Malaysia); Ratnavelu, K. [Department of Mathematics, Kazi Nazrul University, B.C.W. Campus, Asansol 713 304, West Bengal (India)
2015-02-15
The effect of plasma environment on the 1s → nlm charge transfer, for arbitrary n, l, and m, in proton-hydrogen collisions has been investigated within the framework of a distorted wave approximation. The effect of external plasma has been incorporated using Debye screening model of the interacting charge particles. Making use of a simple variationally determined hydrogenic wave function, it has been possible to obtain the scattering amplitude in closed form. A detailed study has been made to investigate the effect of external plasma environment on the differential and total cross sections for electron capture into different angular momentum states for the incident energy in the range of 20–1000 keV. For the unscreened case, our results are in close agreement with some of the most accurate results available in the literature.
13. Polarization and charge transfer in the hydration of chloride ions
International Nuclear Information System (INIS)
Zhao Zhen; Rogers, David M.; Beck, Thomas L.
2010-01-01
A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The quantum theory of atoms in molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. The clusters extracted from the AMOEBA simulations exhibit high probabilities of anisotropic solvation for chloride ions in bulk water. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared to the quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2-level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.
14. Charge transfer in gold--alkali-metal systems
International Nuclear Information System (INIS)
Watson, R.E.; Weinert, M.
1994-01-01
Based on conventional electronegativity arguments, gold--alkali-metal compounds are expected to be among the most ''ionic'' of metallic compounds. The concepts of ionicity and charge transfer are difficult to quantify. However, the changes in bonding in the 50/50 Au--alkali-metal systems between the elemental metals and the compounds are so severe that observations can readily be made concerning their character. The results, as obtained from self-consistent electronic-structure calculations, lead to the apparently odd observation that the electron density at the alkali-metal sites in the compound increases significantly and this involves high l componennts in the charge density. This increase, however, can be attributed to Au-like orbitals spatially overlapping the alkali-metal sites. In a chemical sense, it is reasonable to consider the alkali-metal transferring charge to these Au orbitals. While normally the difference in heats of formation between muffin-tin and full-potential calculations for transition-metal--transition-metal and transition-metal--main-group (e.g., Al) compounds having high site symmetry are small, for the gold--alkali-metal systems, the changes in bonding in the compounds cause differences of ∼0.5 eV/atom between the two classes of potential. Any serious estimate of the electronic structure in these systems must account for these aspherical bonding charges. The origin of the semiconducting behavior of the heavy-alkali-metal Au compounds is shown to arise from a combination of the Au-Au separations and the ionic character of the compounds; the light-alkali-metal Au compounds, with their smaller Au-Au separations, do not have a semiconducting gap. Core-level shifts and isomer shifts are also briefly discussed
15. Quantum computing based on space states without charge transfer
International Nuclear Information System (INIS)
Vyurkov, V.; Filippov, S.; Gorelik, L.
2010-01-01
An implementation of a quantum computer based on space states in double quantum dots is discussed. There is no charge transfer in qubits during a calculation, therefore, uncontrolled entanglement between qubits due to long-range Coulomb interaction is suppressed. Encoding and processing of quantum information is merely performed on symmetric and antisymmetric states of the electron in double quantum dots. Other plausible sources of decoherence caused by interaction with phonons and gates could be substantially suppressed in the structure as well. We also demonstrate how all necessary quantum logic operations, initialization, writing, and read-out could be carried out in the computer.
16. Negative thermal expansion induced by intermetallic charge transfer.
Science.gov (United States)
Azuma, Masaki; Oka, Kengo; Nabetani, Koichiro
2015-06-01
Suppression of thermal expansion is of great importance for industry. Negative thermal expansion (NTE) materials which shrink on heating and expand on cooling are therefore attracting keen attention. Here we provide a brief overview of NTE induced by intermetallic charge transfer in A-site ordered double perovskites SaCu 3 Fe 4 O 12 and LaCu 3 Fe 4- x Mn x O 12 , as well as in Bi or Ni substituted BiNiO 3 . The last compound shows a colossal dilatometric linear thermal expansion coefficient exceeding -70 × 10 -6 K -1 near room temperature, in the temperature range which can be controlled by substitution.
17. Collisions of fast multicharged ions in gas targets: charge transfer and ionization
International Nuclear Information System (INIS)
Schlachter, A.S.
1981-05-01
Measurements of cross sections for charge transfer and ionization of H 2 and rare-gas targets have been made with fast, highly stripped projectiles in charge states as high as 59+. We have found an empirical scaling rule for electron-capture cross section in H 2 valid at energies above 275 keV/amu. Similar scaling might exist for other target gases. Cross sections are generally in good agreement with theory. We have found a scaling rule for electron loss from H in collisions with a fast highly stripped projectile, based on Olson's classical-trajectory Monte-Carlo calculations, and confirmed by measurements in an H 2 target. We have found a similar scaling rule for net ionization of rare-gas targets, based on Olson's CTMC calculations and the independent-electron model. Measurements are essentially consistent with the scaled cross sections. Calculations and measurements of recoil-ion charge-state spectra show large cross sections for the production of highly charged slow recoil ions
18. Charge transfer between acenes and PbS nanocrystals
Energy Technology Data Exchange (ETDEWEB)
Dissanayake, D M N M [Solid State Electronics Laboratory, University of Michigan, Ann Arbor, MI 48109-2122 (United States); Hatton, R A [Department of Chemistry, University of Warwick, Coventry CV4 7AL (United Kingdom); Lutz, T [Departments of Chemistry and Physics, Imperial College, London SW7 2AY (United Kingdom); Curry, R J; Silva, S R P [Advanced Technology Institute, University of Surrey, Guildford GU2 7XH (United Kingdom)], E-mail: [email protected]
2009-05-13
Organic-inorganic hybrid heterojunctions have potential as the basis for future photovoltaic devices. Herein, we report the results of investigations exploring the possibility of using pentacene and tetracene as photoelectron donors in conjunction with PbS nanocrystals (PbS-NCs). Photoinduced charge transfer was probed using external quantum efficiency measurements on acene:PbS-NC hybrid photovoltaic devices in conjunction with photoluminescence studies of the corresponding bilayer films. It is shown that photoelectron transfer from pentacene to the PbS-NCs is inefficient as compared to that between tetracene and PbS-NCs. The latter case can be rationalized in terms of the energy level alignment at the heterojunction assuming a common vacuum level. However, in the case of pentacene:PbS-NC junctions an interfacial energy level shift must be considered in order to explain the observations.
19. Net air emissions from electric vehicles: the effect of carbon price and charging strategies.
Science.gov (United States)
Peterson, Scott B; Whitacre, J F; Apt, Jay
2011-03-01
Plug-in hybrid electric vehicles (PHEVs) may become part of the transportation fleet on time scales of a decade or two. We calculate the electric grid load increase and emissions due to vehicle battery charging in PJM and NYISO with the current generation mix, the current mix with a 50/tonne CO(2) price, and this case but with existing coal generators retrofitted with 80% CO(2) capture. We also examine all new generation being natural gas or wind+gas. PHEV fleet percentages between 0.4 and 50% are examined. Vehicles with small (4 kWh) and large (16 kWh) batteries are modeled with driving patterns from the National Household Transportation Survey. Three charging strategies and three scenarios for future electric generation are considered. When compared to 2020 CAFE standards, net CO(2) emissions in New York are reduced by switching from gasoline to electricity; coal-heavy PJM shows somewhat smaller benefits unless coal units are fitted with CCS or replaced with lower CO(2) generation. NO(X) is reduced in both RTOs, but there is upward pressure on SO(2) emissions or allowance prices under a cap. 20. Charge Transfer Based Colorimetric Detection of Silver Ion Energy Technology Data Exchange (ETDEWEB) Han, Seung Choul; Kim, Kwang Seob; Choi, Soon Kyu; Oh, Jinho; Lee, Jae Wook [Dong-A Univ., Busan (Korea, Republic of) 2014-05-15 We have demonstrated the colorimetric chemosensor for detection of Ag{sup +} via formation of nanoparticles which is based on the intramolecular CT interaction between the electron-rich (2,6-dialkoxynaphthalene; Np) moiety and the electron-deficient (methyl viologen; MV{sup 2+}) moiety of a single sensor molecule. Under irradiation of light, Ag{sup +} was reduced to very small silver nanoparticle by CT interaction in the presence of OEGs as flexible recognition moiety of Ag{sup +} and stabilizer for Ag nanoparticles, thus Ag nanoparticles resulted to reddish brown in the color change of sensor solution, gradually. Therefore, the charge-transfer interaction between an electron-deficient and an electron-rich units existing at a sensor molecule can be regarded as a new and efficient method to construct various colorimetric chemosensors. Donor.acceptor interactions or charge transfer (CT) interactions are an important class of non-covalent interactions and have been widely exploited in self-assembling systems. Beyond molecular chemistry, supramolecular chemistry aims at constituting highly complex, functional chemical systems from components held together by intermolecular forces. Chemosensors are the molecules of abiotic origin that bind selectively and reversibly with the analyte with concomitant change in one or more properties of the system. The recognition and signaling of ionic and neutral species of varying complexity is one of the most intensively studied areas of contemporary supramolecular chemistry. 1. Near thermal charge transfer between Ar+2 and N2 International Nuclear Information System (INIS) Holzscheiter, H.M.; Church, D.A. 1981-01-01 The near thermal charge transfer reaction of Ar +2 with N 2 has been studied at total pressures below 10 -7 Torr using a stored ion technique. Ar +2 ions produced by electron impact double ionization of Ar gas were selectively stored for times the order of seconds in a split-ring Penning-type ion trap. The decay with time of the initial ion sample number in a mixture of Ar and N 2 gases was fit to the sum of two exponentials, corresponding to different reaction rates for the 3 P and 1 D low-lying Ar +2 levels. The observed Ar +2 number decrease is attributed to the double-charge transfer process Ar +2 +N 2 →Ar+N 2 +2 →Ar+N + +N + in accord with recent flow-tube measurements. A rate constant for the metastable Ar +2 ( 1 D) level reaction with a value k( 1 D)=1.4 x 10 -9 cm 3 /sec is obtained, using the previously measured rate constant for the Ar +2 ( 3 P) state 2. Excited State Structural Dynamics of Carotenoids and Charge Transfer Systems International Nuclear Information System (INIS) Van Tassle, Aaron Justin 2006-01-01 This dissertation describes the development and implementation of a visible/near infrared pump/mid-infrared probe apparatus. Chapter 1 describes the background and motivation of investigating optically induced structural dynamics, paying specific attention to solvation and the excitation selection rules of highly symmetric molecules such as carotenoids. Chapter 2 describes the development and construction of the experimental apparatus used throughout the remainder of this dissertation. Chapter 3 will discuss the investigation of DCM, a laser dye with a fluorescence signal resulting from a charge transfer state. By studying the dynamics of DCM and of its methyl deuterated isotopomer (an otherwise identical molecule), we are able to investigate the origins of the charge transfer state and provide evidence that it is of the controversial twisted intramolecular (TICT) type. Chapter 4 introduces the use of two-photon excitation to the S1 state, combined with one-photon excitation to the S2 state of the carotenoid beta-apo-8'-carotenal. These 2 investigations show evidence for the formation of solitons, previously unobserved in molecular systems and found only in conducting polymers Chapter 5 presents an investigation of the excited state dynamics of peridinin, the carotenoid responsible for the light harvesting of dinoflagellates. This investigation allows for a more detailed understanding of the importance of structural dynamics of carotenoids in light harvesting 3. Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states. Science.gov (United States) Sirjoosingh, Andrew; Hammes-Schiffer, Sharon 2011-03-24 The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions. 4. ChemNet: A Transferable and Generalizable Deep Neural Network for Small-Molecule Property Prediction Energy Technology Data Exchange (ETDEWEB) Goh, Garrett B.; Siegel, Charles M.; Vishnu, Abhinav; Hodas, Nathan O. 2017-12-08 With access to large datasets, deep neural networks through representation learning have been able to identify patterns from raw data, achieving human-level accuracy in image and speech recognition tasks. However, in chemistry, availability of large standardized and labelled datasets is scarce, and with a multitude of chemical properties of interest, chemical data is inherently small and fragmented. In this work, we explore transfer learning techniques in conjunction with the existing Chemception CNN model, to create a transferable and generalizable deep neural network for small-molecule property prediction. Our latest model, ChemNet learns in a semi-supervised manner from inexpensive labels computed from the ChEMBL database. When fine-tuned to the Tox21, HIV and FreeSolv dataset, which are 3 separate chemical tasks that ChemNet was not originally trained on, we demonstrate that ChemNet exceeds the performance of existing Chemception models, contemporary MLP models that trains on molecular fingerprints, and it matches the performance of the ConvGraph algorithm, the current state-of-the-art. Furthermore, as ChemNet has been pre-trained on a large diverse chemical database, it can be used as a universal “plug-and-play” deep neural network, which accelerates the deployment of deep neural networks for the prediction of novel small-molecule chemical properties. 5. Integer Charge Transfer and Hybridization at an Organic Semiconductor/Conductive Oxide Interface KAUST Repository Gruenewald, Marco; Schirra, Laura K.; Winget, Paul; Kozlik, Michael; Ndione, Paul F.; Sigdel, Ajaya K.; Berry, Joseph J.; Forker, Roman; Bredas, Jean-Luc; Fritz, Torsten; Monti, Oliver L. A. 2015-01-01 with localized states (the shallow donors) in the substrate and charge back-donation, resulting in an effectively integer charge transfer across the interface. Charge transfer is thus not merely a question of locating the Fermi level above the PTCDA electron 6. Charge transfer of O3+ ions with atomic hydrogen International Nuclear Information System (INIS) Wang, J.G.; Stancil, P.C.; Turner, A.R.; Cooper, D.L. 2003-01-01 Charge transfer processes due to collisions of ground state O 3+ (2s 2 2p 2 P) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with existing experimental and theoretical data shows our results to be in better agreement with the measurements than the previous calculations, although problems with some of the state-selective measurements are noted. Our calculations demonstrate that rotational coupling is not important for the total cross section, but for state-selective cross sections, its relevance increases with energy. For the ratios of triplet to singlet cross sections, significant departures from a statistical value are found, generally in harmony with experiment 7. Charge transfer of O3+ ions with atomic hydrogen Science.gov (United States) Wang, J. G.; Stancil, P. C.; Turner, A. R.; Cooper, D. L. 2003-01-01 Charge transfer processes due to collisions of ground state O3+(2s22p 2P) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with existing experimental and theoretical data shows our results to be in better agreement with the measurements than the previous calculations, although problems with some of the state-selective measurements are noted. Our calculations demonstrate that rotational coupling is not important for the total cross section, but for state-selective cross sections, its relevance increases with energy. For the ratios of triplet to singlet cross sections, significant departures from a statistical value are found, generally in harmony with experiment. 8. Charge Transfer in Collisions of S^4+ with He. Science.gov (United States) Wang, J. G.; Stancil, P. C.; Turner, A. R.; Cooper, D. L.; Schultz, D. R.; Rakovic, M. J.; Fritsch, W.; Zygelman, B. 2001-05-01 Charge transfer processes due to collisions of ground state S^4+ ions with atomic helium were investigated for energies between 0.1 meV/u and 10 MeV/u. Total and state-selective cross sections and rate coefficients were obtained utilizing the quantum-mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling, classical trajectory Monte Carlo (CTMC), and continuum distorted wave methods. The MOCC calculations utilized ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. A number of variants of the CTMC approach were also explored. Previous data are limited to an earlier Landau-Zener calculation of the total rate coefficient for which our results are two orders of magnitude larger. An observed multichannel interference effect in the MOCC results will also be discussed. 9. Angular distribution in proton-hydrogen charge-transfer collisions International Nuclear Information System (INIS) Glembocki, O.; Halpern, A.M. 1977-01-01 Theoretical angular distributions for p-H charge transfer to the 1s state for energies of 1 keV and above have been examined and compared for three approximation schemes: the plane-wave Born approximation of Jackson and Schiff (JS), the Coulomb projected Born approximation of Geltman (G), and the distorted-wave eikonal approximation of one of the authors (D). The sharp dip in the forward distribution characteristic of JS is found to exist in G and D as well. As expected, G and D give identical results for all but the lowest energies. In the cases of G and D the dip, which is located close to that of JS, disappears and then reappears as the energy rises. Analytic high-energy limits for the angular dependence in both the JS and G cases have been found and are discussed 10. Laser-induced charge transfer in the CH6+ quasimolecule International Nuclear Information System (INIS) Errea, L.F.; Mendez, L.; Riera, A. 1985-01-01 The charge transfer cross section is calculated for C 6+ +CH(1s) collisions, through photon assisted 5gsigma--6hsigma, 5gsigma--4fsigma, 5gsigma--4fπ, and 5gsigma--4dsigma transitions. The theory developed by Copeland and Tang, and ourselves, is employed, and the validity of the approximations used is tested. The four processes considered have widely different characteristics with regards to the laser wavelength needed, the collision dynamics and the applicability of back-of-the-envelope estimates based on the Landau--Zener approximation. We point out the relevance of those processes to the impurity diagnostics of magnetically confined fusion plasmas and to the development of short wavelength lasers 11. Scaling of the helium--nitrogen charge transfer laser International Nuclear Information System (INIS) Collins, C.B.; Cunningham, A.J. 1975-01-01 The scaling to high powers of the nitrogen ion laser pumped by charge transfer from He + 2 is reported. Intense emission has been found from three laser lines at 3914, 4278, and 4709 A upon discharge of a fast-pulsed electron beam gun, APEX-1, into several atmospheres of a mixture of helium and nitrogen. Excitation current densities were 1.3 kA/cm 2 at 1 MV over a 1times10-cm transverse geometry. The efficiency of the 4278-A laser emission was found to be proportional to the total pressure raised to the 1.2 power. Outputs of 36 mJ have been obtained from the 16-cm 3 working volume at 30-atm pressure and a peak efficiency of 1.6% relative to the energy lost by the electron beam in this radiating volume has been achieved 12. Charge-transfer collisions involving few-electron systems International Nuclear Information System (INIS) Kirchner, T. 2016-01-01 Ion-atom collision systems that involve more than one electron constitute nonseparable few-body problems, whose full solution is difficult to say the least. At impact energies well below 1 keV/amu an expansion of the stationary scattering wave function in terms of a limited number of products of nuclear and molecular state wave functions (amended to satisfy scattering boundary conditions) is feasible and usually sufficient to obtain accurate charge-transfer cross sections provided the electronic wave functions include configuration interaction. At energies above 1 keV/amu this approach becomes inefficient and close-coupling methods within the semi classical approximation are better suited to treat the problem. For bare-ion collisions from helium target atoms explicit solutions of the two-electron time-dependent Schrödinger equation can be achieved, but are computationally costly and cannot be extended to problems which involve more than two electrons. 13. Positron annihilation studies of some charge transfer molecular complexes CERN Document Server El-Sayed, A; Boraei, A A A 2000-01-01 Positron annihilation lifetimes were measured for some solid charge transfer (CT) molecular complexes of quinoline compounds (2,6-dimethylquinoline, 6-methoxyquinoline, quinoline, 6-methylquinoline, 3-bromoquinoline and 2-chloro-4-methylquinoline) as electron donor and picric acid as an electron acceptor. The infrared spectra (IR) of the solid complexes clearly indicated the formation of the hydrogen-bonding CT-complexes. The annihilation spectra were analyzed into two lifetime components using PATFIT program. The values of the average and bulk lifetimes divide the complexes into two groups according to the non-bonding ionization potential of the donor (electron donating power) and the molecular weight of the complexes. Also, it is found that the ionization potential of the donors and molecular weight of the complexes have a conspicuous effect on the average and bulk lifetime values. The bulk lifetime values of the complexes are consistent with the formation of stable hydrogen-bonding CT-complexes as inferred... 14. Photoinduced Charge Transfer from Titania to Surface Doping Site. Science.gov (United States) Inerbaev, Talgat; Hoefelmeyer, James D; Kilin, Dmitri S 2013-05-16 We evaluate a theoretical model in which Ru is substituting for Ti at the (100) surface of anatase TiO 2 . Charge transfer from the photo-excited TiO 2 substrate to the catalytic site triggers the photo-catalytic event (such as water oxidation or reduction half-reaction). We perform ab-initio computational modeling of the charge transfer dynamics on the interface of TiO 2 nanorod and catalytic site. A slab of TiO 2 represents a fragment of TiO 2 nanorod in the anatase phase. Titanium to ruthenium replacement is performed in a way to match the symmetry of TiO 2 substrate. One molecular layer of adsorbed water is taken into consideration to mimic the experimental conditions. It is found that these adsorbed water molecules saturate dangling surface bonds and drastically affect the electronic properties of systems investigated. The modeling is performed by reduced density matrix method in the basis of Kohn-Sham orbitals. A nano-catalyst modeled through replacement defect contributes energy levels near the bottom of the conduction band of TiO 2 nano-structure. An exciton in the nano-rod is dissipating due to interaction with lattice vibrations, treated through non-adiabatic coupling. The electron relaxes to conduction band edge and then to the Ru cite with faster rate than hole relaxes to the Ru cite. These results are of the importance for an optimal design of nano-materials for photo-catalytic water splitting and solar energy harvesting. 15. Exciplex: An Intermolecular Charge-Transfer Approach for TADF. Science.gov (United States) Sarma, Monima; Wong, Ken-Tsung 2018-04-03 Organic materials that display thermally activated delayed fluorescence (TADF) are a striking class of functional materials that have witnessed a booming progress in recent years. In addition to pure TADF emitters achieved by the subtle manipulations of intramolecular charge transfer processes with sophisticated molecular structures, a new class of efficient TADF-based OLEDs with emitting layer formed by blending electron donor and acceptor molecules that involve intermolecular charge transfer have also been fabricated. In contrast to pure TADF materials, the exciplex-based systems can realize small ΔEST (0-0.05 eV) much more easily since the electron and hole are positioned on two different molecules, thereby giving small exchange energy. Consequently, exciplex-based OLEDs have the prospective to maximize the TADF contribution and achieve theoretical 100% internal quantum efficiency. Therefore, the challenging issue of achieving small ΔEST in organic systems could be solved. In this article, we summarize and discuss the latest and most significant developments regarding these rapidly evolving functional materials, wherein the majority of the reported exciplex forming systems are categorized into two sub-groups, viz. (a) exciplex as TADF emitters and (b) those as hosts for fluorescent, phosphorescent and TADF dopants according to their structural features and applications. The working mechanisms of the direct electroluminescence from the donor/acceptor interface and the exciplex-forming systems as co-host for the realization of high efficiency OLEDs are reviewed and discussed. This article delivers a summary of the current progresses and achievements of exciplex-based researches and points out the future challenges to trigger more research endeavors to this growing field. 16. Charge amplification and transfer processes in the gas electron multiplier International Nuclear Information System (INIS) Bachmann, S.; Bressan, A.; Ropelewski, L.; Sauli, F.; Sharma, A.; Moermann, D. 1999-01-01 We report the results of systematic investigations on the operating properties of detectors based on the gas electron multiplier (GEM). The dependence of gain and charge collection efficiency on the external fields has been studied in a range of values for the hole diameter and pitch. The collection efficiency of ionization electrons into the multiplier, after an initial increase, reaches a plateau extending to higher values of drift field the larger the GEM voltage and its optical transparency. The effective gain, fraction of electrons collected by an electrode following the multiplier, increases almost linearly with the collection field, until entering a steeper parallel plate multiplication regime. The maximum effective gain attainable increases with the reduction in the hole diameter, stabilizing to a constant value at a diameter approximately corresponding to the foil thickness. Charge transfer properties appear to depend only on ratios of fields outside and within the channels, with no interaction between the external fields. With proper design, GEM detectors can be optimized to satisfy a wide range of experimental requirements: tracking of minimum ionizing particles, good electron collection with small distortions in high magnetic fields, improved multi-track resolution and strong ion feedback suppression in large volume and time-projection chambers 17. Doping graphene films via chemically mediated charge transfer Directory of Open Access Journals (Sweden) Ishikawa Ryousuke 2011-01-01 Full Text Available Abstract Transparent conductive films (TCFs are critical components of a myriad of technologies including flat panel displays, light-emitting diodes, and solar cells. Graphene-based TCFs have attracted a lot of attention because of their high electrical conductivity, transparency, and low cost. Carrier doping of graphene would potentially improve the properties of graphene-based TCFs for practical industrial applications. However, controlling the carrier type and concentration of dopants in graphene films is challenging, especially for the synthesis of p-type films. In this article, a new method for doping graphene using the conjugated organic molecule, tetracyanoquinodimethane (TCNQ, is described. Notably, TCNQ is well known as a powerful electron accepter and is expected to favor electron transfer from graphene into TCNQ molecules, thereby leading to p-type doping of graphene films. Small amounts of TCNQ drastically improved the resistivity without degradation of optical transparency. Our carrier doping method based on charge transfer has a huge potential for graphene-based TCFs. 18. Classical/quantum correspondence in state selective charge transfer and excitation reactions involving highly charged ions and hydrogen International Nuclear Information System (INIS) Purkait, M 2009-01-01 State selective charge transfer and excitation cross sections for collisions of Ne q+ (q = 1-10) with atomic hydrogen are calculated within the framework of Classical Trajectory Monte Carlo (CTMC) method and Boundary Corrected Continuum Intermediate State (BCCIS) approximation. 19. Charge Transfer and Support Effects in Heterogeneous Catalysis Energy Technology Data Exchange (ETDEWEB) Hervier, Antoine [Univ. of California, Berkeley, CA (United States) 2011-12-21 The kinetic, electronic and spectroscopic properties of two-dimensional oxide-supported catalysts were investigated in order to understand the role of charge transfer in catalysis. Pt/TiO2 nanodiodes were fabricated and used as catalysts for hydrogen oxidation. During the reaction, the current through the diode, as well as its I-V curve, were monitored, while gas chromatography was used to measure the reaction rate. The current and the turnover rate were found to have the same temperature dependence, indicating that hydrogen oxidation leads to the non-adiabatic excitation of electrons in Pt. A fraction of these electrons have enough energy to ballistically transport through Pt and overcome the Schottky barrier at the interface with TiO2. The yield for this phenomenon is on the order of 10-4 electrons per product molecule formed, similar to what has been observed for CO oxidation and for the adsorption of many different molecules. The same Pt/TiO2 system was used to compare currents in hydrogen oxidation and deuterium oxidation. The current through the diode under deuterium oxidation was found to be greater than under hydrogen oxidation by a factor of three. Weighted by the difference in turnover frequencies for the two isotopes, this would imply a chemicurrent yield 5 times greater for D2 compared to H2, contrary to what is expected given the higher mass of D2. Reversible changes in the rectification factor of the diode are observed when switching between D2 and H2. These changes are a likely cause for the differences in current between the two isotopes. In the nanodiode experiments, surface chemistry leads to charge flow, suggesting the possibility of creating charge flow to tune surface chemistry. This was done first by exposing a Pt/Si diode to visible light while using it as a catalyst for H2 oxidation. Absorption of the light in the Si, combined with 20. Experimental evidence of state-selective charge transfer in inductively coupled plasma-atomic emission spectrometry International Nuclear Information System (INIS) Chan, George C.-Y.; Hieftje, Gary M. 2004-01-01 State-selective charge-transfer behavior was observed for Fe, Cr, Mn and Cu in inductively coupled plasma (ICP)-atomic emission spectrometry. Charge transfer from Ar + to Fe, Cr and Mn is state-selective because of inefficient collisional mixing of the quasiresonant charge-transfer energy levels with nearby levels. This low efficiency is the consequence of differences in electronic configuration of the core electrons. The reason for state-selective charge-transfer behavior to Cu is not clear, although a tentative explanation based on efficiency of intramultiplet and intermultiplet mixing for this special case is offered 1. Effect of Molecular Packing and Charge Delocalization on the Nonradiative Recombination of Charge-Transfer States in Organic Solar Cells KAUST Repository Chen, Xiankai 2016-09-05 In organic solar cells, a major source of energy loss is attributed to nonradiative recombination from the interfacial charge transfer states to the ground state. By taking pentacene–C60 complexes as model donor–acceptor systems, a comprehensive theoretical understanding of how molecular packing and charge delocalization impact these nonradiative recombination rates at donor–acceptor interfaces is provided. 2. Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks. Science.gov (United States) Porta, Alberto; Bari, Vlasta; De Maria, Beatrice; Takahashi, Anielle C M; Guzzetti, Stefano; Colombo, Riccardo; Catai, Aparecida M; Raimondi, Ferdinando; Faes, Luca 2017-11-01 Objective: Indexes assessing the balance between redundancy and synergy were hypothesized to be helpful in characterizing cardiovascular control from spontaneous beat-to-beat variations of heart period (HP), systolic arterial pressure (SAP), and respiration (R). Methods: Net redundancy/synergy indexes were derived according to predictability and transfer entropy decomposition strategies via a multivariate linear regression approach. Indexes were tested in two protocols inducing modifications of the cardiovascular regulation via baroreflex loading/unloading (i.e., head-down tilt at -25° and graded head-up tilt at 15°, 30°, 45°, 60°, 75°, and 90°, respectively). The net redundancy/synergy of SAP and R to HP and of HP and R to SAP were estimated over stationary sequences of 256 successive values. Results: We found that: 1) regardless of the target (i.e., HP or SAP) redundancy was prevalent over synergy and this prevalence was independent of type and magnitude of the baroreflex challenge; 2) the prevalence of redundancy disappeared when decoupling inputs from output via a surrogate approach; 3) net redundancy was under autonomic control given that it varied in proportion to the vagal withdrawal during graded head-up tilt; and 4) conclusions held regardless of the decomposition strategy. Conclusion: Net redundancy indexes can monitor changes of cardiovascular control from a perspective completely different from that provided by more traditional univariate and multivariate methods. Significance: Net redundancy measures might provide a practical tool to quantify the reservoir of effective cardiovascular regulatory mechanisms sharing causal influences over a target variable. Objective: Indexes assessing the balance between redundancy and synergy were hypothesized to be helpful in characterizing cardiovascular control from spontaneous beat-to-beat variations of heart period (HP), systolic arterial pressure (SAP), and respiration (R). Methods: Net redundancy 3. Graphene-ferromagnet interfaces: hybridization, magnetization and charge transfer. Science.gov (United States) Abtew, Tesfaye; Shih, Bi-Ching; Banerjee, Sarbajit; Zhang, Peihong 2013-03-07 Electronic and magnetic properties of graphene-ferromagnet interfaces are investigated using first-principles electronic structure methods in which a single layer graphene is adsorbed on Ni(111) and Co(111) surfaces. Due to the symmetry matching and orbital overlap, the hybridization between graphene pπ and Ni (or Co) d(z(2)) states is very strong. This pd hybridization, which is both spin and k dependent, greatly affects the electronic and magnetic properties of the interface, resulting in a significantly reduced (by about 20% for Ni and 10% for Co) local magnetic moment of the top ferromagnetic layer at the interface and an induced spin polarization on the graphene layer. The calculated induced magnetic moment on the graphene layer agrees well with a recent experiment. In addition, a substantial charge transfer across the graphene-ferromagnet interfaces is observed. We also investigate the effects of thickness of the ferromagnet slab on the calculated electronic and magnetic properties of the interface. The strength of the pd hybridization and the thickness-dependent interfacial properties may be exploited to design structures with desirable magnetic and transport properties for spintronic applications. 4. Versatile charge transfer through anthraquinone films for electrochemical sensing applications International Nuclear Information System (INIS) Venarusso, Luna B.; Tammeveski, Kaido; Maia, Gilberto 2011-01-01 Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were employed to study the effect of anthraquinone (AQ) films on the charge transfer rate of β-nicotinamide adenine dinucleotide (NAD + ), dopamine (DA), and ferricyanide on glassy carbon (GC) electrodes in solutions of different pH. Maximum blocking action on the Fe(CN) 6 3- redox probe was observed at pH 7 and open-circuit potential (OCP). However, maximum electron hopping effect was observed at pH 9 at both -0.58 V and -0.85 V for Fe(CN) 6 3- , pH 7 at -0.58 V for NAD + , and pH 9 at -0.58 V for DA, suggesting that electron hopping in AQ films on a GC surface is dependent on both pH and electrode potential. These findings lend support for the application of these films in the detection of soluble redox probes such as NAD + and DA at biological pH values (from 7 to 9). 5. Low-energy charge transfer excitations in NiO International Nuclear Information System (INIS) Sokolov, V I; Yermakov, A Ye; Uimin, M A; Gruzdev, N B; Pustovarov, V A; Churmanov, V N; Ivanov, V Yu; Sokolov, P S; Baranov, A N; Moskvin, A S 2012-01-01 Comparative analysis of photoluminescence (PL) and photoluminescence excitation (PLE) spectra of NiO poly- and nanocrystals in the spectral range 2-5.5 eV reveals two PLE bands peaked near 3.7 and 4.6 eV with a dramatic rise in the low-temperature PLE spectral weight of the 3.7 eV PLE band in the nanocrystalline NiO as compared with its polycrystalline counterpart. In frames of a cluster model approach we assign the 3.7 eV PLE band to the low-energy bulk-forbidden p-d (t 1g (π)-e g ) charge transfer (CT) transition which becomes the allowed one in the nanocrystalline state while the 4.6 eV PLE band is related to a bulk allowed d-d (e g -e g ) CT transition scarcely susceptible to the nanocrystallization. The PLE spectroscopy of the nanocrystalline materials appears to be a novel informative technique for inspection of different CT transitions. 6. Vibrational spectra of charge transfer complexes of lead phthalocyanine International Nuclear Information System (INIS) Oza, A.T.; Patel, S.G.; Patel, R.G.; Prajapati, S.M.; Vaidya, Rajiv 2005-01-01 Infrared spectra of six charge transfer complexes of lead phthalocyanine (PbPc), namely, PbPc-I 2 , PbPc-TCNQ, PbPc-DDQ, PbPc-chloranil, PbPc-TCNE and PbPc-TNF, where TCNQ=7,7,8,8-tetracyano-1,4-quinodimethane, DDQ=2,3-dichloro-5,6-dicyano-p-benzoquinone, TCNE=tetracyano-p-ethylene and TNF=2,4,5,7-tetranitro-9-fluorenone have been studied in the range of 400-4000 cm -1 . The analysis of featureless absorption is carried out for studying transition across the Peierls gap of 0.225 eV. The electronic absorption envelopes at 1500, 1100 and 3400 cm -1 are found to have Gaussian shapes and not the degenerate oscillators, as found in purely organic conductors. There is a pairing of two electrons on phthalocyanine ligand as required in Little's model, and consequently, the electronic absorption envelope is a doublet. Electronic absorption envelope is a doublet showing two peaks at 1500 and 1100 cm -1 , indicating a two-electron problem in PbPc. Metal-ligand vibrations between 400 and 700 cm -1 lead to indirect transition between the valence and conduction bands and phonon-mediated coupling between metal chains and the side chains 7. Versatile charge transfer through anthraquinone films for electrochemical sensing applications Energy Technology Data Exchange (ETDEWEB) Venarusso, Luna B. [Department of Chemistry, Universidade Federal de Mato Grosso do Sul, Caixa Postal 549, Campo Grande, MS 79070-900 (Brazil); Tammeveski, Kaido [Institute of Chemistry, University of Tartu, Ravila 14a, 50411 Tartu (Estonia); Maia, Gilberto, E-mail: [email protected] [Department of Chemistry, Universidade Federal de Mato Grosso do Sul, Caixa Postal 549, Campo Grande, MS 79070-900 (Brazil) 2011-10-01 Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were employed to study the effect of anthraquinone (AQ) films on the charge transfer rate of {beta}-nicotinamide adenine dinucleotide (NAD{sup +}), dopamine (DA), and ferricyanide on glassy carbon (GC) electrodes in solutions of different pH. Maximum blocking action on the Fe(CN){sub 6}{sup 3-} redox probe was observed at pH 7 and open-circuit potential (OCP). However, maximum electron hopping effect was observed at pH 9 at both -0.58 V and -0.85 V for Fe(CN){sub 6}{sup 3-}, pH 7 at -0.58 V for NAD{sup +}, and pH 9 at -0.58 V for DA, suggesting that electron hopping in AQ films on a GC surface is dependent on both pH and electrode potential. These findings lend support for the application of these films in the detection of soluble redox probes such as NAD{sup +} and DA at biological pH values (from 7 to 9). 8. Magnetically coupled resonance wireless charging technology principles and transfer mechanisms Science.gov (United States) Zhou, Jiehua; Wan, Jian; Ma, Yinping 2017-05-01 With the tenure of Electric-Vehicle rising around the world, the charging methods have been paid more and more attention, the current charging mode mainly has the charging posts and battery swapping station. The construction of the charging pile or battery swapping station not only require lots of manpower, material costs but the bare conductor is also easy to generate electric spark hidden safety problems, still occupies large space. Compared with the wired charging, wireless charging mode is flexible, unlimited space and location factors and charging for vehicle safety and quickly. It complements the traditional charging methods in adaptability and the independent charge deficiencies. So the researching the wireless charging system have an important practical significance and application value. In this paper, wireless charging system designed is divided into three parts: the primary side, secondary side and resonant coupling. The main function of the primary side is to generate high-frequency alternating current, so selecting CLASS-E amplifier inverter structure through the research on full bridge, half-bridge and power amplification circuit. Addition, the wireless charging system is susceptible to outside interference, frequency drift phenomenon. Combined with the wireless energy transmission characteristics, resonant parts adopt resonant coupling energy transmission scheme and the Series-Series coupling compensation structure. For the electric vehicle charging power and voltage requirements, the main circuit is a full bridge inverter and Boost circuit used as the secondary side. 9. Analysis of matters associated with the transferring of object-oriented applications to platform .Net using C# programming language Science.gov (United States) Sarsimbayeva, S. M.; Kospanova, K. K. 2015-11-01 The article provides the discussion of matters associated with the problems of transferring of object-oriented Windows applications from C++ programming language to .Net platform using C# programming language. C++ has always been considered to be the best language for the software development, but the implicit mistakes that come along with the tool may lead to infinite memory leaks and other errors. The platform .Net and the C#, made by Microsoft, are the solutions to the issues mentioned above. The world economy and production are highly demanding applications developed by C++, but the new language with its stability and transferability to .Net will bring many advantages. An example can be presented using the applications that imitate the work of queuing systems. Authors solved the problem of transferring of an application, imitating seaport works, from C++ to the platform .Net using C# in the scope of Visual Studio. 10. Charge-transfer cross sections in collisions of ground-state Ca and H+ Science.gov (United States) Dutta, C. M.; Oubre, C.; Nordlander, P.; Kimura, M.; Dalgarno, A. 2006-03-01 We have investigated collisions of Ca(4s2) with H+ in the energy range of 200eV/u-10keV/u using the semiclassical molecular-orbital close-coupling (MOCC) method with 18 coupled molecular states ( 11Σ+1 and seven Π+1 states) to determine charge-transfer cross sections. Except for the incoming channel 6Σ+1 , the molecular states all correspond to charge-transfer channels. Inclusion of Ca2+-H- is crucial in the configuration-interaction calculation for generating the molecular wave functions and potentials. Because of the Coulomb attraction, the state separating to Ca2+-H- creates many avoided crossings, even though at infinite separation it lies energetically above all other states that we included. Because of the avoided crossings between the incoming channel 6Σ+1 and the energetically close charge-transfer channel 7Σ+1 the charge-transfer interaction occurs at long range. This makes calculations of charge-transfer cross sections by the MOCC method very challenging. The total charge-transfer cross sections increase monotonically from 3.4×10-15cm2 at 200eV/u to 4.5×10-15cm2 at 10keV/u . Charge transfer occurs mostly to the excited Ca+(5p) state in the entire energy range, which is the sum of the charge transfer to 7Σ+1 and 4Π+1 . It accounts for ˜47% of the total charge transfer cross sections at 200eV/u . However, as the energy increases, transfer to Ca+(4d) increases, and at 10keV/u the charge-transfer cross sections for Ca+(5p) and Ca+(4d) become comparable, each giving ˜38% of the total cross section. 11. Charge-transfer cross sections in collisions of ground-state Ca and H+ International Nuclear Information System (INIS) Dutta, C. M.; Oubre, C.; Nordlander, P.; Kimura, M.; Dalgarno, A. 2006-01-01 We have investigated collisions of Ca(4s 2 ) with H + in the energy range of 200 eV/u-10 keV/u using the semiclassical molecular-orbital close-coupling (MOCC) method with 18 coupled molecular states (11 1 Σ + and seven 1 Π + states) to determine charge-transfer cross sections. Except for the incoming channel 6 1 Σ + , the molecular states all correspond to charge-transfer channels. Inclusion of Ca 2+ -H - is crucial in the configuration-interaction calculation for generating the molecular wave functions and potentials. Because of the Coulomb attraction, the state separating to Ca 2+ -H - creates many avoided crossings, even though at infinite separation it lies energetically above all other states that we included. Because of the avoided crossings between the incoming channel 6 1 Σ + and the energetically close charge-transfer channel 7 1 Σ + the charge-transfer interaction occurs at long range. This makes calculations of charge-transfer cross sections by the MOCC method very challenging. The total charge-transfer cross sections increase monotonically from 3.4x10 -15 cm 2 at 200 eV/u to 4.5x10 -15 cm 2 at 10 keV/u. Charge transfer occurs mostly to the excited Ca + (5p) state in the entire energy range, which is the sum of the charge transfer to 7 1 Σ + and 4 1 Π + . It accounts for ∼47% of the total charge transfer cross sections at 200 eV/u. However, as the energy increases, transfer to Ca + (4d) increases, and at 10 keV/u the charge-transfer cross sections for Ca + (5p) and Ca + (4d) become comparable, each giving ∼38% of the total cross section 12. Correlation between charge transfer and exchange coupling in carbon-based magnetic materials Energy Technology Data Exchange (ETDEWEB) Nguyen, Anh Tuan, E-mail: [email protected] [Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi (Viet Nam); Science and Technology Department, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi (Viet Nam); Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan (Japan); Nguyen, Van Thanh; Nguyen, Huy Sinh [Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi (Viet Nam); Pham, Thi Tuan Anh [Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi (Viet Nam); Faculty of Science, College of Hai Duong, Nguyen Thi Due, Hai Duong (Viet Nam); Do, Viet Thang [Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi (Viet Nam); Faculty of Science, Haiphong University, 171 Phan Dang Luu, Kien An, Hai Phong (Viet Nam); Dam, Hieu Chi [Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan (Japan) 2015-10-15 Several forms of carbon-based magnetic materials, i.e. single radicals, radical dimers, and alternating stacks of radicals and diamagnetic molecules, have been investigated using density-functional theory with dispersion correction and full geometry optimization. Our calculated results demonstrate that the C{sub 31}H{sub 15} (R{sub 4}) radical has a spin of ½. However, in its [R{sub 4}]{sub 2} dimer structure, the net spin becomes zero due to antiferromagnetic spin-exchange between radicals. To avoid antiferromagnetic spin-exchange of identical face-to-face radicals, eight alternating stacks, R{sub 4}/D{sub 2m}/R{sub 4} (with m = 3-10), were designed. Our calculated results show that charge transfer (Δn) between R{sub 4} radicals and the diamagnetic molecule D{sub 2m} occurs with a mechanism of spin exchange (J) in stacks. The more electrons that transfer from R{sub 4} to D{sub 2m}, the stronger the ferromagnetic spin-exchange in stacks. In addition, our calculated results show that Δn can be tailored by adjusting the electron affinity (E{sub a}) of D{sub 2m}. The correlation between Δn, E{sub a}, m, and J is discussed. These results give some hints for the design of new ferromagnetic carbon-based materials. 13. About application of the 'rough' net method for decision of the neutron transfer transient equation International Nuclear Information System (INIS) Seleznev, E.F.; Tarasenko, V.V. 1995-01-01 Method of the decision of a transient equation of the neutrons transfer is developed, which at preservation of necessary accuracy permits considerably to speed up a finding of the decision up to modeling of processes in reactor in real time. The transient equation of neutrons transfer in one-group diffusion approximation is decided by the finite-difference method. The calculating model of reactor is divided into rather large zones, where the currents on internal borders are away, and on external borders ones are a sum of currents on the borders of small-sized zones. For the decision of an equation in finite-difference kind the numerical scheme 'Time - integrate' is used, which permits to search the decision in a half-explicit kind with rather large temporary step. The decision for density of neutrons flux is determine by the SOR method. Under the conducted preliminary analysis of an algorithm efficiency it is possible to conclude, that the time of the decision on a computer can be reduced in 3 and more times, in depending on 'roughness' of a calculated net in comparison with computation on a complete net. The realized algorithm can be used as for scientific researches, and as neutron-physical block of the simulator. 6 refs., 1 fig 14. Charge transfer and ionization occurring in proton- and helium ion-atom collisions International Nuclear Information System (INIS) DuBois, R.D. 1985-12-01 Two examples are presented where specific channels have been identified that are responsible for single and double target ionization via direct coulomb ionization or charge transfer processes. Using ratios of absolute cross sections that have been measured for these processes it was shown that an independent electron model should be appropriate for calculating direct double target ionization but generally appears to be inadequate in calculating charge transfer plus ionization and double charge transfer cross sections. At present such detailed information can be obtained only in limited cases. However cross sections with detailed final charge state information should provide stringent tests for present and future theoretical work. 22 refs., 2 figs 15. ARCHITECTURE OF A CHARGE-TRANSFER STATE REGULATING LIGHT HARVESTING IN A PLANT ANTENNA PROTEIN Energy Technology Data Exchange (ETDEWEB) Fleming, Graham; Ahn, Tae Kyu; Avenson, Thomas J.; Ballottari, Matteo; Cheng, Yuan-Chung; Niyogi, Krishna K.; Bassi, Roberto; Fleming, Graham R. 2008-04-02 Energy-dependent quenching of excess absorbed light energy (qE) is a vital mechanism for regulating photosynthetic light harvesting in higher plants. All of the physiological characteristics of qE have been positively correlated with charge-transfer between coupled chlorophyll and zeaxanthin molecules in the light-harvesting antenna of photosystem II (PSII). In this work, we present evidence for charge-transfer quenching in all three of the individual minor antenna complexes of PSII (CP29, CP26, and CP24), and we conclude that charge-transfer quenching in CP29 involves a de-localized state of an excitonically coupled chlorophyll dimer. We propose that reversible conformational changes in CP29 can `tune? the electronic coupling between the chlorophylls in this dimer, thereby modulating the energy of the chlorophylls-zeaxanthin charge-transfer state and switching on and off the charge-transfer quenching during qE. 16. Crystal growth of new charge-transfer salts based on π-conjugated donor molecules Energy Technology Data Exchange (ETDEWEB) Morherr, Antonia, E-mail: [email protected] [Physikalisches Institut, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main (Germany); Witt, Sebastian [Physikalisches Institut, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main (Germany); Chernenkaya, Alisa [Graduate School Materials Science in Mainz, 55128 Mainz (Germany); Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz (Germany); Bäcker, Jan-Peter [Physikalisches Institut, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main (Germany); Schönhense, Gerd [Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz (Germany); Bolte, Michael [Institut für anorganische Chemie, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main (Germany); Krellner, Cornelius [Physikalisches Institut, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main (Germany) 2016-09-01 New charge transfer crystals of π-conjugated, aromatic molecules (phenanthrene and picene) as donors were obtained by physical vapor transport. The melting behavior, optimization of crystal growth and the crystal structure are reported for charge transfer salts with (fluorinated) tetracyanoquinodimethane (TCNQ-F{sub x}, x=0, 2, 4), which was used as acceptor material. The crystal structures were determined by single-crystal X-ray diffraction. Growth conditions for different vapor pressures in closed ampules were applied and the effect of these starting conditions for crystal size and quality is reported. The process of charge transfer was investigated by geometrical analysis of the crystal structure and by infrared spectroscopy on single crystals. With these three different acceptor strengths and the two sets of donor materials, it is possible to investigate the distribution of the charge transfer systematically. This helps to understand the charge transfer process in this class of materials with π-conjugated donor molecules. 17. Dynamical interaction of He atoms with metal surfaces: Charge transfer processes International Nuclear Information System (INIS) Flores, F.; Garcia Vidal, F.J.; Monreal, R. 1993-01-01 A self-consistent Kohn-Sham LCAO method is presented to calculate the charge transfer processes between a He * -atom and metal surfaces. Intra-atomic correlation effects are taken into account by considering independently each single He-orbital and by combining the different charge transfer processes into a set of dynamical rate equations for the different ion charge fractions. Our discussion reproduces qualitatively the experimental evidence and gives strong support to the method presented here. (author). 24 refs, 4 figs 18. Dynamics of the excited state intramolecular charge transfer International Nuclear Information System (INIS) Joo, T.; Kim, C.H. 2006-01-01 The 6-dodecanoyl-2-dimethylaminonaphtalene (laurdan), a derivative of 6-propanoyl- 2-dimethylaminonaphthalene (prodan), has been used as a fluorescent probe in cell imaging, especially in visualizing the lipid rafts by the generalized polarization (GP) images, where GP=(I 440 -I 490 )/(I 440 +I 490 ) with I being the fluorescence intensity. The fluorescence spectrum of laurdan is sensitive to its dipolar environment due to the intramolecular charge transfer (ICT) process in S 1 state, which results in a dual emission from the locally excited (LE) and the ICT states. The ICT process and the solvation of the ICT state are very sensitive to the dipolar nature of the environment. In this work, the ICT of laurdan in ethanol has been studied by femtosecond time resolved fluorescence (TRF), especially TRF spectra measurement without the conventional spectral reconstruction method. TRF probes the excited states exclusively, a unique advantage over the pump/probe transient absorption technique, although time resolution of the TRF is generally lower than transient absorption and the TRF spectra measurement was possible only though the spectral reconstruction. Over the years, critical advances in TRF technique have been made in our group to achieve <50 fs time resolution with direct full spectra measurement capability. Detailed ICT and the subsequent solvation processes can be visualized unambiguously from the TRF spectra. Fig. 1 shows the TRF spectra of laurdan in ethanol at several time delays. Surprisingly, two bands at 433 and 476 nm are clearly visible in the TRF spectra of laurdan even at T = 0 fs. As time increases, the band at 476 nm shifts to the red while its intensity increases. The band at 433 nm also shifts slightly to the red, but loses intensity as time increases. The intensity of the 476 nm band reaches maximum at around 5 ps, where it is roughly twice as intense as that at 0 fs, and stays constant until lifetime decay is noticeable. The spectra were fit by 19. Charge-transfer interactions of Cr species with DNA. Science.gov (United States) Nowicka, Anna M; Matysiak-Brynda, Edyta; Hepel, Maria 2017-10-01 Interactions of Cr species with nucleic acids in living organisms depend strongly on Cr oxidation state and the environmental conditions. As the effects of these interactions range from benign to pre-mutagenic to carcinogenic, careful assessment of the hazard they pose to human health is necessary. We have investigated methods that would enable quantifying the DNA damage caused by Cr species under varying environmental conditions, including UV, O 2 , and redox potential, using simple instrumental techniques which could be in future combined into a field-deployable instrumentation. We have employed electrochemical quartz crystal nanogravimetry (EQCN), cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) to evaluate the extent of DNA damage expressed in terms of guanine oxidation yield (η) and changes in specific characteristics provided by these techniques. The effects of the interactions of Cr species with DNA were analyzed using a model calf thymus DNA (ctDNA) film on a gold electrode (Au@ctDNA) in different media, including: (i) Cr(VI), (ii) Cr(VI) reduced at -0.2V, (iii) Cr(III)+UV radiation+O 2 , and Cr(III), obtaining the η values: 7.4±1.4, 1.5±0.4, 1.1±0.31%, and 0%, respectively, thus quantifying the hazard posed. The EIS measurements have enabled utilizing the decrease in charge-transfer resistance (R ct ) for ferri/ferrocyanide redox probe at an Au@ctDNA electrode to assess the oxidative ctDNA damage by Cr(VI) species. In this case, circular dichroism indicates an extensive damage to the ctDNA hydrogen bonding. On the other hand, Cr(III) species have not induced any damage to ctDNA, although the EQCN measurements show an electrostatic binding to DNA. Copyright © 2017 Elsevier Inc. All rights reserved. 20. Charged-particle transfer reactions and nuclear astrophysics problems International Nuclear Information System (INIS) Artemov, S.V.; Yarmukhamedov, R.; Yuldashev, B.S.; Burtebaev, N.; Duysebaev, A.; Kadyrzhanov, K.K. 2002-01-01 In the report a review of the recent results of calculation of the astrophysical S-factors S(E) for the D(α, γ) 6 Li, 3 He(α, γ) 7 Be, 7 Be(p, γ) 8 Be, 12,13 C(p, γ) 13, 14 N and 12 C(p,γ) 16 O* reactions at extremely low energies E, including value E=0 , performed within the framework of a new method taking into account the additional information about the nuclear vertex constant (Nc) (or the respective asymptotic normalization coefficient) are presented. The required values of Nc can be obtained from an analysis of measured differential cross-sections of proton and α-particle transfer reactions (for example A( 3 He,d)B, 6 Li(d, 6 Li)d, 6 Li(α, 6 Li)α, 12 C( 6 Li, d) 16 O* etc.). A comparative analysis between the results obtained by different authors is also done. Taking into account an important role of the NVC's values for the nuclear astrophysical A(p, γ)B and A(α, γ)B reactions, a possibility of obtaining the reliable NVC values for the virtual decay B→A+p and B→A+α from the analysis of differential cross sections both sub- and above-barrier A( 3 He, d) and A( 6,7 Li, 2,3 H)B reactions is discussed in detail. In this line the use the isochronous cyclotron U-150 M, the 'DC-60' heavy ion machine and electrostatic charge-exchanging accelerator UKP-2-1 of Institute of Nuclear Physics of National Nuclear Center of the Republic of Kazakhstan for carrying out the needed experiments is considered and the possibility of the obtained data application for the astrophysical interest is also discussed 1. Self-interaction and charge transfer in organic semiconductors Energy Technology Data Exchange (ETDEWEB) Koerzdoerfer, Thomas 2009-12-18 This work concentrates on the problem of self-interaction, which is one of the most serious problems of commonly used approximative density functionals. As a major result of this work, it is demonstrated that self-interaction plays a decisive role for the performance of different approximative functionals in predicting accurate electronic properties of organic molecular semiconductors. In search for a solution to the self-interaction problem, a new concept for correcting commonly used density functionals for self-interaction is introduced and applied to a variety of systems, spanning small molecules, extended molecular chains, and organic molecular semiconductors. It is further shown that the performance of functionals that are not free from self-interaction can vary strongly for different systems and observables of interest, thus entailing the danger of misinterpretation of the results obtained from those functionals. The underlying reasons for the varying performance of commonly used density functionals are discussed thoroughly in this work. Finally, this thesis provides strategies that allow to analyze the reliability of commonly used approximations to the exchange-correlation functional for particular systems of interest. This cumulative dissertation is divided into three parts. Part I gives a short introduction into DFT and its time-dependent extension (TDDFT). Part II provides further insights into the self-interaction problem, presents a newly developed concept for the correction of self-interaction, gives an introduction into the publications, and discusses their basic results. Finally, the four publications on self-interaction and charge-transfer in extended molecular systems and organic molecular semiconductors are collected in Part III. (orig.) 2. Receptor-Mediated Melanoma Targeting with Radiolabeled α-Melanocyte-Stimulating Hormone: Relevance of the Net Charge of the Ligand Directory of Open Access Journals (Sweden) Alex N. Eberle 2017-04-01 Full Text Available A majority of melanotic and amelanotic melanomas overexpress melanocortin type 1 receptors (MC1Rs for α-melanocyte-stimulating hormone. Radiolabeled linear or cyclic analogs of α-MSH have a great potential as diagnostic or therapeutic tools for the management of malignant melanoma. Compounds such as [111In]DOTA-NAP-amide exhibit high affinity for the MC1R in vitro, good tumor uptake in vivo, but they may suffer from relatively high kidney uptake and retention in vivo. We have shown previously that the introduction of negative charges into radiolabeled DOTA-NAP-amide peptide analogs may enhance their excretion and reduce kidney retention. To address the question of where to place negative charges within the ligand, we have extended these studies by designing two novel peptides, Ac-Nle-Asp-His-d-Phe-Arg-Trp-Gly-Lys(DOTA-d-Asp-d-Asp-OH (DOTA-NAP-d-Asp-d-Asp with three negative charges at the C-terminal end (overall net charge of the molecule −2 and DOTA-Gly-Tyr(P-Nle-Asp-His-d-Phe-Arg-Trp-NH2 (DOTA-Phospho-MSH2-9 with two negative charges in the N-terminal region (net charge −1. The former peptide showed markedly reduced receptor affinity and biological activity by >10-fold compared to DOTA-NAP-amide as reference compound, and the latter peptide displayed similar bioactivity and receptor affinity as the reference compound. The uptake by melanoma tumor tissue of [111In]DOTA-Phospho-MSH2-9 was 7.33 ± 0.47 %ID/g 4 h after injection, i.e., almost equally high as with [111In]DOTA-NAP-amide. The kidney retention was 2.68 ± 0.18 %ID/g 4 h after injection and hence 44% lower than that of [111In]DOTA-NAP-amide. Over an observation period from 4 to 48 h, the tumor-to-kidney ratio of [111In]DOTA-Phospho-MSH2-9 was 35% more favorable than that of the reference compound. In a comparison of DOTA-NAP-d-Asp-d-Asp, DOTA-Phospho-MSH2-9 and DOTA-NAP-amide with five previously published analogs of DOTA-NAP-amide that altogether cover a range 3. Voltammetry for the charge transfer at two immiscible electrolyte solutions interface International Nuclear Information System (INIS) Kihara, S.; Suzuki, M.; Maeda, K.; Ogura, K.; Matsui, M.; Yoshida, Z. 1989-01-01 The voltammetry for the charge transfer (VCT) at the interface of immicible solutions is a very powerful method for understanding the dynamic features of the charge transfer because of its unmatched advantage that the transfer energy and the number of charges transferred can be measured simultaneously and in situ. In the present paper, several novel systems for electron transfer are outlined, and the following topics are discussed based on results obtained by the current scan polarography at the solution dropping electrode developed as a technique for VCT: the relation between the half-wave potential in VCT for ion transfer and the characteristics of the ion transferred; the relation between the half-wave potential in VCT for electron transfer and the electrochemical nature of a redox couple added in water and that added in organic solution; and the ion transfer through a liquid membrane promoted by electron transfer. Observations are presented and discussion is made on the characteristics of ion transfer polarograms, those of electron transfer polarograms, and ion transfer promoted by electron transfer at a liquid/membrane interface. (N.K.) 4. Design of a Software for Calculating Isoelectric Point of a Polypeptide According to Their Net Charge Using the Graphical Programming Language LabVIEW Science.gov (United States) Tovar, Glomen 2018-01-01 A software to calculate the net charge and to predict the isoelectric point (pI) of a polypeptide is developed in this work using the graphical programming language LabVIEW. Through this instrument the net charges of the ionizable residues of the chains of the proteins are calculated at different pH values, tabulated, pI is predicted and an Excel… 5. Cost-Effectiveness Comparison of Coupler Designs of Wireless Power Transfer for Electric Vehicle Dynamic Charging Directory of Open Access Journals (Sweden) Weitong Chen 2016-11-01 Full Text Available This paper presents a cost-effectiveness comparison of coupler designs for wireless power transfer (WPT, meant for electric vehicle (EV dynamic charging. The design comparison of three common types of couplers is first based on the raw material cost, output power, transfer efficiency, tolerance of horizontal offset, and flux density. Then, the optimal cost-effectiveness combination is selected for EV dynamic charging. The corresponding performances of the proposed charging system are compared and analyzed by both simulation and experimentation. The results verify the validity of the proposed dynamic charging system for EVs. 6. Reduced Charge Transfer Exciton Recombination in Organic Semiconductor Heterojunctions by Molecular Doping Science.gov (United States) Deschler, Felix; da Como, Enrico; Limmer, Thomas; Tautz, Raphael; Godde, Tillmann; Bayer, Manfred; von Hauff, Elizabeth; Yilmaz, Seyfullah; Allard, Sybille; Scherf, Ullrich; Feldmann, Jochen 2011-09-01 We investigate the effect of molecular doping on the recombination of electrons and holes localized at conjugated-polymer-fullerene interfaces. We demonstrate that a low concentration of p-type dopant molecules (<4% weight) reduces the interfacial recombination via charge transfer excitons and results in a favored formation of separated carriers. This is observed by the ultrafast quenching of photoluminescence from charge transfer excitons and the increase in photoinduced polaron density by ˜70%. The results are consistent with a reduced formation of emissive charge transfer excitons, induced by state filling of tail states. 7. Robust Stacking-Independent Ultrafast Charge Transfer in MoS2/WS2 Bilayers. Science.gov (United States) Ji, Ziheng; Hong, Hao; Zhang, Jin; Zhang, Qi; Huang, Wei; Cao, Ting; Qiao, Ruixi; Liu, Can; Liang, Jing; Jin, Chuanhong; Jiao, Liying; Shi, Kebin; Meng, Sheng; Liu, Kaihui 2017-12-26 Van der Waals-coupled two-dimensional (2D) heterostructures have attracted great attention recently due to their high potential in the next-generation photodetectors and solar cells. The understanding of charge-transfer process between adjacent atomic layers is the key to design optimal devices as it directly determines the fundamental response speed and photon-electron conversion efficiency. However, general belief and theoretical studies have shown that the charge transfer behavior depends sensitively on interlayer configurations, which is difficult to control accurately, bringing great uncertainties in device designing. Here we investigate the ultrafast dynamics of interlayer charge transfer in a prototype heterostructure, the MoS 2 /WS 2 bilayer with various stacking configurations, by optical two-color ultrafast pump-probe spectroscopy. Surprisingly, we found that the charge transfer is robust against varying interlayer twist angles and interlayer coupling strength, in time scale of ∼90 fs. Our observation, together with atomic-resolved transmission electron characterization and time-dependent density functional theory simulations, reveals that the robust ultrafast charge transfer is attributed to the heterogeneous interlayer stretching/sliding, which provides additional channels for efficient charge transfer previously unknown. Our results elucidate the origin of transfer rate robustness against interlayer stacking configurations in optical devices based on 2D heterostructures, facilitating their applications in ultrafast and high-efficient optoelectronic and photovoltaic devices in the near future. 8. Charge separation in photoinitiated electron transfer reactions induced by a polyelectrolyte International Nuclear Information System (INIS) Meyerstein, D.; Rabani, J.; Matheson, M.S.; Meisel, D. 1978-01-01 When uncharged molecules quench the luminescence of Ru(bpy) 3 /sup 2+*/ by electron transfer to the quencher, the addition of poly(vinyl sulfate) (PVS) may, through its potential field, affect the rate of quenching, enhance the net separated charge yield, and slow the back reaction of the separated photoredox products. In all such cases that we have studied the quenching rate in the presence of PVS was reduced to about 60% of the rate measured in the absence of PVS. For two neutral species, iron(III) nitrilotriacetate (FeNTA) and cobalt(III) acetylacetonate (Co(acac) 3 ), photoreduction of the quencher was observed, and the redox yield escaping geminate recombination was substantially increased by added PVS. In the case of FeNTA the rate of the bulk back reaction was not changed appreciably by the presence of PVS owing to the rapid neutralization of Fe(NTA) - by protonation. For Co(acac) 3 the rate of the bulk back reaction was decreased by several orders of magnitude and the back reaction was shown to occur via the enolate form of the ligand which is released to the bulk solution. 4 figures, 4 tables 9. b-Cyclodextrin-assisted intervalence charge transfer in mixed- valent Indian Academy of Sciences (India) Administrator The study of intramolecular electron transfer in redox active binuclear transition metal complexes is of great fundamental importance and is an area of contemporary research interest. Though there are many reports on the role of bridging ligands (BL) in tuning metal–metal interactions and intramolecular electron transfers in ... 10. Engineering Interfacial Charge Transfer in CsPbBr3 Perovskite Nanocrystals by Heterovalent Doping KAUST Repository Begum, Raihana; Parida, Manas R.; Abdelhady, Ahmed L.; Banavoth, Murali; AlYami, Noktan; Ahmed, Ghada H.; Hedhili, Mohamed N.; Bakr, Osman; Mohammed, Omar F. 2016-01-01 Since compelling device efficiencies of perovskite solar cells have been achieved, investigative efforts have turned to understand other key challenges in these systems, such as engineering interfacial energy-level alignment and charge transfer (CT 11. Multiple nucleon transfer in damped nuclear collisions. [Lectures, mass charge, and linear and angular momentum transport Energy Technology Data Exchange (ETDEWEB) Randrup, J. 1979-07-01 This lecture discusses a theory for the transport of mass, charge, linear, and angular momentum and energy in damped nuclear collisions, as induced by multiple transfer of individual nucleons. 11 references. 12. Positronium Inhibition and Quenching by Organic Electron Acceptors and Charge Transfer Complexes DEFF Research Database (Denmark) Jansen, P.; Eldrup, Morten Mostgaard; Jensen, Bror Skytte 1975-01-01 Positron lifetime measurements were performed on a series of organic electron acceptors and charge-transfer complexes in solution. The acceptors cause both positronium (Ps) inhibition (with maybe one exception) and quenching, but when an acceptor takes part in a charge-transfer complex...... in terms of the spur reaction model of Ps formation. Correlation was also made to gas phase reaction between electron acceptors and free electron, as well as to pulse radiolysis data.... 13. Synthesis and photophysical properties of a novel terephthalic PH sensor based on internal charge transfer International Nuclear Information System (INIS) Miladinova, Polya M. 2016-01-01 A novel fluorescence sensing derivative of 2-aminodimethylterephthalate configured as a “fluorophore-receptor” system was synthesized and investigated. Due to the internal charge transfer, the designed fluorophore was able to act as a pH-probe via an “off-on” fluorescence sensing mechanism. The sensor activity toward protons as cations and hydroxide as anions in DMF was studied by monitoring the changes of the fluorescence intensity. Keywords: 2-aminoterephthalic derivative, ICT (internal charge transfer), pH sensor. 14. High Pressure Optical Studies of the Thallous Halides and of Charge-Transfer Complexes Science.gov (United States) Jurgensen, Charles Willard High pressure was used to study the insulator -to-metal transition in sulfur and the thallous halides and to study the intermolecular interactions in charge -transfer complexes. The approach to the band overlap insulator -to-metal transition was studied in three thallous halides and sulfur by optical absorption measurements of the band gap as a function of pressure. The band gap of sulfur continuously decreases with pressure up to the insulator -to-metal transition which occurs between 450 and 485 kbars. The results on the thallous halides indicate that the indirect gap decreases more rapidly than the direct gap; the closing of the indirect gap is responsible for the observed insulator -to-metal transitions. High pressure electronic and vibrational spectroscopic measurements on the solid-state complexes of HMB-TCNE were used to study the intermolecular interactions of charge -transfer complexes. The vibrational frequency shifts indicate that the degree of charge transfer increases with pressure which is independently confirmed by an increase in the molar absorptivity of the electronic charge-transfer peak. Induction and dispersion forces contribute towards a red shift of the charge-transfer peak; however, charge-transfer resonance contributes toward a blue shift and this effect is dominant for the HMB-TCNE complexes. High pressure electronic spectra were used to study the effect of intermolecular interactions on the electronic states of TCNQ and its complexes. The red shifts with pressure of the electronic spectra of TCNQ and (TCNQ)(' -) in polymer media and of crystalline TCNQ can be understood in terms of Van der Waals interactions. None of the calculations which considered intradimer distance obtained the proper behavior for either the charge-transfer of the locally excited states of the complexes. The qualitative behavior of both states can be interpreted as the effect of increased mixing of the locally excited and charge transfer states. 15. The influence of electric charge transferred during electro-mechanical reshaping on mechanical behavior of cartilage Science.gov (United States) Protsenko, Dimitry E.; Lim, Amanda; Wu, Edward C.; Manuel, Cyrus; Wong, Brian J. F. 2011-03-01 Electromechanical reshaping (EMR) of cartilage has been suggested as an alternative to the classical surgical techniques of modifying the shape of facial cartilages. The method is based on exposure of mechanically deformed cartilaginous tissue to a low level electric field. Electro-chemical reactions within the tissue lead to reduction of internal stress, and establishment of a new equilibrium shape. The same reactions offset the electric charge balance between collagen and proteoglycan matrix and interstitial fluid responsible for maintenance of cartilage mechanical properties. The objective of this study was to investigate correlation between the electric charge transferred during EMR and equilibrium elastic modulus. We used a finite element model based on the triphasic theory of cartilage mechanical properties to study how electric charges transferred in the electro-chemical reactions in cartilage can change its mechanical responses to step displacements in unconfined compression. The concentrations of the ions, the strain field and the fluid and ion velocities within the specimen subject to an applied mechanical deformation were estimated and apparent elastic modulus (the ratio of the equilibrium axial stress to the axial strain) was calculated as a function of transferred charge. The results from numerical calculations showed that the apparent elastic modulus decreases with increase in electric charge transfer. To compare numerical model with experimental observation we measured elastic modulus of cartilage as a function of electric charge transferred in electric circuit during EMR. Good correlation between experimental and theoretical data suggests that electric charge disbalance is responsible for alteration of cartilage mechanical properties. 16. Proton transfer to charged platinum electrodes. A molecular dynamics trajectory study. Science.gov (United States) Wilhelm, Florian; Schmickler, Wolfgang; Spohr, Eckhard 2010-05-05 A recently developed empirical valence bond (EVB) model for proton transfer on Pt(111) electrodes (Wilhelm et al 2008 J. Phys. Chem. C 112 10814) has been applied in molecular dynamics (MD) simulations of a water film in contact with a charged Pt surface. A total of seven negative surface charge densities σ between -7.5 and -18.9 µC cm(-2) were investigated. For each value of σ, between 30 and 84 initial conditions of a solvated proton within a water slab were sampled, and the trajectories were integrated until discharge of a proton occurred on the charged surfaces. We have calculated the mean rates for discharge and for adsorption of solvated protons within the adsorbed water layer in contact with the metal electrode as a function of surface charge density. For the less negative values of σ we observe a Tafel-like exponential increase of discharge rate with decreasing σ. At the more negative values this exponential increase levels off and the discharge process is apparently transport limited. Mechanistically, the Tafel regime corresponds to a stepwise proton transfer: first, a proton is transferred from the bulk into the contact water layer, which is followed by transfer of a proton to the charged surface and concomitant discharge. At the more negative surface charge densities the proton transfer into the contact water layer and the transfer of another proton to the surface and its discharge occur almost simultaneously. 17. Electron transfer and decay processes of highly charged iodine ions International Nuclear Information System (INIS) Sakaue, Hiroyuki A.; Danjo, Atsunori; Hosaka, Kazumoto 2005-01-01 In the present experimental work we have investigated multi-electron transfer processes in I q+ (q=10, 15, 20 and 25) + Ne, Ar, Kr and Xe collisions at 1.5q keV energy. The branching ratios between Auger and radiative decay channels have been measured in decay processes of multiply excited states formed by multi-electron transfer collisions. It has been shown that, in all the multi-electron transfer processes investigated, the Auger decays are far dominant over the radiative decay processes and the branching ratios are clearly characterized by the average principal quantum number of the initial excited states of projectile ions. We could express the branching ratios in high Rydberg states formed in multi-electron transfer processes by using the decay probability of one Auger electron emission. (author) 18. CNDO/SCF molecular orbital structural studies and charge transfer ... African Journals Online (AJOL) dimethoxy- diquinone (DQ) has been discussed and compared with some related compounds. The electron transfer between DQ and uracil was studied in ethanol as an interaction medium. The ionization potentials and the electron affinities of the ... 19. High Power Wireless Transfer : For Charging High Power Batteries OpenAIRE Gill, Himmat 2017-01-01 Wireless power transfer (WPT) is developing with emerging of new technologies that has made it possible to transfer electricity over certain distances without any physical contact, offering significant benefits to modern automation systems, medical applications, consumer electronic, and especially in electric vehicle systems. The goal of this study is to provide a brief review of existing compensation topologies for the loosely coupled transformer. The technique used to simulate a co... 20. Incorporation of charge transfer into the explicit polarization fragment method by grand canonical density functional theory. Science.gov (United States) Isegawa, Miho; Gao, Jiali; Truhlar, Donald G 2011-08-28 Molecular fragmentation algorithms provide a powerful approach to extending electronic structure methods to very large systems. Here we present a method for including charge transfer between molecular fragments in the explicit polarization (X-Pol) fragment method for calculating potential energy surfaces. In the conventional X-Pol method, the total charge of each fragment is preserved, and charge transfer between fragments is not allowed. The description of charge transfer is made possible by treating each fragment as an open system with respect to the number of electrons. To achieve this, we applied Mermin's finite temperature method to the X-Pol wave function. In the application of this method to X-Pol, the fragments are open systems that partially equilibrate their number of electrons through a quasithermodynamics electron reservoir. The number of electrons in a given fragment can take a fractional value, and the electrons of each fragment obey the Fermi-Dirac distribution. The equilibrium state for the electrons is determined by electronegativity equalization with conservation of the total number of electrons. The amount of charge transfer is controlled by re-interpreting the temperature parameter in the Fermi-Dirac distribution function as a coupling strength parameter. We determined this coupling parameter so as to reproduce the charge transfer energy obtained by block localized energy decomposition analysis. We apply the new method to ten systems, and we show that it can yield reasonable approximations to potential energy profiles, to charge transfer stabilization energies, and to the direction and amount of charge transferred. © 2011 American Institute of Physics 1. Charge transfer in DNA: role of base pairing Czech Academy of Sciences Publication Activity Database Kratochvílová, Irena; Bunček, M.; Schneider, Bohdan 2009-01-01 Roč. 38, Suppl. (2009), S123-S123 ISSN 0175-7571. [EBSA European Biophysics Congress /7./. Genoa, 11.07.2009-15.07.2009] Institutional research plan: CEZ:AV0Z10100520; CEZ:AV0Z50520701 Keywords : DNA * charge transport * base pairing Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.437, year: 2009 2. Identification of the Heat Transfer Coefficient at the Charge Surface Heated on the Chamber Furnace Directory of Open Access Journals (Sweden) Gołdasz A. 2017-06-01 Full Text Available The inverse method was applied to determine the heat flux reaching the charge surface. The inverse solution was based upon finding the minimum of the error norm between the measured and calculated temperatures. The charge temperature field was calculated with the finite element method by solving the heat transfer equation for a square charge made of 15HM steel heated on all its surfaces. On the basis of the mean value of heat flux, the value of the heat transfer coefficient at each surface was determined depending on the surface temperature of the material heated. 3. Charge transfer and bond lengths in YBa2Cu3-xMxO6+y International Nuclear Information System (INIS) Jorgensen, J.D.; Rhyne, J.J.; Neumann, D.A.; Miceli, P.F.; Tarascon, J.M.; Greene, L.H.; Barboux, P. 1989-01-01 We discuss the effects of doping on the Cu chain sites in YBa 2 Cu 3-x M x O 6+y . The relationship between bond lengths obtained from neutron scattering and charge transfer is evaluated in terms of bond valence. In particular, it is concluded that removing an oxygen from the chains transfers one electron to the planes. 24 refs., 3 figs 4. Using metal complex-labeled peptides for charge transfer-based biosensing with semiconductor quantum dots Science.gov (United States) Medintz, Igor L.; Pons, Thomas; Trammell, Scott A.; Blanco-Canosa, Juan B.; Dawson, Philip E.; Mattoussi, Hedi 2009-02-01 Luminescent colloidal semiconductor quantum dots (QDs) have unique optical and photonic properties and are highly sensitive to charge transfer in their surrounding environment. In this study we used synthetic peptides as physical bridges between CdSe-ZnS core-shell QDs and some of the most common redox-active metal complexes to understand the charge transfer interactions between the metal complexes and QDs. We found that QD emission underwent quenching that was highly dependent on the choice of metal complex used. We also found that quenching traces the valence or number of metal complexes brought into close proximity of the nanocrystal surface. Monitoring of the QD absorption bleaching in the presence of the metal complex provided insight into the charge transfer mechanism. The data suggest that two distinct charge transfer mechanisms can take place. One directly to the QD core states for neutral capping ligands and a second to surface states for negatively charged capping ligands. A basic understanding of the proximity driven charge-transfer and quenching interactions allowed us to construct proteolytic enzyme sensing assemblies with the QD-peptide-metal complex conjugates. 5. Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics † Science.gov (United States) Chen, Wei; Shen, Jana K. 2014-01-01 Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: 1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? 2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK a values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via co-titrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle-mesh Ewald, considering the known artifacts due to charge-compensating background plasma. PMID:25142416 6. Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics. Science.gov (United States) Chen, Wei; Shen, Jana K 2014-10-15 Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma. Copyright © 2014 Wiley Periodicals, Inc. 7. Integer Charge Transfer and Hybridization at an Organic Semiconductor/Conductive Oxide Interface KAUST Repository Gruenewald, Marco 2015-02-11 We investigate the prototypical hybrid interface formed between PTCDA and conductive n-doped ZnO films by means of complementary optical and electronic spectroscopic techniques. We demonstrate that shallow donors in the vicinity of the ZnO surface cause an integer charge transfer to PTCDA, which is clearly restricted to the first monolayer. By means of DFT calculations, we show that the experimental signatures of the anionic PTCDA species can be understood in terms of strong hybridization with localized states (the shallow donors) in the substrate and charge back-donation, resulting in an effectively integer charge transfer across the interface. Charge transfer is thus not merely a question of locating the Fermi level above the PTCDA electron-transport level but requires rather an atomistic understanding of the interfacial interactions. The study reveals that defect sites and dopants can have a significant influence on the specifics of interfacial coupling and thus on carrier injection or extraction. 8. Photoinduced partial charge transfer between conjugated polymer and fullerene in solutions International Nuclear Information System (INIS) Lin Hongzhen; Weng Yufeng; Huang Hongmin; He Qingguo; Zheng Min; Bai Fenglian 2004-01-01 Photoinduced charge transfer between a conjugated polymer and C 60 and the related processes were investigated in dilute solutions. The substantial fluorescence quenching is correlated with the efficient exciton diffusion within the polymer chains, according to which a sphere-of-action mechanism is proposed. An emissive exciplex was found formed between the conjugated polymer and fullerene in a nonpolar solvent, indicating the occurrence of a photoinduced partial charge transfer process. The low-energy sites in the polymer are believed to play a crucial role in the partial charge transfer. The asymmetry of the exciplex provides a method for evaluating the tendency of photoinduced charge separation between the donor and the acceptor. This method allows screening candidates for photovoltaic applications 9. Net trophic transfer efficiencies of polychlorinated biphenyl congeners to lake trout (Salvelinus namaycush) from its prey Science.gov (United States) Madenjian, Charles P.; David, Solomon R.; Rediske, Richard R.; O’Keefe, James P. 2012-01-01 Lake trout (Salvelinus namaycush) were fed bloater (Coregonus hoyi) in eight laboratory tanks over a 135-d experiment. At the start of the experiment, four to nine fish in each tank were sacrificed, and the concentrations of 75 polychlorinated biphenyl (PCB) congeners within these fish were determined. Polychlorinated biphenyl congener concentrations were also determined in the 10 lake trout remaining in each of the eight tanks at the end of the experiment as well as in the bloater fed to the lake trout. Each lake trout was weighed at the start and the end of the experiment, and the amount of food eaten by the lake trout was recorded. Using these measurements, net trophic transfer efficiency (γ) from the bloater to the lake trout in each of the eight tanks was calculated for each of the 75 congeners. Results showed that γ did not vary significantly with the degree of chlorination of the PCB congeners, and γ averaged 0.66 across all congeners. However,γ did show a slight, but significant, decrease as logKOW increased from 6.0 to 8.2. Activity level of the lake trout did not have a significant effect on γ. 10. Photophysics of charge transfer in a polyfluorene/violanthrone blend Science.gov (United States) Cabanillas-Gonzalez, J.; Virgili, T.; Lanzani, G.; Yeates, S.; Ariu, M.; Nelson, J.; Bradley, D. D. C. 2005-01-01 We present a study of the photophysical and photovoltaic properties of blends of violanthrone in poly[9, 9-bis (2-ethylhexyl)-fluorene-2, 7-diyl ] (PF2/6) . Photoluminescence quenching and photocurrent measurements show moderate efficiencies for charge generation, characteristic of such polymer/dye blends. Pump-probe measurements on blend films suggest that while ˜47% of the total exciton population dissociates within 4ps of photoexcitation, only ˜32% subsequently results in the formation of dye anions. We attribute the discrepancy to the likely formation of complex species with long lifetimes, such as stabilized interface charge pairs or exciplexes. This conclusion is supported by the appearance of a long lifetime component of 2.4ns in the dynamics of the photoinduced absorption signal associated to polarons in photoinduced absorption bands centered at 560nm . 11. An abnormally slow proton transfer reaction in a simple HBO derivative due to ultrafast intramolecular-charge transfer events. Science.gov (United States) Alarcos, Noemí; Gutierrez, Mario; Liras, Marta; Sánchez, Félix; Douhal, Abderrazzak 2015-07-07 We report on the steady-state, picosecond and femtosecond time-resolved studies of a charge and proton transfer dye 6-amino-2-(2'-hydroxyphenyl)benzoxazole (6A-HBO) and its methylated derivative 6-amino-2-(2'-methoxyphenyl)benzoxazole (6A-MBO), in different solvents. With femtosecond resolution and comparison with the photobehaviour of 6A-MBO, we demonstrate for 6A-HBO in solution, the photoproduction of an intramolecular charge-transfer (ICT) process at S1 taking place in ∼140 fs or shorter, followed by solvent relaxation in the charge transferred species. The generated structure (syn-enol charge transfer conformer) experiences an excited-state intramolecular proton-transfer (ESIPT) reaction to produce a keto-type tautomer. This subsequent proton motion occurs in 1.2 ps (n-heptane), 14 ps (DCM) and 35 ps (MeOH). In MeOH, it is assisted by the solvent molecules and occurs through tunneling for which we got a large kinetic isotope effect (KIE) of about 13. For the 6A-DBO (deuterated sample in CD3OD) the global proton-transfer reaction takes place in 200 ps, showing a remarkable slow KIE regime. The slow ESIPT reaction in DCM (14 ps), not through tunnelling as it is not sensitive to OH/OD exchange, has however to overcome an energy barrier using intramolecular as well as solvent coordinates. The rich ESIPT dynamics of 6A-HBO in the used solutions is governed by an ICT reaction, triggered by the amino group, and it is solvent dependent. Thus, the charge injection to a 6A-HBO molecular frame makes the ICT species more stable, and the phenol group less acidic, slowing down the subsequent ESIPT reaction. Our findings bring new insights into the coupling between ICT and ESIPT reactions on the potential-energy surfaces of several barriers. 12. Impact of fuel-dependent electricity retail charges on the value of net-metered PV applications in vertically integrated systems International Nuclear Information System (INIS) Nikolaidis, Alexandros I.; Milidonis, Andreas; Charalambous, Charalambos A. 2015-01-01 Retail electricity charges inevitably influence the financial rationale of using net-metered photovoltaic (PV) applications since their structure as well as their level may vary significantly over the life-cycle of a customer-sited PV generation system. This subsequently introduces a further uncertainty for a ratepayer considering a net-metered PV investment. To thoroughly comprehend this uncertainty, the paper employs a top-down approach – in vertically integrated environments – to model the volatility of partially hedged electricity charges and its subsequent impact on the value of bill savings from net-metered PV systems. Besides the utility's pricing strategy and rate structures, particular emphasis is given in modeling the fossil fuel mix component that introduces a significant source of uncertainty on electricity charges and thus on the value of bill savings of net-metered, customer-sited, PV applications. - Highlights: • A top-down approach of developing traditional electricity charges is provided. • The combined effect of pricing strategies, rate structures and fuels is examined. • Fossil fuel prices can substantially affect the net metering compensation. • A financial risk assessment for net-metered PV systems is performed 13. Complexes with charge transfer and ion-radical salts in catalysis Energy Technology Data Exchange (ETDEWEB) Krylov, O V [AN SSSR, Moscow. Inst. Khimicheskoj Fiziki 1978-01-01 Considered are the data experimentally proving formation of complexes with charge transfer as intermediate complexes in homogeneous and heterogeneous catalysis. Catalytic activity correlations with charge transfer energy (and in heterogeneous catalysis with width of semiconductor forbidden band can be useful while selection of catalysts (MoO/sub 3//MgO; V/sub 2/O/sub 5//MgO; MoO/sub 3//Al/sub 2/O/sub 3/; V/sub 2/O/sub 5//Al/sub 2/O/sub 3/). A review of papers on catalytic activity of the previously prepared complexes with charge transfer and ion-radical salts is given. The use of alkali metal complexes with aromatic compounds showed their high activity in hydrogenation reactions and proved principle possibility of activation of hydrogen and hydrocarbons by the systems which do not contain transfer metals. 14. Estimating Net Primary Productivity Beneath Snowpack Using Snowpack Radiative Transfer Modeling and Global Satellite Data Science.gov (United States) Barber, D. E.; Peterson, M. C. 2002-05-01 Sufficient photosynthetically active radiation (PAR) penetrates snow for plants to grow beneath snowpack during late winter or early spring in tundra ecosystems. During the spring in this ecosystem, the snowpack creates an environment with higher humidity and less variable and milder temperatures than on the snow-free land. Under these conditions, the amount of PAR available is likely to be the limiting factor for plant growth. Current methods for determining net primary productivity (NPP) of tundra ecosystems do not account for this plant growth beneath snowpack, apparently resulting in underestimating plant production there. We are currently in the process of estimating the magnitude of this early growth beneath snow for tundra ecosystems. Our method includes a radiative transfer model that simulates diffuse and direct PAR penetrating snowpack based on downwelling PAR values and snow depth data from global satellite databases. These PAR levels are convolved with plant growth for vegetation that thrives beneath snowpacks, such as lichen. We expect to present the net primary production for Cladonia species (a common Arctic lichen) that has the capability of photosynthesizing at low temperatures beneath snowpack. This method may also be used to study photosynthesis beneath snowpacks in other hardy plants. Lichens are used here as they are common in snow-covered regions, flourish under snowpack, and provide an important food source for tundra herbivores (e.g. caribou). In addition, lichens are common in arctic-alpine environments and our results can be applied to these ecosystems as well. Finally, the NPP of lichen beneath snowpack is relatively well understood compared to other plants, making it ideal vegetation for this first effort at estimating the potential importance of photosynthesis at large scales. We are examining other candidate plants for their photosynthetic potential beneath snowpack at this time; however, little research has been done on this topic. We 15. Net-Charge Fluctuations in Pb-Pb collisions at\\sqrt{s_{NN}}= 2.76$TeV CERN Document Server Abelev, Betty; Adamova, Dagmar; Adare, Andrew Marshall; Aggarwal, Madan; Aglieri Rinella, Gianluca; Agocs, Andras Gabor; Agostinelli, Andrea; Aguilar Salazar, Saul; Ahammed, Zubayer; Ahmad, Arshad; Ahmad, Nazeer; Ahn, Sang Un; Akindinov, Alexander; Aleksandrov, Dmitry; Alessandro, Bruno; Alfaro Molina, Jose Ruben; Alici, Andrea; Alkin, Anton; Almaraz Avina, Erick Jonathan; Alme, Johan; Alt, Torsten; Altini, Valerio; Altinpinar, Sedat; Altsybeev, Igor; Andrei, Cristian; Andronic, Anton; Anguelov, Venelin; Anielski, Jonas; Anticic, Tome; Antinori, Federico; Antonioli, Pietro; Aphecetche, Laurent Bernard; Appelshauser, Harald; Arbor, Nicolas; Arcelli, Silvia; Armesto, Nestor; Arnaldi, Roberta; Aronsson, Tomas Robert; Arsene, Ionut Cristian; Arslandok, Mesut; Augustinus, Andre; Averbeck, Ralf Peter; Awes, Terry; Aysto, Juha Heikki; Azmi, Mohd Danish; Bach, Matthias Jakob; Badala, Angela; Baek, Yong Wook; 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Grelli, Alessandro; Grigoras, Alina Gabriela; Grigoras, Costin; Grigoriev, Vladislav; Grigoryan, Ara; Grigoryan, Smbat; Grinyov, Boris; Grion, Nevio; Grosse-Oetringhaus, Jan Fiete; Grossiord, Jean-Yves; Grosso, Raffaele; Guber, Fedor; Guernane, Rachid; Guerra Gutierrez, Cesar; Guerzoni, Barbara; Guilbaud, Maxime Rene Joseph; Gulbrandsen, Kristjan Herlache; Gunji, Taku; Gupta, Anik; Gupta, Ramni; Gutbrod, Hans; Haaland, Oystein Senneset; Hadjidakis, Cynthia Marie; Haiduc, Maria; Hamagaki, Hideki; Hamar, Gergoe; Hanratty, Luke David; Hansen, Alexander; Harmanova, Zuzana; Harris, John William; Hartig, Matthias; Hasegan, Dumitru; Hatzifotiadou, Despoina; Hayrapetyan, Arsen; Heckel, Stefan Thomas; Heide, Markus Ansgar; Helstrup, Haavard; Herghelegiu, Andrei Ionut; Herrera Corral, Gerardo Antonio; Herrmann, Norbert; Hess, Benjamin Andreas; Hetland, Kristin Fanebust; Hicks, Bernard; Hille, Per Thomas; Hippolyte, Boris; Horaguchi, Takuma; Hori, Yasuto; Hristov, Peter Zahariev; Hrivnacova, Ivana; 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Lara, Camilo Ernesto; Lardeux, Antoine Xavier; Lazzeroni, Cristina; Le Bornec, Yves; Lea, Ramona; Lechman, Mateusz; Lee, Graham Richard; Lee, Ki Sang; Lee, Sung Chul; Lefevre, Frederic; Lehnert, Joerg Walter; Leistam, Lars; Lemmon, Roy Crawford; Lenti, Vito; Leon Monzon, Ildefonso; Leon Vargas, Hermes; Leoncino, Marco; Levai, Peter; Lien, Jorgen; Lietava, Roman; Lindal, Svein; Lindenstruth, Volker; Lippmann, Christian; Lisa, Michael Annan; Liu, Lijiao; Loggins, Vera; Loginov, Vitaly; Lohn, Stefan Bernhard; Lohner, Daniel; Loizides, Constantinos; Loo, Kai Krister; Lopez, Xavier Bernard; Lopez Torres, Ernesto; Lovhoiden, Gunnar; Lu, Xianguo; Luettig, Philipp; Lunardon, Marcello; Luo, Jiebin; Luparello, Grazia; Luquin, Lionel; Luzzi, Cinzia; Ma, Rongrong; Maevskaya, Alla; Mager, Magnus; Mahapatra, Durga Prasad; Maire, Antonin; Mal'Kevich, Dmitry; Malaev, Mikhail; Maldonado Cervantes, Ivonne Alicia; Malinina, Ludmila; Malzacher, Peter; Mamonov, Alexander; Manceau, Loic Henri Antoine; Manko, Vladislav; Manso, Franck; Manzari, Vito; Mao, Yaxian; Marchisone, Massimiliano; Mares, Jiri; Margagliotti, Giacomo Vito; Margotti, Anselmo; Marin, Ana Maria; Marin Tobon, Cesar Augusto; Markert, Christina; Martashvili, Irakli; Martinengo, Paolo; Martinez, Mario Ivan; Martinez Davalos, Arnulfo; Martinez Garcia, Gines; Martynov, Yevgen; Mas, Alexis Jean-Michel; Masciocchi, Silvia; Masera, Massimo; Masoni, Alberto; Mastroserio, Annalisa; Matthews, Zoe Louise; Matyja, Adam Tomasz; Mayer, Christoph; Mazer, Joel; Mazzoni, Alessandra Maria; Meddi, Franco; Menchaca-Rocha, Arturo Alejandro; Mercado Perez, Jorge; Meres, Michal; Miake, Yasuo; Milano, Leonardo; Milosevic, Jovan; Mischke, Andre; Mishra, Aditya Nath; Miskowiec, Dariusz; Mitu, Ciprian Mihai; Mlynarz, Jocelyn; Mohanty, Bedangadas; Molnar, Levente; Montano Zetina, Luis Manuel; Monteno, Marco; Montes, Esther; Moon, Taebong; Morando, Maurizio; Moreira De Godoy, Denise Aparecida; Moretto, Sandra; Morsch, Andreas; Muccifora, Valeria; Mudnic, Eugen; Muhuri, Sanjib; Mukherjee, Maitreyee; Muller, Hans; Munhoz, Marcelo; Musa, Luciano; Musso, Alfredo; Nandi, Basanta Kumar; Nania, Rosario; Nappi, Eugenio; Nattrass, Christine; Naumov, Nikolay; Navin, Sparsh; Nayak, Tapan Kumar; Nazarenko, Sergey; Nazarov, Gleb; Nedosekin, Alexander; Nicassio, Maria; Niculescu, Mihai; Nielsen, Borge Svane; Niida, Takafumi; Nikolaev, Sergey; Nikolic, Vedran; Nikulin, Sergey; Nikulin, Vladimir; Nilsen, Bjorn Steven; Nilsson, Mads Stormo; Noferini, Francesco; Nomokonov, Petr; Nooren, Gerardus; Novitzky, Norbert; Nyanin, Alexandre; Nyatha, Anitha; Nygaard, Casper; Nystrand, Joakim Ingemar; Oeschler, Helmut Oskar; Oh, Saehanseul; Oh, Sun Kun; Oleniacz, Janusz; Oppedisano, Chiara; Ortona, Giacomo; Oskarsson, Anders Nils Erik; Otwinowski, Jacek Tomasz; Oyama, Ken; Pachmayer, Yvonne Chiara; Pachr, Milos; Padilla, Fatima; Pagano, Paola; Paic, Guy; Painke, Florian; Pajares, Carlos; Pal, Susanta Kumar; Palaha, Arvinder Singh; Palmeri, Armando; Papikyan, Vardanush; Pappalardo, Giuseppe; Park, Woo Jin; Passfeld, Annika; Patalakha, Dmitri Ivanovich; Paticchio, Vincenzo; Pavlinov, Alexei; Pawlak, Tomasz Jan; Peitzmann, Thomas; Pereira Da Costa, Hugo Denis Antonio; Pereira De Oliveira Filho, Elienos; Peresunko, Dmitri; Perez Lara, Carlos Eugenio; Perez Lezama, Edgar; Perini, Diego; Perrino, Davide; Peryt, Wiktor Stanislaw; Pesci, Alessandro; Peskov, Vladimir; Pestov, Yury; Petracek, Vojtech; Petran, Michal; Petris, Mariana; Petrov, Plamen Rumenov; Petrovici, Mihai; Petta, Catia; Piano, Stefano; Piccotti, Anna; Pikna, Miroslav; Pillot, Philippe; Pinazza, Ombretta; Pinsky, Lawrence; Pitz, Nora; Piuz, Francois; Piyarathna, Danthasinghe; Ploskon, Mateusz Andrzej; Pluta, Jan Marian; Pochybova, Sona; Podesta Lerma, Pedro Luis Manuel; Poghosyan, Martin; Polichtchouk, Boris; Pop, Amalia; Porteboeuf-Houssais, Sarah; Pospisil, Vladimir; Potukuchi, Baba; Prasad, Sidharth Kumar; Preghenella, Roberto; Prino, Francesco; Pruneau, Claude Andre; Pshenichnov, Igor; Puchagin, Sergey; Puddu, Giovanna; Pujahari, Prabhat Ranjan; Pulvirenti, Alberto; Punin, Valery; Putis, Marian; Putschke, Jorn Henning; Quercigh, Emanuele; Qvigstad, Henrik; Rachevski, Alexandre; Rademakers, Alphonse; Raiha, Tomi Samuli; Rak, Jan; Rakotozafindrabe, Andry Malala; Ramello, Luciano; Ramirez Reyes, Abdiel; Raniwala, Rashmi; Raniwala, Sudhir; Rasanen, Sami Sakari; Rascanu, Bogdan Theodor; Rathee, Deepika; Read, Kenneth Francis; Real, Jean-Sebastien; Redlich, Krzysztof; Rehman, Attiq Ur; Reichelt, Patrick; Reicher, Martijn; Renfordt, Rainer Arno Ernst; Reolon, Anna Rita; Reshetin, Andrey; Rettig, Felix Vincenz; Revol, Jean-Pierre; Reygers, Klaus Johannes; Riccati, Lodovico; Ricci, Renato Angelo; Richert, Tuva; Richter, Matthias Rudolph; Riedler, Petra; Riegler, Werner; Riggi, Francesco; Rodrigues Fernandes Rabacal, Bartolomeu; Rodriguez Cahuantzi, Mario; Rodriguez Manso, Alis; Roed, Ketil; Rohr, David; Rohrich, Dieter; Romita, Rosa; Ronchetti, Federico; Rosnet, Philippe; Rossegger, Stefan; Rossi, Andrea; Roy, Christelle Sophie; Roy, Pradip Kumar; Rubio Montero, Antonio Juan; Rui, Rinaldo; Russo, Riccardo; Ryabinkin, Evgeny; Rybicki, Andrzej; Sadovsky, Sergey; Safarik, Karel; Sahoo, Raghunath; Sahu, Pradip Kumar; Saini, Jogender; Sakaguchi, Hiroaki; Sakai, Shingo; Sakata, Dosatsu; Salgado, Carlos Albert; Salzwedel, Jai; Sambyal, Sanjeev Singh; Samsonov, Vladimir; Sanchez Castro, Xitzel; Sandor, Ladislav; Sandoval, Andres; Sano, Masato; Sano, Satoshi; Santo, Rainer; Santoro, Romualdo; Sarkamo, Juho Jaako; Scapparone, Eugenio; Scarlassara, Fernando; Scharenberg, Rolf Paul; Schiaua, Claudiu Cornel; Schicker, Rainer Martin; Schmidt, Christian Joachim; Schmidt, Hans Rudolf; Schreiner, Steffen; Schuchmann, Simone; Schukraft, Jurgen; Schutz, Yves Roland; Schwarz, Kilian Eberhard; Schweda, Kai Oliver; Scioli, Gilda; Scomparin, Enrico; Scott, Patrick Aaron; Scott, Rebecca; Segato, Gianfranco; Selyuzhenkov, Ilya; Senyukov, Serhiy; Seo, Jeewon; Serci, Sergio; Serradilla, Eulogio; Sevcenco, Adrian; Shabetai, Alexandre; Shabratova, Galina; Shahoyan, Ruben; Sharma, Natasha; Sharma, Satish; Shigaki, Kenta; Shimomura, Maya; Shtejer, Katherin; Sibiriak, Yury; Siciliano, Melinda; Sicking, Eva; Siddhanta, Sabyasachi; Siemiarczuk, Teodor; Silvermyr, David Olle Rickard; Silvestre, Catherine; Simatovic, Goran; Simonetti, Giuseppe; Singaraju, Rama Narayana; Singh, Ranbir; Singha, Subhash; Singhal, Vikas; Sinha, Bikash; Sinha, Tinku; Sitar, Branislav; Sitta, Mario; Skaali, Bernhard; Skjerdal, Kyrre; Smakal, Radek; Smirnov, Nikolai; Snellings, Raimond; Sogaard, Carsten; Soltz, Ron Ariel; Son, Hyungsuk; Song, Jihye; Song, Myunggeun; Soos, Csaba; Soramel, Francesca; Sputowska, Iwona; Spyropoulou-Stassinaki, Martha; Srivastava, Brijesh Kumar; Stachel, Johanna; Stan, Ionel; Stefanek, Grzegorz; Stefanini, Giorgio; Steinpreis, Matthew; Stenlund, Evert Anders; Steyn, Gideon Francois; Stiller, Johannes Hendrik; Stocco, Diego; Stolpovskiy, Mikhail; Strabykin, Kirill; Strmen, Peter; Suaide, Alexandre Alarcon do Passo; Subieta Vasquez, Martin Alfonso; Sugitate, Toru; Suire, Christophe Pierre; Sukhorukov, Mikhail; Sultanov, Rishat; Sumbera, Michal; Susa, Tatjana; Szanto de Toledo, Alejandro; Szarka, Imrich; Szczepankiewicz, Adam; Szostak, Artur Krzysztof; Szymanski, Maciej; Takahashi, Jun; Tapia Takaki, Daniel Jesus; Tarazona Martinez, Alfonso; Tauro, Arturo; Tejeda Munoz, Guillermo; Telesca, Adriana; Terrevoli, Cristina; Thader, Jochen Mathias; Thomas, Deepa; Tieulent, Raphael Noel; Timmins, Anthony; Toia, Alberica; Torii, Hisayuki; Tosello, Flavio; Trubnikov, Victor; Trzaska, Wladyslaw Henryk; Tsuji, Tomoya; Tumkin, Alexandr; Turrisi, Rosario; Tveter, Trine Spedstad; Ulery, Jason Glyndwr; Ullaland, Kjetil; Ulrich, Jochen; Uras, Antonio; Urban, Jozef; Urciuoli, Guido Marie; Usai, Gianluca; Vajzer, Michal; Vala, Martin; Valencia Palomo, Lizardo; Vallero, Sara; van der Kolk, Naomi; van Leeuwen, Marco; Vande Vyvre, Pierre; Vannucci, Luigi; Vargas, Aurora Diozcora; Varma, Raghava; Vasileiou, Maria; Vasiliev, Andrey; Vechernin, Vladimir; Veldhoen, Misha; Venaruzzo, Massimo; Vercellin, Ermanno; Vergara, Sergio; Vernet, Renaud; Verweij, Marta; Vickovic, Linda; Viesti, Giuseppe; Vikhlyantsev, Oleg; Vilakazi, Zabulon; Villalobos Baillie, Orlando; Vinogradov, Alexander; Vinogradov, Leonid; Vinogradov, Yury; Virgili, Tiziano; Viyogi, Yogendra; Vodopianov, Alexander; Voloshin, Kirill; Voloshin, Sergey; Volpe, Giacomo; von Haller, Barthelemy; Vranic, Danilo; Øvrebekk, Gaute; Vrlakova, Janka; Vulpescu, Bogdan; Vyushin, Alexey; Wagner, Boris; Wagner, Vladimir; Wan, Renzhuo; Wang, Dong; Wang, Mengliang; Wang, Yifei; Wang, Yaping; Watanabe, Kengo; Weber, Michael; Wessels, Johannes; Westerhoff, Uwe; Wiechula, Jens; Wikne, Jon; Wilde, Martin Rudolf; Wilk, Alexander; Wilk, Grzegorz Andrzej; Williams, Crispin; Windelband, Bernd Stefan; Xaplanteris Karampatsos, Leonidas; Yaldo, Chris G; Yamaguchi, Yorito; Yang, Hongyan; Yang, Shiming; Yasnopolsky, Stanislav; Yi, JunGyu; Yin, Zhongbao; Yoo, In-Kwon; Yoon, Jongik; Yu, Weilin; Yuan, Xianbao; Yushmanov, Igor; Zach, Cenek; Zampolli, Chiara; Zaporozhets, Sergey; Zarochentsev, Andrey; Zavada, Petr; Zaviyalov, Nikolai; Zbroszczyk, Hanna Paulina; Zelnicek, Pierre; Zgura, Sorin Ion; Zhalov, Mikhail; Zhang, Haitao; Zhang, Xiaoming; Zhou, Daicui; Zhou, Fengchu; Zhou, You; Zhu, Jianhui; Zhu, Xiangrong; Zichichi, Antonino; Zimmermann, Alice; Zinovjev, Gennady; Zoccarato, Yannick Denis; Zynovyev, Mykhaylo; Zyzak, Maksym 2013-04-10 We report the first measurement of the net-charge fluctuations in Pb-Pb collisions at$\\sqrt{s_{NN}}$= 2.76 TeV, measured with the ALICE detector at the CERN Large Hadron Collider. The dynamical fluctuations per unit entropy are observed to decrease when going from peripheral to central collisions. An additional reduction in the amount of fluctuations is seen in comparison to the results from lower energies. We examine the dependence of fluctuations on the pseudo-rapidity interval, which may account for the dilution of fluctuations during the evolution of the system. We find that the ALICE data points are between the theoretically predicted values for a hadron gas and a Quark-Gluon Plasma. 16. A differential dielectric spectroscopy setup to measure the electric dipole moment and net charge of colloidal quantum dots Energy Technology Data Exchange (ETDEWEB) Kortschot, R. J.; Bakelaar, I. A.; Erné, B. H.; Kuipers, B. W. M., E-mail: [email protected] [Van ' t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH Utrecht (Netherlands) 2014-03-15 A sensitive dielectric spectroscopy setup is built to measure the response of nanoparticles dispersed in a liquid to an alternating electric field over a frequency range from 10{sup −2} to 10{sup 7} Hz. The measured complex permittivity spectrum records both the rotational dynamics due to a permanent electric dipole moment and the translational dynamics due to net charges. The setup consists of a half-transparent capacitor connected in a bridge circuit, which is balanced on pure solvent only, using a software-controlled compensating voltage. In this way, the measured signal is dominated by the contributions of the nanoparticles rather than by the solvent. We demonstrate the performance of the setup with measurements on a dispersion of colloidal CdSe quantum dots in the apolar liquid decalin. 17. A differential dielectric spectroscopy setup to measure the electric dipole moment and net charge of colloidal quantum dots. Science.gov (United States) Kortschot, R J; Bakelaar, I A; Erné, B H; Kuipers, B W M 2014-03-01 A sensitive dielectric spectroscopy setup is built to measure the response of nanoparticles dispersed in a liquid to an alternating electric field over a frequency range from 10(-2) to 10(7) Hz. The measured complex permittivity spectrum records both the rotational dynamics due to a permanent electric dipole moment and the translational dynamics due to net charges. The setup consists of a half-transparent capacitor connected in a bridge circuit, which is balanced on pure solvent only, using a software-controlled compensating voltage. In this way, the measured signal is dominated by the contributions of the nanoparticles rather than by the solvent. We demonstrate the performance of the setup with measurements on a dispersion of colloidal CdSe quantum dots in the apolar liquid decalin. 18. Charge Transfer Properties Through Graphene Layers in Gas Detectors CERN Document Server Thuiner, P.; Jackman, R.B.; Müller, H.; Nguyen, T.T.; Oliveri, E.; Pfeiffer, D.; Resnati, F.; Ropelewski, L.; Smith, J.A.; van Stenis, M.; Veenhof, R. 2016-01-01 Graphene is a single layer of carbon atoms arranged in a honeycomb lattice with remarkable mechanical, electrical and optical properties. For the first time graphene layers suspended on copper meshes were installed into a gas detector equipped with a gaseous electron multiplier. Measurements of low energy electron and ion transfer through graphene were conducted. In this paper we describe the sample preparation for suspended graphene layers, the testing procedures and we discuss the preliminary results followed by a prospect of further applications. 19. Experimental determination of net protein charge and A(tot) and K(a) of nonvolatile buffers in canine plasma. Science.gov (United States) Constable, Peter D; Stämpfli, Henry R 2005-01-01 Acid-base abnormalities frequently are present in sick dogs. The mechanism for an acid-base disturbance can be determined with the simplified strong ion approach, which requires accurate values for the total concentration of plasma nonvolatile buffers (A(tot)) and the effective dissociation constant for plasma weak acids (K(a)). The aims of this study were to experimentally determine A(tot) and K(a) values for canine plasma. Plasma was harvested from 10 healthy dogs; the concentrations of quantitatively important strong ions (Na+, K+, Ca2+, Mg2+, Cl-, L-lactate) and nonvolatile buffer ions (total protein, albumin, phosphate) were determined; and the plasma was tonometered with CO2 at 37 degrees C. Strong ion difference (SID) was calculated from the measured strong ion concentrations, and nonlinear regression was used to estimate values for A(tot) and K(a), which were validated with data from an in vitro and in vivo study. Mean (+/- SD) values for canine plasma were A(tot) = (17.4 +/- 8.6) mM (equivalent to 0.273 mmol/g of total protein or 0.469 mmol/g of albumin); K(a) = (0.17 +/- 0.11) x 10(-7); pK(a) = 7.77. The calculated SID for normal canine plasma (pH = 7.40; P(CO2) = 37 mm Hg; [total protein] = 64 g/L) was 27 mEq/L. The net protein charge for normal canine plasma was 0.25 mEq/g of total protein or 0.42 mEq/g of albumin. Application of the experimentally determined values for A(tot), K(a), and net protein charge should improve understanding of the mechanism for complex acid-base disturbances in dogs. 20. Experimental determination of net protein charge and A(tot) and K(a) of nonvolatile buffers in human plasma. Science.gov (United States) Staempfli, Henry R; Constable, Peter D 2003-08-01 The mechanism for an acid-base disturbance can be determined by using the strong ion approach, which requires species-specific values for the total concentration of plasma nonvolatile buffers (Atot) and the effective dissociation constant for plasma weak acids (Ka). The aim of this study was to experimentally determine Atot and Ka values for human plasma by using in vitro CO2 tonometry. Plasma Pco2 was systematically varied from 25 to 145 Torr at 37 degrees C, thereby altering plasma pH over the physiological range of 6.90-7.55, and plasma pH, Pco2, and concentrations of quantitatively important strong ions (Na+, K+, Ca2+, Mg2+, Cl-, lactate) and buffer ions (total protein, albumin, phosphate) were measured. Strong ion difference was estimated, and nonlinear regression was used to calculate Atot and Ka from the measured pH and Pco2 and estimated strong ion difference; the Atot and Ka values were then validated by using a published data set (Figge J, Rossing TH, and Fencl V, J Lab Clin Med 117: 453-467, 1991). The values (mean +/- SD) were as follows: Atot = 17.2 +/- 3.5 mmol/l (equivalent to 0.224 mmol/g of protein or 0.378 mmol/g of albumin); Ka = 0.80 +/- 0.60 x 10-7; negative log of Ka = 7.10. Mean estimates were obtained for strong ion difference (37 meq/l) and net protein charge (13+.0 meq/l). The experimentally determined values for Atot, Ka, and net protein charge should facilitate the diagnosis and treatment of acid-base disturbances in critically ill humans. 1. Experimental determination of net protein charge, [A]tot, and Ka of nonvolatile buffers in bird plasma. Science.gov (United States) Stämpfli, Henry; Taylor, Michael; McNicoll, Carl; Gancz, Ady Y; Constable, Peter D 2006-06-01 The quantitative mechanistic acid-base approach to clinical assessment of acid-base status requires species-specific values for [A]tot (the total concentration of nonvolatile buffers in plasma) and Ka (the effective dissociation constant for weak acids in plasma). The aim of this study was to determine [A]tot and Ka values for plasma in domestic pigeons. Plasma from 12 healthy commercial domestic pigeons was tonometered with 20% CO2 at 37 degrees C. Plasma pH, Pco2, and plasma concentrations of strong cations (Na, K, Ca), strong anions (Cl, L-lactate), and nonvolatile buffer ions (total protein, albumin, phosphate) were measured over a pH range of 6.8-7.7. Strong ion difference (SID) (SID5=Na+K+Ca-Cl-lactate) was used to calculate [A]tot and Ka from the measured pH and Pco2 and SID5. Mean (+/-SD) values for bird plasma were as follows: [A]tot=7.76+/-2.15 mmol/l (equivalent to 0.32 mmol/g of total protein, 0.51 mmol/g of albumin, 0.23 mmol/g of total solids); Ka=2.15+/-1.15x10(-7); and pKa=6.67. The net protein charge at normal pH (7.43) was estimated to be 6 meq/l; this value indicates that pigeon plasma has a much lower anion gap value than mammals after adjusting for high mean L-lactate concentrations induced by restraint during blood sampling. This finding indicates that plasma proteins in pigeons have a much lower net anion charge than mammalian plasma protein. An incidental finding was that total protein concentration measured by a multianalyzer system was consistently lower than the value for total solids measured by refractometer. 2. Process techniques of charge transfer time reduction for high speed CMOS image sensors International Nuclear Information System (INIS) Cao Zhongxiang; Li Quanliang; Han Ye; Qin Qi; Feng Peng; Liu Liyuan; Wu Nanjian 2014-01-01 This paper proposes pixel process techniques to reduce the charge transfer time in high speed CMOS image sensors. These techniques increase the lateral conductivity of the photo-generated carriers in a pinned photodiode (PPD) and the voltage difference between the PPD and the floating diffusion (FD) node by controlling and optimizing the N doping concentration in the PPD and the threshold voltage of the reset transistor, respectively. The techniques shorten the charge transfer time from the PPD diode to the FD node effectively. The proposed process techniques do not need extra masks and do not cause harm to the fill factor. A sub array of 32 × 64 pixels was designed and implemented in the 0.18 μm CIS process with five implantation conditions splitting the N region in the PPD. The simulation and measured results demonstrate that the charge transfer time can be decreased by using the proposed techniques. Comparing the charge transfer time of the pixel with the different implantation conditions of the N region, the charge transfer time of 0.32 μs is achieved and 31% of image lag was reduced by using the proposed process techniques. (semiconductor devices) 3. Non-Markovian reduced dynamics of ultrafast charge transfer at an oligothiophene–fullerene heterojunction Energy Technology Data Exchange (ETDEWEB) Hughes, Keith H., E-mail: [email protected] [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Cahier, Benjamin [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Martinazzo, Rocco [Dipartimento di Chimica Università degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Tamura, Hiroyuki [WPI-Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt/Main (Germany) 2014-10-17 Highlights: • Quantum dynamical study of exciton dissociation at a heterojunction interface. • The non-Markovian quantum dynamics involves a highly structured spectral density. • Spectral density is reconstructed from an effective mode transformation of the Hamiltonian. • The dynamics is studied using the hierarchical equations of motion approach. • It was found that the temperature has little effect on the charge transfer. - Abstract: We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene–fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway. 4. Electrostatic sensors applied to the measurement of electric charge transfer in gas-solids pipelines International Nuclear Information System (INIS) Woodhead, S R; Denham, J C; Armour-Chelu, D I 2005-01-01 This paper describes the development of a number of electric charge sensors. The sensors have been developed specifically to investigate triboelectric charge transfer which takes place between particles and the pipeline wall, when powdered materials are conveyed through a pipeline using air. A number of industrial applications exist for such gas-solids pipelines, including pneumatic conveyors, vacuum cleaners and dust extraction systems. The build-up of electric charge on pipelines and powdered materials can lead to electrostatic discharge and so is of interest from a safety viewpoint. The charging of powders can also adversely affect their mechanical handling characteristics and so is of interest to handling equipment engineers. The paper presents the design of the sensors, the design of the electric charge test rig and electric charge measurement test results 5. Contribution of the net charge to the regulatory effects of amino acids and epsilon-poly(L-lysine) on the gelatinization behavior of potato starch granules. Science.gov (United States) Ito, Azusa; Hattori, Makoto; Yoshida, Tadashi; Takahashi, Koji 2006-01-01 The effects of lysine (Lys), monosodium glutamate (GluNa), glycine, alanine and epsilon-poly(L-lysine) (PL) with different degrees of polymerization on the gelatinization behavior of potato starch granules were investigated by DSC, viscosity and swelling measurements, microscopic observation, and measurement of the retained amino acid amount to clarify the contribution of the net charge to their regulatory effects on the gelatinization behavior. The amino acids and PL each contributed to an increase in the gelatinization temperature, and a decrease in the peak viscosity and swelling. These effects strongly depended on the absolute value of their net charge. The disappearance of a negative or positive net charge by adjusting the pH value weakened the contribution. The swelling index and size of the potato starch granules changed according to replacement of the swelling medium. The amino acids and PL were easily retained by the swollen potato starch granules according to replacement of the outer solution of the starch granules. 6. Analysis of solar radiation transfer: A method to estimate the porosity of a plastic shading net International Nuclear Information System (INIS) Abdel-Ghany, A.M.; Al-Helal, I.M. 2011-01-01 Plastic nets with opaque threads are frequently used for shading agricultural structures under high solar radiation conditions. A parameter that is often used to define a net is the net porosity (Π). Value of Π is usually estimated by one of three methods: image processing, direct beam transmittance, or solar radiation balance (hereafter radiation balance). Image processing is a rather slow process because it requires scanning the net sample at high resolution. The direct beam transmittance and radiation balance methods greatly overestimate Π because some of the solar radiation incident on the thread surfaces is forward scattered and add a considerable amount of radiation to that transmitted from the net pores directly. In this study, the radiation balance method was modified to estimate Π precisely. The amount of solar radiation scattered forward on the thread surfaces was estimated separately. Thus, the un-scattered solar radiation transmitted from the net pores directly, which describes the net porosity, Π could be estimated. This method, in addition to the image processing and the direct beam transmittance methods were used to estimate Π for different types of nets that are commonly used for shading structures in summer. Values of Π estimated by using the proposed method were in good accordance with those measured by the image processing method at a resolution of 4800 dpi. The direct beam transmittance and the radiation balance methods resulted in overestimation errors in the values of Π. This error strongly depends on the color of the net. The estimated errors were +14% for a green net and +37% for a white net when using the radiation balance method, and were +16% and +38%, respectively, when using the direct beam transmittance method. In the image processing method, a resolution of 2400 dpi is sufficient to estimate Π precisely and the higher resolutions showed no significant effect on the value of Π. 7. Electroluminescence from charge transfer states in Donor/Acceptor solar cells DEFF Research Database (Denmark) Sherafatipour, Golenaz; Madsen, Morten Charge photocurrent generation is a key process in solar energy conversion systems. Effective dissociation of the photo-generated electron-hole pairs (excitons) has a strong influence on the efficiency of the organic solar cells. Charge dissociation takes place at the donor/acceptor interface via...... which the maximum open-circuit voltage can be estimated, and further can be used in the modeling and optimization of the OPV devices. [1] C. Deibe, T. Strobe, and V. Dyakonov, “Role of the charge transfer state in organic donor-acceptor solar cells,” Adv. Mater., vol. 22, pp. 4097–4111, 2010. [2] K...... charge transfer (CT) excitons, which is Coulombically bound interfacial electron- hole pairs residing at the donor/acceptor heterojunctions. The CT state represents an intermediate state between the exciton dissociation and recombination back to the ground state. Since the recombination of photo... 8. A two-dimensional position sensitive gas chamber with scanned charge transfer readout International Nuclear Information System (INIS) Gomez, F.; Iglesias, A.; Lobato, R.; Mosquera, J.; Pardo, J.; Pena, J.; Pazos, A.; Pombar, M.; Rodriguez, A. 2003-01-01 We have constructed and tested a two-dimensional position sensitive parallel-plate gas ionization chamber with scanned charge transfer readout. The scan readout method described here is based on the development of a new position-dependent charge transfer technique. It has been implemented by using gate strips perpendicularly oriented to the collector strips. This solution reduces considerably the number of electronic readout channels needed to cover large detector areas. The use of a 25 μm thick kapton etched circuit allows high charge transfer efficiency with a low gating voltage, consequently needing a very simple commutating circuit. The present prototype covers 8x8 cm 2 with a pixel size of 1.27x1.27 mm 2 . Depending on the intended use and beam characteristics a smaller effective pixel is feasible and larger active areas are possible. This detector can be used for X-ray or other continuous beam intensity profile monitoring 9. High-energy behavior of the charge-transfer cross section in the eikonal approximation International Nuclear Information System (INIS) Dewangan, D.P. 1982-01-01 In the now popular version of the eikonal theory of charge transfer, the eikonal wave function does not satisfy the proper boundary conditions and the charge-transfer amplitude is uncertain by an undefined phase factor. The inclusion of the internuclear potential in a consistent way, in the eikonal theory overcomes theses difficulties. However, it also changes the high-energy asymptotic form of proton-hydrogen charge-transfer cross section from sigma/sub eik/ approx.(23/48) sigma/sub BK/ by a small amount to sigma/sub G/approx.(20.109/48)sigma/sub BK/ where sigma/sub BK/ is the Brinkman-Kramers cross section 10. Polyoxometalate active charge-transfer material for mediated redox flow battery Energy Technology Data Exchange (ETDEWEB) Anderson, Travis Mark; Hudak, Nicholas; Staiger, Chad; Pratt, Harry 2017-01-17 Redox flow batteries including a half-cell electrode chamber coupled to a current collecting electrode are disclosed herein. In a general embodiment, a separator is coupled to the half-cell electrode chamber. The half-cell electrode chamber comprises a first redox-active mediator and a second redox-active mediator. The first redox-active mediator and the second redox-active mediator are circulated through the half-cell electrode chamber into an external container. The container includes an active charge-transfer material. The active charge-transfer material has a redox potential between a redox potential of the first redox-active mediator and a redox potential of the second redox-active mediator. The active charge-transfer material is a polyoxometalate or derivative thereof. The redox flow battery may be particularly useful in energy storage solutions for renewable energy sources and for providing sustained power to an electrical grid. 11. Charge-transfer channel in quantum dot-graphene hybrid materials Science.gov (United States) Cao, Shuo; Wang, Jingang; Ma, Fengcai; Sun, Mengtao 2018-04-01 The energy band theory of a classical semiconductor can qualitatively explain the charge-transfer process in low-dimensional hybrid colloidal quantum dot (QD)-graphene (GR) materials; however, the definite charge-transfer channels are not clear. Using density functional theory (DFT) and time-dependent DFT, we simulate the hybrid QD-GR nanostructure, and by constructing its orbital interaction diagram, we show the quantitative coupling characteristics of the molecular orbitals (MOs) of the hybrid structure. The main MOs are derived from the fragment MOs (FOs) of GR, and the Cd13Se13 QD FOs merge with the GR FOs in a certain proportion to afford the hybrid system. Upon photoexcitation, electrons in the GR FOs jump to the QD FOs, leaving holes in the GR FOs, and the definite charge-transfer channels can be found by analyzing the complex MOs coupling. The excited electrons and remaining holes can also be localized in the GR or the QD or transfer between the QD and GR with different absorption energies. The charge-transfer process for the selected excited states of the hybrid QD-GR structure are testified by the charge difference density isosurface. The natural transition orbitals, charge-transfer length analysis and 2D site representation of the transition density matrix also verify the electron-hole delocalization, localization, or coherence chacracteristics of the selected excited states. Therefore, our research enhances understanding of the coupling mechanism of low-dimensional hybrid materials and will aid in the design and manipulation of hybrid photoelectric devices for practical application in many fields. 12. Charge Transfer Properties Through Graphene for Applications in Gaseous Detectors CERN Document Server Franchino, S.; Hall-Wilton, R.; Jackman, R.B.; Muller, H.; Nguyen, T.T.; de Oliveira, R.; Oliveri, E.; Pfeiffer, D.; Resnati, F.; Ropelewski, L.; Smith, J.; van Stenis, M.; Streli, C.; Thuiner, P.; Veenhof, R. 2016-07-11 Graphene is a single layer of carbon atoms arranged in a honeycomb lattice with remarkable mechanical and electrical properties. Regarded as the thinnest and narrowest conductive mesh, it has drastically different transmission behaviours when bombarded with electrons and ions in vacuum. This property, if confirmed in gas, may be a definitive solution for the ion back-flow problem in gaseous detectors. In order to ascertain this aspect, graphene layers of dimensions of about 2x2cm$^2, grown on a copper substrate, are transferred onto a flat metal surface with holes, so that the graphene layer is freely suspended. The graphene and the support are installed into a gaseous detector equipped with a triple Gaseous Electron Multiplier (GEM), and the transparency properties to electrons and ions are studied in gas as a function of the electric fields. The techniques to produce the graphene samples are described, and we report on preliminary tests of graphene-coated GEMs. 13. Improving radiation hardness in space-based Charge-Coupled Devices through the narrowing of the charge transfer channel Science.gov (United States) Hall, D. J.; Skottfelt, J.; Soman, M. R.; Bush, N.; Holland, A. 2017-12-01 Charge-Coupled Devices (CCDs) have been the detector of choice for imaging and spectroscopy in space missions for several decades, such as those being used for the Euclid VIS instrument and baselined for the SMILE SXI. Despite the many positive properties of CCDs, such as the high quantum efficiency and low noise, when used in a space environment the detectors suffer damage from the often-harsh radiation environment. High energy particles can create defects in the silicon lattice which act to trap the signal electrons being transferred through the device, reducing the signal measured and effectively increasing the noise. We can reduce the impact of radiation on the devices through four key methods: increased radiation shielding, device design considerations, optimisation of operating conditions, and image correction. Here, we concentrate on device design operations, investigating the impact of narrowing the charge-transfer channel in the device with the aim of minimising the impact of traps during readout. Previous studies for the Euclid VIS instrument considered two devices, the e2v CCD204 and CCD273, the serial register of the former having a 50 μm channel and the latter having a 20 μm channel. The reduction in channel width was previously modelled to give an approximate 1.6× reduction in charge storage volume, verified experimentally to have a reduction in charge transfer inefficiency of 1.7×. The methods used to simulate the reduction approximated the charge cloud to a sharp-edged volume within which the probability of capture by traps was 100%. For high signals and slow readout speeds, this is a reasonable approximation. However, for low signals and higher readout speeds, the approximation falls short. Here we discuss a new method of simulating and calculating charge storage variations with device design changes, considering the absolute probability of capture across the pixel, bringing validity to all signal sizes and readout speeds. Using this method, we 14. Evidence for charge transfer in Bi-based superconductors studied by positron annihilation International Nuclear Information System (INIS) Tang, Z.; Wang, S.J.; Gao, X.H.; Ce, G.C.; Zhao, Z.X. 1993-01-01 We have measured Doppler-broadening annihilation radiation (DBAR) spectra and positron lifetimes in normal and superconducting states for three kinds of Bi-based superconductors: Bi2212, Pb-doped Bi2223, Pb- and F-doped Bi2223. The difference spectra after deconvolution between two states show a sharpening effect with increasing temperature; the F-doped sample has the greatest amplitude in difference spectra but nearly the same positron lifetimes as the Pb-doped sample. The results are interpreted in terms of charge transfer between the Cu-O and Bi-O planes. The role of oxygen defects in charge transfer is discussed. (orig.) 15. Charge transfer and excitation in high-energy ion-atom collisions International Nuclear Information System (INIS) Schlachter, A.S.; Berkner, K.H.; McDonald, R.J. 1986-11-01 Coincidence measurements of charge transfer and simultaneous projectile electron excitation provide insight into correlated two-electron processes in energetic ion-atom collisions. Projectile excitation and electron capture can occur simultaneously in a collision of a highly charged ion with a target atom; this process is called resonant transfer and excitation (RTE). The intermediate excited state which is thus formed can subsequently decay by photon emission or by Auger-electron emission. Results are shown for RTE in both the K shell of Ca ions and the L shell of Nb ions, for simultaneous projectile electron loss and excitation, and for the effect of RTE on electron capture 16. Photoinduced charge transfer within polyaniline-encapsulated quantum dots decorated on graphene. Science.gov (United States) Nguyen, Kim Truc; Li, Dehui; Borah, Parijat; Ma, Xing; Liu, Zhaona; Zhu, Liangliang; Grüner, George; Xiong, Qihua; Zhao, Yanli 2013-08-28 A new method to enhance the stability of quantum dots (QDs) in aqueous solution by encapsulating them with conducting polymer polyaniline was reported. The polyaniline-encapsulated QDs were then decorated onto graphene through π-π interactions between graphene and conjugated polymer shell of QDs, forming stable polyaniline/QD/graphene hybrid. A testing electronic device was fabricated using the hybrid in order to investigate the photoinduced charge transfer between graphene and encapsulated QDs within the hybrid. The charge transfer mechanism was explored through cyclic voltammetry and spectroscopic studies. The hybrid shows a clear response to the laser irradiation, presenting a great advantage for further applications in optoelectronic devices. 17. Symmetric resonance double charge transfer in Kr++ + Kr and Xe++ + Xe systems International Nuclear Information System (INIS) Okuno, K.; Koizumi, T.; Kaneko, Y. 1978-01-01 Cross sections of processes Kr ++ + Kr → Ke + Kr ++ and Xe ++ + Xe → Xe + Xe ++ were measured by the injected-ion-drift-tube technique from 0.04 to 20 eV. For both cases, the cross section below 1 eV coincides with the orbiting cross sections with a charge-transfer probability 1/2. Above 1 eV, the energy dependence of the cross sectcion is like that for single charge transfer. Mobilities of Kr ++ and Xe ++ in He are presented also 18. Heat transfer from the evaporator outlet to the charge of thermostatic expansion valves DEFF Research Database (Denmark) Langmaack, Lasse Nicolai; Knudsen, Hans-Jørgen Høgaard 2006-01-01 outlet with a special mounting strap. The heat transfer is quite complex because it takes place both directly through the contact points between bulb and pipe and indirectly through the mounting strap The TXV has to react to temperature changes at the evaporator outlet. Therefore, the dynamic behavior...... of the valve (and thereby the whole refrigeration system) depends greatly on the heat transfer between the evaporator outlet tube and the charge in the bulb. In this paper a model for the overall heat transfer between the pipe and the charge is presented. Geometrical data and material properties have been kept...... been found to predict the time constant for the temperature development in the bulb within 1-10 %. Furthermore it has been found that app. 20% of the heat transfer takes place trough the mounting strap.... 19. Structural dynamics of a noncovalent charge transfer complex from femtosecond stimulated Raman spectroscopy. Science.gov (United States) Fujisawa, Tomotsumi; Creelman, Mark; Mathies, Richard A 2012-09-06 Femtosecond stimulated Raman spectroscopy is used to examine the structural dynamics of photoinduced charge transfer within a noncovalent electron acceptor/donor complex of pyromellitic dianhydride (PMDA, electron acceptor) and hexamethylbenzene (HMB, electron donor) in ethylacetate and acetonitrile. The evolution of the vibrational spectrum reveals the ultrafast structural changes that occur during the charge separation (Franck-Condon excited state complex → contact ion pair) and the subsequent charge recombination (contact ion pair → ground state complex). The Franck-Condon excited state is shown to have significant charge-separated character because its vibrational spectrum is similar to that of the ion pair. The charge separation rate (2.5 ps in ethylacetate and ∼0.5 ps in acetonitrile) is comparable to solvation dynamics and is unaffected by the perdeuteration of HMB, supporting the dominant role of solvent rearrangement in charge separation. On the other hand, the charge recombination slows by a factor of ∼1.4 when using perdeuterated HMB, indicating that methyl hydrogen motions of HMB mediate the charge recombination process. Resonance Raman enhancement of the HMB vibrations in the complex reveals that the ring stretches of HMB, and especially the C-CH(3) deformations are the primary acceptor modes promoting charge recombination. 20. Transverse Schottky spectra and beam transfer functions of coasting ion beams with space charge International Nuclear Information System (INIS) Paret, Stefan 2010-01-01 A study of the transverse dynamics of coasting ion beams with moderate space charge is presented in this work. From the dispersion relation with linear space charge, an analytic model describing the impact of space charge on transverse beam transfer functions (BTFs) and the stability limits of a beam is derived. The dielectric function obtained in this way is employed to describe the transverse Schottky spectra with linear space charge as well. The difference between the action of space charge and impedances is highlighted. The setup and the results of an experiment performed in the heavy ion synchrotron SIS-18 at GSI to detect space-charge effects at different beam intensities are explicated. The measured transverse Schottky spectra and BTFs are compared with the linear space-charge model. The stability diagrams constructed from the BTFs are presented. The space-charge parameters evaluated from the Schottky and BTF measurements are compared with estimations based on measured beam parameters. The impact of collective effects on the Schottky and BTF diagnostics is also investigated through numerical simulations. For this purpose the self-field of beams with linear and non-linear transverse density-distributions is computed on a twodimensional grid. The noise of the random particle distribution causes fluctuations of the dipole moment of the beam which produce the Schottky spectrum. BTFs are simulated by exciting the beam with transverse kicks. The simulation results are used to verify the space-charge model. (orig.) 1. Transverse Schottky spectra and beam transfer functions of coasting ion beams with space charge Energy Technology Data Exchange (ETDEWEB) Paret, Stefan 2010-02-22 A study of the transverse dynamics of coasting ion beams with moderate space charge is presented in this work. From the dispersion relation with linear space charge, an analytic model describing the impact of space charge on transverse beam transfer functions (BTFs) and the stability limits of a beam is derived. The dielectric function obtained in this way is employed to describe the transverse Schottky spectra with linear space charge as well. The difference between the action of space charge and impedances is highlighted. The setup and the results of an experiment performed in the heavy ion synchrotron SIS-18 at GSI to detect space-charge effects at different beam intensities are explicated. The measured transverse Schottky spectra and BTFs are compared with the linear space-charge model. The stability diagrams constructed from the BTFs are presented. The space-charge parameters evaluated from the Schottky and BTF measurements are compared with estimations based on measured beam parameters. The impact of collective effects on the Schottky and BTF diagnostics is also investigated through numerical simulations. For this purpose the self-field of beams with linear and non-linear transverse density-distributions is computed on a twodimensional grid. The noise of the random particle distribution causes fluctuations of the dipole moment of the beam which produce the Schottky spectrum. BTFs are simulated by exciting the beam with transverse kicks. The simulation results are used to verify the space-charge model. (orig.) 2. Transfer of energy or charge between quasi-zero-dimensional nanostructures Czech Academy of Sciences Publication Activity Database Král, Karel; Menšík, Miroslav 2016-01-01 Roč. 45, č. 4 (2016), s. 243-255 ISSN 2332-4309 R&D Projects: GA ČR(CZ) GA14-05053S; GA MŠk(CZ) LD14011; GA MŠk LH12236 Institutional support: RVO:68378271 ; RVO:61389013 Keywords : charge transfer * electron-phonon interaction * energy transfer * nanostructures * quantum dots Subject RIV: BM - Solid Matter Physics ; Magnetism; CD - Macromolecular Chemistry (UMCH-V) Impact factor: 0.171, year: 2016 3. Correction: Towards the rationalization of catalytic activity values by means of local hyper-softness on the catalytic site: a criticism about the use of net electric charges. Science.gov (United States) Martínez-Araya, Jorge Ignacio; Grand, André; Glossman-Mitnik, Daniel 2016-01-28 Correction for 'Towards the rationalization of catalytic activity values by means of local hyper-softness on the catalytic site: a criticism about the use of net electric charges' by Jorge Ignacio Martínez-Araya et al., Phys. Chem. Chem. Phys., 2015, DOI: 10.1039/c5cp03822g. 4. Coupled quantum treatment of vibrationally inelastic and vibronic charge transfer in proton-O2 collisions International Nuclear Information System (INIS) Gianturco, F.A.; Palma, A.; Semprini, E.; Stefani, F.; Baer, M. 1990-01-01 A three-dimensional quantum-mechanical study of vibrational, state-resolved differential cross sections (DCS) for the direct inelastic and for the charge-transfer scattering channels has been carried out for the H + +O 2 system. The collision energy considered was E c.m. =23.0 eV, which is the same as that examined by Noll and Toennies in their experiments [J. Chem. Phys. 85, 3313 (1986)]. The scattering treatment employed was the charge-transfer infinite-order sudden approximation (CT IOSA) with the vibrational states correctly expanded over the relevant adiabatic basis for each of the two electronic channels. The state-to-state DCS are found to follow closely the behavior of the experimental quantities, both in the inelastic and the charge-transfer channels. Moreover, a careful comparison between the measured relative probabilities and computed values allows us to test in minute detail the efficiency of the scattering model and the reliability of the potential-energy surfaces employed. It is found that vibrational energy transfer is overestimated in the vibrational inelastic channels while in the charge-transfer inelastic channels the same energy transfer is slightly underestimated by the calculations. The total flux distribution, however, is found to be in very good accord with experiments. Angular distributions are also well reproduced both by the DCS and by the average energy-transfer values. The study of some of the CT IOSA quantities also allows us to establish clearly the importance of nonadiabatic transitions in enhancing vibrational inelasticity in the present system 5. Changes in wetting and contact charge transfer by femtosecond laser-ablation of polyimide Energy Technology Data Exchange (ETDEWEB) Guo, X.D., E-mail: [email protected] [Department of Physics and Technology, Allegaten 55, 5020 Bergen, University of Bergen (Norway); Dai, Y.; Gong, M. [Department of Physics, Shanghai 200444, Shanghai University (China); Qu, Y.G. [Center for Geobiology, Allegaten 41, 5020 Bergen, University of Bergen (Norway); Helseth, L.E. [Department of Physics and Technology, Allegaten 55, 5020 Bergen, University of Bergen (Norway) 2015-09-15 Highlights: • Laser ablation significantly reduced the triboelectric charging of polyimide films. • Hierarchical micro/nanostructures formed on the surface of the sample. • Structural anisotropy leads to spatially varying contact angles of water droplets. • Raman spectroscopy revealed a carbonization of the polyimide sample. • The corresponding loss of insulation may explain the reduction of charge transfer. - Abstract: In this study it is demonstrated that the triboelectric charging of polyimide thin films is significantly reduced by using a femtosecond laser to nanostructure its. It is found that the contact charge transfer between laser-ablated Kapton and aluminum is almost negligible, and even much lower than the significant current occurring when non-treated Kapton touches the metal. Scanning electron microscopy demonstrates that laser ablation produces a hierarchical micro and nanostructure, and it is found that the structural anisotropy leads to spatially varying contact angles of water droplets residing on the surface. Raman spectra suggest that the centers of the laser-ablated tracks are carbonized; therefore, the loss of insulation can be responsible for the reduction of charge transfer. 6. Charge transfer to a dielectric target by guided ionization waves using electric field measurements NARCIS (Netherlands) Slikboer, E.T.; Garcia-Caurel, E.; Guaitella, O.; Sobota, A. 2017-01-01 A kHz-operated atmospheric pressure plasma jet is investigated by measuring charge transferred to a dielectric electro-optic surface (BSO crystal) allowing for the measurement of electric field by exploiting the Pockels effect. The electric field values, distribution of the surface discharge and 7. Mechanism and Dynamics of Charge Transfer in Donor-Bridge-Acceptor Systems NARCIS (Netherlands) Gorczak-Vos, N. 2016-01-01 Photoinduced charge transfer in organic materials is a fundamental process in various biological and technological areas. Donor-bridge-acceptor (DBA) molecules are used as model systems in numerous theoretical and experimental work to systematically study and unravel the underlying mechanisms of 8. Simple heuristic derivation of some charge-transfer probabilities at asymptotically high incident velocities International Nuclear Information System (INIS) Spruch, L.; Shakeshaft, R. 1984-01-01 For asymptotically high incident velocities we provide simple, heuristic, almost classical, derivations of the cross section for forward charge transfer, and of the ratio of the cross section for capture to the elastic-scattering cross section for the projectile scattered through an angle close to π/3 9. Surface characterization and surface electronic structure of organic quasi-one-dimensional charge transfer salts DEFF Research Database (Denmark) Sing, M.; Schwingenschlögl, U.; Claessen, R. 2003-01-01 We have thoroughly characterized the surfaces of the organic charge-transfer salts TTF-TCNQ and (TMTSF)(2)PF6 which are generally acknowledged as prototypical examples of one-dimensional conductors. In particular x-ray-induced photoemission spectroscopy turns out to be a valuable nondestructive... 10. Charge distribution effects in polyatomic reactants involved in simple electron transfer reactions Czech Academy of Sciences Publication Activity Database Fawcett, W. R.; Chavis, G. J.; Hromadová, Magdaléna 2008-01-01 Roč. 53, č. 23 (2008), s. 6787-6792 ISSN 0013-4686 Institutional research plan: CEZ:AV0Z40400503 Keywords : electron transfer kinetics * charge distribution effects * double - layer effects in electrode kinetics Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.078, year: 2008 11. Integer charge transfer at the tetrakis(dimethylamino)ethylene/Au interface DEFF Research Database (Denmark) Lindell, L.; Unge, Mikael; Osikowicz, W. 2008-01-01 In organic-based electronics, interfacial properties have a profound impact on device performance. The lineup of energy levels is usually dependent on interface dipoles, which may arise from charge transfer reactions. In many applications, metal-organic junctions are prepared under ambient... 12. Charge transfer state in DBP:C70 organic solar cells DEFF Research Database (Denmark) Sherafatipour, Golenaz; Benduhn, Johannes; Spoltore, Donato -acceptor interface via delocalized charge-transfer (CT) states, which represents an intermediate state between the exciton dissociation and recombination back to the ground state. In this work we perform the electroluminescence (EL) created by bimolecular free career recombination and sensitive external quantum... 13. Elastic, excitation, ionization and charge transfer cross sections of current interest in fusion energy research Energy Technology Data Exchange (ETDEWEB) Schultz, D.R.; Krstic, P.S. [Oak Ridge National Lab. TN (United States). Physics Div. 1997-01-01 Due to the present interest in modeling and diagnosing the edge and divertor plasma regions in magnetically confined fusion devices, we have sought to provide new calculations regarding the elastic, excitation, ionization, and charge transfer cross sections in collisions among relevant ions, neutrals, and isotopes in the low-to intermediate-energy regime. We summarize here some of our recent work. (author) 14. Charge transfer to the continuum by heavy ions in atomic hydrogen International Nuclear Information System (INIS) Sellin, I.A. 1981-01-01 Design and installation of an atomic hydrogen target for measurements of charge transfer to the continuum by heavy ions are discussed. The design consists of a tungsten gas cell operated at temperatures of 2500 to 2600 0 K. Initial testing is underway 15. Mechanism of the Primary Charge Transfer Reaction in the Cytochrome bc1 Complex DEFF Research Database (Denmark) Barragan, Angela M; Schulten, Klaus; Solov'yov, Ilia A 2016-01-01 , the quinol-protein interaction, which initiates the Q-cycle, has not yet been completely described. Furthermore, the initial charge transfer reactions of the Q-cycle lack a physical description. The present investigation utilizes classical molecular dynamics simulations in tandem with quantum density... 16. The description of charge transfer in fast negative ions scattering on water covered Si(100) surfaces Energy Technology Data Exchange (ETDEWEB) Chen, Lin; Qiu, Shunli; Liu, Pinyang; Xiong, Feifei; Lu, Jianjie; Liu, Yuefeng; Li, Guopeng; Liu, Yiran; Ren, Fei; Xiao, Yunqing; Gao, Lei; Zhao, Qiushuang; Ding, Bin; Li, Yuan [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China); Guo, Yanling, E-mail: [email protected] [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China); Chen, Ximeng, E-mail: [email protected] [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China) 2016-11-30 Highlights: • We first observe that negative-ion fractions present no variation with the doping concentration, which is very different from the results of low energy Li neutralization from doped Si samples. • Our work shows that the affinity levels and collision time significantly counteract the band gap effect on negative ion formation. The work will improve our understanding on electron transfer on semiconductor surfaces associated with doping. • In addition, we build a complete theoretical framework to quantitatively calculate the negative-ion fractions. • Our work is related to charge transfer on semiconductor surfaces, which will be of interest to a broad audience due to the wide necessity of the knowledge of charge exchange on semiconductor surfaces in different fields. - Abstract: Doping has significantly affected the characteristics and performance of semiconductor electronic devices. In this work, we study the charge transfer processes for 8.5–22.5 keV C{sup −} and F{sup −} ions scattering on H{sub 2}O-terminated p-type Si(100) surfaces with two different doping concentrations. We find that doping has no influence on negative-ion formation for fast collisions in this relatively high energy range. Moreover, we build a model to calculate negative ion fractions including the contribution from positive ions. The calculations support the nonadiabatic feature of charge transfer. 17. Symmetry-breaking intramolecular charge transfer in the excited state of meso-linked BODIPY dyads KAUST Repository Whited, Matthew T.; Patel, Niral M.; Roberts, Sean T.; Allen, Kathryn; Djurovich, Peter I.; Bradforth, Stephen E.; Thompson, Mark E. 2012-01-01 We report the synthesis and characterization of symmetric BODIPY dyads where the chromophores are attached at the meso position, using either a phenylene bridge or direct linkage. Both molecules undergo symmetry-breaking intramolecular charge transfer in the excited state, and the directly linked dyad serves as a visible-light-absorbing analogue of 9,9′-bianthryl. 18. Reduced Charge Transfer Exciton Recombination in Organic Semiconductor Heterojunctions by Molecular Doping NARCIS (Netherlands) Deschler, Felix; Da Como, Enrico; Limmer, Thomas; Tautz, Raphael; Godde, Tillmann; Bayer, Manfred; von Hauff, Elizabeth; Yilmaz, Seyfullah; Allard, Sybille; Scherf, Ullrich; Feldmann, Jochen 2011-01-01 We investigate the effect of molecular doping on the recombination of electrons and holes localized at conjugated-polymer–fullerene interfaces. We demonstrate that a low concentration of p-type dopant molecules (<4% weight) reduces the interfacial recombination via charge transfer excitons and 19. Enhanced intersystem crossing via a high energy charge transfer state in a perylenediimide-perylenemonoimide dyad NARCIS (Netherlands) Veldman, D.; Chopin-Cado, S.M.A; Meskers, S.C.J.; Janssen, R.A.J. 2008-01-01 The electronic relaxation processes of a photoexcited linear perylenediimide-perylenemonoimide (PDI-PMI) acceptor-donor dyad were studied. PDI-PMI serves as a model compound for donor-acceptor systems in photovoltaic devices and has been designed to have a high-energy PDI--PMI + charge transfer (CT) 20. Charge transfer between hydrogen(deuterium) ions and atoms in metal vapors International Nuclear Information System (INIS) Alvarez T, I.; Cisneros G, C. 1981-01-01 The current state of the experiments on charge transfer between hydrogen (deuterium) ions and atoms in metal vapors are given. Emphasis is given to describing different experimental techniques. The results of calculations if available, are compared with existing experimental data. (author) 1. Radiative charge-transfer lifetime of the excited state of (NaCa)+ International Nuclear Information System (INIS) Makarov, Oleg P.; Cote, R.; Michels, H.; Smith, W.W. 2003-01-01 New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom-ion trap under high-vacuum conditions. We study the collisional cooling of laser precooled Ca + ions by ultracold Na atoms. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A 1 Σ + state of the (NaCa) + molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using complete active space self-consistent field and Moeller-Plesset second-order perturbation theory with an extended Gaussian basis, 6-311+G (3df). The semiclassical charge-transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition, we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be 2.3x10 -16 cm 3 /sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher (1.1x10 -8 cm 3 /sec and 2.3x10 -9 cm 3 /sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer 2. Effects of Charge-Transfer Excitons on the Photophysics of Organic Semiconductors Science.gov (United States) Hestand, Nicholas J. The field of organic electronics has received considerable attention over the past several years due to the promise of novel electronic materials that are cheap, flexible and light weight. While some devices based on organic materials have already emerged on the market (e.g. organic light emitting diodes), a deeper understanding of the excited states within the condensed phase is necessary both to improve current commercial products and to develop new materials for applications that are currently in the commercial pipeline (e.g. organic photovoltaics, wearable displays, and field effect transistors). To this end, a model for pi-conjugated molecular aggregates and crystals is developed and analyzed. The model considers two types of electronic excitations, namely Frenkel and charge-transfer excitons, both of which play a prominent role in determining the nature of the excited states within tightly-packed organic systems. The former consist of an electron-hole pair bound to the same molecule while in the later the electron and hole are located on different molecules. The model also considers the important nuclear reorganization that occurs when the system switches between electronic states. This is achieved using a Holstein-style Hamiltonian that includes linear vibronic coupling of the electronic states to the nuclear motion associated with the high frequency vinyl-stretching and ring-breathing modes. Analysis of the model reveals spectroscopic signatures of charge-transfer mediated J- and H-aggregation in systems where the photophysical properties are determined primarily by charge-transfer interactions. Importantly, such signatures are found to be sensitive to the relative phase of the intermolecular electron and hole transfer integrals, and the relative energy of the Frenkel and charge-transfer states. When the charge-transfer integrals are in phase and the energy of the charge-transfer state is higher than the Frenkel state, the system exhibits J 3. Temperature dependence of positronium reactivities with charge transfer molecules in bilayer membranes International Nuclear Information System (INIS) Jean, Y.C.; Yu, C.; Wang, Y.Y.; Yeh, Y.Y. 1984-01-01 Rate constants for positronium atoms reacting chemically with charge-transfer molecules such as p-benzoquinone, nitrobenzene, and coenzyme Q-10 in a model bilayer membrane, dipalmitoylphosphatidylcholine (DPPC), have been measured at temperatures between 23 and 65 0 C. A strong variation of the positronium chemical reactivities, k/sub Ps/ was observed in these systems: k/sub Ps/ increases with increasing temperature until the pretransition temperature of the membrane reaches a maximum value near the main transition temperature and decreases at temperatures higher than the main transition temperature. This variation is interpreted in terms of fluidity and permeability changes associated with the phase transitions of membranes and in terms of charge-transfer-complex formation between the solubilized molecules and the polar head of the membrane. These results demonstrate that positronium and its annihilation characteristics can be employed to investigate charge transport phenomena and microstructural changes of real biological membranes 4. A schematic model for energy and charge transfer in the chlorophyll complex DEFF Research Database (Denmark) Bohr, Henrik; Malik, F.B. 2011-01-01 A theory for simultaneous charge and energy transfer in the carotenoid-chlorophyll-a complex is presented here and discussed. The observed charge transfer process in these chloroplast complexes is reasonably explained in terms of this theory. In addition, the process leads to a mechanism to drive...... an electron in a lower to a higher-energy state, thus providing a mechanism for the ejection of the electron to a nearby molecule (chlorophyll) or into the environment. The observed lifetimes of the electronically excited states are in accord/agreement with the investigations of Sundström et al....... and are in the range of pico-seconds and less. The change in electronic charge distribution in internuclear space as the system undergoes an electronic transition to a higher-energy state could, under appropriate physical conditions, lead to oscillating dipoles capable of transmitting energy from the carotenoid-chlorophylls... 5. Charge Transfer Effect on Raman and Surface Enhanced Raman Spectroscopy of Furfural Molecules. Science.gov (United States) Wan, Fu; Shi, Haiyang; Chen, Weigen; Gu, Zhaoliang; Du, Lingling; Wang, Pinyi; Wang, Jianxin; Huang, Yingzhou 2017-08-02 The detection of furfural in transformer oil through surface enhanced Raman spectroscopy (SERS) is one of the most promising online monitoring techniques in the process of transformer aging. In this work, the Raman of individual furfural molecules and SERS of furfural-M x (M = Ag, Au, Cu) complexes are investigated through density functional theory (DFT). In the Raman spectrum of individual furfural molecules, the vibration mode of each Raman peak is figured out, and the deviation from experimental data is analyzed by surface charge distribution. In the SERS of furfural-M x complexes, the influence of atom number and species on SERS chemical enhancement factors (EFs) are studied, and are further analyzed by charge transfer effect. Our studies strengthen the understanding of charge transfer effect in the SERS of furfural molecules, which is important in the online monitoring of the transformer aging process through SERS. 6. Extraordinary Mechanism of the Diels-Alder Reaction: Investigation of Stereochemistry, Charge Transfer, Charge Polarization, and Biradicaloid Formation. Science.gov (United States) Sexton, Thomas; Kraka, Elfi; Cremer, Dieter 2016-02-25 The Diels-Alder reaction between 1,3-butadiene and ethene is investigated from far-out in the entrance channel to the very last step in the exit channel thus passing two bifurcation points and extending the range of the reaction valley studied with URVA (Unified Reaction Valley Approach) by 300% compared to previous studies. For the first time, the pre- and postchemical steps of the reaction are analyzed at the same level of theory as the actual chemical processes utilizing the path curvature and its decomposition into internal coordinate or curvilinear coordinate components. A first smaller charge transfer to the dienophile facilitates the rotation of gauche butadiene into its cis form. The actual chemical processes are initiated by a second larger charge transfer to the dienophile that facilitates pyramidalization of the reacting carbon centers, bond equalization, and biradicaloid formation of the reactants. The transition state is aromatically stabilized and moved by five path units into the entrance channel in line with the Hammond-Leffler postulate. The pseudorotation of the boat form into the halfchair of cyclohexene is analyzed. Predictions are made for the Diels-Alder reaction based on a 11-phase mechanism obtained by the URVA analysis. 7. Charge transfer in dissociating iodomethane and fluoromethane molecules ionized by intense femtosecond X-ray pulses Directory of Open Access Journals (Sweden) Rebecca Boll 2016-07-01 Full Text Available Ultrafast electron transfer in dissociating iodomethane and fluoromethane molecules was studied at the Linac Coherent Light Source free-electron laser using an ultraviolet-pump, X-ray-probe scheme. The results for both molecules are discussed with respect to the nature of their UV excitation and different chemical properties. Signatures of long-distance intramolecular charge transfer are observed for both species, and a quantitative analysis of its distance dependence in iodomethane is carried out for charge states up to I21+. The reconstructed critical distances for electron transfer are in good agreement with a classical over-the-barrier model and with an earlier experiment employing a near-infrared pump pulse. 8. Ion-atom charge-transfer system for a heavy-ion-beam pumped laser International Nuclear Information System (INIS) Ulrich, A.; Gernhaeuser, R.; Kroetz, W.; Wieser, J.; Murnick, D.E. 1994-01-01 An Ar target to which Cs vapor could be added, excited by a pulsed beam of 100-MeV 32 S ions, was studied as a prototype ion-atom charge-transfer system for pumping short-wavelength lasers. Low-velocity Ar 2+ ions were efficiently produced; a huge increase in the intensity of the Ar II 4d-4p spectral lines was observed when Cs vapor was added to the argon. This observation is explained by a selective charge transfer of the Cs 6s electron into the upper levels of the observed transitions. A rate constant of (1.4±0.2)x10 -9 cm 3 /s for the transfer process was determined 9. Synthetic system mimicking the energy transfer and charge separation of natural photosynthesis Energy Technology Data Exchange (ETDEWEB) Gust, D.; Moore, T.A. 1985-05-01 A synthetic molecular triad consisting of a porphyrin P linked to both a quinone Q and a carotenoid polyene C has been prepared as a mimic of natural photosynthesis for solar energy conversion purposes. Laser flash excitation of the porphyrin moiety yields a charge-separated state Csup(+.)-P-Qsup(-.) within 100 ps with a quantum yield of more than 0.25. This charge-separated state has a lifetime on the microsecond time scale in suitable solvents. The triad also models photosynthetic antenna function and photoprotection from singlet oxygen damge. The successful biomimicry of photosynthetic charge separation is in part the result of multistep electron transfers which rapidly separate the charges and leave the system at high potential, but with a considerable barrier to recombination. 10. Theoretical Study of the Charge-Transfer State Separation within Marcus Theory DEFF Research Database (Denmark) Volpi, Riccardo; Nassau, Racine; Nørby, Morten Steen 2016-01-01 We study, within Marcus theory, the possibility of the charge-transfer (CT) state splitting at organic interfaces and a subsequent transport of the free charge carriers to the electrodes. As a case study we analyze model anthracene-C60 interfaces. Kinetic Monte Carlo (KMC) simulations on the cold...... CT state were performed at a range of applied electric fields, and with the fields applied at a range of angles to the interface to simulate the action of the electric field in a bulk heterojunction (BHJ) interface. The results show that the inclusion of polarization in our model increases CT state...... dissociation and charge collection. The effect of the electric field on CT state splitting and free charge carrier conduction is analyzed in detail with and without polarization. Also, depending on the relative orientation of the anthracene and C60 molecules at the interface, CT state splitting shows different... 11. Active pixel sensor having intra-pixel charge transfer with analog-to-digital converter Science.gov (United States) Fossum, Eric R. (Inventor); Mendis, Sunetra K. (Inventor); Pain, Bedabrata (Inventor); Nixon, Robert H. (Inventor); Zhou, Zhimin (Inventor) 2003-01-01 An imaging device formed as a monolithic complementary metal oxide semiconductor integrated circuit in an industry standard complementary metal oxide semiconductor process, the integrated circuit including a focal plane array of pixel cells, each one of the cells including a photogate overlying the substrate for accumulating photo-generated charge in an underlying portion of the substrate, a readout circuit including at least an output field effect transistor formed in the substrate, and a charge coupled device section formed on the substrate adjacent the photogate having a sensing node connected to the output transistor and at least one charge coupled device stage for transferring charge from the underlying portion of the substrate to the sensing node and an analog-to-digital converter formed in the substrate connected to the output of the readout circuit. 12. Charge and energy transfer interplay in hybrid sensitized solar cells mediated by graphene quantum dots International Nuclear Information System (INIS) Mihalache, Iuliana; Radoi, Antonio; Mihaila, Mihai; Munteanu, Cornel; Marin, Alexandru; Danila, Mihai; Kusko, Mihaela; Kusko, Cristian 2015-01-01 Highlights: • We report a one pot synthesis metod of GQD with controlled size and optoelectronic properties. • An improvement of common N3-DSSC characteristics is achieved when GQDs are used as co-sensitiser. • The role of GQD as cosensitisers in hybrid DSSC was investigated and the interplay between charge and energy transfer phenomena mediated by GQDs was demonstrated. • The GQDs presence determines an inhibition of the recombination processes at the TiO 2 /electrolyte interface. - Abstract: We explored the role of graphene quantum dots (GQDs) as co-sensitizers in hybrid dye sensitized solar cell (DSSC) architectures, focusing on various concurring mechanisms, such as: charge transfer, energy transfer and recombination rate, towards light harvesting improvement. GQDs were prepared by the hydrothermal method that allows the tuning of electronic levels and optical properties by employing appropriate precursors and synthesis conditions. The aim was to realize a type II alignment for TiO 2 /GQD/dye hybrid configuration, using standard N3 Ru-dye in order to improve charge transfer. When GQDs were used as co-sensitizers together with N3 Ru-dye, an improvement in power conversion efficiency was achieved, as shown by electrical measurements. The experimental analysis indicates that this improvement arises from the interplay of various mechanisms mediated by GQDs: (i) enhancement of charge separation and collection due to the cascaded alignment of the energy levels; (ii) energy transfer from GQDs to N3 Ru-dye due to the overlap between GQD photoluminescence and N3 Ru-dye absorption spectra; and (iii) reduction of the electron recombination to the redox couple due to the inhibition of the back electron transfer to the electrolyte by the GQDs 13. Energy and charge transfer cascade in methylammonium lead bromide perovskite nanoparticle aggregates. Science.gov (United States) Bouduban, Marine E F; Burgos-Caminal, Andrés; Ossola, Rachele; Teuscher, Joël; Moser, Jacques-E 2017-06-01 Highly photoluminescent hybrid lead halide perovskite nanoparticles have recently attracted wide interest in the context of high-stake applications, such as light emitting diodes (LEDs), light emitting transistors and lasers. In addition, they constitute ideal model systems to explore energy and charge transport phenomena occurring at the boundaries of nanocrystalline grains forming thin films in high-efficiency perovskite solar cells (PSCs). Here we report a complete photophysical study of CH 3 NH 3 PbBr 3 perovskite nanoparticles suspended in chlorobenzene and highlight some important interaction properties. Colloidal suspensions under study were constituted of dispersed aggregates of quasi-2D platelets of a range of thicknesses, decorated with 3D-like spherical nanoparticles. These types of nanostructures possess different optical properties that afford a handle for probing them individually. The photophysics of the colloidal particles was studied by femtosecond pump-probe spectroscopy and time-correlated single-photon counting. We show here that a cascade of energy and exciton-mediated charge transfer occurs between nanostructures: upon photoexcitation, localized excitons within one nanostructure can either recombine on a ps timescale, yielding a short-lived emission, or form charge-transfer states (CTSs) across adjacent domains, resulting in longer-lived photoluminescence in the millisecond timescale. Furthermore, CTSs exhibit a clear signature in the form of a strong photoinduced electroabsorption evidenced in femtosecond transient absorption measurements. Charge transfer dynamics at the surface of the nanoparticles have been studied with various quenchers in solution. Efficient hole transfer to N , N , N ', N '-tetrakis(4-methoxyphenyl)benzidine (MeO-TPD) and 1,4-bis(diphenyl-amino)benzene (BDB) donors was attested by the quenching of the nanoparticles emission. The charge transfer rate was limited by the organic layer used to stabilize the nanoparticles 14. A low-spin Fe(III) complex with 100-ps ligand-to-metal charge transfer photoluminescence DEFF Research Database (Denmark) Chabera, Pavel; Liu, Yizhu; Prakash, Om 2017-01-01 Transition-metal complexes are used as photosensitizers(1), in light-emitting diodes, for biosensing and in photocatalysis(2). A key feature in these applications is excitation from the ground state to a charge-transfer state(3,4); the long charge-transfer-state lifetimes typical for complexes... 15. Photo-induced charge transfer at heterogeneous interfaces: Dye-sensitized tin disulfide, the theory and the experiment International Nuclear Information System (INIS) Lanzafame, J.M. 1993-01-01 The study of photo-induced charge transfer is an endeavor that spans the entire industrial period of man's history. Its great importance demands an ever greater understanding of its underlying principles. The work discussed here attempts to probe elementary aspects of the charge transfer process. Investigations into the theory of charge transfer reactions are made in an attempt to isolate the relevant parameters. An analytical discussion is made of a simple Golden Rule type rate equation to describe the transfer kinetics. Then a quantum simulation is carried out to follow the wavefunction propagation as a test of the applicability of the assumptions made in deriving the simpler rate equation. Investigation of charge transfer at surfaces is bet served by the application of ultrafast optical spectroscopies to probe carrier dynamics. A discussion of the properties of the short pulse laser systems employed is included along with a discussion of the different optical spectroscopies available. These tools are then brought to bear upon dye-sensitized SnS 2 , a model system for the study of charge injection processes. The unique properties of the semiconductor are discussed with respect to the charge transfer process. The unique properties of the semiconductor are discussed with respect to the charge transfer process. The optical experiments performed on the dye/SnS 2 systems elucidate the fundamental carrier dynamics and these dynamics are discussed within the theoretical framework to provide a complete picture of the charge transfer kinetics 16. Study Of Higher Moments Of Net-Electric Charge & Net-Proton Number Fluctuations In Pb+Pb Collisions At\\sqrt{s_{NN}}$=2.76 TeV In ALICE At LHC CERN Document Server Behera, Nirbhay Kumar Lattice QCD predicts that at extreme temperature and energy density, QCD matter will undergo a phase transition from hadronic matter to partonic matter called as QGP. One of the fundamental goals of heavy ion collision experiments to map the QCD phase diagram as a function of temperature (T) and baryo-chemical potential ($\\mu_{B}$). There are many proposed experimental signatures of QGP and fluctuations study are regarded as sensitive tool for it. It is proposed that fluctuation of conserved quantities like net-charge and net-proton can be used to map the QCD phase diagram. The mean ($\\mu$), sigma ($\\sigma$), skewness (S) and kurtosis ($\\kappa$) of the distribution of net charge and net proton are believed to be sensitive probes in fluctuation analysis. It has been argued that critical phenomena are signaled with increase and divergence of correlation length. The dependence of$n^{th}$order higher moments (cumulants,$c_{n}$) with the correlation length$\\xi$is as$c_{n}\\sim\\xi^{2.5n-3}. At LHC energy, the... 17. Communication: Modeling of concentration dependent water diffusivity in ionic solutions: Role of intermolecular charge transfer Energy Technology Data Exchange (ETDEWEB) Yao, Yi; Berkowitz, Max L., E-mail: [email protected], E-mail: [email protected]; Kanai, Yosuke, E-mail: [email protected], E-mail: [email protected] [Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 (United States) 2015-12-28 The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na{sup +} and K{sup +} ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications. 18. Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroanilin DEFF Research Database (Denmark) Eriksen, J.J.; Sauer, S.P.A.; Mikkelsen, K.V. 2013-01-01 We investigate the failure of Time{Dependent Density Functional Theory (TDDFT) with the CAM{B3LYP exchange{correlation (xc) functional coupled to the Polarizable Embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge{transfer excitation in para...... the electric dipole moments in the gas phase and for 100 solvent congurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic...... to benchmark results of TDDFT calculations with CAM-B3LYP for intramolecular charge{transfer excitations in molecular systems similar to pNA against higher{level ab initio wave function methods, like, e.g., CCSD, prior to their use. Using the calculated change in dipole moment upon excitation as a measure... 19. Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme International Nuclear Information System (INIS) Theophilou, Iris; Tassi, M.; Thanos, S. 2014-01-01 Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations 20. State-selective charge transfer cross sections for light ion impact of atomic hydrogen Energy Technology Data Exchange (ETDEWEB) Schultz, D. R. [University of North Texas; Stancil, Phillip C. [University of Georgia, Athens; Havener, C. C. [Oak Ridge National Laboratory (ORNL) 2015-01-01 Owing to the utility of diagnosing plasma properties such as impurity concentration and spatial distribution, and plasma temperature and rotation, by detection of photon emission following capture of electrons from atomic hydrogen to excited states of multiply charged ions, new calculations of state-selective charge transfer involving light ions have been carried out using the atomic orbital close-coupling and the classical trajectory Monte Carlo methods. By comparing these with results of other approaches applicable in a lower impact energy regime, and by benchmarking them using key experimental data, knowledge of the cross sections can be made available across the range parameters needed by fusion plasma diagnostics. 1. Fermi level alignment in molecular nanojunctions and its relation to charge transfer DEFF Research Database (Denmark) Stadler, Robert; Jacobsen, Karsten Wedel 2006-01-01 The alignment of the Fermi level of a metal electrode within the gap of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a molecule is a key quantity in molecular electronics, which can vary the electron transparency of a single-molecule junction...... by orders of magnitude. We present a quantitative analysis of the relation between this level alignment (which can be estimated from charging free molecules) and charge transfer for bipyridine and biphenyl dithiolate (BPDT) molecules attached to gold leads based on density functional theory calculations...... end of the gap in the transmission function for bipyridine and at its lower end for BPDT.... 2. Molecular control of photoexcited charge transfer and recombination at a quaterthiophene/zinc oxide interface International Nuclear Information System (INIS) Mou Weiwei; Nakano, Aiichiro; Ohmura, Satoshi; Shimojo, Fuyuki 2012-01-01 Nonadiabatic quantum molecular dynamics simulations are performed to study photoexcited charge transfer (CT) and charge recombination (CR) at an interface between a conjugated oligomer donor, quaterthiophene (QT), and an inorganic acceptor (ZnO). Simulations reveal a detrimental effect of static disorder in QT conformation on the efficiency of hybrid QT/ZnO solar cells due to increased CR. On the contrary, dynamic disorder (i.e., fluctuation of carbon-hydrogen bonds in QT) is essential for high efficiency by assisting CT. The separate controllability of CT and CR at the molecular level has impacts on molecular design for efficient solar cells and explains recent experimental observations. 3. Energy and charge transfer dynamics between Alq3 and CdSeS nanocrystals. Science.gov (United States) Zhang, Shuping; Liu, Yuqiang; Yang, Yanqiang 2010-03-01 The photoluminescence properties of the blend films consisting of organic small molecules and nanocrystals (NCs)--Alq3 and CdSeS NCs--were studied by steady-state and time-resolved photoluminescence (PL) spectroscopy with different excited wavelengths. Both the fluorescence intensity and lifetime are intensively dependent on the NC concentration. The detailed analysis of experiment data proves that Forster energy transfer from the Alq3 to the NCs exists simultaneously with the charge transfer and both compete with each other in the blend films. 4. Temperature-dependent kinetics of charge transfer, hydrogen-atom transfer, and hydrogen-atom expulsion in the reaction of CO+ with CH4 and CD4. Science.gov (United States) Melko, Joshua J; Ard, Shaun G; Johnson, Ryan S; Shuman, Nicholas S; Guo, Hua; Viggiano, Albert A 2014-09-18 We have determined the rate constants and branching ratios for the reactions of CO(+) with CH4 and CD4 in a variable-temperature selected ion flow tube. We find that the rate constants are collisional for all temperatures measured (193-700 K for CH4 and 193-500 K for CD4). For the CH4 reaction, three product channels are identified, which include charge transfer (CH4(+) + CO), H-atom transfer (HCO(+) + CH3), and H-atom expulsion (CH3CO(+) + H). H-atom transfer is slightly preferred to charge transfer at low temperature, with the charge-transfer product increasing in contribution as the temperature is increased (H-atom expulsion is a minor product for all temperatures). Analogous products are identified for the CD4 reaction. Density functional calculations on the CO(+) + CH4 reaction were also conducted, revealing that the relative temperature dependences of the charge-transfer and H-atom transfer pathways are consistent with an initial charge transfer followed by proton transfer. 5. Dependence of charge transfer phenomena during solid-air two-phase flow on particle disperser Science.gov (United States) Tanoue, Ken-ichiro; Suedomi, Yuuki; Honda, Hirotaka; Furutani, Satoshi; Nishimura, Tatsuo; Masuda, Hiroaki 2012-12-01 An experimental investigation of the tribo-electrification of particles has been conducted during solid-air two-phase turbulent flow. The current induced in a metal plate by the impact of polymethylmethacrylate (PMMA) particles in a high-speed air flow was measured for two different plate materials. The results indicated that the contact potential difference between the particles and a stainless steel plate was positive, while for a nickel plate it was negative. These results agreed with theoretical contact charge transfer even if not only the particle size but also the kind of metal plate was changed. The specific charge of the PMMA particles during solid-air two-phase flow using an ejector, a stainless steel branch pipe, and a stainless steel straight pipe was measured using a Faraday cage. Although the charge was negative in the ejector, the particles had a positive specific charge at the outlet of the branch pipe, and this positive charge increased in the straight pipe. The charge decay along the flow direction could be reproduced by the charging and relaxation theory. However, the proportional coefficients in the theory changed with the particle size and air velocity. Therefore, an unexpected charge transfer occurred between the ejector and the branch pipe, which could not be explained solely by the contact potential difference. In the ejector, an electrical current in air might have been produced by self-discharge of particles with excess charge between the nickel diffuser in the ejector and the stainless steel nozzle or the stainless steel pipe due to a reversal in the contact potential difference between the PMMA and the stainless steel. The sign of the current depended on the particle size, possibly because the position where the particles impacted depended on their size. When dual coaxial glass pipes were used as a particle disperser, the specific charge of the PMMA particles became more positive along the particle flow direction due to the contact 6. Photodissociation and charge transfer dynamics of negative ions studied with femtosecond photoelectron spectroscopy Energy Technology Data Exchange (ETDEWEB) Zanni, Martin Thomas [Univ. of California, Berkeley, CA (United States) 1999-12-01 This dissertation presents studies aimed at understanding the potential energy surfaces and dynamics of isolated negative ions, and the effects of solvent on each. Although negative ions play important roles in atmospheric and solution phase chemistry, to a large extent the ground and excited state potential energy surfaces of gas phase negative ions are poorly characterized, and solvent effects even less well understood. In an effort to fill this gap, the author's coworkers and the author have developed a new technique, anion femtosecond photoelectron spectroscopy, and applied it to gas phase photodissociation and charge transfer processes. Studies are presented that (1) characterize the ground and excited states of isolated and clustered anions, (2) monitor the photodissociation dynamics of isolated and clustered anions, and (3) explore the charge-transfer-to-solvent states of atomic iodide clustered with polar and non-polar solvents. 7. Bands dispersion and charge transfer in β-BeH2 Science.gov (United States) Trivedi, D. K.; Galav, K. L.; Joshi, K. B. 2018-04-01 Predictive capabilities of ab-initio method are utilised to explore bands dispersion and charge transfer in β-BeH2. Investigations are carried out using the linear combination of atomic orbitals method at the level of density functional theory. The crystal structure and related parameters are settled by coupling total energy calculations with the Murnaghan equation of state. Electronic bands dispersion from PBE-GGA is reported. The PBE-GGA, and PBE0 hybrid functional, show that β-BeH2 is a direct gap semiconductor with 1.18 and 2.40 eV band gap. The band gap slowly decreases with pressure and beyond l00 GPa overlap of conduction and valence bands at the r point is observed. Charge transfer is studied by means of Mullikan population analysis. 8. Charge transfer complex in diketopyrrolopyrrole polymers and fullerene blends: Implication for organic solar cell efficiency Science.gov (United States) Moghe, D.; Yu, P.; Kanimozhi, C.; Patil, S.; Guha, S. 2012-02-01 Copolymers based on diketopyrrolopyrrole (DPP) have recently gained potential in organic photovoltaics. When blended with another acceptor such as PCBM, intermolecular charge transfer occurs which may result in the formation of charge transfer (CT) states. We present here the spectral photocurrent characteristics of two donor-acceptor DPP based copolymers, PDPP-BBT and TDPP-BBT, blended with PCBM to identify the CT states. The spectral photocurrent measured using Fourier-transform photocurrent spectroscopy (FTPS) and monochromatic photocurrent (PC) methods are compared with P3HT:PCBM, where the CT state is well known. PDPP-BBT:PCBM shows a stable CT state while TDPP-BBT does not. Our analysis shows that the larger singlet state energy difference between TDPP-BBT and PCBM along with the lower optical gap of TDPP-BBT obliterates the formation of a midgap CT state resulting in an enhanced photovoltaic efficiency over PDPP-BBT:PCBM. 9. Study on charge transfer reaction of several organic molecules with accelerated rare gas ions International Nuclear Information System (INIS) Takahasi, Makoto; Okuda, Sachiko; Arai, Eiichi; Ichinose, Akira; Takakubo, Masaaki. 1984-01-01 Observing the charge transfer mass spectra of ethylbenzene, cyclobutane and methanol in Ar and Xe ion impacts, we investigated the dependence of the secondary ion peak intensities (normalized to primary ion current and target pressure) on the translational energy of primary ions (0-3500 eV).In the case of ethylbenzene, several maxima of the secondary i on peak intensities were observed in Ar and Xe ion impacts. The correlation between the maxima and the primary ion energy was examined in terms of near adiabatic theory of Massey. Supplementary studies on the energy distribution of primary ion, charge transfer cross section between methanol and Xe ion, and final product analysis in rare gas ion irradiation on cyclobutane were described. (author) 10. Oxidation and Metal-Insertion in Molybdenite Surfaces: Evaluation of Charge-Transfer Mechanisms and Dynamics Energy Technology Data Exchange (ETDEWEB) Ramana, Chintalapalle V.; Becker, U.; Shutthanandan, V.; Julien, C. M. 2008-06-05 Molybdenum sulfide (MoS2), an important representative member of the layered transition-metal dichalcogenides, has been of special importance to the research community of geochemistry, materials and environmental chemistry, and industrial science and technology. Understanding the oxidation behavior and charge-transfer mechanisms in MoS2 is important to gain better insight into the degradation of this mineral in the environment. On the other hand understanding the insertion of metals into molybdenite and evaluation of charge-transfer mechanism and dynamics is quite important to utilize these minerals in technological applications. Furthermore, such a detailed investigation of thermal oxidation behavior and intercalation process will provide a basis to further explore and model the mechanism of adsorption of metal ions on to geomedia. Therefore, the present work was performed to understand the oxidation and intercalation processes of molybdenite surfaces. The results obtained, using a wide variety of analytical techniques, are presented and discussed in this paper. 11. Photodissociation and charge transfer dynamics of negative ions studied with femtosecond photoelectron spectroscopy International Nuclear Information System (INIS) Zanni, Martin T. 1999-01-01 This dissertation presents studies aimed at understanding the potential energy surfaces and dynamics of isolated negative ions, and the effects of solvent on each. Although negative ions play important roles in atmospheric and solution phase chemistry, to a large extent the ground and excited state potential energy surfaces of gas phase negative ions are poorly characterized, and solvent effects even less well understood. In an effort to fill this gap, the author's coworkers and the author have developed a new technique, anion femtosecond photoelectron spectroscopy, and applied it to gas phase photodissociation and charge transfer processes. Studies are presented that (1) characterize the ground and excited states of isolated and clustered anions, (2) monitor the photodissociation dynamics of isolated and clustered anions, and (3) explore the charge-transfer-to-solvent states of atomic iodide clustered with polar and non-polar solvents 12. Highly mobile charge-transfer excitons in two-dimensional WS2/tetracene heterostructures Science.gov (United States) Zhu, Tong; Yuan, Long; Zhao, Yan; Zhou, Mingwei; Wan, Yan; Mei, Jianguo; Huang, Libai 2018-01-01 Charge-transfer (CT) excitons at heterointerfaces play a critical role in light to electricity conversion using organic and nanostructured materials. However, how CT excitons migrate at these interfaces is poorly understood. We investigate the formation and transport of CT excitons in two-dimensional WS2/tetracene van der Waals heterostructures. Electron and hole transfer occurs on the time scale of a few picoseconds, and emission of interlayer CT excitons with a binding energy of ~0.3 eV has been observed. Transport of the CT excitons is directly measured by transient absorption microscopy, revealing coexistence of delocalized and localized states. Trapping-detrapping dynamics between the delocalized and localized states leads to stretched-exponential photoluminescence decay with an average lifetime of ~2 ns. The delocalized CT excitons are remarkably mobile with a diffusion constant of ~1 cm2 s−1. These highly mobile CT excitons could have important implications in achieving efficient charge separation. PMID:29340303 13. Impact of speciation on the electron charge transfer properties of nanodiamond drug carriers. Science.gov (United States) Sun, Baichuan; Barnard, Amanda S 2016-08-07 Unpassivated diamond nanoparticles (bucky-diamonds) exhibit a unique surface reconstruction involving graphitization of certain crystal facets, giving rise to hybrid core-shell particles containing both aromatic and aliphatic carbon. Considerable effort is directed toward eliminating the aromatic shell, but persistent graphitization of subsequent subsurface-layers makes perdurable purification a challenge. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the impact of different fractions of aromatic and aliphatic carbon on the charge transfer properties of the ensembles of bucky-diamonds. By predicting quality factors for a variety of cases, we find that perfect purification is not necessary to preserve selectivity, and there is a clear motivation for purifying samples to improve the sensitivity of charge transfer reactions. This may prove useful in designing drug delivery systems where the release of (selected) drugs needs to be sensitive to specific conditions at the point of delivery. 14. Muon transfer from muonic hydrogen to heavier atoms; Transfert de charge muonique Energy Technology Data Exchange (ETDEWEB) Dupays, A 2004-06-01 This work concerns muon transfer from muonic hydrogen to heavier atoms. Recently, a method of measurement of the hyperfine structure of ground-state muonic hydrogen based on the collision energy dependence of the muon transfer rate to oxygen has been proposed. This proposal is based on measurements which where performed at the Paul Scherrer Institute in the early nineties which indicate that the muon transfer from muonic hydrogen to oxygen increases by a factor of 4 going from thermal to 0.12 eV energies. The motivation of our calculations was to confirm this behaviour. To study the collision energy dependence of the muon transfer rate, we have used a time-independent close-coupling method. We have set up an hyperspherical elliptic formalism valid for nonzero total angular momentum which allows accurate computations of state-to-state reactive and charge exchange processes. We have applied this formalism to muon-transfer process to oxygen and neon. The comparison with experimental results is in both cases excellent. Finally, the neon transfer rate dependence with energy suggests to use neon instead of oxygen to perform a measurement of the hyperfine structure of muonic hydrogen. The results of accurate calculations of the muon transfer rates from muonic protium and deuterium atoms to nitrogen, oxygen and neon are also reported. Very good agreement with measured rates is obtained and for the three systems, the isotopic effect is perfectly reproduced. (author) 15. Oxygen-assisted charge transfer between ZnO quantum dots and graphene. Science.gov (United States) Guo, Wenhao; Xu, Shuigang; Wu, Zefei; Wang, Ning; Loy, M M T; Du, Shengwang 2013-09-23 Efficient charge transfer between ZnO quantum dots (QDs) and graphene is demonstrated by decorating ZnO QDs on top of graphene, with the assistance of oxygen molecules from the air. The electrical response of the device to UV light is greatly enhanced, and a photoconductive gain of up to 10(7) can be obtained. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 16. Oxidation and metal-insertion in molybdenite surfaces: evaluation of charge-transfer mechanisms and dynamics Directory of Open Access Journals (Sweden) Shutthanandan V 2008-06-01 Full Text Available Abstract Molybdenum disulfide (MoS2, a layered transition-metal dichalcogenide, has been of special importance to the research community of geochemistry, materials and environmental chemistry, and geotechnical engineering. Understanding the oxidation behavior and charge-transfer mechanisms in MoS2 is important to gain better insight into the degradation of this mineral in the environment. In addition, understanding the insertion of metals into molybdenite and evaluation of charge-transfer mechanism and dynamics is important to utilize these minerals in technological applications. Furthermore, a detailed investigation of thermal oxidation behavior and metal-insertion will provide a basis to further explore and model the mechanism of adsorption of metal ions onto geomedia. The present work was performed to understand thermal oxidation and metal-insertion processes of molybdenite surfaces. The analysis was performed using atomic force microscopy (AFM, scanning electron microscopy (SEM, transmission electron microscopy (TEM, Rutherford backscattering spectrometry (RBS, and nuclear reaction analysis (NRA. Structural studies using SEM and TEM indicate the local-disordering of the structure as a result of charge-transfer process between the inserted lithium and the molybdenite layer. Selected area electron diffraction measurements indicate the large variations in the diffusivity of lithium confirming that the charge-transfer is different along and perpendicular to the layers in molybdenite. Thermal heating of molybenite surface in air at 400°C induces surface oxidation, which is slow during the first hour of heating and then increases significantly. The SEM results indicate that the crystals formed on the molybdenite surface as a result of thermal oxidation exhibit regular thin-elongated shape. The average size and density of the crystals on the surface is dependent on the time of annealing; smaller size and high density during the first one-hour and 17. Oxidation and metal-insertion in molybdenite surfaces: evaluation of charge-transfer mechanisms and dynamics. Science.gov (United States) Ramana, C V; Becker, U; Shutthanandan, V; Julien, C M 2008-06-05 Molybdenum disulfide (MoS2), a layered transition-metal dichalcogenide, has been of special importance to the research community of geochemistry, materials and environmental chemistry, and geotechnical engineering. Understanding the oxidation behavior and charge-transfer mechanisms in MoS2 is important to gain better insight into the degradation of this mineral in the environment. In addition, understanding the insertion of metals into molybdenite and evaluation of charge-transfer mechanism and dynamics is important to utilize these minerals in technological applications. Furthermore, a detailed investigation of thermal oxidation behavior and metal-insertion will provide a basis to further explore and model the mechanism of adsorption of metal ions onto geomedia.The present work was performed to understand thermal oxidation and metal-insertion processes of molybdenite surfaces. The analysis was performed using atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Rutherford backscattering spectrometry (RBS), and nuclear reaction analysis (NRA).Structural studies using SEM and TEM indicate the local-disordering of the structure as a result of charge-transfer process between the inserted lithium and the molybdenite layer. Selected area electron diffraction measurements indicate the large variations in the diffusivity of lithium confirming that the charge-transfer is different along and perpendicular to the layers in molybdenite. Thermal heating of molybenite surface in air at 400 degrees C induces surface oxidation, which is slow during the first hour of heating and then increases significantly. The SEM results indicate that the crystals formed on the molybdenite surface as a result of thermal oxidation exhibit regular thin-elongated shape. The average size and density of the crystals on the surface is dependent on the time of annealing; smaller size and high density during the first one-hour and significant 18. Lifetimes of partial charge transfer exciplexes of 9-cyanophenanthrene and 9-cyanoanthracene OpenAIRE Dolotova, Elena; Dogadkin, Denis; Soboleva, Irina; Kuzmin, Michael; Nicolet, Olivier; Vauthey, Eric 2003-01-01 The fluorescence decays of several exciplexes with partial charge transfer have been investigated in solvents of various polarity. The measured lifetimes are found to be in reasonable agreement with the activation enthalpy and entropy of exciplex decay obtained earlier from the temperature dependence of the exciplex emission quantum yields. For exciplexes with 9-cyanophenanthrene substantial contribution of the higher local excited state into the exciplex electronic structure is found and bor... 19. Imidazole as a parent π-conjugated backbone in charge-transfer chromophores Directory of Open Access Journals (Sweden) Jiří Kulhánek 2012-01-01 Full Text Available Research activities in the field of imidazole-derived push–pull systems featuring intramolecular charge transfer (ICT are reviewed. Design, synthetic pathways, linear and nonlinear optical properties, electrochemistry, structure–property relationships, and the prospective application of such D-π-A organic materials are described. This review focuses on Y-shaped imidazoles, bi- and diimidazoles, benzimidazoles, bis(benzimidazoles, imidazole-4,5-dicarbonitriles, and imidazole-derived chromophores chemically bound to a polymer chain. 20. Development and capital investment tasks involved in the production of charge transfer equipment International Nuclear Information System (INIS) Simon, Sandor 1983-01-01 Stringent requirements had to be considered in the course of the production development of charge transfer equipment. The production of structures demanding extremely high endurance was based on extensive co-operation. Special alloys were needed for parts and bearings, special heat-treatment was required at certain sections for large dimensions etc. Appropriate mashine stock, assembly and test hall have been built for assembling and testing the equipment with both 440 and 100 MW.(Sz.J.) 1. Charge transfer collisions of Si^3+ with H at low energies Science.gov (United States) Joseph, D. C.; Gu, J. P.; Saha, B. C. 2009-11-01 Charge transfer of positively charged ions with atomic hydrogen is important not only in magnetically confined plasmas between impurity ions and H atoms from the chamber walls influences the overall ionization balance and effects the plasma cooling but also in astrophysics, where it plays a key role in determining the properties of the observed gas. It also provides a recombination mechanism for multiply charged ions in X-ray ionized astronomical environments. We report an investigation using the molecular-orbital close-coupling (MOCC) method, both quantum mechanically and semi-classically, in the adiabatic representation. Ab initio adiabatic potentials and coupling matrix elements--radial and angular--are calculated using the MRD-CI method. Comparison of our results with other theoretical as well as experimental findings will be discussed. 2. Computational models of an inductive power transfer system for electric vehicle battery charge Science.gov (United States) Anele, A. O.; Hamam, Y.; Chassagne, L.; Linares, J.; Alayli, Y.; Djouani, K. 2015-09-01 One of the issues to be solved for electric vehicles (EVs) to become a success is the technical solution of its charging system. In this paper, computational models of an inductive power transfer (IPT) system for EV battery charge are presented. Based on the fundamental principles behind IPT systems, 3 kW single phase and 22 kW three phase IPT systems for Renault ZOE are designed in MATLAB/Simulink. The results obtained based on the technical specifications of the lithium-ion battery and charger type of Renault ZOE show that the models are able to provide the total voltage required by the battery. Also, considering the charging time for each IPT model, they are capable of delivering the electricity needed to power the ZOE. In conclusion, this study shows that the designed computational IPT models may be employed as a support structure needed to effectively power any viable EV. 3. Computational models of an inductive power transfer system for electric vehicle battery charge International Nuclear Information System (INIS) Anele, A O; Hamam, Y; Djouani, K; Chassagne, L; Alayli, Y; Linares, J 2015-01-01 One of the issues to be solved for electric vehicles (EVs) to become a success is the technical solution of its charging system. In this paper, computational models of an inductive power transfer (IPT) system for EV battery charge are presented. Based on the fundamental principles behind IPT systems, 3 kW single phase and 22 kW three phase IPT systems for Renault ZOE are designed in MATLAB/Simulink. The results obtained based on the technical specifications of the lithium-ion battery and charger type of Renault ZOE show that the models are able to provide the total voltage required by the battery. Also, considering the charging time for each IPT model, they are capable of delivering the electricity needed to power the ZOE. In conclusion, this study shows that the designed computational IPT models may be employed as a support structure needed to effectively power any viable EV. (paper) 4. Charge-Transfer States in Organic Solar Cells: Understanding the Impact of Polarization, Delocalization, and Disorder KAUST Repository Zheng, Zilong 2017-05-08 We investigate the impact of electronic polarization, charge delocalization, and energetic disorder on the charge-transfer (CT) states formed at a planar C60/pentacene interface. The ability to examine large complexes containing up to seven pentacene molecules and three C60 molecules allows us to take explicitly into account the electronic polarization effects. These complexes are extracted from a bilayer architecture modeled by molecular dynamics simulations and evaluated by means of electronic-structure calculations based on long-range-separated functionals (ωB97XD and BNL) with optimized range-separation parameters. The energies of the lowest charge-transfer states derived for the large complexes are in very good agreement with the experimentally reported values. The average singlet-triplet energy splittings of the lowest CT states are calculated not to exceed 10 meV. The rates of geminate recombination as well as of dissociation of the triplet excitons are also evaluated. In line with experiment, our results indicate that the pentacene triplet excitons generated through singlet fission can dissociate into separated charges on a picosecond time scale, despite the fact that their energy in C60/pentacene heterojunctions is slightly lower than the energies of the lowest CT triplet states. 5. Charge transfer through DNA/DNA duplexes and DNA/RNA hybrids: complex theoretical and experimental studies. Science.gov (United States) Kratochvílová, Irena; Vala, Martin; Weiter, Martin; Špérová, Miroslava; Schneider, Bohdan; Páv, Ondřej; Šebera, Jakub; Rosenberg, Ivan; Sychrovský, Vladimír 2013-01-01 Oligonucleotides conduct electric charge via various mechanisms and their characterization and understanding is a very important and complicated task. In this work, experimental (temperature dependent steady state fluorescence spectroscopy, time-resolved fluorescence spectroscopy) and theoretical (Density Functional Theory) approaches were combined to study charge transfer processes in short DNA/DNA and RNA/DNA duplexes with virtually equivalent sequences. The experimental results were consistent with the theoretical model - the delocalized nature of HOMO orbitals and holes, base stacking, electronic coupling and conformational flexibility formed the conditions for more effective short distance charge transfer processes in RNA/DNA hybrids. RNA/DNA and DNA/DNA charge transfer properties were strongly connected with temperature affected structural changes of molecular systems - charge transfer could be used as a probe of even tiny changes of molecular structures and settings. © 2013. Published by Elsevier B.V. All rights reserved. 6. Density functional theory for the description of charge-transfer processes at TTF/TCNQ interfaces KAUST Repository Van Regemorter, Tanguy; Guillaume, Maxime; Sini, Gjergji; Sears, John S.; Geskin, Victor; Bré das, Jean-Luc; Beljonne, David; Cornil, Jé rô me 2012-01-01 In the field of organic electronics, a central issue is to assess how the frontier electronic levels of two adjacent organic layers align with respect to one another at the interface. This alignment can be driven by the presence of a partial charge transfer and the formation of an interface dipole; it plays a key role for instance in determining the rates of exciton dissociation or exciton formation in organic solar cells or light-emitting diodes, respectively. Reliably modeling the processes taking place at these interfaces remains a challenge for the computational chemistry community. Here, we review our recent theoretical work on the influence of the choice of density functional theory (DFT) methodology on the description of the charge-transfer character in the ground state of TTF/ TCNQ model complexes and interfaces. Starting with the electronic properties of the isolated TTF and TCNQ molecules and then considering the charge transfer and resulting interface dipole in TTF/TCNQ donor-acceptor stacks and bilayers, we examine the impact of the choice of DFT functional in describing the interfacial electronic structure. Finally, we employ computations based on periodic boundary conditions to highlight the impact of depolarization effects on the interfacial dipole moment. © Springer-Verlag 2012. 7. Development of highly accurate approximate scheme for computing the charge transfer integral Energy Technology Data Exchange (ETDEWEB) Pershin, Anton; Szalay, Péter G. [Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest (Hungary) 2015-08-21 The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature. 8. A two-dimensional position sensitive gas chamber with scanned charge transfer readout Energy Technology Data Exchange (ETDEWEB) Gomez, F. E-mail: [email protected]; Iglesias, A.; Lobato, R.; Mosquera, J.; Pardo, J.; Pena, J.; Pazos, A.; Pombar, M.; Rodriguez, A 2003-10-21 We have constructed and tested a two-dimensional position sensitive parallel-plate gas ionization chamber with scanned charge transfer readout. The scan readout method described here is based on the development of a new position-dependent charge transfer technique. It has been implemented by using gate strips perpendicularly oriented to the collector strips. This solution reduces considerably the number of electronic readout channels needed to cover large detector areas. The use of a 25 {mu}m thick kapton etched circuit allows high charge transfer efficiency with a low gating voltage, consequently needing a very simple commutating circuit. The present prototype covers 8x8 cm{sup 2} with a pixel size of 1.27x1.27 mm{sup 2}. Depending on the intended use and beam characteristics a smaller effective pixel is feasible and larger active areas are possible. This detector can be used for X-ray or other continuous beam intensity profile monitoring. 9. Overcoming the Cut-Off Charge Transfer Bandgaps at the PbS Quantum Dot Interface KAUST Repository El-Ballouli, Ala'a O. 2015-11-17 Light harvesting from large size of semiconductor PbS quantum dots (QDs) with a bandgap of less than 1 eV is one of the greatest challenges precluding the development of PbS QD-based solar cells because the interfacial charge transfer (CT) from such QDs to the most commonly used electron acceptor materials is very inefficient, if it occurs at all. Thus, an alternative electron-accepting unit with a new driving force for CT is urgently needed to harvest the light from large-sized PbS QDs. Here, a cationic porphyrin is utilized as a new electron acceptor unit with unique features that bring the donor–acceptor components into close molecular proximity, allowing ultrafast and efficient electron transfer for QDs of all sizes, as inferred from the drastic photoluminescence quenching and the ultrafast formation of the porphyrin anionic species. The time-resolved results clearly demonstrate the possibility of modulating the electron transfer process between PbS QDs and porphyrin moieties not only by the size quantization effect but also by the interfacial electrostatic interaction between the positively charged porphyrin and the negatively charged QDs. This approach provides a new pathway for engineering QD-based solar cells that make the best use of the diverse photons making up the Sun\\'s broad irradiance spectrum. 10. Charge transfer in photorechargeable composite films of TiO2 and polyaniline Science.gov (United States) Nomiyama, Teruaki; Sasabe, Kenichi; Sakamoto, Kenta; Horie, Yuji 2015-07-01 A photorechargeable battery (PRB) is a photovoltaic device having an energy storage function in a single cell. The photoactive electrode of PRB is a bilayer film consisting of bare porous TiO2 and a TiO2-polyaniline (PANi) mixture that work as a photovoltaic current generator and an electrochemical energy storage by ion dedoping, respectively. To study the charge transfer between TiO2 and PANi, the photorechargeable quantum efficiency QE ([electron count on discharge]/[incident photon count on photocharge]) was measured by varying the thickness LS of the TiO2-PANi mixture. The quantum efficiency QEuv for UV photons had a maximum of ˜7% at LS ˜ 7 µm. The time constant τTP for the charge transfer was about 10-1 s, which was longer ten times or more than the lifetime of excited electrons within TiO2. These facts reveal that the main rate-limiting factor in the photocharging process is the charge transfer between TiO2 and PANi. 11. Tuning electronic properties of graphene nanoflake polyaromatic hydrocarbon through molecular charge-transfer interactions Science.gov (United States) Sharma, Vaishali; Dabhi, Shweta D.; Shinde, Satyam; Jha, Prafulla K. 2018-05-01 By means of first principles calculation we have tuned the electronic properties of graphene nanoflake polyaromatic hydrocarbon via molecular charge transfer. Acceptor/donor Tetracyanoquinodimethane (TCNQ) and Tetrathiafulvalene (TTF) organic molecules are adsorbed on polyaromatic hydrocarbons (PAH) in order to introduce the charge transfer. The substrate's n- or p- type nature depends on the accepting/donating behavior of dopant molecules. Two different classes of PAH (extended form of triangulene) namely Bow-tie graphene nanoflake (BTGNF) and triangular zigzag graphene nanoflake (TZGNF). It is revealed that all the TCNQ and TTF modified graphene nanoflakes exhibit significant changes in HOMO-LUMO gap in range from 0.58 eV to 0.64 eV and 0.01 eV to 0.05 eV respectively. The adsorption energies are in the range of -0.05 kcal/mol to -2.6 kcal/mol. The change in work function is also calculated and discussed, the maximum charge transfer is for TCNQ adsorbed BTGNF. These alluring findings in the tuning of electronic properties will be advantageous for promoting graphene nanoflake polyaromatic hydrocarbon for their applications in electronic devices. 12. Density functional theory for the description of charge-transfer processes at TTF/TCNQ interfaces KAUST Repository Van Regemorter, Tanguy 2012-09-15 In the field of organic electronics, a central issue is to assess how the frontier electronic levels of two adjacent organic layers align with respect to one another at the interface. This alignment can be driven by the presence of a partial charge transfer and the formation of an interface dipole; it plays a key role for instance in determining the rates of exciton dissociation or exciton formation in organic solar cells or light-emitting diodes, respectively. Reliably modeling the processes taking place at these interfaces remains a challenge for the computational chemistry community. Here, we review our recent theoretical work on the influence of the choice of density functional theory (DFT) methodology on the description of the charge-transfer character in the ground state of TTF/ TCNQ model complexes and interfaces. Starting with the electronic properties of the isolated TTF and TCNQ molecules and then considering the charge transfer and resulting interface dipole in TTF/TCNQ donor-acceptor stacks and bilayers, we examine the impact of the choice of DFT functional in describing the interfacial electronic structure. Finally, we employ computations based on periodic boundary conditions to highlight the impact of depolarization effects on the interfacial dipole moment. © Springer-Verlag 2012. 13. Models of charge transport and transfer in molecular switch tunnel junctions of bistable catenanes and rotaxanes International Nuclear Information System (INIS) Flood, Amar H.; Wong, Eric W.; Stoddart, J. Fraser 2006-01-01 The processes by which charge transfer can occur play a foundational role in molecular electronics. Here we consider simplified models of the transfer processes that could be present in bistable molecular switch tunnel junction (MSTJ) devices during one complete cycle of the device from its low- to high- and back to low-conductance state. The bistable molecular switches, which are composed of a monolayer of either switchable catenanes or rotaxanes, exist in either a ground-state co-conformation or a metastable one in which the conduction properties of the two co-conformations, when measured at small biases (+0.1 V), are significantly different irrespective of whether transport is dominated by tunneling or hopping. The voltage-driven generation (±2 V) of molecule-based redox states, which are sufficiently long-lived to allow the relative mechanical movements necessary to switch between the two co-conformations, rely upon unequal charge transfer rates on to and/or off of the molecules. Surface-enhanced Raman spectroscopy has been used to image the ground state of the bistable rotaxane in MSTJ-like devices. Consideration of these models provide new ways of looking at molecular electronic devices that rely, not only on nanoscale charge-transport, but also upon the bustling world of molecular motion in mechanically interlocked bistable molecules 14. Photoinduced charge and energy transfer in dye-doped conjugated polymers International Nuclear Information System (INIS) Veldman, Dirk; Bastiaansen, Jolanda J.A.M.; Langeveld-Voss, Bea M.W.; Sweelssen, Joergen; Koetse, Marc M.; Meskers, Stefan C.J.; Janssen, Rene A.J. 2006-01-01 Conjugated polymer-molecular dye blends of MDMO-PPV (poly[2-methoxy-5-(3',7'-dimethyloctyloxy)-1,4-phenylenevinylene]) and PF1CVTP (poly[9,9-dioctylfluorene-2,7-diyl-alt-2,5-bis(2-thienyl-1-cyanovinyl) -1-(3',7= '-dimethyloctyloxy)-4-methoxybenzene-5'',5''-diyl]) with three dipyrrometheneboron difluoride (bodipy) dyes were studied by (time-resolved) fluorescence and photoinduced absorption spectroscopy to determine quantitatively the relation between the electronic HOMO and LUMO levels and the occurrence of energy or charge transfer after optical excitation. We find that for MDMO-PPV photoinduced charge transfer to the dyes occurs, while photoexcitation of PF1CVTP exclusively results in energy transfer. The differences can be rationalized by assuming that the energy of the charge separated state is 0.33-0.45 eV higher than the energy determined from oxidation and reduction potentials of donor and acceptor, respectively. This provides an important design rule to identify appropriate materials for polymer solar cells that can have a high open-circuit voltage 15. Charge-transfer complexes and their role in exciplex emission and near-infrared photovoltaics. Science.gov (United States) Ng, Tsz-Wai; Lo, Ming-Fai; Fung, Man-Keung; Zhang, Wen-Jun; Lee, Chun-Sing 2014-08-20 Charge transfer and interactions at organic heterojunctions (OHJs) are known to have critical influences on various properties of organic electronic devices. In this Research News article, a short review is given from the electronic viewpoint on how the local molecular interactions and interfacial energetics at P/N OHJs contribute to the recombination/dissociation of electron-hole pairs. Very often, the P-type materials donate electrons to the N-type materials, giving rise to charge-transfer complexes (CTCs) with a P(δ+) -N(δ-) configuration. A recently observed opposite charge-transfer direction in OHJs is also discussed (i.e., N-type material donates electrons to P-type material to form P(δ-) -N(δ+) ). Recent studies on the electronic structures of CTC-forming material pairs are also summarized. The formation of P(δ-) -N(δ+) -type CTCs and their correlations with exciplex emission are examined. Furthermore, the potential applications of CTCs in NIR photovoltaic devices are reviewed. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 16. Microchip-calorimetry of organic charge transfer complex which shows superconductivity at low temperatures Energy Technology Data Exchange (ETDEWEB) Muraoka, Yuki [Department of Chemistry, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043 (Japan); Yamashita, Satoshi [RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198 (Japan); Yamamoto, Takashi [Department of Chemistry, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043 (Japan); Nakazawa, Yasuhiro, E-mail: [email protected] [Department of Chemistry, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043 (Japan); Institute for Molecular Science, Nishigonaka 38, Myodaiji, Okazaki 444-8585 (Japan) 2012-03-20 Highlights: Black-Right-Pointing-Pointer Organic charge transfer salt of {kappa}-(BEDT-TTF){sub 2}Cu[N(CN){sub 2}]Br shows superconductivity. Black-Right-Pointing-Pointer We succeeded to detect thermal anomaly microchip device TCG3880. Black-Right-Pointing-Pointer Development details of the calorimeter and the detection system is presented. Black-Right-Pointing-Pointer The magnetic fields dependence shows typical character of layered superconductor. - Abstract: We carried out thermodynamic measurements of organic charge transfer complex of {kappa}-(BEDT-TTF){sub 2}Cu[N(CN){sub 2}]Br, where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene by TCG3880 chip device in order to examine capability of the chip calorimeter at low temperature region and under magnetic fields. TCG3880 chip is mounted on a {sup 3}He cryostat available in combination with a superconductive magnet up to 7 T. Thermal anomalies related to the glass-like freezing of ethylene groups of BEDT-TTF molecules and the superconductive transition were observed. A frequency dependence of the thermal anomaly of the glass formation and a magnetic fields dependence of the thermal anomaly of the superconductive transition are reported. The results presented in this work demonstrate that the TCG3880 is quite useful for thermodynamic investigations of the organic charge transfer complex with much reduced sample quantity as compared with those of relaxation and adiabatic calorimetry. 17. The charge transfer characteristic of tetraphenylporphyrin iron chloride Langmuir–Blodgett films International Nuclear Information System (INIS) Du, Y.; Li, Z.H.; Qi, P.; Wang, F.; Liu, D. 2013-01-01 The charge transfer characteristic of tetraphenylporphyrin iron (III) chloride (FeP) Langmuir–Blodgett (LB) films on the surface of the ITO glass electrode was reported. When the cyclic voltammetry (CV) scanning was running, the charge transfer characteristic was controlled by the oxidation–reduction process of Fe(III)/Fe(II). The charge transfer characteristic was related to the following factors: the cross-sectional area, relative to the electrode, of FeP as the electron donor (or acceptor). The greater the cross-sectional area of the aggregation of FeP as the electron donor (or acceptor) was, the larger the number of the donated (or accepted) electrons was. The projected area of the cross-section on the ITO electrode. The greater the projected area was, the larger the number of the donated (or accepted) electrons was. The distance between the center of the electron donor (or acceptor) of FeP and the surface of ITO electrode. The smaller the distance was, the greater the rate of donating (or accepting) electrons was. The monolayer coverage, which formed because of the FeP lying on the ITO surface in the form of the monomer and aggregate, was more sensitive to detect oxygen 18. Overcoming the Cut-Off Charge Transfer Bandgaps at the PbS Quantum Dot Interface KAUST Repository El-Ballouli, Ala'a O.; Alarousu, Erkki; Kirmani, Ahmad R.; Amassian, Aram; Bakr, Osman; Mohammed, Omar F. 2015-01-01 Light harvesting from large size of semiconductor PbS quantum dots (QDs) with a bandgap of less than 1 eV is one of the greatest challenges precluding the development of PbS QD-based solar cells because the interfacial charge transfer (CT) from such QDs to the most commonly used electron acceptor materials is very inefficient, if it occurs at all. Thus, an alternative electron-accepting unit with a new driving force for CT is urgently needed to harvest the light from large-sized PbS QDs. Here, a cationic porphyrin is utilized as a new electron acceptor unit with unique features that bring the donor–acceptor components into close molecular proximity, allowing ultrafast and efficient electron transfer for QDs of all sizes, as inferred from the drastic photoluminescence quenching and the ultrafast formation of the porphyrin anionic species. The time-resolved results clearly demonstrate the possibility of modulating the electron transfer process between PbS QDs and porphyrin moieties not only by the size quantization effect but also by the interfacial electrostatic interaction between the positively charged porphyrin and the negatively charged QDs. This approach provides a new pathway for engineering QD-based solar cells that make the best use of the diverse photons making up the Sun's broad irradiance spectrum. 19. A novel transferable individual tree crown delineation model based on Fishing Net Dragging and boundary classification Science.gov (United States) Liu, Tao; Im, Jungho; Quackenbush, Lindi J. 2015-12-01 This study provides a novel approach to individual tree crown delineation (ITCD) using airborne Light Detection and Ranging (LiDAR) data in dense natural forests using two main steps: crown boundary refinement based on a proposed Fishing Net Dragging (FiND) method, and segment merging based on boundary classification. FiND starts with approximate tree crown boundaries derived using a traditional watershed method with Gaussian filtering and refines these boundaries using an algorithm that mimics how a fisherman drags a fishing net. Random forest machine learning is then used to classify boundary segments into two classes: boundaries between trees and boundaries between branches that belong to a single tree. Three groups of LiDAR-derived features-two from the pseudo waveform generated along with crown boundaries and one from a canopy height model (CHM)-were used in the classification. The proposed ITCD approach was tested using LiDAR data collected over a mountainous region in the Adirondack Park, NY, USA. Overall accuracy of boundary classification was 82.4%. Features derived from the CHM were generally more important in the classification than the features extracted from the pseudo waveform. A comprehensive accuracy assessment scheme for ITCD was also introduced by considering both area of crown overlap and crown centroids. Accuracy assessment using this new scheme shows the proposed ITCD achieved 74% and 78% as overall accuracy, respectively, for deciduous and mixed forest. 20. Charge-transfer mobility and electrical conductivity of PANI as conjugated organic semiconductors. Science.gov (United States) Zhang, Yahong; Duan, Yuping; Song, Lulu; Zheng, Daoyuan; Zhang, Mingxing; Zhao, Guangjiu 2017-09-21 The intramolecular charge transfer properties of a phenyl-end-capped aniline tetramer (ANIH) and a chloro-substituted derivative (ANICl) as organic semiconductors were theoretically studied through the first-principles calculation based on the Marcus-Hush theory. The reorganization energies, intermolecular electronic couplings, angular resolution anisotropic mobilities, and density of states of the two crystals were evaluated. The calculated results demonstrate that both ANIH and ANICl crystals show the higher electron transfer mobilities than the hole-transfer mobilities, which means that the two crystals should prefer to function as n-type organic semiconductors. Furthermore, the angle dependence mobilities of the two crystals show remarkable anisotropic character. The maximum mobility μ max of ANIH and ANICl crystals is 1.3893 and 0.0272 cm 2 V -1 s -1 , which appear at the orientation angles near 176°/356° and 119°/299° of a conducting channel on the a-b reference plane. It is synthetically evaluated that the ANIH crystal possesses relatively lower reorganization energy, higher electronic coupling, and electron transfer mobility, which means that the ANIH crystal may be the more ideal candidate as a high performance n-type organic semiconductor material. The systematic theoretical studies on organic crystals should be conducive to evaluating the charge-transport properties and designing higher performance organic semiconductor materials. 1. Charge transfer dynamics from adsorbates to surfaces with single active electron and configuration interaction based approaches Energy Technology Data Exchange (ETDEWEB) Ramakrishnan, Raghunathan, E-mail: [email protected] [Institute of Physical Chemistry, National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel (Switzerland); Nest, Mathias [Theoretische Chemie, Technische Universität München, Lichtenbergstr. 4, 85747 Garching (Germany) 2015-01-13 Highlights: • We model electron dynamics across cyano alkanethiolates attached to gold cluster. • We present electron transfer time scales from TD-DFT and TD-CI based simulations. • Both DFT and CI methods qualitatively predict the trend in time scales. • TD-CI predicts the experimental relative time scale very accurately. - Abstract: We employ wavepacket simulations based on many-body time-dependent configuration interaction (TD-CI), and single active electron theories, to predict the ultrafast molecule/metal electron transfer time scales, in cyano alkanethiolates bonded to model gold clusters. The initial states represent two excited states where a valence electron is promoted to one of the two virtual π{sup ∗} molecular orbitals localized on the cyanide fragment. The ratio of the two time scales indicate the efficiency of one charge transfer channel over the other. In both our one-and many-electron simulations, this ratio agree qualitatively with each other as well as with the previously reported experimental time scales (Blobner et al., 2012), measured for a macroscopic metal surface. We study the effect of cluster size and the description of electron correlation on the charge transfer process. 2. Charge transfer luminescence of Yb3+ ions in LiY1-xYbxP4O12 phosphates International Nuclear Information System (INIS) Stryganyuk, G; Zazubovich, S; Voloshinovskii, A; Pidzyrailo, M; Zimmerer, G; Peters, R; Petermann, K 2007-01-01 Spectral-kinetic studies have been performed for LiY 1-x Yb x P 4 O 12 (x = 0; 0.1; 0.9) phosphates at T = 8-320 K using synchrotron radiation for excitation within the 5-17 eV energy range. Mechanisms for the excitation of Yb 3+ charge transfer and f-f luminescence are discussed. The quasimolecular character of Yb 3+ charge transfer luminescence (CTL) is pointed out. The central Yb 2+ ion and hole delocalized over the surrounding ligands are proposed for consideration as a 'charge transfer cluster' (Yb 2+ CT cluster). Possible mechanisms of Yb 3+ CTL quenching are presumed 3. Layer-dependent surface potential of phosphorene and anisotropic/layer-dependent charge transfer in phosphorene-gold hybrid systems. Science.gov (United States) Xu, Renjing; Yang, Jiong; Zhu, Yi; Yan, Han; Pei, Jiajie; Myint, Ye Win; Zhang, Shuang; Lu, Yuerui 2016-01-07 The surface potential and the efficiency of interfacial charge transfer are extremely important for designing future semiconductor devices based on the emerging two-dimensional (2D) phosphorene. Here, we directly measured the strong layer-dependent surface potential of mono- and few-layered phosphorene on gold, which is consistent with the reported theoretical prediction. At the same time, we used an optical way photoluminescence (PL) spectroscopy to probe charge transfer in the phosphorene-gold hybrid system. We firstly observed highly anisotropic and layer-dependent PL quenching in the phosphorene-gold hybrid system, which is attributed to the highly anisotropic/layer-dependent interfacial charge transfer. 4. Charge-exchange breakup of the deuteron with the production of two protons and spin structure of the amplitude of the nucleon charge transfer reaction International Nuclear Information System (INIS) Glagolev, V.V.; Lyuboshits, V.L.; Lyuboshits, V.V.; Piskunov, N.M. 1999-01-01 In the framework of the impulse approximation, the relation between the effective cross section of the charge-exchange breakup of a fast deuteron d + a → (pp) + b and the effective cross section of the charge transfer process n + a → p + b is discussed. In doing so, the effects of the proton identity (Fermi-statistics) and of the Coulomb and strong interactions of protons in the final state are taken into account. The distribution over relative momenta of the protons, produced in the charge-exchange process d + p → (pp) + n in the forward direction, is investigated. At the transfer momenta being close to zero the effective cross section of the charge-exchange breakup of a fast deuteron, colliding with the proton target, is determined only by the spin-flip part of the amplitude of the charge transfer reaction n + p → p + n at the zero angle. It is shown that the study of the process d + p → (pp) + n in a beam of the polarized (aligned) deuterons allows one, in principle, to separate two spin-dependent terms in the amplitude of the charge transfer reaction n + p → p + n, one of which does not conserve and the other one conserves the projection of the nucleon spin onto the direction of momentum at the transition of the neutron into the proton 5. Deflection effects and charge transfer in inner-shell vacancy production International Nuclear Information System (INIS) Swafford, G.L. 1978-01-01 A method used in the calculation of inner shell ionization in asymmetric ion-atom collisions is extended to include projectile deflection effects and charge transfer to the projectile. Work is done in an independent electron model (Hartree-Fock) for the target, and the interaction is treated with the projectile as a time-dependent perturbation of the system. It is shown tht the time-dependent problem can be solved for the projectile moving along the classical hyperbolic trajectory that results from the nuclear repulsion. The method is very efficient due to the utilization the target-centered expansion of the system wave function. This means that all the required matrix elements can be pretabulated and are then available for use at all impact parameters. The method is first applied to the impact-parameter dependence of K-shell ionization by protons incident upon copper in the energy range 0.5 to 2 MeV. Excellent agreement with the experiments of Andersen et al., is found at the lower energy. Less satisfactory agreement is obtained in the higher energy region. Next the projectile is considered to move in a straight line path with constant velocity, and extend the method to include charge transfer between the target inner shells and the K-shell of the projectile. A critical feature of the results is the recognition of the importance of target continuum states of energy approximately equal to the kinetic energy (in the target frame) of the electron on the projectile. An approach is developed to properly include such resonance states in our pseudostate calculation. Selected numerical results are presented to illustrate the method and to demonstrate the projectile energy and nuclear charge dependence of the charge transfer cross sections 6. Electronic and vibronic properties of a discotic liquid-crystal and its charge transfer complex Energy Technology Data Exchange (ETDEWEB) Haverkate, Lucas A.; Mulder, Fokko M. [Reactor Institute Delft, Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629JB Delft (Netherlands); Zbiri, Mohamed, E-mail: [email protected]; Johnson, Mark R. [Institut Laue Langevin, 38042 Grenoble Cedex 9 (France); Carter, Elizabeth [Vibrational Spectroscopy Facility, School of Chemistry, The University of Sydney, NSW 2008 (Australia); Kotlewski, Arek; Picken, S. [ChemE-NSM, Faculty of Chemistry, Delft University of Technology, 2628BL/136 Delft (Netherlands); Kearley, Gordon J. [Bragg Institute, Australian Nuclear Science and Technology Organisation, Menai, NSW 2234 (Australia) 2014-01-07 Discotic liquid crystalline (DLC) charge transfer (CT) complexes combine visible light absorption and rapid charge transfer characteristics, being favorable properties for photovoltaic (PV) applications. We present a detailed study of the electronic and vibrational properties of the prototypic 1:1 mixture of discotic 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT6) and 2,4,7-trinitro-9-fluorenone (TNF). It is shown that intermolecular charge transfer occurs in the ground state of the complex: a charge delocalization of about 10{sup −2} electron from the HAT6 core to TNF is deduced from both Raman and our previous NMR measurements [L. A. Haverkate, M. Zbiri, M. R. Johnson, B. Deme, H. J. M. de Groot, F. Lefeber, A. Kotlewski, S. J. Picken, F. M. Mulder, and G. J. Kearley, J. Phys. Chem. B 116, 13098 (2012)], implying the presence of permanent dipoles at the donor-acceptor interface. A combined analysis of density functional theory calculations, resonant Raman and UV-VIS absorption measurements indicate that fast relaxation occurs in the UV region due to intramolecular vibronic coupling of HAT6 quinoidal modes with lower lying electronic states. Relatively slower relaxation in the visible region the excited CT-band of the complex is also indicated, which likely involves motions of the TNF nitro groups. The fast quinoidal relaxation process in the hot UV band of HAT6 relates to pseudo-Jahn-Teller interactions in a single benzene unit, suggesting that the underlying vibronic coupling mechanism can be generic for polyaromatic hydrocarbons. Both the presence of ground state CT dipoles and relatively slow relaxation processes in the excited CT band can be relevant concerning the design of DLC based organic PV systems. 7. Synthesis of Stable Interfaces on SnO2 Surfaces for Charge-Transfer Applications Science.gov (United States) Benson, Michelle C. The commercial market for solar harvesting devices as an alternative energy source requires them to be both low-cost and efficient to replace or reduce the dependence on fossil fuel burning. Over the last few decades there has been promising efforts towards improving solar devices by using abundant and non-toxic metal oxide nanomaterials. One particular metal oxide of interest has been SnO2 due to its high electron mobility, wide-band gap, and aqueous stability. However SnO2 based solar cells have yet to reach efficiency values of other metal oxides, like TiO2. The advancement of SnO2 based devices is dependent on many factors, including improved methods of surface functionalization that can yield stable interfaces. This work explores the use of a versatile functionalization method through the use of the Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) reaction. The CuAAC reaction is capable of producing electrochemically, photochemically, and electrocatalytically active surfaces on a variety of SnO2 materials. The resulting charge-transfer characteristics were investigated as well as an emphasis on understanding the stability of the resulting molecular linkage. We determined the CuAAC reaction is able to proceed through both azide-modified and alkyne-modified surfaces. The resulting charge-transfer properties showed that the molecular tether was capable of supporting charge separation at the interface. We also investigated the enhancement of electron injection upon the introduction of an ultra-thin ZrO2 coating on SnO2. Several complexes were used to fully understand the charge-transfer capabilities, including model systems of ferrocene and a ruthenium coordination complex, a ruthenium mononuclear water oxidation catalyst, and a commercial ruthenium based dye. 8. Molecular orbital (SCF-Xα-SW) theory of metal-metal charge transfer processes in minerals - II. Application to Fe2+ --> Ti4+ charge transfer transitions in oxides and silicates Science.gov (United States) Sherman, David M. 1987-01-01 A molecular orbital description, based on Xα-Scattered wave calculations on a (FeTiO10)14− cluster, is given for Fe2+ → Ti4+ charge transfer transitions in minerals. The calculated energy for the lowest Fe2+ → Ti4+ metal-metal charge transfer transition is 18040 cm−1 in reasonable agreement with energies observed in the optical spectra of Fe-Ti oxides and silicates. As in the case of Fe2+ → Fe3+ charge transfer in mixed-valence iron oxides and silicates, Fe2+ → Ti4+ charge transfer is associated with Fe-Ti bonding across shared polyhedral edges. Such bonding results from the overlap of the Fe(t 2g ) and Ti(t 2g ) 3d orbitals. 9. Bane of Hydrogen-Bond Formation on the Photoinduced Charge-Transfer Process in Donor–Acceptor Systems KAUST Repository Alsam, Amani Abdu 2017-03-14 Controlling the ultrafast dynamical process of photoinduced charge transfer at donor acceptor interfaces remains a major challenge for physical chemistry and solar cell communities. The process is complicated by the involvement of other complex dynamical processes, including hydrogen bond formation, energy transfer, and solvation dynamics occurring on similar time scales. In this study, we explore the remarkable impact of hydrogen-bond formation on the interfacial charge transfer between a negatively charged electron donating anionic porphyrin and a positively charged electron accepting pi-conjugated polymer, as a model system in solvents with different polarities and capabilities for hydiogen bonding using femtosecond transient absorption spectroscopy. Unlike the conventional understanding of the key role of hydrogen bonding in promoting the charge-transfer process, our steadystate and time-resolved results reveal that the intervening hydrogen-bonding environment and, consequently, the probable longer spacing between the donor and acceptor molecules significantly hinders the charge-transfer process between them. These results show that site-specific hydrogen bonding and geometric considerations between donor and acceptor can be exploited to control both the charge-transfer dynamics and its efficiency not only at donor acceptor interfaces but also in complex biological systems. 10. An Electronic Structure Approach to Charge Transfer and Transport in Molecular Building Blocks for Organic Optoelectronics Science.gov (United States) Hendrickson, Heidi Phillips A fundamental understanding of charge separation in organic materials is necessary for the rational design of optoelectronic devices suited for renewable energy applications and requires a combination of theoretical, computational, and experimental methods. Density functional theory (DFT) and time-dependent (TD)DFT are cost effective ab-initio approaches for calculating fundamental properties of large molecular systems, however conventional DFT methods have been known to fail in accurately characterizing frontier orbital gaps and charge transfer states in molecular systems. In this dissertation, these shortcomings are addressed by implementing an optimally-tuned range-separated hybrid (OT-RSH) functional approach within DFT and TDDFT. The first part of this thesis presents the way in which RSH-DFT addresses the shortcomings in conventional DFT. Environmentally-corrected RSH-DFT frontier orbital energies are shown to correspond to thin film measurements for a set of organic semiconducting molecules. Likewise, the improved RSH-TDDFT description of charge transfer excitations is benchmarked using a model ethene dimer and silsesquioxane molecules. In the second part of this thesis, RSH-DFT is applied to chromophore-functionalized silsesquioxanes, which are currently investigated as candidates for building blocks in optoelectronic applications. RSH-DFT provides insight into the nature of absorptive and emissive states in silsesquioxanes. While absorption primarily involves transitions localized on one chromophore, charge transfer between chromophores and between chromophore and silsesquioxane cage have been identified. The RSH-DFT approach, including a protocol accounting for complex environmental effects on charge transfer energies, was tested and validated against experimental measurements. The third part of this thesis addresses quantum transport through nano-scale junctions. The ability to quantify a molecular junction via spectroscopic methods is crucial to their 11. Physical adsorption and charge transfer of molecular Br2 on graphene. Science.gov (United States) Chen, Zheyuan; Darancet, Pierre; Wang, Lei; Crowther, Andrew C; Gao, Yuanda; Dean, Cory R; Taniguchi, Takashi; Watanabe, Kenji; Hone, James; Marianetti, Chris A; Brus, Louis E 2014-03-25 We present a detailed study of gaseous Br2 adsorption and charge transfer on graphene, combining in situ Raman spectroscopy and density functional theory (DFT). When graphene is encapsulated by hexagonal boron nitride (h-BN) layers on both sides, in a h-BN/graphene/h-BN sandwich structure, it is protected from doping by strongly oxidizing Br2. Graphene supported on only one side by h-BN shows strong hole doping by adsorbed Br2. Using Raman spectroscopy, we determine the graphene charge density as a function of pressure. DFT calculations reveal the variation in charge transfer per adsorbed molecule as a function of coverage. The molecular adsorption isotherm (coverage versus pressure) is obtained by combining Raman spectra with DFT calculations. The Fowler-Guggenheim isotherm fits better than the Langmuir isotherm. The fitting yields the adsorption equilibrium constant (∼0.31 Torr(-1)) and repulsive lateral interaction (∼20 meV) between adsorbed Br2 molecules. The Br2 molecule binding energy is ∼0.35 eV. We estimate that at monolayer coverage each Br2 molecule accepts 0.09 e- from single-layer graphene. If graphene is supported on SiO2 instead of h-BN, a threshold pressure is observed for diffusion of Br2 along the (somewhat rough) SiO2/graphene interface. At high pressure, graphene supported on SiO2 is doped by adsorbed Br2 on both sides. 12. Coil Design for High Misalignment Tolerant Inductive Power Transfer System for EV Charging Directory of Open Access Journals (Sweden) Kafeel Ahmed Kalwar 2016-11-01 Full Text Available The inductive power transfer (IPT system for electric vehicle (EV charging has acquired more research interest in its different facets. However, the misalignment tolerance between the charging coil (installed in the ground and pick-up coil (mounted on the car chassis, has been a challenge and fundamental interest in the future market of EVs. This paper proposes a new coil design QDQ (Quad D Quadrature that maintains the high coupling coefficient and efficient power transfer during reasonable misalignment. The QDQ design makes the use of four adjacent circular coils and one square coil, for both charging and pick-up side, to capture the maximum flux at any position. The coil design has been modeled in JMAG software for calculation of inductive parameters using the finite element method (FEM, and its hardware has been tested experimentally at various misaligned positions. The QDQ coils are shown to be capable of achieving good coupling coefficient and high efficiency of the system until the misalignment displacement reaches 50% of the employed coil size. 13. Ultrafast dynamics of solvation and charge transfer in a DNA-based biomaterial. Science.gov (United States) Choudhury, Susobhan; Batabyal, Subrata; Mondol, Tanumoy; Sao, Dilip; Lemmens, Peter; Pal, Samir Kumar 2014-05-01 Charge migration along DNA molecules is a key factor for DNA-based devices in optoelectronics and biotechnology. The association of a significant amount of water molecules in DNA-based materials for the intactness of the DNA structure and their dynamic role in the charge-transfer (CT) dynamics is less documented in contemporary literature. In the present study, we have used a genomic DNA-cetyltrimethyl ammonium chloride (CTMA) complex, a technological important biomaterial, and Hoechest 33258 (H258), a well-known DNA minor groove binder, as fluorogenic probe for the dynamic solvation studies. The CT dynamics of CdSe/ZnS quantum dots (QDs; 5.2 nm) embedded in the as-prepared and swollen biomaterial have also been studied and correlated with that of the timescale of solvation. We have extended our studies on the temperature-dependent CT dynamics of QDs in a nanoenvironment of an anionic, sodium bis(2-ethylhexyl)sulfosuccinate reverse micelle (AOT RMs), whereby the number of water molecules and their dynamics can be tuned in a controlled manner. A direct correlation of the dynamics of solvation and that of the CT in the nanoenvironments clearly suggests that the hydration barrier within the Arrhenius framework essentially dictates the charge-transfer dynamics. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 14. Single-crystal charge transfer interfaces for efficient photonic devices (Conference Presentation) Science.gov (United States) Alves, Helena; Pinto, Rui M.; Maçôas, Ermelinda M. S.; Baleizão, Carlos; Santos, Isabel C. 2016-09-01 Organic semiconductors have unique optical, mechanical and electronic properties that can be combined with customized chemical functionality. In the crystalline form, determinant features for electronic applications such as molecular purity, the charge mobility or the exciton diffusion length, reveal a superior performance when compared with materials in a more disordered form. Combining crystals of two different conjugated materials as even enable a new 2D electronic system. However, the use of organic single crystals in devices is still limited to a few applications, such as field-effect transistors. In 2013, we presented the first system composed of single-crystal charge transfer interfaces presenting photoconductivity behaviour. The system composed of rubrene and TCNQ has a responsivity reaching 1 A/W, corresponding to an external quantum efficiency of nearly 100%. A similar approach, with a hybrid structure of a PCBM film and rubrene single crystal also presents high responsivity and the possibility to extract excitons generated in acceptor materials. This strategy led to an extended action towards the near IR. By adequate material design and structural organisation of perylediimides, we demonstrate that is possible to improve exciton diffusion efficiency. More recently, we have successfully used the concept of charge transfer interfaces in phototransistors. These results open the possibility of using organic single-crystal interfaces in photonic applications. 15. Single Molecule Spectroelectrochemistry of Interfacial Charge Transfer Dynamics In Hybrid Organic Solar Cell Energy Technology Data Exchange (ETDEWEB) Pan, Shanlin [Univ. of Alabama, Tuscaloosa, AL (United States) 2014-11-16 Our research under support of this DOE grant is focused on applied and fundamental aspects of model organic solar cell systems. Major accomplishments are: 1) we developed a spectroelectorchemistry technique of single molecule single nanoparticle method to study charge transfer between conjugated polymers and semiconductor at the single molecule level. The fluorescence of individual fluorescent polymers at semiconductor surfaces was shown to exhibit blinking behavior compared to molecules on glass substrates. Single molecule fluorescence excitation anisotropy measurements showed the conformation of the polymer molecules did not differ appreciably between glass and semiconductor substrates. The similarities in molecular conformation suggest that the observed differences in blinking activity are due to charge transfer between fluorescent polymer and semiconductor, which provides additional pathways between states of high and low fluorescence quantum efficiency. Similar spectroelectrochemistry work has been done for small organic dyes for understand their charge transfer dynamics on various substrates and electrochemical environments; 2) We developed a method of transferring semiconductor nanoparticles (NPs) and graphene oxide (GO) nanosheets into organic solvent for a potential electron acceptor in bulk heterojunction organic solar cells which employed polymer semiconductor as the electron donor. Electron transfer from the polymer semiconductor to semiconductor and GO in solutions and thin films was established through fluorescence spectroscopy and electroluminescence measurements. Solar cells containing these materials were constructed and evaluated using transient absorption spectroscopy and dynamic fluorescence techniques to understand the charge carrier generation and recombination events; 3) We invented a spectroelectorchemistry technique using light scattering and electroluminescence for rapid size determination and studying electrochemistry of single NPs in an 16. Bane of Hydrogen-Bond Formation on the Photoinduced Charge-Transfer Process in Donor–Acceptor Systems KAUST Repository Alsam, Amani Abdu; Adhikari, Aniruddha; Parida, Manas R.; Aly, Shawkat Mohammede; Bakr, Osman; Mohammed, Omar F. 2017-01-01 Controlling the ultrafast dynamical process of photoinduced charge transfer at donor acceptor interfaces remains a major challenge for physical chemistry and solar cell communities. The process is complicated by the involvement of other complex 17. State-selective charge transfer and excitation in ion-ion interactions at intermediate and high energies International Nuclear Information System (INIS) Samanta, R; Purkait, M 2012-01-01 Boundary Corrected Continuum Intermediate State (BCCIS) approximation and Classical Trajectory Monte Carlo (CTMC) methods are applied to calculate the charge transfer and excitation cross sections for ion-ion collisions. 18. Low energy cross section data for ion-molecule reactions in hydrogen systems and for charge transfer of multiply charged ions with atoms and molecules International Nuclear Information System (INIS) Okuno, Kazuhiko 2007-04-01 Systematic cross section measurements for ion-molecule reactions in hydrogen systems and for charge transfer of multiply charged ions in low energy collisions with atoms and molecules have been performed continuously by the identical apparatus installed with an octo-pole ion beam guide (OPIG) since 1980 till 2004. Recently, all of accumulated cross section data for a hundred collision systems has been entered into CMOL and CHART of the NIFS atomic and molecular numerical database together with some related cross section data. In this present paper, complicated ion-molecule reactions in hydrogen systems are revealed and the brief outlines of specific properties in low energy charge transfer collisions of multiply charged ions with atoms and molecules are introduced. (author) 19. A statewide teleradiology system reduces radiation exposure and charges in transferred trauma patients. Science.gov (United States) Watson, Justin J J; Moren, Alexis; Diggs, Brian; Houser, Ben; Eastes, Lynn; Brand, Dawn; Bilyeu, Pamela; Schreiber, Martin; Kiraly, Laszlo 2016-05-01 Trauma transfer patients routinely undergo repeat imaging because of inefficiencies within the radiology system. In 2009, the virtual private network (VPN) telemedicine system was adopted throughout Oregon allowing virtual image transfer between hospitals. The startup cost was a nominal3,000 per hospital. A retrospective review from 2007 to 2012 included 400 randomly selected adult trauma transfer patients based on a power analysis (200 pre/200 post). The primary outcome evaluated was reduction in repeat computed tomography (CT) scans. Secondary outcomes included cost savings, emergency department (ED) length of stay (LOS), and spared radiation. All data were analyzed using Mann-Whitney U and chi-square tests. P less than .05 indicated significance. Spared radiation was calculated as a weighted average per body region, and savings was calculated using charges obtained from Oregon Health and Science University radiology current procedural terminology codes. Four-hundred patients were included. Injury Severity Score, age, ED and overall LOS, mortality, trauma type, and gender were not statistically different between groups. The percentage of patients with repeat CT scans decreased after VPN implementation: CT abdomen (13.2% vs 2.8%, P < .01) and cervical spine (34.4% vs 18.2%, P < .01). Post-VPN, the total charges saved in 2012 for trauma transfer patients was \$333,500, whereas the average radiation dose spared per person was 1.8 mSV. Length of stay in the ED for patients with Injury Severity Score less than 15 transferring to the ICU was decreased (P < .05). Implementation of a statewide teleradiology network resulted in fewer total repeat CT scans, significant savings, decrease in radiation exposure, and decreased LOS in the ED for patients with less complex injuries. The potential for health care savings by widespread adoption of a VPN is significant. Copyright © 2016 Elsevier Inc. All rights reserved.
20. Refrigerant charge, pressure drop, and condensation heat transfer in flattened tubes
Energy Technology Data Exchange (ETDEWEB)
Wilson, M J; Newell, T A; Chato, J C [University of Illinois, Urbana, IL (United States). Dept. of Mechanical and Industrial Engineering; Infante Ferreira, C A [Delft University of Technology (Netherlands). Laboratory for Refrigeration and Indoor Climate Control
2003-06-01
Horizontal smooth and microfinned copper tubes with an approximate diameter of 9 mm were successively flattened in order to determine changes in flow field characteristics as a round tube is altered into a flattened tube profile. Refrigerants R134a and R410A were investigated over a mass flux range from 75 to 400 kg m{sup -2} s{sup -}2{sup 1} and a quality range from approximately 10-80%. For a given refrigerant mass flow rate, the results show that a significant reduction in refrigerant charge is possible. Pressure drop results show increases of pressure drop at a given mass flux and quality as a tube profile is flattened. Heat transfer results indicate enhancement of the condensation heat transfer coefficient as a tube is flattened. Flattened tubes with an 18{sup o} helix angle displayed the highest heat transfer coefficients. Smooth tubes and axial microfin tubes displayed similar levels of heat transfer enhancement. Heat transfer enhancement is dependent on the mass flux, quality and tube profile. (author)
1. Theoretical perspectives on electron transfer and charge separation events in photochemical water cleavage systems
International Nuclear Information System (INIS)
Kozak, J.J.; Lenoir, P.M.; Musho, M.K.; Tembe, B.L.
1984-01-01
We study in this paper the dynamics induced by models for photochemical water cleavage systems, focusing on the spatial and temporal factors influencing electron transfer and charge separation processes in such systems. The reaction-diffusion theory is formulated in full generality and the consequences explored in a number of spatio-temporal regimes, viz. the spatially homogeneous system in the long-time limit (i.e. the steady state for a well-stirred system), the spatially homogeneous system in evolution, and the spatially inhomogeneous system in evolution (where, in the latter study, we consider electron transfer at the cluster surface to be governed by a rate constant that reflects the localized nature of such processes). The results of numerical simulations are presented for all three cases and used to highlight the importance of heterogeneous environments in enhancing the cage escape yield of charge separated species, and to demonstrate the dependence of the hydrogen yield on the localization of electron-transfer processes in the vicinity of the microcatalyst surface
2. Excitation and charge transfer in low-energy hydrogen atom collisions with neutral iron
Science.gov (United States)
Barklem, P. S.
2018-05-01
Data for inelastic processes due to hydrogen atom collisions with iron are needed for accurate modelling of the iron spectrum in late-type stars. Excitation and charge transfer in low-energy Fe+H collisions is studied theoretically using a previously presented method based on an asymptotic two-electron linear combination of atomic orbitals model of ionic-covalent interactions in the neutral atom-hydrogen-atom system, together with the multi-channel Landau-Zener model. An extensive calculation including 166 covalent states and 25 ionic states is presented and rate coefficients are calculated for temperatures in the range 1000-20 000 K. The largest rates are found for charge transfer processes to and from two clusters of states around 6.3 and 6.6 eV excitation, corresponding in both cases to active 4d and 5p electrons undergoing transfer. Excitation and de-excitation processes among these two sets of states are also significant. Full Tables and rate coefficient data are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/612/A90
3. Low-Energy Charge Transfer in Multiply-Charged Ion-Atom Collisions Studied with the Combined SCVB-MOCC Approach
OpenAIRE
Cooper, D. L.; Stancil, P. C.; Turner, A. R.; Wang, J. G.; Clarke, N. J.; Zygelman, B.
2002-01-01
A survey of theoretical studies of charge transfer involving collisions of multiply-charged ions with atomic neutrals (H and He) is presented. The calculations utilized the quantum-mechanical molecular-orbital close-coupling (MOCC) approach where the requisite potential curves and coupling matrix elements have been obtained with the spin-coupled valence bond (SCVB) method. Comparison is made among various collision partners, for equicharged systems, where it is illustrated that even for total...
4. Charge transfer and partial pinning at the contacts as the origin of a double dip in the transfer characteristics of graphene-based field-effect transistors
International Nuclear Information System (INIS)
Di Bartolomeo, Antonio; Giubileo, Filippo; Santandrea, Salvatore; Romeo, Francesco; Citro, Roberta; Schroeder, Thomas; Lupina, Grzegorz
2011-01-01
We discuss the origin of an additional dip other than the charge neutrality point observed in the transfer characteristics of graphene-based field-effect transistors with a Si/SiO 2 substrate used as the back-gate. The double dip is proved to arise from charge transfer between the graphene and the metal electrodes, while charge storage at the graphene/SiO 2 interface can make it more evident. Considering a different Fermi energy from the neutrality point along the channel and partial charge pinning at the contacts, we propose a model which explains all the features observed in the gate voltage loops. We finally show that the double dip enhanced hysteresis in the transfer characteristics can be exploited to realize graphene-based memory devices.
5. Study of the cold charge transfer state separation at the TQ1/PC71 BM interface.
Science.gov (United States)
Volpi, Riccardo; Linares, Mathieu
2017-05-30
Charge transfer (CT) state separation is one of the most critical processes in the functioning of an organic solar cell. In this article, we study a bilayer of TQ1 and PC 71 BM molecules presenting disorder at the interface, obtained by means of Molecular Dynamics. The study of the CT state splitting can be first analyzed through the CT state splitting diagram, introduced in a previous work. Through this analysis, we identify the possibility of CT state splitting within Marcus Theory in function of the electric field. Once the right range of electric fields has been identified, we perform Kinetic Monte Carlo simulations to estimate percentages and times for the CT state splitting and the free charge carriers collection. Statistical information extracted from these simulations allows us to highlight the importance of polarization and to test the limits of the predictions given by the CT state splitting diagram. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
6. Charge transfer properties and photoelectrocatalytic activity of TiO{sub 2}/MWCNT hybrid
Energy Technology Data Exchange (ETDEWEB)
Jiang Liaochuan [Nano Science Research Center, School of Chemistry and Chemical Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640 (China); Zhang Weide, E-mail: [email protected] [Nano Science Research Center, School of Chemistry and Chemical Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640 (China)
2010-12-15
The vertically aligned multiwalled carbon nanotube (MWCNT) arrays on tantalum foils were successfully coated with TiO{sub 2} nanoparticles by a hydrothermal process. The prepared TiO{sub 2}/MWCNT hybrid was characterized by scanning electron microscopy and transmission electron microscopy. The charge transfer properties and photocatalytic degradation of rhodamine B with and without bias potential under UV irradiation were investigated. The MWCNTs promoted the separation of photoinduced carriers in the TiO{sub 2}, thus enhanced photocatalytic activity. Applying bias potential on the photoanode further enhanced its catalytic activity. The efficient charge transportation and high photoelectrocatalytic activity towards degradation of rhodamine B made this hybrid material promising for photocatalyst and for the development of photoelectrical devices.
7. Charge-Transfer Effects in Ligand Exchange Reactions of Au25 Monolayer-Protected Clusters.
Science.gov (United States)
Carducci, Tessa M; Blackwell, Raymond E; Murray, Royce W
2015-04-16
Reported here are second-order rate constants of associative ligand exchanges of Au25L18 nanoparticles (L = phenylethanethiolate) of various charge states, measured by proton nuclear magnetic resonance at room temperature and below. Differences in second-order rate constants (M(-1) s(-1)) of ligand exchange (positive clusters ∼1.9 × 10(-5) versus negative ones ∼1.2 × 10(-4)) show that electron depletion retards ligand exchange. The ordering of rate constants between the ligands benzeneselenol > 4-bromobenzene thiol > benzenethiol reveals that exchange is accelerated by higher acidity and/or electron donation capability of the incoming ligand. Together, these observations indicate that partial charge transfer occurs between the nanoparticle and ligand during the exchange and that this is a rate-determining effect in the process.
8. ANISOTROPY EFFECTS IN SINGLE-ELECTRON TRANSFER BETWEEN LASER-EXCITED ATOMS AND HIGHLY-CHARGED IONS
NARCIS (Netherlands)
Recent collision experiments are reviewed in which one-electron transfer between laser excited target atoms and (highly charged) keV-ions has been studied. Especially results showing a dependence of the charge exchange on the initial target orbital alignment are discussed. The question to what
9. Charge transfer and injection barrier at the metal-organic interfaces
Science.gov (United States)
Yan, Li
2002-09-01
The metal-organic interface plays a critical role in determining the functionality and performance of many innovative organic based devices. It has attracted extensive research interests in recent years. This thesis presents investigations of the electronic structures of organic materials, such as tris-(8-hydroxyquinoline) aluminum (Alq3) and copper phthalocyanine (CuPc), during their interface formation with metals. The characterization is accomplished by X-ray and ultraviolet photoelectron spectroscopes (XPS and UPS) and inverse photoelectron spectroscopy (IPES). As discussed herein, both occupied and unoccupied electronic states at the interfaces are carefully examined in different aspects. In Chapter 4, the charge transfer and chemical reaction at various metal/Alq3 interfaces are investigated using XPS and UPS to study the electron injection into the Alga film. Electron transfer from the low work function metal and Al/LiF(CsF) bilayer to the Alga has been observed. The role of the dielectric and possible chemistry at the interface are discussed in comparison of the low work function metals. Further in Chapter 5, the origin of the metal-interface dipole and the estimation of charge injection barrier is explored using several organic materials. A thermodynamic equilibrium model is extended to explain the relation between the charge transfer process ad the interface dipole. Further, in Chapter 6 the combination of XPS, UPS and IPES detailed the evolution of both occupied and unoccupied energy states during the alkali metal doping. The energy gap modification in organic due to metal doping is observed directly for the spectra. Chapter 7 provides stability study of the organic thin films under x-ray and UV light. The results verify the usability of UPS and XPS for the organic materials used in the thesis. Chapter 7 also shows the secondary ion mass spectroscopy results of metal diffusion in organic thin films.
10. Interface charge transfer process in ZnO:Mn/ZnS nanocomposites
Energy Technology Data Exchange (ETDEWEB)
Stefan, M.; Toloman, D., E-mail: [email protected]; Popa, A. [National Institute for R & D of Isotopic and Molecular Technology (Romania); Mesaros, A. [Technical University of Cluj-Napoca, Superconductivity, Spintronics and Surface Science Center – C4S (Romania); Vasile, O. R. [University “Politehnica” from Bucharest, Faculty of Applied Chemistry and Material Science (Romania); Leostean, C.; Pana, O. [National Institute for R & D of Isotopic and Molecular Technology (Romania)
2016-03-15
ZnO:Mn/ZnS nanocomposites were prepared by seed-mediated growth of ZnS QDs onto the preformed ZnO:Mn nanoparticles. The formation of the nanocomposite structure has been evidenced by XRD, HRTEM, and XPS. The architecture of the nanocomposite with outer ZnS QDs around ZnO:Mn cores is sustained by the sulfur and oxygen depth profiles resulted from XPS. When the two components are brought together, the band gap of ZnS component decreases while that of ZnO:Mn increases. It is the result of interface charge transfer from ZnO:Mn to ZnS QDs. Here ZnO:Mn valence states are extended through the interface into unoccupied gap states of ZnS. The energy band setup is modified from a type II into a type I band alignment. The process is accompanied by enhancement of composite UV emission of PL spectra as compared to its counterparts. The charge transfer from valence band also determines the increase of the core-polarization effect of sshell electrons at Mn{sup 2+} nucleus, thus determining the increase of the hyperfine field through the reduction of the covalency degree of Zn(Mn)–O bonds. The quantum confinement in ZnS QDs promotes the ferromagnetic coupling of singly occupied states due to Zn vacancies determining a superparamagnetic behavior of the ensemble. When the nanocomposites are formed, due to interface charge transfer effects, an increased number of filled cation vacancies in ZnS QDs develop, thus disrupting the pre-existing ferromagnetic coupling between spins resulting in a significant reduction of the overall saturation magnetization. The possibility to modulate nanocomposite properties by controlling the interface interactions may be foreseen in these types of materials.
11. Theoretical Investigation of OCN(-) Charge Transfer Complexes in Condensed Phase Media: Spectroscopic Properties in Amorphous Ice
Science.gov (United States)
Park, Jin-Young; Woon, David E.
2004-01-01
Density functional theory (DFT) calculations of cyanate (OCN(-)) charge-transfer complexes were performed to model the "XCN" feature observed in interstellar icy grain mantles. OCN(-) charge-transfer complexes were formed from precursor combinations of HNCO or HOCN with either NH3 or H2O. Three different solvation strategies for realistically modeling the ice matrix environment were explored, including (1) continuum solvation, (2) pure DFT cluster calculations, and (3) an ONIOM DFT/PM3 cluster calculation. The model complexes were evaluated by their ability to reproduce seven spectroscopic measurements associated with XCN: the band origin of the OCN(-) asymmetric stretching mode, shifts in that frequency due to isotopic substitutions of C, N, O, and H, plus two weak features. The continuum solvent field method produced results consistent with some of the experimental data but failed to account for other behavior due to its limited capacity to describe molecular interactions with solvent. DFT cluster calculations successfully reproduced the available spectroscopic measurements very well. In particular, the deuterium shift showed excellent agreement in complexes where OCN(-) was fully solvated. Detailed studies of representative complexes including from two to twelve water molecules allowed the exploration of various possible solvation structures and provided insights into solvation trends. Moreover, complexes arising from cyanic or isocyanic acid in pure water suggested an alternative mechanism for the formation of OCN(-) charge-transfer complexes without the need for a strong base such as NH3 to be present. An extended ONIOM (B3LYP/PM3) cluster calculation was also performed to assess the impact of a more realistic environment on HNCO dissociation in pure water.
12. Interfacial electronic charge transfer and density of states in short period Cu/Cr multilayers; TOPICAL
International Nuclear Information System (INIS)
Barbee, T W; Bello, A F; Klepeis, J E; Van Buuren, T
1999-01-01
Nanometer period metallic multilayers are ideal structures to investigate electronic phenomena at interfaces between metal films since interfacial atoms comprise a large atomic fraction of the samples. The Cu/Cr binary pair is especially suited to study the interfaces in metals since these elements are mutually insoluble, thus eliminating mixing effects and compound formation and the lattice mismatch is very small. This allows the fabrication of high structural quality Cu/Cr multilayers that have a structure which can be approximated in calculations based on idealized atomic arrangements. The electronic structure of the Cu and the Cr layers in several samples of thin Cu/Cr multilayers were studied using x-ray absorption spectroscopy (XAS). Total electron yield was measured and used to study the white lines at the Cu L(sub 2) and L(sub 3) absorption edges. The white lines at the Cu absorption edges are strongly related to the unoccupied d-orbitals and are used to calculate the amount of charge transfer between the Cr and Cu atoms in interfaces. Analysis of the Cu white lines show a charge transfer of 0.026 electrons/interfacial Cu atom to the interfacial Cr atoms. In the Cu XAS spectra we also observe a van Hove singularity between the L(sub 2) and L(sub 3) absorption edges as expected from the structural analysis. The absorption spectra are compared to partial density of states obtained from a full-potential linear muffin-tin orbital calculation. The calculations support the presence of charge transfer and indicate that it is localized to the first two interfacial layers in both Cu and Cr
13. Fragment-orbital tunneling currents and electronic couplings for analysis of molecular charge-transfer systems.
Science.gov (United States)
Hwang, Sang-Yeon; Kim, Jaewook; Kim, Woo Youn
2018-04-04
In theoretical charge-transfer research, calculation of the electronic coupling element is crucial for examining the degree of the electronic donor-acceptor interaction. The tunneling current (TC), representing the magnitudes and directions of electron flow, provides a way of evaluating electronic couplings, along with the ability of visualizing how electrons flow in systems. Here, we applied the TC theory to π-conjugated organic dimer systems, in the form of our fragment-orbital tunneling current (FOTC) method, which uses the frontier molecular-orbitals of system fragments as diabatic states. For a comprehensive test of FOTC, we assessed how reasonable the computed electronic couplings and the corresponding TC densities are for the hole- and electron-transfer databases HAB11 and HAB7. FOTC gave 12.5% mean relative unsigned error with regard to the high-level ab initio reference. The shown performance is comparable with that of fragment-orbital density functional theory, which gave the same error by 20.6% or 13.9% depending on the formulation. In the test of a set of nucleobase π stacks, we showed that the original TC expression is also applicable to nondegenerate cases under the condition that the overlap between the charge distributions of diabatic states is small enough to offset the energy difference. Lastly, we carried out visual analysis on the FOTC densities of thiophene dimers with different intermolecular alignments. The result depicts an intimate topological connection between the system geometry and electron flow. Our work provides quantitative and qualitative grounds for FOTC, showing it to be a versatile tool in characterization of molecular charge-transfer systems.
14. Molecular distortion and charge transfer effects in ZnPc/Cu(111)
KAUST Repository
Amin, B.; Nazir, S.; Schwingenschlö gl, Udo
2013-01-01
The adsorption geometry and electronic properties of a zinc-phthalocyanine molecule on a Cu(111) substrate are studied by density functional theory. In agreement with experiment, we find remarkable distortions of the molecule, mainly as the central Zn atom tends towards the substrate to minimize the Zn-Cu distance. As a consequence, the Zn-N chemical bonding and energy levels of the molecule are significantly modified. However, charge transfer induces metallic states on the molecule and therefore is more important for the ZnPc/Cu(111) system than the structural distortions.
15. Specific optical signalling of anions via intramolecular charge transfer pathway based on acridinedione fluorophore
International Nuclear Information System (INIS)
Thiagarajan, Viruthachalam; Ramamurthy, Perumal
2007-01-01
We present a simple but highly specific acridinedione fluorophore (ADD-1) that acts both as a fluorescent and colorimetric sensor for anions in acetonitrile. The specific optical signalling of ADD-1 is due to the formation of new distinct intramolecular charge transfer (ICT) emitting states in the presence of AcO - (490 nm), H 2 PO 4 - (440 nm), and F - (510 nm) over other anions. Presence of F - shows a colour change that is perceptible to the naked eye, from colourless to an intense fluorescent green due to the deprotonation of acridinedione ring amino hydrogen
16. Electronic, structural and chemical effects of charge-transfer at organic/inorganic interfaces
Science.gov (United States)
Otero, R.; Vázquez de Parga, A. L.; Gallego, J. M.
2017-07-01
During the last decade, interest on the growth and self-assembly of organic molecular species on solid surfaces spread over the scientific community, largely motivated by the promise of cheap, flexible and tunable organic electronic and optoelectronic devices. These efforts lead to important advances in our understanding of the nature and strength of the non-bonding intermolecular interactions that control the assembly of the organic building blocks on solid surfaces, which have been recently reviewed in a number of excellent papers. To a large extent, such studies were possible because of a smart choice of model substrate-adsorbate systems where the molecule-substrate interactions were purposefully kept low, so that most of the observed supramolecular structures could be understood simply by considering intermolecular interactions, keeping the role of the surface always relatively small (although not completely negligible). On the other hand, the systems which are more relevant for the development of organic electronic devices include molecular species which are electron donors, acceptors or blends of donors and acceptors. Adsorption of such organic species on solid surfaces is bound to be accompanied by charge-transfer processes between the substrate and the adsorbates, and the physical and chemical properties of the molecules cannot be expected any longer to be the same as in solution phase. In recent years, a number of groups around the world have started tackling the problem of the adsorption, self- assembly and electronic and chemical properties of organic species which interact rather strongly with the surface, and for which charge-transfer must be considered. The picture that is emerging shows that charge transfer can lead to a plethora of new phenomena, from the development of delocalized band-like electron states at molecular overlayers, to the existence of new substrate-mediated intermolecular interactions or the strong modification of the chemical
17. Laser-induced charge transfer in the HeH2+ quasimolecule
International Nuclear Information System (INIS)
Errea, L.F.; Mendez, L.; Riera, A.
1983-01-01
In a recent publication, the charge transfer cross section for He 2+ +H(ls) collisions through photon-assisted 2psigma--3dsigma transitions was calculated; this calculation, however, contained several errors whose quantitative--even qualitative effect on the results is not obvious. We present a correct evaluation of this laser-induced cross section, which turns out to be larger, and present a maximum for longer wavelengths, than the values previously reported. In addition, we have checked the applicability of perturbation theory, of the stationary phase, uniform and Landau--Zener approximations, and the importance of potentially competitive photon-assisted reactions
18. Effective interactions between concentration fluctuations and charge transfer in chemically ordering liquid alloys
International Nuclear Information System (INIS)
Akdeniz, Z.; Tosi, M.P.
1992-08-01
The correlations between long-wavelength fluctuations of concentration in a liquid binary alloy are determined by a balance between an elastic strain free energy and an Ornstein-Zernike effective interaction. The latter is extracted from thermodynamic data in the case of the Li-Pb system, which is well known to chemically order with stoichiometric composition corresponding to Li 4 Pb. Strong attractive interactions between concentration fluctuations near the composition of chemical ordering originate from electronic charge transfer, which is estimated from the electron-ion partial structure factors as functions of composition in the liquid alloy. (author). 20 refs, 2 figs
19. On the charge transfer between single-walled carbon nanotubes and graphene
International Nuclear Information System (INIS)
Rao, Rahul; Pierce, Neal; Dasgupta, Archi
2014-01-01
It is important to understand the electronic interaction between single-walled carbon nanotubes (SWNTs) and graphene in order to use them efficiently in multifunctional hybrid devices. Here, we deposited SWNT bundles on graphene-covered copper and SiO 2 substrates by chemical vapor deposition and investigated the charge transfer between them by Raman spectroscopy. Our results revealed that, on both copper and SiO 2 substrates, graphene donates electrons to the SWNTs, resulting in p-type doped graphene and n-type doped SWNTs.
20. Surface charges and J H Poynting’s disquisitions on energy transfer in electrical circuits
Science.gov (United States)
Matar, M.; Welti, R.
2017-11-01
In this paper we review applications given by J H Poynting (1884) on the transfer of electromagnetic energy in DC circuits. These examples were strongly criticized by O Heaviside (1887). Heaviside stated that Poynting had a misconception about the nature of the electric field in the vicinity of a wire through which a current flows. The historical review of this conflict and its resolution based on the consideration of electrical charges on the surface of the wires can be useful for student courses on electromagnetism or circuit theory.
1. Study of charge transfer complexes of menadione (vitamin K 3) with a series of anilines
Science.gov (United States)
Pal, Purnendu; Saha, Avijit; Mukherjee, Asok K.; Mukherjee, Dulal C.
2004-01-01
Menadione (vitamin K 3) has been shown to form charge transfer complexes with N, N-dimethyl aniline, N, N-dimethyl p-toluidine and N, N-dimethyl m-toluidine in CCl 4 medium. The CT transition energies are well correlated with the ionisation potentials of the anilines. The formation constants of the complexes have been determined at a number of temperatures from which the enthalpies and entropies of formation have been obtained. The formation constants exhibit a very good linear free energy relationship (Hammett) at all the temperatures studied.
2. Formation of an intermolecular charge-transfer compound in UHV codeposited tetramethoxypyrene and tetracyanoquinodimethane
DEFF Research Database (Denmark)
Medjanik, K.; Perkert, S.; Naghavi, S.
2010-01-01
Ultrahigh vacuum (UHV)-deposited films of the mixed phase of tetramethoxypyrene and tetracyanoquinodimethane (TMP -TCNQ ) on gold have been studied using ultraviolet photoelectron spectroscopy (UPS), x-ray diffraction (XRD), infrared (IR) spectroscopy, and scanning tunneling spectroscopy (STS......). The formation of an intermolecular charge-transfer (CT) compound is evident from the appearance of new reflexes in XRD (d =0.894nm and d =0.677nm). A softening of the CN stretching vibration (redshift by 7 cm⊃-1) of TCNQ is visible in the IR spectra, being indicative of a CT on the order of 0.3e from TMP...
3. Metallic conductivity in a disordered charge-transfer salt derived from cis-BET-TTF
Energy Technology Data Exchange (ETDEWEB)
Rovira, C. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Tarres, J. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Ribera, E. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Veciana, J. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Canadell, E. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Molins, E. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Mas, M. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain); Laukhin, V. [Inst. de Ciencia de Materials de Barcelona (CSIC) (Spain)]|[Rossijskaya Akademiya Nauk, Chernogolovka (Russian Federation). Inst. Khimicheskoj Fiziki; Doublet, M.L. [Lab. de Structure et Dynamique (CNRS), Univ. de Montpellier 2 (France); Cowan, D.O. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Chemistry; Yang, S. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Chemistry
1997-02-28
The first example of a metallic charge-transfer salt derived from cis-bis(ethylenethio)-tetrathiafulvalene (BET-TTF) is reported. (BET-TTF){sub 2}SCN and (BET-TTF)SCN salts were obtained by electrocrystallization starting from trans-BET-TTF. X-ray crystal structure of the mixed-valence salt revealed that trans-cis isomerization occurs upon one electron oxidation. In spite of the structural disorder in both BET-TTF and the counterion, 2:1 salt is metallic down to 60 K and then resistance increases slowly down to 4 K. (orig.)
4. Laser-induced charge transfer in the HeH/sup 2 +/ quasimolecule
Energy Technology Data Exchange (ETDEWEB)
Errea, L.F.; Mendez, L.; Riera, A.
1983-11-01
In a recent publication, the charge transfer cross section for He/sup 2 +/+H(ls) collisions through photon-assisted 2psigma--3dsigma transitions was calculated; this calculation, however, contained several errors whose quantitative--even qualitative effect on the results is not obvious. We present a correct evaluation of this laser-induced cross section, which turns out to be larger, and present a maximum for longer wavelengths, than the values previously reported. In addition, we have checked the applicability of perturbation theory, of the stationary phase, uniform and Landau--Zener approximations, and the importance of potentially competitive photon-assisted reactions.
5. Ab initio study of H + + H 2 collisions: Elastic/inelastic and charge transfer processes
Science.gov (United States)
Saieswari, A.; Kumar, Sanjay
2007-12-01
An ab initio full configuration interaction study has been undertaken to obtain the global potential energy surfaces for the ground and the first excited electronic state of the H + + H 2 system employing Dunning's cc-pVQZ basis set. Using the ab initio approach the corresponding quasi-diabatic potential energy surfaces and coupling potentials have been obtained. A time-independent quantum mechanical study has been also undertaken for both the inelastic and charge transfer processes at the experimental collision energy Ec.m. = 20.0 eV and the preliminary results show better agreement with the experimental data as compared to the earlier available theoretical studies.
6. Estimation of instantaneous heat transfer coefficients for a direct-injection stratified-charge rotary engine
Science.gov (United States)
Lee, C. M.; Addy, H. E.; Bond, T. H.; Chun, K. S.; Lu, C. Y.
1987-01-01
The main objective of this report was to derive equations to estimate heat transfer coefficients in both the combustion chamber and coolant pasage of a rotary engine. This was accomplished by making detailed temperature and pressure measurements in a direct-injection stratified-charge rotary engine under a range of conditions. For each sppecific measurement point, the local physical properties of the fluids were calculated. Then an empirical correlation of the coefficients was derived by using a multiple regression program. This correlation expresses the Nusselt number as a function of the Prandtl number and Reynolds number.
7. Spectroscopy of charge transfer complexes of four amino acids as organic two-dimensional conductors
International Nuclear Information System (INIS)
Padhiyar, Ashvin; Patel, A J; Oza, A T
2007-01-01
It is found in this study that four amino acids, namely asparagine, arginine, histidine and glutamine form two-dimensional conducting systems which are charge transfer complexes (CTCs) with organic acceptors like TCNQ, TCNE, chloranil, DDQ, TNF and iodine. It is verified using optical absorption edges that these are 2d conductors like transition metal dichalcogenides obeying absorption functions different from 1d and 3d conductors. This 2d nature is related to the network of intermolecular H-bonding in these complexes, which leads to a global H-bonded network resulting in the absence of local deformation due to the relaxation of strain
8. Charge-transfer complexes between p-toluidine and iodine in solution: a kinetic study
International Nuclear Information System (INIS)
Beggiato, G.; Casalbore, G.; Marconi, G.; Baraldi, C.
1985-01-01
The kinetics of charge-transfer interaction between p-toluidine and iodine in methylene chloride was investigated in depth. The thermal process of formation of the 'inner' complex was found to proceed to an equilibrium. The photochemical process follows a different reaction coordinate, going through the formation of an exciplex between the excited 'outer' complex and the amine ground state. In both cases the same ionic complex (Am 2 I + I - 3 , where Am stands for p-toluidine) was detected as the final product. (Author)
9. Molecular distortion and charge transfer effects in ZnPc/Cu(111)
KAUST Repository
Amin, B.
2013-04-23
The adsorption geometry and electronic properties of a zinc-phthalocyanine molecule on a Cu(111) substrate are studied by density functional theory. In agreement with experiment, we find remarkable distortions of the molecule, mainly as the central Zn atom tends towards the substrate to minimize the Zn-Cu distance. As a consequence, the Zn-N chemical bonding and energy levels of the molecule are significantly modified. However, charge transfer induces metallic states on the molecule and therefore is more important for the ZnPc/Cu(111) system than the structural distortions.
10. Absolute Charge Transfer and Fragmentation Cross Sections in He2+-C60 Collisions
International Nuclear Information System (INIS)
Rentenier, A.; Moretto-Capelle, P.; Bordenave-Montesquieu, D.; Bordenave-Montesquieu, A.; Ruiz, L. F.; Diaz-Tendero, S.; Alcami, M.; Martin, F.; Zarour, B.; Hanssen, J.; Hervieux, P.-A.; Politis, M. F.
2008-01-01
We have determined absolute charge transfer and fragmentation cross sections in He 2+ +C 60 collisions in the impact-energy range 0.1-250 keV by using a combined experimental and theoretical approach. We have found that the cross sections for the formation of He + and He 0 are comparable in magnitude, which cannot be explained by the sole contribution of pure single and double electron capture but also by contribution of transfer-ionization processes that are important even at low impact energies. The results show that multifragmentation is important only at impact energies larger than 40 keV; at lower energies, sequential C 2 evaporation is the dominant process
11. Femtosecond stimulated Raman evidence for charge-transfer character in pentacene singlet fission.
Science.gov (United States)
Hart, Stephanie M; Silva, W Ruchira; Frontiera, Renee R
2018-02-07
Singlet fission is a spin-allowed process in which an excited singlet state evolves into two triplet states. We use femtosecond stimulated Raman spectroscopy, an ultrafast vibrational technique, to follow the molecular structural evolution during singlet fission in order to determine the mechanism of this process. In crystalline pentacene, we observe the formation of an intermediate characterized by pairs of excited state peaks that are red- and blue-shifted relative to the ground state features. We hypothesize that these features arise from the formation of cationic and anionic species due to partial transfer of electron density from one pentacene molecule to a neighboring molecule. These observations provide experimental evidence for the role of states with significant charge-transfer character which facilitate the singlet fission process in pentacene. Our work both provides new insight into the singlet fission mechanism in pentacene and demonstrates the utility of structurally-sensitive time-resolved spectroscopic techniques in monitoring ultrafast processes.
12. Charge transfer through single molecule contacts: How reliable are rate descriptions?
Directory of Open Access Journals (Sweden)
Denis Kast
2011-08-01
Full Text Available Background: The trend for the fabrication of electrical circuits with nanoscale dimensions has led to impressive progress in the field of molecular electronics in the last decade. However, a theoretical description of molecular contacts as the building blocks of future devices is challenging, as it has to combine the properties of Fermi liquids in the leads with charge and phonon degrees of freedom on the molecule. Outside of ab initio schemes for specific set-ups, generic models reveal the characteristics of transport processes. Particularly appealing are descriptions based on transfer rates successfully used in other contexts such as mesoscopic physics and intramolecular electron transfer. However, a detailed analysis of this scheme in comparison with numerically exact solutions is still elusive.Results: We show that a formulation in terms of transfer rates provides a quantitatively accurate description even in domains of parameter space where strictly it is expected to fail, e.g., at lower temperatures. Typically, intramolecular phonons are distributed according to a voltage driven steady state that can only roughly be captured by a thermal distribution with an effective elevated temperature (heating. An extension of a master equation for the charge–phonon complex, to effectively include the impact of off-diagonal elements of the reduced density matrix, provides very accurate solutions even for stronger electron–phonon coupling.Conclusion: Rate descriptions and master equations offer a versatile model to describe and understand charge transfer processes through molecular junctions. Such methods are computationally orders of magnitude less expensive than elaborate numerical simulations that, however, provide exact solutions as benchmarks. Adjustable parameters obtained, e.g., from ab initio calculations allow for the treatment of various realizations. Even though not as rigorously formulated as, e.g., nonequilibrium Green’s function
13. Charge Transfer Processes in Collisions of Si4+ Ions with He Atoms at Intermediate Energies
Science.gov (United States)
Suzuki, R.; Watanabe, A.; Sato, H.; Gu, J. P.; Hirsch, G.; Buenker, R. J.; Kimura, M.; Stancil, P. C.
Charge transfer in collisions of Si4+ ions with He atoms below 100 keV/u is studied by using a molecular orbital representation within both the semiclassical and quantal representations. Single transfer reaction Si4++He →Si3++He+ has been studied by a number of theoretical investigations. In addition to the reaction (1), the first semiclassical MOCC calculations are performed for the double transfer channel Si4++HE→Si2++He2+ Nine molecular states that connect both with single and double electron transfer processes are considered in the present model. Electronic states and corresponding couplings are determined by the multireference single- and double- excitation configuration interaction method. The present cross sections tie well with the earlier calculations of Stancil et al., Phys. Rev. A 55, 1064 (1997) at lower energies, but show a rather different magnitude from those of Bacchus-Montabonel and Ceyzeriat, Phys. Rev. A 58, 1162 (1998). The present rate constant is found to be significantly different from the experimental finding of Fang and Kwong, Phys. Rev. A 59, 342 (1996) at 4,600 K, and hence does not support the experiment.
14. 129I Moessbauer spectroscopic study of several n-σ charge-transfer complexes of iodine with thioethers
International Nuclear Information System (INIS)
Sakai, Hiroshi; Matsuyama, Tomochika; Maeda, Yutaka
1986-01-01
129 I Moessbauer studies have been made of n-σ charge-transfer complexes of iodine with thioethers, such as thiane, 1,4-oxathiane, and 1,4-dithiane. The spectra of these complexes consist of two sets of quadrupole octets, corresponding to the bridging and terminal iodine atoms. The transferred charges from the thioethers are localized on the terminal iodine atoms, and the bridging iodine atoms have slightly positive charges. This result can be well explained in terms of a covalent bond between the sulfur and bridging iodine atoms or the MO treatment of a delocalized three-center four-electron bonding. The contributions of the dative structure to the ground state are estimated to be 36, 28, and 24 % for thiane-iodine, 1,4-oxathiane-iodine, and 1,4-dithiane-iodine respectively. The nature of the charge-transfer bond is discussed in comparison with amine-iodine complexes. (author)
15. Spectroscopic studies of charge transfer complexes of some amino aromatic donors with some acceptors
International Nuclear Information System (INIS)
Al-Ani, S.S.
1989-01-01
Charge transfer (C.T.) complexes are the products of the weak reversible interactions between electron donors and electron acceptors. Sixteen novel C.T. complexes were studied and discussed. These complexes were formed from aromatic electron donors with various electron acceptors in absolute ethyl alcohol at 20 0 C. Electronic absorption spectra of these complexes and their donors and acceptors were taken. New charge transfer absorption bands appeared for these complexes in the UV-VIS region. The donors used are tetramethyl diamino benzophenone, P-amino-N:N-dimethyl aniline, tetramethyl-diamino-diphenylmethane, P-amino-azobenzene and benzidine, while the acceptors are iodine, bromine, picric acid, 2,4-dinitrophenol, trifluoroacetic acid and trichloroacetic acid. The results showed a disappearance of some donors and acceptors absorption bands. The energy of C.T. bands were calculated from which the ionization potentials of donors were obtained. The results showed that energies of C.T. Bands for complexes of a given donor with a series of acceptors are very similar. Some C.T. complexes showed low value of energy and high values of electrical conductivity. These are ionic complexes rather than molecular ones. 4 tabs.; 2 figs.; 99 refs
16. Observation of excited state charge transfer with fs/ps-CARS
Energy Technology Data Exchange (ETDEWEB)
Blom, Alex Jason [Iowa State Univ., Ames, IA (United States)
2009-01-01
Excited state charge transfer processes are studied using the fs/ps-CARS probe technique. This probe allows for multiplexed detection of Raman active vibrational modes. Systems studied include Michler's Ketone, Coumarin 120, 4-dimethylamino-4'-nitrostilbene, and several others. The vibrational spectrum of the para di-substituted benzophenone Michler's Ketone in the first excited singlet state is studied for the first time. It is found that there are several vibrational modes indicative of structural changes of the excited molecule. A combined experimental and theoretical approach is used to study the simplest 7-amino-4-methylcoumarin, Coumarin 120. Vibrations observed in FTIR and spontaneous Raman spectra are assigned using density functional calculations and a continuum solvation model is used to predict how observed modes are affected upon inclusion of a solvent. The low frequency modes of the excited state charge transfer species 4-dimethylamino-4{prime}-nitrostilbene are studied in acetonitrile. Results are compared to previous work on this molecule in the fingerprint region. Finally, several partially completed projects and their implications are discussed. These include the two photon absorption of Coumarin 120, nanoconfinement in cyclodextrin cavities and sensitization of titania nanoparticles.
17. Experimental and modeling study on charge storage/transfer mechanism of graphene-based supercapacitors
Science.gov (United States)
Ban, Shuai; Jing, Xie; Zhou, Hongjun; Zhang, Lei; Zhang, Jiujun
2014-12-01
A symmetrical graphene-based supercapacitor is constructed for studying the charge-transfer mechanism within the graphene-based electrodes using both experiment measurements and molecular simulation. The in-house synthesized graphene is characterized by XRD, SEM and BET measurements for morphology and surface area. It is observed that the electric capacity of graphene electrode can be reduced by both high internal resistance and limited mass transfer. Computer modeling is conducted at the molecular level to characterize the diffusion behavior of electrolyte ions to the interior of electrode with emphasis on the unique 2D confinement imposed by graphene layers. Although graphene powder poses a moderate internal surface of 400 m2 g-1, the capacitance performance of graphene electrode can be as good as that of commercial activated carbon which has an overwhelming surface area of 1700 m2 g-1. An explanation to this abnormal correlation is that graphene material has an intrinsic capability of adaptively reorganizing its microporous structure in response to intercalation of ions and immergence of electrolyte solvent. The accessible surface of graphene is believed to be dramatically enlarged for ion adsorption during the charging process of capacitor.
18. Excitation and charge transfer in low-energy hydrogen atom collisions with neutral oxygen
Science.gov (United States)
Barklem, P. S.
2018-02-01
Excitation and charge transfer in low-energy O+H collisions is studied; it is a problem of importance for modelling stellar spectra and obtaining accurate oxygen abundances in late-type stars including the Sun. The collisions have been studied theoretically using a previously presented method based on an asymptotic two-electron linear combination of atomic orbitals (LCAO) model of ionic-covalent interactions in the neutral atom-hydrogen-atom system, together with the multichannel Landau-Zener model. The method has been extended to include configurations involving excited states of hydrogen using an estimate for the two-electron transition coupling, but this extension was found to not lead to any remarkably high rates. Rate coefficients are calculated for temperatures in the range 1000-20 000 K, and charge transfer and (de)excitation processes involving the first excited S-states, 4s.5So and 4s.3So, are found to have the highest rates. Data are available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/vizbin/qcat?J/A+A/610/A57. The data are also available at http://https://github.com/barklem/public-data
19. Charge Transfer Mechanism in Titanium-Doped Microporous Silica for Photocatalytic Water-Splitting Applications
Directory of Open Access Journals (Sweden)
Wendi Sapp
2016-02-01
Full Text Available Solar energy conversion into chemical form is possible using artificial means. One example of a highly-efficient fuel is solar energy used to split water into oxygen and hydrogen. Efficient photocatalytic water-splitting remains an open challenge for researchers across the globe. Despite significant progress, several aspects of the reaction, including the charge transfer mechanism, are not fully clear. Density functional theory combined with density matrix equations of motion were used to identify and characterize the charge transfer mechanism involved in the dissociation of water. A simulated porous silica substrate, using periodic boundary conditions, with Ti4+ ions embedded on the inner pore wall was found to contain electron and hole trap states that could facilitate a chemical reaction. A trap state was located within the silica substrate that lengthened relaxation time, which may favor a chemical reaction. A chemical reaction would have to occur within the window of photoexcitation; therefore, the existence of a trapping state may encourage a chemical reaction. This provides evidence that the silica substrate plays an integral part in the electron/hole dynamics of the system, leading to the conclusion that both components (photoactive materials and support of heterogeneous catalytic systems are important in optimization of catalytic efficiency.
20. K-shell-hole production, multiple-hole production, charge transfer, and antisymmetry
International Nuclear Information System (INIS)
1980-01-01
In calculating K-shell-hole production when an ion collides with an atom, account must be taken of the fact that processes involving electrons other than the K-shell electron can occur. For example, after making a K-shell hole an L-shell electron may be knocked into it, or an L-shell vacancy may be produced and the K-shell electron promoted to that vacancy in the ''Fermi sea'' of the target-atom orbitals. In 1973 a theorem was proved by one of the present authors demonstrating that all these multielectron processes cancel in an independent-particle model for the target atom. In this paper it is shown that the same thing occurs for hole production by charge transfer to the ion. The authors demonstrate that multihole production does not obey this simple rule and that the probability for multihole production is not the product of independent single-electron probabilities. The correct expressions that should be used for these processes are given, together with new results for charge-transfer processes accompanied by hole production
1. Theory of interfacial charge-transfer complex photophysics in π-conjugated polymer-fullerene blends
Science.gov (United States)
Aryanpour, K.; Psiachos, D.; Mazumdar, S.
2010-03-01
We present a theory of the electronic structure and photophysics of 1:1 blends of derivatives of polyparaphenylenevinylene and fullerenes [1]. Within the same Coulomb-correlated Hamiltonian applied previously to interacting chains of single-component π-conjugated polymers [2], we find an exciplex state that occurs below the polymer's optical exciton. Weak absorption from the ground state occurs to the exciplex. We explain transient photoinduced absorptions in the blend [3], observed for both above-gap and below-gap photoexcitations, within our theory. Photoinduced absorptions for above-gap photoexcitation are from the optical exciton as well as the exciplex, while for below-gap photoexcitation induced absorptions are from the exciplex alone. In neither case are free polarons generated in the time scale of the experiment. Importantly, the photophysics of films of single-component π-conjugated polymers and blends can both be understood by extending Mulliken's theory of ground state charge-transfer to the case of excited state charge-transfer. [1] K. Aryanpour, D. Psiachos, and S. Mazumdar, arXiv:0908.0366 [2] D. Psiachos and S. Mazumdar, Phys. Rev. B. 79 155106 (2009) [3] T. Drori et al., Phys. Rev. Lett. 101, 037402 (2008)
2. Momentum transfer theory of non-conservative charged particle transport in crossed electric and magnetic fields
International Nuclear Information System (INIS)
Vrhovac, S.B.; Petrovic, Z.Lj.
1995-01-01
Momentum - transfer approximation is applied to momentum and energy balance equations describing reacting particle swarms in gases in crossed electric and magnetic fields. Transport coefficients of charged particles undergoing both inelastic and reactive, non-particle-conserving collisions with a gas of neutral molecules are calculated. Momentum - transfer theory (MTT) has been developed mainly by Robson and collaborators. It has been applied to a single reactive gas and mixtures of reactive gases in electric field only. MTT has also been applied in crossed electric and magnetic fields recently and independently of our work but the reactive collisions were not considered. Consider a swarm of electrons of charge e and mass m moving with velocity rvec v through a neutral gas under the influence of an applied electric rvec E and magnetic rvec B field. The collision processes which we shall investigate are limited to elastic, inelastic and reactive collisions of electrons with gas molecules. Here we interpret reactive collisions as collisions which produce change in number of the swarm particles. Reactive collisions involve creation (ionization by electron impact) or loss (electron attachment) of swarm particles. We consider only single ionization in approximation of the mass ratio m/m 0 0 are masses of electrons and neutral particles, respectively. We assume that the stage of evolution of the swarm is the hydrodynamic limit (HDL). In HDL, the space - time dependence of all properties is carried by the number density n of swarm particles
3. Spectroscopic and theoretical investigations on intramolecular charge transfer phenomenon in 1-3-dioxolane derivative
Science.gov (United States)
Zhang, Zhiyong; Zhang, Zhongzhi; Luo, Yijing; Sun, Shanshan; Zhang, Guangqing
2018-02-01
High fluorescence quantum yield (FQY) and large Stokes shift (SS) cannot be easily achieved simultaneously by traditional PICT or TICT fluorescent probe. However, an 1-3-dioxolane derivative named 5-methyl-8,9-dihydro-5H-[1,3]dioxolo[4,5-b]carbazol-6(7H)-one (MDDCO) features both high FQY and large SS. The purpose of this study is to search the mechanism behind this phenomenon by theoretical method. Simulated structure changes and charge transfer suggest ICT process in MDDCO is similar to PLICT (Planarized Intramolecular Charge Transfer) process. Calculated UV-Vis spectra and fluorescence spectra show that PLICT-like state (S1 state) of MDDCO leads to large SS. Computed transient-absorption spectra and radiative decay rates indicate that PLICT-like state is key factor for high FQY of MDDCO. These findings suggest that PLICT-like state in 1,3-dioxolane derivatives can achieve both large SS and high FQY, which presents a new method for high-performance fluorescent probe design.
4. Observation of excited state charge transfer with fs/ps-CARS
International Nuclear Information System (INIS)
Blom, Alex Jason
2009-01-01
Excited state charge transfer processes are studied using the fs/ps-CARS probe technique. This probe allows for multiplexed detection of Raman active vibrational modes. Systems studied include Michler's Ketone, Coumarin 120, 4-dimethylamino-4(prime)-nitrostilbene, and several others. The vibrational spectrum of the para di-substituted benzophenone Michler's Ketone in the first excited singlet state is studied for the first time. It is found that there are several vibrational modes indicative of structural changes of the excited molecule. A combined experimental and theoretical approach is used to study the simplest 7-amino-4-methylcoumarin, Coumarin 120. Vibrations observed in FTIR and spontaneous Raman spectra are assigned using density functional calculations and a continuum solvation model is used to predict how observed modes are affected upon inclusion of a solvent. The low frequency modes of the excited state charge transfer species 4-dimethylamino-4(prime)-nitrostilbene are studied in acetonitrile. Results are compared to previous work on this molecule in the fingerprint region. Finally, several partially completed projects and their implications are discussed. These include the two photon absorption of Coumarin 120, nanoconfinement in cyclodextrin cavities and sensitization of titania nanoparticles
5. Frenkel-Charge-Transfer exciton intermixing theory for molecular crystals with two isolated Frenkel exciton states.
Science.gov (United States)
We develop an analytical theory for the intra-intermolecular exciton intermixing in periodic 1D chains of planar organic molecules with two isolated low-lying Frenkel exciton states, typical of copper phthalocyanine (CuPc) and other transition metal phthalocyanine molecules. We formulate the Hamiltonian and use the exact Bogoliubov diagonalization procedure to derive the eigen energy spectrum for the two lowest intramolecular Frenkel excitons coupled to the intermolecular charge transfer (CT) exciton state. By comparing our theoretical spectrum with available experimental CuPc absorption data, we obtain the parameters of the Frenkel-CT exciton intermixing in CuPc thin films. The two Frenkel exciton states here are spaced apart by 0.26 eV, and the charge transfer exciton state is 50 meV above the lowest Frenkel exciton. Both Frenkel excitons are strongly mixed with the CT exciton, showing the coupling constant 0.17 eV in agreement with earlier electron transport experiments. Our results can be used for the proper interpretation of the physical properties of crystalline phthalocyanines. DOE-DE-SC0007117 (I.B.), UNC-GA ROI Grant (A.P.).
6. Differential charge-transfer cross sections for systems with energetically degenerate or near-degenerate channels
International Nuclear Information System (INIS)
Nguyen, H.; Bredy, R.; Camp, H.A.; DePaola, B.D.; Awata, T.
2004-01-01
Resolution plays a vital role in spectroscopic studies. In the usual recoil-ion momentum spectroscopy (RIMS), Q-value resolution is relied upon to distinguish between different collision channels: The better the Q-value resolution, the better one is able to resolve energetically similar channels. Although traditional COLTRIMS greatly improves Q-value resolution by cooling the target and thus greatly reducing the initial target momentum spread, the resolution of the technique is still limited by target temperature. However, with the recent development in RIMS, namely, magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) superior recoil ion momentum resolution as well as charge transfer measurements with laser excited targets have become possible. Through MOTRIMS, methods for the measurements of target excited state fraction and kinematically complete relative charge transfer cross sections have been developed, even for some systems having energetically degenerate or nearly degenerate channels. In the present work, the systems of interest having energy degeneracies or near degeneracies are Rb + , K + , and Li + colliding with trapped Rb(5l), where l=s and p
7. Real-time observation of intersystem crossing induced by charge recombination during bimolecular electron transfer reactions
KAUST Repository
Alsam, Amani Abdu
2016-09-21
Real-time probing of intersystem crossing (ISC) and triplet-state formation after photoinduced electron transfer (ET) is a particularly challenging task that can be achieved by time-resolved spectroscopy with broadband capability. Here, we examine the mechanism of charge separation (CS), charge recombination (CR) and ISC of bimolecular photoinduced electron transfer (PET) between poly[(9,9-di(3,3′-N,N’-trimethyl-ammonium) propyl fluorenyl-2,7-diyl)-alt-co-(9,9-dioctyl-fluorenyl-2,7-diyl)] diiodide salt (PFN) and dicyanobenzene (DCB) using time-resolved spectroscopy. PET from PFN to DCB is confirmed by monitoring the transient absorption (TA) and infrared spectroscopic signatures for the radical ion pair (DCB─•-PFN+•). In addition, our time-resolved results clearly demonstrate that CS takes place within picoseconds followed by CR within nanoseconds. The ns-TA data exhibit the clear spectroscopic signature of PFN triplet-triplet absorption, induced by the CR of the radical ion pairs (DCB─•-PFN+•). As a result, the triplet state of PFN (3PFN*) forms and subsequently, the ground singlet state is replenished within microseconds. © 2016
8. Excited State Structural Dynamics of Carotenoids and ChargeTransfer Systems
Energy Technology Data Exchange (ETDEWEB)
Van Tassle, Aaron Justin [Univ. of California, Berkeley, CA (United States)
2006-01-01
This dissertation describes the development andimplementation of a visible/near infrared pump/mid-infrared probeapparatus. Chapter 1 describes the background and motivation ofinvestigating optically induced structural dynamics, paying specificattention to solvation and the excitation selection rules of highlysymmetric molecules such as carotenoids. Chapter 2 describes thedevelopment and construction of the experimental apparatus usedthroughout the remainder of this dissertation. Chapter 3 will discuss theinvestigation of DCM, a laser dye with a fluorescence signal resultingfrom a charge transfer state. By studying the dynamics of DCM and of itsmethyl deuterated isotopomer (an otherwise identical molecule), we areable to investigate the origins of the charge transfer state and provideevidence that it is of the controversial twisted intramolecular (TICT)type. Chapter 4 introduces the use of two-photon excitation to the S1state, combined with one-photon excitation to the S2 state of thecarotenoid beta-apo-8'-carotenal. These 2 investigations show evidencefor the formation of solitons, previously unobserved in molecular systemsand found only in conducting polymers Chapter 5 presents an investigationof the excited state dynamics of peridinin, the carotenoid responsiblefor the light harvesting of dinoflagellates. This investigation allowsfor a more detailed understanding of the importance of structuraldynamics of carotenoids in light harvesting.
9. Heat exchange between a microparticle and plasma. Contribution of charge transfer processes
International Nuclear Information System (INIS)
Uglov, A.A.; Gnedovets, A.G.
1983-01-01
Heat- and mass-transfer in interaction of a microparticle with a dense plasma have been considered analytically. At that, calculation methods developed as applied to probe diagnostics of slightly ionized plasma are also used in the case of relatively high degrees of ionization, at which heat flows of plasma charged particles Qe and Qi become comparable with molecular ones. High efficiency of energy transfer during electron and ion collisions with a microparticle is due to the following: 1) effective cross section of ion collision with a microparticle, which acquires in a quasineutral plasma the potential phisub(f) < 0, surpasses the geometric one; the maximum contribution of electron and ion constituent is achieved when the cross section ion collisions with a microparticle is linearly connected with its potential, 2) with a charged microparticle electrons from distribution function ''tail'' collide, their energy exceeds potential barrier near the surface and, consequently, the mean heat energy; 3) besides the energy of a microparticle thermal movement during electron recombination and ion neutralization on its surface the heat Qsub(e) and Qsub(i), which considerably exceed the heat of molecular adsorption and mean heat energy of plasma particles at kT approximately 1 eV, are transmitted to the microparticle
10. Electronic properties of Fe charge transfer complexes – A combined experimental and theoretical approach
International Nuclear Information System (INIS)
Ferreira, Hendrik; Eschwege, Karel G. von; Conradie, Jeanet
2016-01-01
Highlights: • Experimental and computational study of Fe II -phen, -bpy & -tpy compleesx. • Close correlations between experimental redox and spectral, and computational data. • Computational methods fast-track DSSC research. - Abstract: Dye-sensitized solar cell technology holds huge potential in renewable electricity generation of the future. Due to demand urgency, ways need to be explored to reduce research time and cost. Against this background, quantum computational chemistry is illustrated to be a reliable tool at the onset of studies in this field, simulating charge transfer, spectral (solar energy absorbed) and electrochemical (ease by which electrons may be liberated) tuning of related photo-responsive dyes. Comparative experimental and theoretical DFT studies were done under similar conditions, involving an extended series of electrochemically altered phenanthrolines, bipyridyl and terpyridyl complexes of Fe II . Fe II/III oxidation waves vary from 0.363 V for tris(3,6-dimethoxybipyridyl)Fe II to 0.894 V (versus Fc/Fc + ) for the 5-nitrophenanthroline complex. Theoretical DFT computed ionization potentials in the bipyridyl sub-series achieved an almost 100% linear correlation with experimental electrochemical oxidation potentials, while the phenanthroline sub-series gave R 2 = 0.95. Apart from the terpyridyl complex which accorded an almost perfect match, in general, TDDFT oscillators were computed at slightly lower energies than what was observed experimentally, while molecular HOMO and LUMO renderings reveal desired complexes with directional charge transfer propensities.
11. Ultrafast spin exchange-coupling torque via photo-excited charge-transfer processes
Science.gov (United States)
Ma, X.; Fang, F.; Li, Q.; Zhu, J.; Yang, Y.; Wu, Y. Z.; Zhao, H. B.; Lüpke, G.
2015-10-01
Optical control of spin is of central importance in the research of ultrafast spintronic devices utilizing spin dynamics at short time scales. Recently developed optical approaches such as ultrafast demagnetization, spin-transfer and spin-orbit torques open new pathways to manipulate spin through its interaction with photon, orbit, charge or phonon. However, these processes are limited by either the long thermal recovery time or the low-temperature requirement. Here we experimentally demonstrate ultrafast coherent spin precession via optical charge-transfer processes in the exchange-coupled Fe/CoO system at room temperature. The efficiency of spin precession excitation is significantly higher and the recovery time of the exchange-coupling torque is much shorter than for the demagnetization procedure, which is desirable for fast switching. The exchange coupling is a key issue in spin valves and tunnelling junctions, and hence our findings will help promote the development of exchange-coupled device concepts for ultrafast coherent spin manipulation.
12. Microgravity and Charge Transfer in the Neuronal Membrane: Implications for Computational Neurobiology
Science.gov (United States)
Wallace, Ron
1995-01-01
Evidence from natural and artificial membranes indicates that the neural membrane is a liquid crystal. A liquid-to-gel phase transition caused by the application of superposed electromagnetic fields to the outer membrane surface releases spin-correlated electron pairs which propagate through a charge transfer complex. The propagation generates Rydberg atoms in the lipid bilayer lattice. In the present model, charge density configurations in promoted orbitals interact as cellular automata and perform computations in Hilbert space. Due to the small binding energies of promoted orbitals, their automata are highly sensitive to microgravitational perturbations. It is proposed that spacetime is classical on the Rydberg scale, but formed of contiguous moving segments, each of which displays topological equivalence. This stochasticity is reflected in randomized Riemannian tensor values. Spacetime segments interact with charge automata as components of a computational process. At the termination of the algorithm, an orbital of high probability density is embedded in a more stabilized microscopic spacetime. This state permits the opening of an ion channel and the conversion of a quantum algorithm into a macroscopic frequency code.
13. Application of double-hybrid density functionals to charge transfer in N-substituted pentacenequinones.
Science.gov (United States)
Sancho-García, J C
2012-05-07
A set of N-heteroquinones, deriving from oligoacenes, have been recently proposed as n-type organic semiconductors with high electron mobilities in thin-film transistors. Generally speaking, this class of compounds self-assembles in neighboring π-stacks linked by weak hydrogen bonds. We aim at theoretically characterizing here the sequential charge transport (hopping) process expected to take place across these arrays of molecules. To do so, we need to accurately address the preferred packing of these materials simultaneously to single-molecule properties related to charge-transfer events, carefully employing dispersion-corrected density functional theory methods to accurately extract the key molecular parameters governing this phenomenon at the nanoscale. This study confirms the great deal of interest around these compounds, since controlled functionalization of model molecules (i.e., pentacene) allows to efficiently tune the corresponding charge mobilities, and the capacity of modern quantum-chemical methods to predict it after rationalizing the underlying structure-property relationships.
14. Hydrated proton and hydroxide charge transfer at the liquid/vapor interface of water
Energy Technology Data Exchange (ETDEWEB)
Soniat, Marielle; Rick, Steven W., E-mail: [email protected] [Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (United States); Kumar, Revati [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70808 (United States)
2015-07-28
The role of the solvated excess proton and hydroxide ions in interfacial properties is an interesting scientific question with applications in a variety of aqueous behaviors. The role that charge transfer (CT) plays in interfacial behavior is also an unsettled question. Quantum calculations are carried out on clusters of water with an excess proton or a missing proton (hydroxide) to determine their CT. The quantum results are applied to analysis of multi-state empirical valence bond trajectories. The polyatomic nature of the solvated excess proton and hydroxide ion results in directionally dependent CT, depending on whether a water molecule is a hydrogen bond donor or acceptor in relation to the ion. With polyatomic molecules, CT also depends on the intramolecular bond distances in addition to intermolecular distances. The hydrated proton and hydroxide affect water’s liquid/vapor interface in a manner similar to monatomic ions, in that they induce a hydrogen-bonding imbalance at the surface, which results in charged surface waters. This hydrogen bond imbalance, and thus the charged waters at the surface, persists until the ion is at least 10 Å away from the interface.
15. Large impact of reorganization energy on photovoltaic conversion due to interfacial charge-transfer transitions.
Science.gov (United States)
Fujisawa, Jun-ichi
2015-05-14
Interfacial charge-transfer (ICT) transitions are expected to be a novel charge-separation mechanism for efficient photovoltaic conversion featuring one-step charge separation without energy loss. Photovoltaic conversion due to ICT transitions has been investigated using several TiO2-organic hybrid materials that show organic-to-inorganic ICT transitions in the visible region. In applications of ICT transitions to photovoltaic conversion, there is a significant problem that rapid carrier recombination is caused by organic-inorganic electronic coupling that is necessary for the ICT transitions. In order to solve this problem, in this work, I have theoretically studied light-to-current conversions due to the ICT transitions on the basis of the Marcus theory with density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. An apparent correlation between the reported incident photon-to-current conversion efficiencies (IPCE) and calculated reorganization energies was clearly found, in which the IPCE increases with decreasing the reorganization energy consistent with the Marcus theory in the inverted region. This activation-energy dependence was systematically explained by the equation formulated by the Marcus theory based on a simple excited-state kinetic scheme. This result indicates that the reduction of the reorganization energy can suppress the carrier recombination and enhance the IPCE. The reorganization energy is predominantly governed by the structural change in the chemical-adsorption moiety between the ground and ICT excited states. This work provides crucial knowledge for efficient photovoltaic conversion due to ICT transitions.
16. Improper ferroelectric polarization in a perovskite driven by intersite charge transfer and ordering
Science.gov (United States)
Chen, Wei-Tin; Wang, Chin-Wei; Wu, Hung-Cheng; Chou, Fang-Cheng; Yang, Hung-Duen; Simonov, Arkadiy; Senn, M. S.
2018-04-01
It is of great interest to design and make materials in which ferroelectric polarization is coupled to other order parameters such as lattice, magnetic, and electronic instabilities. Such materials will be invaluable in next-generation data storage devices. Recently, remarkable progress has been made in understanding improper ferroelectric coupling mechanisms that arise from lattice and magnetic instabilities. However, although theoretically predicted, a compact lattice coupling between electronic and ferroelectric (polar) instabilities has yet to be realized. Here we report detailed crystallographic studies of a perovskite HgAMn3A'Mn4BO12 that is found to exhibit a polar ground state on account of such couplings that arise from charge and orbital ordering on both the A'- and B-sites, which are themselves driven by a highly unusual MnA '-MnB intersite charge transfer. The inherent coupling of polar, charge, orbital, and hence magnetic degrees of freedom make this a system of great fundamental interest, and demonstrating ferroelectric switching in this and a host of recently reported hybrid improper ferroelectrics remains a substantial challenge.
17. Hydrated proton and hydroxide charge transfer at the liquid/vapor interface of water
International Nuclear Information System (INIS)
Soniat, Marielle; Rick, Steven W.; Kumar, Revati
2015-01-01
The role of the solvated excess proton and hydroxide ions in interfacial properties is an interesting scientific question with applications in a variety of aqueous behaviors. The role that charge transfer (CT) plays in interfacial behavior is also an unsettled question. Quantum calculations are carried out on clusters of water with an excess proton or a missing proton (hydroxide) to determine their CT. The quantum results are applied to analysis of multi-state empirical valence bond trajectories. The polyatomic nature of the solvated excess proton and hydroxide ion results in directionally dependent CT, depending on whether a water molecule is a hydrogen bond donor or acceptor in relation to the ion. With polyatomic molecules, CT also depends on the intramolecular bond distances in addition to intermolecular distances. The hydrated proton and hydroxide affect water’s liquid/vapor interface in a manner similar to monatomic ions, in that they induce a hydrogen-bonding imbalance at the surface, which results in charged surface waters. This hydrogen bond imbalance, and thus the charged waters at the surface, persists until the ion is at least 10 Å away from the interface
18. Simulation of charge transfer and orbital rehybridization in molecular and condensed matter systems
Science.gov (United States)
Nistor, Razvan A.
The mixing and shifting of electronic orbitals in molecules, or between atoms in bulk systems, is crucially important to the overall structure and physical properties of materials. Understanding and accurately modeling these orbital interactions is of both scientific and industrial relevance. Electronic orbitals can be perturbed in several ways. Doping, adding or removing electrons from systems, can change the bond-order and the physical properties of certain materials. Orbital rehybridization, driven by either thermal or pressure excitation, alters the short-range structure of materials and changes their long-range transport properties. Macroscopically, during bond formation, the shifting of electronic orbitals can be interpreted as a charge transfer phenomenon, as electron density may pile up around, and hence, alter the effective charge of, a given atom in the changing chemical environment. Several levels of theory exist to elucidate the mechanisms behind these orbital interactions. Electronic structure calculations solve the time-independent Schrodinger equation to high chemical accuracy, but are computationally expensive and limited to small system sizes and simulation times. Less fundamental atomistic calculations use simpler parameterized functional expressions called force-fields to model atomic interactions. Atomistic simulations can describe systems and time-scales larger and longer than electronic-structure methods, but at the cost of chemical accuracy. In this thesis, both first-principles and phenomenological methods are addressed in the study of several encompassing problems dealing with charge transfer and orbital rehybridization. Firstly, a new charge-equilibration method is developed that improves upon existing models to allow next-generation force-fields to describe the electrostatics of changing chemical environments. Secondly, electronic structure calculations are used to investigate the doping dependent energy landscapes of several high
19. Intra-molecular Charge Transfer and Electron Delocalization in Non-fullerene Organic Solar Cells
Energy Technology Data Exchange (ETDEWEB)
Wu, Qinghe [Department of Chemistry, Key Laboratory for Preparation and Application of Ordered Structural Materials of Guangdong Province, Shantou University, Guangdong 515063, P. R. China; Zhao, Donglin [Department of Chemistry, The James Franck Institute, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States; Goldey, Matthew B. [Institute for Molecular Engineering, The University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States; Filatov, Alexander S. [Department of Chemistry, The James Franck Institute, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States; Sharapov, Valerii [Department of Chemistry, The James Franck Institute, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States; Colón, Yamil J. [Institute for Molecular Engineering, Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States; Institute for Molecular Engineering, The University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States; Cai, Zhengxu [Department of Chemistry, The James Franck Institute, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States; Chen, Wei [Institute for Molecular Engineering, Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States; Institute for Molecular Engineering, The University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States; de Pablo, Juan [Institute for Molecular Engineering, Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States; Institute for Molecular Engineering, The University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States; Galli, Giulia [Institute for Molecular Engineering, Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States; Institute for Molecular Engineering, The University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, United States; Yu, Luping [Department of Chemistry, The James Franck Institute, The University of Chicago, 929 E 57th Street, Chicago, Illinois 60637, United States
2018-03-02
Two types of electron acceptors were synthesized by coupling two kinds of electron-rich cores with four equivalent perylene diimides (PDIs) at the a position. With fully aromatic cores, TPB and TPSe have pi-orbitals spread continuously over the whole aromatic conjugated backbone, unlike TPC and TPSi, which contain isolated PDI units due to the use of a tetrahedron carbon or silicon linker. Density functional theory calculations of the projected density of states showed that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for TPB are localized in separate regions of space. Further, the LUMO of TPB shows a greater contribution from the orbitals belonging to the connective core of the molecules than that of TPC. Overall, the properties of the HOMO and LUMO point at increased intra-molecular delocalization of negative charge carriers for TPB and TPSe than for TPC and TPSi and hence at a more facile intra-molecular charge transfer for the former. The film absorption and emission spectra showed evidences for the inter -molecular electron delocalization in TPB and TPSe, which is consistent with the network structure revealed by X-ray diffraction studies on single crystals of TPB. These features benefit the formation of charge transfer states and/or facilitate charge transport. Thus, higher electron mobility and higher charge dissociation probabilities under J(sc) condition were observed in blend films of TPB:PTB7-Th and TPSe:PTB7-Th than those in TPC:PTB7Th and TPSi:PTB7-Th blend films. As a result, the J(sc) and fill factor values of 15.02 mA/cm(2), 0.58 and 14.36 mA/cm(2), 0.55 for TPB- and TPSe-based solar cell are observed, whereas those for TPC and TPSi are 11.55 mA/cm2, 0.47 and 10.35 mA/cm(2), 0.42, respectively.
20. Heat transfer performance of a pulsating heat pipe charged with acetone-based mixtures
Science.gov (United States)
Wang, Wenqing; Cui, Xiaoyu; Zhu, Yue
2017-06-01
Pulsating heat pipes (PHPs) are used as high efficiency heat exchangers, and the selection of working fluids in PHPs has a great impact on the heat transfer performance. This study investigates the thermal resistance characteristics of the PHP charged with acetone-based binary mixtures, where deionized water, methanol and ethanol were added to and mixed with acetone, respectively. The volume mixing ratios were 2:1, 4:1 and 7:1, and the heating power ranged from 10 to 100 W with filling ratios of 45, 55, 62 and 70%. At a low filling ratio (45%), the zeotropic characteristics of the binary mixtures have an influence on the heat transfer performance of the PHP. Adding water, which has a substantially different boiling point compared with that of acetone, can significantly improve the anti-dry-out ability inside the PHP. At a medium filling ratio (55%), the heat transfer performance of the PHP is affected by both phase transition characteristics and physical properties of working fluids. At high heating power, the thermal resistance of the PHP with acetone-water mixture is between that with pure acetone and pure water, whereas the thermal resistance of the PHP with acetone-methanol and acetone-ethanol mixtures at mixing ratios of 2:1 and 4:1 is less than that with the corresponding pure fluids. At high filling ratios (62 and 70%), the heat transfer performance of the PHP is mainly determined by the properties of working fluids that affects the flow resistance. Thus, the PHP with acetone-methanol and acetone-ethanol mixtures that have a lower flow resistance shows better heat transfer performance than that with acetone-water mixture.
1. Molecular Engineering for Enhanced Charge Transfer in Thin-Film Photoanode.
Science.gov (United States)
Kim, Jeong Soo; Kim, Byung-Man; Kim, Un-Young; Shin, HyeonOh; Nam, Jung Seung; Roh, Deok-Ho; Park, Jun-Hyeok; Kwon, Tae-Hyuk
2017-10-11
We developed three types of dithieno[3,2-b;2',3'-d]thiophene (DTT)-based organic sensitizers for high-performance thin photoactive TiO 2 films and investigated the simple but powerful molecular engineering of different types of bonding between the triarylamine electron donor and the conjugated DTT π-bridge by the introduction of single, double, and triple bonds. As a result, with only 1.3 μm transparent and 2.5-μm TiO 2 scattering layers, the triple-bond sensitizer (T-DAHTDTT) shows the highest power conversion efficiency (η = 8.4%; V OC = 0.73 V, J SC = 15.4 mA·cm -2 , and FF = 0.75) in an iodine electrolyte system under one solar illumination (AM 1.5, 1000 W·m -2 ), followed by the single-bond sensitizer (S-DAHTDTT) (η = 7.6%) and the double-bond sensitizer (D-DAHTDTT) (η = 6.4%). We suggest that the superior performance of T-DAHTDTT comes from enhanced intramolecular charge transfer (ICT) induced by the triple bond. Consequently, T-DAHTDTT exhibits the most active photoelectron injection and charge transport on a TiO 2 film during operation, which leads to the highest photocurrent density among the systems studied. We analyzed these correlations mainly in terms of charge injection efficiency, level of photocharge storage, and charge-transport kinetics. This study suggests that the molecular engineering of a triple bond between the electron donor and the π-bridge of a sensitizer increases the performance of dye-sensitized solar cell (DSC) with a thin photoactive film by enhancing not only J SC through improved ICT but also V OC through the evenly distributed sensitizer surface coverage.
2. Vibrational inelastic and charge transfer processes in H++H2 system: An ab initio study
Science.gov (United States)
Amaran, Saieswari; Kumar, Sanjay
2007-12-01
State-resolved differential cross sections, total and integral cross sections, average vibrational energy transfer, and the relative probabilities are computed for the H++H2 system using the newly obtained ab initio potential energy surfaces at the full CI/cc-pVQZ level of accuracy which allow for both the direct vibrational inelastic and the charge transfer processes. The quantum dynamics is treated within the vibrational close-coupling infinite-order-sudden approximation approach using the two ab initio quasidiabatic potential energy surfaces. The computed collision attributes for both the processes are compared with the available state-to-state scattering experiments at Ec.m.=20eV. The results are in overall good agreement with most of the observed scattering features such as rainbow positions, integral cross sections, and relative vibrational energy transfers. A comparison with the earlier theoretical study carried out on the semiempirical surfaces (diatomics in molecules) is also made to illustrate the reliability of the potential energy surfaces used in the present work.
3. Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine
Science.gov (United States)
Lee, Chi M.; Schock, Harold J.
1988-01-01
Currently, the heat transfer equation used in the rotary combustion engine (RCE) simulation model is taken from piston engine studies. These relations have been empirically developed by the experimental input coming from piston engines whose geometry differs considerably from that of the RCE. The objective of this work was to derive equations to estimate heat transfer coefficients in the combustion chamber of an RCE. This was accomplished by making detailed temperature and pressure measurements in a direct injection stratified charge (DISC) RCE under a range of conditions. For each specific measurement point, the local gas velocity was assumed equal to the local rotor tip speed. Local physical properties of the fluids were then calculated. Two types of correlation equations were derived and are described in this paper. The first correlation expresses the Nusselt number as a function of the Prandtl number, Reynolds number, and characteristic temperature ratio; the second correlation expresses the forced convection heat transfer coefficient as a function of fluid temperature, pressure and velocity.
4. Theoretical studies of charge transfer and proton transfer complex formation between 3,5-dinitrobenzic acid and 1,2-dimethylimidazole
Science.gov (United States)
2018-05-01
Natural atomic charge analysis and molecular electrostatic potential (MEP) surface analysis of hydrogen bonded charge transfer (HBCT) and proton transfer (PT) complex of 3,5-dinitrobenzoic acid (DNBA) and 1,2-dimethylimidazole (DMI) have been investigated by theoretical modelling using widely employed DFT/B3LYP/6-311G(d,p) level of theory. Along with this analysis, Hirshfeld surface study of the intermolecular interactions and associated 2D finger plot for reported PT complex between DNBA and DMI have been explored.
5. Charge transfer in carbon nanotube actuators investigated using in situ Raman spectroscopy
International Nuclear Information System (INIS)
Gupta, S.; Hughes, M.; Windle, A.H.; Robertson, J.
2004-01-01
Charge transfer dynamics on the surface of single-wall carbon nanotube sheets is investigated using in situ Raman spectroscopy in order to understand the actuation mechanism of an electrochemical actuator and to determine associated parameters. We built an actuator from single-wall carbon nanotube mat and studied its actuation in several alkali metal (Li, Na, and K) and alkaline earth (Ca) halide and sulfate solutions in order to clarify the role of counterion as mobile ions in the film. The variation of bonding with applied potential was monitored using in situ Raman spectroscopy. This is because Raman can detect changes in C-C bond length: the radial breathing mode at ∼190 cm-1 varies inversely with the nanotube diameter, and the G band at ∼1590 cm-1 varies with the axial bond length. In addition, the intensities of both the modes vary with the emptying/depleting or filling of the bonding and antibonding states due to electrochemical charge injection. We discussed the variation of peak height and wave numbers of these modes providing valuable information concerning electrochemical charge injection on the carbon nanotube mat surface. We found in-plane microscopic compressive strain (∼-0.25%) and the equivalent charge transfer per carbon atom (f c ∼-0.005) as an upper bound for the actuators studied hereby. It is demonstrated that though the present analysis does comply with the proposition for the actuation principle made earlier, the quantitative estimates are significantly lower if compared with those of reported values. Furthermore, the extent of variation, i.e., coupled electro-chemo-mechanical response of single-wall carbon nanotubes (SWNT) mat depended upon the type of counterion used (Group I versus Group II). The cyclic voltammetry and ac electrochemical impedance spectroscopy results were described briefly, which help to demonstrate well-developed capacitive behavior of SWNT mat and to estimate the specific capacitances as well. Summarizing, the
6. Design of a software for calculating isoelectric point of a polypeptide according to their net charge using the graphical programming language LabVIEW.
Science.gov (United States)
Tovar, Glomen
2018-01-01
A software to calculate the net charge and to predict the isoelectric point (pI) of a polypeptide is developed in this work using the graphical programming language LabVIEW. Through this instrument the net charges of the ionizable residues of the polypeptide chains of the proteins are calculated at different pH values, tabulated, pI is predicted and an Excel (-xls) type file is generated. In this work, the experimental values of the pIs (pI) of different proteins are compared with the values of the pIs (pI) calculated graphically, achieving a correlation coefficient (R) of 0.934746 which represents a good reliability for a p program can constitute an instrument applicable in the laboratory, facilitating the calculation to graduate students and junior researchers. © 2017 by The International Union of Biochemistry and Molecular Biology, 46(1):39-46, 2018. © 2017 The International Union of Biochemistry and Molecular Biology.
7. Scientific Computation Application Partnerships in Materials and Chemical Sciences, Charge Transfer and Charge Transport in Photoactivated Systems, Developing Electron-Correlated Methods for Excited State Structure and Dynamics in the NWChem Software Suite
Energy Technology Data Exchange (ETDEWEB)
Cramer, Christopher J. [Univ. of Minnesota, Minneapolis, MN (United States)
2017-11-12
Charge transfer and charge transport in photoactivated systems are fundamental processes that underlie solar energy capture, solar energy conversion, and photoactivated catalysis, both organometallic and enzymatic. We developed methods, algorithms, and software tools needed for reliable treatment of the underlying physics for charge transfer and charge transport, an undertaking with broad applicability to the goals of the fundamental-interaction component of the Department of Energy Office of Basic Energy Sciences and the exascale initiative of the Office of Advanced Scientific Computing Research.
8. Low-Energy Charge Transfer in Multiply-Charged Ion-Atom Collisions Studied with the Combined SCVB-MOCC Approach
Directory of Open Access Journals (Sweden)
B. Zygelman
2002-03-01
Full Text Available A survey of theoretical studies of charge transfer involving collisions of multiply-charged ions with atomic neutrals (H and He is presented. The calculations utilized the quantum-mechanical molecular-orbital close-coupling (MOCC approach where the requisite potential curves and coupling matrix elements have been obtained with the spin-coupled valence bond (SCVB method. Comparison is made among various collision partners, for equicharged systems, where it is illustrated that even for total charge transfer cross sections, scaling-laws do not exist for low-energy collisions (i.e. < 1 keV/amu. While various empirical scaling-laws are well known in the intermediateand high-energy regimes, the multi-electron configurations of the projectile ions results in a rich and varied low-energy dependence, requiring an explicit calculation for each collision-partner pair. Future charge transfer problems to be addressed with the combined SCVB-MOCC approach are briefly discussed.
9. Effect of the Net Charge Distribution on the Aqueous Solution Properties of Polyampholytes Effet de la répartition de la charge nette sur les propriétés des solutions aqueuses de polyampholytes
Directory of Open Access Journals (Sweden)
Candau F.
2006-12-01
Full Text Available The zwitterion nature of ampholytic polymers provides features that are useful in environmental and industrial applications, e. g. ion-exchange membrane, as flocculants in sewage treatment and in oil recovery processes. In the latter case, the increase in viscosity which is observed in the presence of brine (anti -polyelectrolyte behavior make them ideal candidates for high salinity media. The aqueous solution properties of a series of ampholytic terpolymers based on sodium-2-acrylamido-2- rilethylpropanesulfonate (NaAMPS, Methacryloyloxyethyltrimethylammonium chloride (MADQUAT and acrylamide (AM, prepared in inverse micro emulsions have been investigated by viscometry and light scattering experiments. The distribution of the net charge among the chains was varied by adjusting the initial monomer composition and the degree of conversion. The effect of this distribution on the solubility of the samples and on the chain conformation was studied. It was found that samples with a narrow distribution of net charges were soluble in water even if the average net charge is small. Addition of salt produces a transition from an extended conformation to a more compact one in qualitative agreement with theoretical predictions. A practically alternated NaAMPS- MADQUAT copolymer prepared in homogeneous solution and with a small average net charge shows a behaviour quite similar to that of the terpolymers. La nature zwitterioniquedes polymères ampholytes présente des caractéristiques qui sont utiles dans les applications environnementales et industrielles, comme les membranes d'échange ionique, les floculants dans le traitement des eaux usées et dans les procédés de récupération de pétrole. Dans ce dernier cas, l'augmentation de viscosité qui est observée en présence de saumure (comportement antipolyélectrolyte en fait des candidats idéaux pour des milieux de salinité élevée. Les propriétés de la solution aqueuse d'une série de terpolym
10. Quantitative description of the relation between protein net charge and protein adsorption to air-water interfaces
NARCIS (Netherlands)
Wierenga, P.A.; Meinders, M.B.J.; Egmond, M.R.; Voragen, A.G.J.; Jongh, H.H.J.de
2005-01-01
In this study a set of chemically engineered variants of ovalbumin was produced to study the effects of electrostatic charge on the adsorption kinetics and resulting surface pressure at the air-water interface. The modification itself was based on the coupling of succinic anhydride to lysine
11. Sodium dodecyl benzene sulphonate mediated tautomerism of Eriochrome Black-T: Effect of charge transfer interaction
Science.gov (United States)
Ghosh, Sumit
2010-11-01
Interaction between anionic surfactant, sodium dodecyl benzene sulphonate, (SDBS) and an anionic dye Eriochrome Black-T, (EBT) has been investigated by visible spectroscopy, conductometry, dynamic light scattering and zeta potential measurements. Spectral changes of EBT observed on addition of SDBS indicate formation of quinone-hydrazone tautomer at pH 7.0, whereas in absence of SDBS this change appears at pH ˜ 9.45. However, at pH 7.0 this change in tautomerism is not observed in presence of sodium dodecyl sulphate (SDS). Experimental results indicate presence of charge transfer interaction between less stable quinone-hydrazone tautomer of EBT and SDBS molecules, which is confirmed using Benesi-Hildebrand and Scott equations.
12. Charge transfer in carbon composites based on fullerenes and exfoliated graphite
Science.gov (United States)
Berezkin, V. I.
2017-07-01
Kinetic processes have been studied in composites based on fullerenes and exfoliated graphite at the initial proportions of components from 1: 16 to 16: 1 in mass. The samples are produced by heat treatment of initial dispersed mixtures in vacuum in the diffusion-adsorption process, their further cold pressing, and annealing. It is shown that the annealing almost does not influence the conduction mechanisms and only induces additional structural defects acting as electron traps. As a whole, the results obtained at the noted proportions of components make it possible to consider the material as a compensated metallic system with a structural disorder in which the charge transfer at temperatures from 4.2 K to room temperature is controlled by quantum interference phenomena. At low temperatures, the effect of a weak localization is observed, and the electron-electron interactions take place at medium and high temperatures.
13. Charge transfer in graphene oxide-dye system for photonic applications
International Nuclear Information System (INIS)
Bongu, Sudhakara Reddy; Bisht, Prem B.; Thu, Tran V.; Sandhu, Adarsh
2014-01-01
The fluorescence of a standard dye Rhodamine 6G (R6G) in solution decreases on addition of reduced graphene oxide (rGO). The absorption spectra and lifetime measurements confirm that no excited-state but a ground-state complex formation is responsible for this effect. For silver decorated rGO (Ag-rGO), the quenching efficiency and ground state complex formation process is small. Z-scan measurements have been done to study the optical nonlinearity at 532 nm under ps time scale. Remarkable reduction in the saturable absorption (SA) effect of R6G indicates no nonlinear contribution from the ground state complex. The results have been explained with varying charge transfer rates and non-fluorescence nature of the complex
14. Charge transfer in rectifying oxide heterostructures and oxide access elements in ReRAM
Energy Technology Data Exchange (ETDEWEB)
Stefanovich, G. B.; Pergament, A. L.; Boriskov, P. P.; Kuroptev, V. A., E-mail: [email protected]; Stefanovich, T. G. [Petrozavodsk State University (Russian Federation)
2016-05-15
The main aspects of the synthesis and experimental research of oxide diode heterostructures are discussed with respect to their use as selector diodes, i.e., access elements in oxide resistive memory. It is shown that charge transfer in these materials differs significantly from the conduction mechanism in p–n junctions based on conventional semiconductors (Si, Ge, A{sup III}–B{sup V}), and the model should take into account the electronic properties of oxides, primarily the low carrier drift mobility. It is found that an increase in the forward current requires an oxide with a small band gap (<1.3 eV) in the heterostructure composition. Heterostructures with Zn, In–Zn (IZO), Ti, Ni, and Cu oxides are studied; it is found that the CuO–IZO heterojunction has the highest forward current density (10{sup 4} A/cm{sup 2}).
15. Charge transfer of He2+ with H in a strong magnetic field
International Nuclear Information System (INIS)
Liu Chun-Lei; Zou Shi-Yang; He Bin; Wang Jian-Guo
2015-01-01
By solving a time-dependent Schrödinger equation (TDSE), we studied the electron capture process in the He 2+ +H collision system under a strong magnetic field in a wide projectile energy range. The strong enhancement of the total charge transfer cross section is observed for the projectile energy below 2.0 keV/u. With the projectile energy increasing, the cross sections will reduce a little and then increase again, compared with those in the field-free case. The cross sections to the states with different magnetic quantum numbers are presented and analyzed where the influence due to Zeeman splitting is obviously found, especially in the low projectile energy region. The comparison with other models is made and the tendency of the cross section varying with the projectile energy is found closer to that from other close coupling models. (paper)
16. Low-energy charge transfer for collisions of Si3+ with atomic hydrogen
Science.gov (United States)
Bruhns, H.; Kreckel, H.; Savin, D. W.; Seely, D. G.; Havener, C. C.
2008-06-01
Cross sections of charge transfer for Si3+ ions with atomic hydrogen at collision energies of ≈40-2500eV/u were carried out using a merged-beam technique at the Multicharged Ion Research Facility at Oak Ridge National Laboratory. The data span an energy range in which both molecular orbital close coupling (MOCC) and classical trajectory Monte Carlo (CTMC) calculations are available. The influence of quantum mechanical effects of the ionic core as predicted by MOCC is clearly seen in our results. However, discrepancies between our experiment and MOCC results toward higher collision energies are observed. At energies above 1000 eV/u good agreement is found with CTMC results.
17. Ab initio study of charge transfer in B2+ low-energy collisions with atomic hydrogen
Science.gov (United States)
Turner, A. R.; Cooper, D. L.; Wang, J. G.; Stancil, P. C.
2003-07-01
Charge transfer processes due to collisions of ground state B2+(2s 2S) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with the existing experiments shows our results to be in good agreement. When EMOCC cross sections with and without rotational coupling are small (400 eV/u, inclusion of rotational coupling increases the total cross section by 50% 80%, improving the agreement between the current calculations and experiments. For state-selective cross sections, rotational coupling induces mixing between different symmetries; however, its effect, especially at low collision energies, is not as important as had been suggested in previous work.
18. Vibrationally-resolved Charge Transfer of O^3+ Ions with Molecular Hydrogen
Science.gov (United States)
Wang, J. G.; Stancil, P. C.; Turner, A. R.; Cooper, D. L.
2003-05-01
Charge transfer processes due to collisions of ground state O^3+ ions with H2 are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. Vibrationally-resolved cross sections for energies between 0.1 eV/u and 2 keV/u using the infinite order sudden approximation (IOSA), vibrational sudden approximation (VSA), and electronic approximation (EA), but including Frank-Condon factors (the centroid approximation) will be presented. Comparison with existing experimental data for total cross sections shows best agreement with IOSA and discrepancies for VSA and EA. Triplet-singlet cross section ratios obtained with IOSA are found generally to be in harmony with experiment. JGW and PCS acknowledge support from NASA grant 11453.
19. Low Energy Charge Transfer for Collisions of Si3+ with Atomic Hydrogen
Energy Technology Data Exchange (ETDEWEB)
Bruhns, H. [Columbia University; Kreckel, H. [Columbia University; Savin, D. W. [Columbia University; Seely, D. G. [Albion College; Havener, Charles C [ORNL
2008-01-01
Cross sections of charge transfer for Si{sup 3+} ions with atomic hydrogen at collision energies of {approx} 40-2500 eV/u were carried out using a merged-beam technique at the Multicharged Ion Research Facility at Oak Ridge National Laboratory. The data span an energy range in which both molecular orbital close coupling (MOCC) and classical trajectory Monte Carlo (CTMC) calculations are available. The influence of quantum mechanical effects of the ionic core as predicted by MOCC is clearly seen in our results. However, discrepancies between our experiment and MOCC results toward higher collision energies are observed. At energies above 1000 eV/u good agreement is found with CTMC results.
20. Ab initio study of charge transfer in B2+ low-energy collisions with atomic hydrogen
International Nuclear Information System (INIS)
Turner, A.R.; Cooper, D.L.; Wang, J.G.; Stancil, P.C.
2003-01-01
Charge transfer processes due to collisions of ground state B 2+ (2s 2 S) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with the existing experiments shows our results to be in good agreement. When E 400 eV/u, inclusion of rotational coupling increases the total cross section by 50%-80%, improving the agreement between the current calculations and experiments. For state-selective cross sections, rotational coupling induces mixing between different symmetries; however, its effect, especially at low collision energies, is not as important as had been suggested in previous work
1. Dielectric Losses and Charge Transfer in Antimony-Doped TlGaS2 Single Crystal
Science.gov (United States)
Asadov, S. M.; Mustafaeva, S. N.
2018-03-01
Effect of semimetallic antimony (0.5 mol % Sb) on the dielectric properties and ac-conductivity of TlGaS2-based single crystals grown by the Bridgman-Stockbarger method has been studied. The experimental results on the frequency dispersion of dielectric coefficients and the conductivity of TlGa0.995Sb0.005S2 single crystals allowed the revealing of the dielectric loss nature, the charge transfer mechanism, and the estimation of the parameters of the states localized in the energy gap. The antimony-doping of the TlGaS2 single crystal leads to an increase in the density of states near the Fermi level and a decrease in the average time and average distance of hopes.
2. Manipulation of charge transfer and transport in plasmonic-ferroelectric hybrids for photoelectrochemical applications
Science.gov (United States)
Wang, Zhijie; Cao, Dawei; Wen, Liaoyong; Xu, Rui; Obergfell, Manuel; Mi, Yan; Zhan, Zhibing; Nasori, Nasori; Demsar, Jure; Lei, Yong
2016-01-01
Utilizing plasmonic nanostructures for efficient and flexible conversion of solar energy into electricity or fuel presents a new paradigm in photovoltaics and photoelectrochemistry research. In a conventional photoelectrochemical cell, consisting of a plasmonic structure in contact with a semiconductor, the type of photoelectrochemical reaction is determined by the band bending at the semiconductor/electrolyte interface. The nature of the reaction is thus hard to tune. Here instead of using a semiconductor, we employed a ferroelectric material, Pb(Zr,Ti)O3 (PZT). By depositing gold nanoparticle arrays and PZT films on ITO substrates, and studying the photocurrent as well as the femtosecond transient absorbance in different configurations, we demonstrate an effective charge transfer between the nanoparticle array and PZT. Most importantly, we show that the photocurrent can be tuned by nearly an order of magnitude when changing the ferroelectric polarization in PZT, demonstrating a versatile and tunable system for energy harvesting. PMID:26753764
3. Charge-transfer interaction mediated organogels from 18β-glycyrrhetinic acid appended pyrene
Directory of Open Access Journals (Sweden)
Jun Hu
2013-12-01
Full Text Available We describe herein the two-component charge-transfer (CT interaction induced organogel formation with 18β-glycyrrhetinic acid appended pyrene (GA-pyrene, 3 as the donor, and 2,4,7-trinitrofluorenone (TNF, 4 as the acceptor. The use of TNF (4 as a versatile electron acceptor in the formation of CT gels is demonstrated through the formation of gels in a variety of solvents. Thermal stability, stoichiometry, scanning electron microscopy (SEM, optical micrographs, and circular dichroism (CD are performed on these CT gels to investigate their thermal and assembly properties. UV–vis, fluorescence, mass spectrometric as well as variable-temperature 1H NMR experiments on these gels suggest that the CT interaction is one of the major driving forces for the formation of these organogels.
4. ZnO nanowires: Synthesis and charge transfer mechanism in the detection of ammonia vapour
Science.gov (United States)
Nancy Anna Anasthasiya, A.; Ramya, S.; Rai, P. K.; Jeyaprakash, B. G.
2018-01-01
ZnO nanowires with hexagonal wurtzite structure were grown on the glass substrate using Successive Ionic Layer Adsorption and Reaction (SILAR) method. Both experimental and theoretical studies demonstrated that NH3 chemisorbed and transferred the charge to the surface of the nanowire via its nitrogen site to the zinc site of ZnO nanowires, leading to the detection of NH3 vapour. The adsorbed ammonia dissociated into NH2 and H due to steric repulsion, and then into N2 and H2 gas. The formation of the N2 gas during the desorption process confirmed by observing peak at 14 and 28 m/z in the GC-MS spectrum.
5. Correlation between the Open-Circuit Voltage and Charge Transfer State Energy in Organic Photovoltaic Cells.
Science.gov (United States)
Zou, Yunlong; Holmes, Russell J
2015-08-26
In order to further improve the performance of organic photovoltaic cells (OPVs), it is essential to better understand the factors that limit the open-circuit voltage (VOC). Previous work has sought to correlate the value of VOC in donor-acceptor (D-A) OPVs to the interface energy level offset (EDA). In this work, measurements of electroluminescence are used to extract the charge transfer (CT) state energy for multiple small molecule D-A pairings. The CT state as measured from electroluminescence is found to show better correlation to the maximum VOC than EDA. The difference between EDA and the CT state energy is attributed to the Coulombic binding energy of the CT state. This correlation is demonstrated explicitly by inserting an insulating spacer layer between the donor and acceptor materials, reducing the binding energy of the CT state and increasing the measured VOC. These results demonstrate a direct correlation between maximum VOC and CT state energy.
6. Charge transfer complex states in diketopyrrolopyrrole polymers and fullerene blends: Implications for organic solar cell efficiency
Science.gov (United States)
Moghe, D.; Yu, P.; Kanimozhi, C.; Patil, S.; Guha, S.
2011-12-01
The spectral photocurrent characteristics of two donor-acceptor diketopyrrolopyrrole (DPP)-based copolymers (PDPP-BBT and TDPP-BBT) blended with a fullerene derivative [6,6]-phenyl C61-butyric acid methyl ester (PCBM) were studied using Fourier-transform photocurrent spectroscopy (FTPS) and monochromatic photocurrent (PC) method. PDPP-BBT:PCBM shows the onset of the lowest charge transfer complex (CTC) state at 1.42 eV, whereas TDPP-BBT:PCBM shows no evidence of the formation of a midgap CTC state. The FTPS and PC spectra of P3HT:PCBM are also compared. The larger singlet state energy difference of TDPP-BBT and PCBM compared to PDPP-BBT/P3HT and PCBM obliterates the formation of a midgap CTC state resulting in an enhanced photovoltaic efficiency over PDPP-BBT:PCBM.
7. Positron annihilation in liquids and in solutions containing electron acceptors and charge-transfer complexes
International Nuclear Information System (INIS)
Jansen, P.
1976-05-01
Positron lifetime measurements and angular correlation measurements were performed in several organic liquids. The results strongly indicate that positronium is contained in a 'bubble' in the liquids. The radius of the bubble can be estimated by using broadness of the narrow component in the angular correlation distribution, and by using the surface tension of the liquids. Both methods give bubble radii from 4-7 A in the solvents investigated. The bubble influences the reaction mechanism between Ps and weak electron acceptors in such a way that the presence of the bubble decreases the reactivity of Ps. Positron lifetime measurements were also performed on a series of mixtures of organic liquids and on electron acceptors and charge-transfer complexes in solution. The results were is agreement with the spur model of Ps formation. (Auth.)
8. The effect of interfacial charge transfer on ferromagnetism in perovskite oxide superlattices
Energy Technology Data Exchange (ETDEWEB)
Yang, F. [Univ. of California, Davis, CA (United States). Department of Chemical Engineering and Materials Science; Gu, M. [Univ. of California, Davis, CA (United States). Department of Chemical Engineering and Materials Science; Arenholz, E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS); Browning, N. D. [Univ. of California, Davis, CA (United States). Department of Molecular and Cellular Biology; Takamura, Y. [Univ. of California, Davis, CA (United States). Department of Chemical Engineering and Materials Science
2012-01-05
We investigate the structural, magnetic, and electrical properties of superlattices composed of the ferromagnetic/metal La0.7Sr0.3MnO3 and non-magnetic/metal La0.5Sr0.5TiO3 grown on (001)-oriented SrTiO3 substrates. Using a combination of bulk magnetometry, soft x-ray magnetic spectroscopy, and scanning transmission electron microscopy, we demonstrate that robust ferromagnetic properties can be maintained in this superlattice system where charge transfer at the interfaces is minimized. Thus, ferromagnetism can be controlled effectively through the chemical identity and the thickness of the individual superlattice layers.
9. Engineering high charge transfer n-doping of graphene electrodes and its application to organic electronics.
Science.gov (United States)
Sanders, Simon; Cabrero-Vilatela, Andrea; Kidambi, Piran R; Alexander-Webber, Jack A; Weijtens, Christ; Braeuninger-Weimer, Philipp; Aria, Adrianus I; Qasim, Malik M; Wilkinson, Timothy D; Robertson, John; Hofmann, Stephan; Meyer, Jens
2015-08-14
Using thermally evaporated cesium carbonate (Cs2CO3) in an organic matrix, we present a novel strategy for efficient n-doping of monolayer graphene and a ∼90% reduction in its sheet resistance to ∼250 Ohm sq(-1). Photoemission spectroscopy confirms the presence of a large interface dipole of ∼0.9 eV between graphene and the Cs2CO3/organic matrix. This leads to a strong charge transfer based doping of graphene with a Fermi level shift of ∼1.0 eV. Using this approach we demonstrate efficient, standard industrial manufacturing process compatible graphene-based inverted organic light emitting diodes on glass and flexible substrates with efficiencies comparable to those of state-of-the-art ITO based devices.
10. Intramolecular Charge-Transfer Interaction of Donor-Acceptor-Donor Arrays Based on Anthracene Bisimide.
Science.gov (United States)
Iwanaga, Tetsuo; Ogawa, Marina; Yamauchi, Tomokazu; Toyota, Shinji
2016-05-20
We designed anthracene bisimide (ABI) derivatives having two triphenylamine (TPA) groups as donor units at the 9,10-positions to form a novel π-conjugated donor-acceptor system. These compounds and their analogues with ethynylene linkers were synthesized by Suzuki-Miyaura and Sonogashira coupling reactions, respectively. In UV-vis spectra, the linker-free derivatives showed broad absorption bands arising from intramolecular charge-transfer interactions. Introducing ethynylene linkers resulted in a considerable red shift of the absorption bands. In fluorescence spectra, the ethynylene derivatives showed intense emission bands at 600-650 nm. Their photophysical and electrochemical properties were compared with those of the corresponding mono TPA derivatives on the basis of theoretical calculations and cyclic voltammetry to evaluate the intramolecular electronic interactions between the donor and acceptor units.
11. Supramolecular fullerene/porphyrin charge transfer interaction studied by absorption spectrophotometric method
Science.gov (United States)
Mukherjee, Partha; Bhattacharya (Banerjee), Shrabanti; Nayak, Sandip K.; Chattopadhyay, Subrata; Bhattacharya, Sumanta
2009-06-01
A detailed UV-Vis spectrometric and thermodynamic studies were done to look insight into the nature of molecular interactions of the electron donor-acceptor complexes of C60 and C70 with 5,10,15,20-tetrakis(octadecyloxyphenyl)-21H,23H-porphyrin (1) in chloroform and toluene. Charge transfer (CT) absorption bands were located in the visible region and vertical ionization potential of 1 was determined utilizing CT transition energy. Low values of oscillator and transition dipole strengths suggested that the complexes were almost of neutral character in ground states. The high binding constant value for the C70-1 complex indicated high selectivity of 1 molecule towards C70. Experimental as well as theoretically determined of enthalpies of formation value substantiated the trend in K values for fullerene-1 complexes.
12. Charge transfer from and to manganese phthalocyanine: bulk materials and interfaces
Directory of Open Access Journals (Sweden)
Florian Rückerl
2017-08-01
Full Text Available Manganese phthalocyanine (MnPc is a member of the family of transition-metal phthalocyanines, which combines interesting electronic behavior in the fields of organic and molecular electronics with local magnetic moments. MnPc is characterized by hybrid states between the Mn 3d orbitals and the π orbitals of the ligand very close to the Fermi level. This causes particular physical properties, different from those of the other phthalocyanines, such as a rather small ionization potential, a small band gap and a large electron affinity. These can be exploited to prepare particular compounds and interfaces with appropriate partners, which are characterized by a charge transfer from or to MnPc. We summarize recent spectroscopic and theoretical results that have been achieved in this regard.
13. Laser-induced charge transfer in the CH/sup 6 +/ quasimolecule
Energy Technology Data Exchange (ETDEWEB)
Errea, L.F.; Mendez, L.; Riera, A.
1985-05-15
The charge transfer cross section is calculated for C/sup 6 +/+CH(1s) collisions, through photon assisted 5gsigma--6hsigma, 5gsigma--4fsigma, 5gsigma--4f..pi.., and 5gsigma--4dsigma transitions. The theory developed by Copeland and Tang, and ourselves, is employed, and the validity of the approximations used is tested. The four processes considered have widely different characteristics with regards to the laser wavelength needed, the collision dynamics and the applicability of back-of-the-envelope estimates based on the Landau--Zener approximation. We point out the relevance of those processes to the impurity diagnostics of magnetically confined fusion plasmas and to the development of short wavelength lasers.
14. The role of molecular mobility in the transfer of charge generated by ionizing radiation in polymers
International Nuclear Information System (INIS)
Khatinov, S.A.; Edrisov, K.M.; Turdybekov, K.M.; Milinchuk, V.K.
1995-01-01
The dependence of radiation-induced electrical conductivity on the irradiation time and temperature was studied for a number of polymers. The character of variation of radiation-induced conductivity with time and temperature correlates with the physical state of a polymer. Defreezing of the segmental mobility in the region of α-relaxation transition leads to a sharp change in radiation-induced conductivity, and the appearance of peaks in the kinetic curves and break points on the Arrhenius plots in conductivity versus temperature coordinates. Molecular mobility plays a determining role in the transfer of charge carriers generated by radiation. This conclusion agrees with the data on the carrier mobility obtained by the time-of-flight methods. 24 refs., 8 figs
15. Annealing bounds to prevent further Charge Transfer Inefficiency increase of the Chandra X-ray CCDs
Energy Technology Data Exchange (ETDEWEB)
Monmeyran, Corentin, E-mail: [email protected] [Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Patel, Neil S., E-mail: [email protected] [Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Bautz, Mark W., E-mail: [email protected] [Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Grant, Catherine E., E-mail: [email protected] [Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Prigozhin, Gregory Y., E-mail: [email protected] [Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Agarwal, Anuradha, E-mail: [email protected] [Microphotonics Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Kimerling, Lionel C., E-mail: [email protected] [Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Microphotonics Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2016-12-15
After the front-illuminated CCDs on board the X-ray telescope Chandra were damaged by radiation after launch, it was decided to anneal them in an effort to remove the defects introduced by the irradiation. The annealing led to an unexpected increase of the Charge Transfer Inefficiency (CTI). The performance degradation is attributed to point defect interactions in the devices. Specifically, the annealing at 30 °C activated the diffusion of the main interstitial defect in the device, the carbon interstitial, which led to its association with a substitutional impurity, ultimately resulting in a stable and electrically active defect state. Because the formation reaction of this carbon interstitial and substitutional impurity associate is diffusion limited, we recommend a higher upper bound for the annealing temperature and duration of any future CCD anneals, that of −50 °C for one day or −60 °C for a week, to prevent further CTI increase.
16. Nanoscale charge transfer in redox proteins and DNA: Towards biomolecular electronics
International Nuclear Information System (INIS)
Artés, Juan Manuel; López-Martínez, Montserrat; Díez-Pérez, Ismael; Sanz, Fausto; Gorostiza, Pau
2014-01-01
Understanding how charges move through and between biomolecules is a fundamental question that constitutes the basis for many biological processes. On the other hand, it has potential applications in the design of sensors based on biomolecules and single molecule devices. In this review we introduce the study of the electron transfer (ET) process in biomolecules, providing an overview of the fundamental theory behind it and the different experimental approaches. The ET in proteins is introduced by reviewing a complete electronic characterization of a redox protein (azurin) using electrochemical scanning tunnelling microscopy (ECSTM). The ET process in DNA is overviewed and results from different experimental approaches are discussed. Finally, future directions in the study of the ET process in biomolecules are introduced as well as examples of possible technological applications
17. Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory
Science.gov (United States)
Gould, Tim; Kronik, Leeor; Pittalis, Stefano
2018-05-01
By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.
18. Robust singlet fission in pentacene thin films with tuned charge transfer interactions.
Science.gov (United States)
Broch, K; Dieterle, J; Branchi, F; Hestand, N J; Olivier, Y; Tamura, H; Cruz, C; Nichols, V M; Hinderhofer, A; Beljonne, D; Spano, F C; Cerullo, G; Bardeen, C J; Schreiber, F
2018-03-05
Singlet fission, the spin-allowed photophysical process converting an excited singlet state into two triplet states, has attracted significant attention for device applications. Research so far has focused mainly on the understanding of singlet fission in pure materials, yet blends offer the promise of a controlled tuning of intermolecular interactions, impacting singlet fission efficiencies. Here we report a study of singlet fission in mixtures of pentacene with weakly interacting spacer molecules. Comparison of experimentally determined stationary optical properties and theoretical calculations indicates a reduction of charge-transfer interactions between pentacene molecules with increasing spacer molecule fraction. Theory predicts that the reduced interactions slow down singlet fission in these blends, but surprisingly we find that singlet fission occurs on a timescale comparable to that in pure crystalline pentacene. We explain the observed robustness of singlet fission in such mixed films by a mechanism of exciton diffusion to hot spots with closer intermolecular spacings.
19. Charge-Transfer Processes in Warm Dense Matter: Selective Spectral Filtering for Laser-Accelerated Ion Beams
Science.gov (United States)
Braenzel, J.; Barriga-Carrasco, M. D.; Morales, R.; Schnürer, M.
2018-05-01
We investigate, both experimentally and theoretically, how the spectral distribution of laser accelerated carbon ions can be filtered by charge exchange processes in a double foil target setup. Carbon ions at multiple charge states with an initially wide kinetic energy spectrum, from 0.1 to 18 MeV, were detected with a remarkably narrow spectral bandwidth after they had passed through an ultrathin and partially ionized foil. With our theoretical calculations, we demonstrate that this process is a consequence of the evolution of the carbon ion charge states in the second foil. We calculated the resulting spectral distribution separately for each ion species by solving the rate equations for electron loss and capture processes within a collisional radiative model. We determine how the efficiency of charge transfer processes can be manipulated by controlling the ionization degree of the transfer matter.
20. Heat transfer enhancement of phase change materials by fins under simultaneous charging and discharging
International Nuclear Information System (INIS)
Joybari, Mahmood Mastani; Haghighat, Fariborz; Seddegh, Saeid; Al-Abidi, Abduljalil A.
2017-01-01
Highlights: • CFD simulation of a finned triplex tube heat exchanger with PCM under simultaneous charging and discharging. • Developed fin configurations for SCD, compatible with natural convection. • More fins enhanced the heat transfer as long as natural convection was not suppressed. • Longer fins enhanced the heat transfer as long as natural convection was not suppressed. • The effect of fin thickness was negligible, similar to non-SCD conditions. - Abstract: Due to the inherent intermittency of renewable energy sources such as solar, latent heat thermal energy storage in phase change materials (PCMs) has received considerable attention. Among several techniques to enhance PCMs’ thermal conductivity, the majority of studies have focused on fin integration due to its simplicity, ease of manufacturing, and low cost. In this study, utilization of extended surfaces (by longitudinal fins) was investigated by development of a numerical model to study the performance of a triplex tube heat exchanger (TTHX) equipped with a PCM under simultaneous charging and discharging (SCD). Governing equations were developed and numerically solved using ANSYS Fluent v16.2. Three conventional fin geometries and six developed fin configurations were compared based on the temperature, liquid fraction, and natural convection behavior under both SCD and non-SCD conditions. The intensity of natural convection was investigated for different fins for the inside heating/outside cooling scenario based on the solid–liquid interface evolution over time. The results indicated that since the buoyancy forces induce upward melted PCM motion, the inner hot tube requires fins on its lower half, while the outer cold one should be extended from its upper half. It was concluded that the case with 3 hot tube fins and 1 cold tube fin is most compatible with natural convection and provides the best performance under SCD conditions.
1. Spectroscopic study of the charge-transfer complexes TiCl4/styrene and TiCl4/polystyrene
Science.gov (United States)
Gonçalves, Norberto S.; Noda, Lúcia. K.
2017-10-01
In this work, solutions of TiCl4/styrene and TiCl4/polystyrene charge-transfer complexes in CHCl3 or CDCl3 were investigated by UV-vis, resonance Raman and 1H NMR spectroscopies in order to study their molecular and electronic structures. Both show a yellow colour due to absorption in the 400 nm region, related to a charge-transfer transition. In Raman spectra, as the excitation approaches the resonance region, the primary enhancement of aromatic ring modes was mainly observed, rather than intensification of the vinylic double-bond stretch. Under the experimental conditions it was observed that formation of polystyrene takes place, as showed by 1H NMR spectra, and the most significant interaction occurs at the aromatic ring, as supported by the results from interaction of TiCl4 with polystyrene, as indicated by the charge-transfer band and resonant intensification of the aromatic ring modes.
2. Direct evidence for radiative charge transfer after inner-shell excitation and ionization of large clusters
Science.gov (United States)
Hans, Andreas; Stumpf, Vasili; Holzapfel, Xaver; Wiegandt, Florian; Schmidt, Philipp; Ozga, Christian; Reiß, Philipp; Ben Ltaief, Ltaief; Küstner-Wetekam, Catmarna; Jahnke, Till; Ehresmann, Arno; Demekhin, Philipp V.; Gokhberg, Kirill; Knie, André
2018-01-01
We directly observe radiative charge transfer (RCT) in Ne clusters by dispersed vacuum-ultraviolet photon detection. The doubly ionized Ne2+-{{{N}}{{e}}}n-1 initial states of RCT are populated after resonant 1s-3p photoexcitation or 1s photoionization of Ne n clusters with ≈ 2800. These states relax further producing Ne+-Ne+-{{{N}}{{e}}}n-2 final states, and the RCT photon is emitted. Ab initio calculations assign the observed RCT signal to the{}{{{N}}{{e}}}2+(2{{{p}}}-2{[}1{{D}}]){--}{{{N}}{{e}}}n-1 initial state, while transitions from other possible initial states are proposed to be quenched by competing relaxation processes. The present results are in agreement with the commonly discussed scenario, where the doubly ionized atom in a noble gas cluster forms a dimer which dissipates its vibrational energy on a picosecond timescale. Our study complements the picture of the RCT process in weakly bound clusters, providing information which is inaccessible by charged particle detection techniques.
3. Charge transfer effects of ions at the liquid water/vapor interface
Energy Technology Data Exchange (ETDEWEB)
Soniat, Marielle; Rick, Steven W., E-mail: [email protected] [Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (United States)
2014-05-14
Charge transfer (CT), the movement of small amounts of electron density between non-bonded pairs, has been suggested as a driving force for a variety of physical processes. Herein, we examine the effect of CT on ion adsorption to the water liquid-vapor interface. Using a CT force field for molecular dynamics, we construct a potential of mean force (PMF) for Na{sup +}, K{sup +}, Cl{sup −}, and I{sup −}. The PMFs were produced with respect to an average interface and an instantaneous interface. An analysis of the PMF relative to the instantaneous surface reveals that the area in which the anions experience a free energy minimum is quite narrow, and the cations feel a steeply repulsive free energy near the interface. CT is seen to have only minor effects on the overall free energy profiles. However, the long-ranged effects of ions are highlighted by the CT model. Due to CT, the water molecules at the surface become charged, even when the ion is over 15 Å away from the surface.
4. Photophysical study of a charge transfer oxazole dye in micelles: Role of surfactant headgroups
Energy Technology Data Exchange (ETDEWEB)
Maiti, Jyotirmay [Department of Chemistry, West Bengal State University, Barasat, Kolkata 700126 (India); Sarkar, Yeasmin; Parui, Partha Pratim [Department of Chemistry, Jadavpur University, Kolkata 700032 (India); Chakraborty, Sandipan [Department of Microbiology, University of Calcutta, Kolkata 700019 (India); Biswas, Suman [Department of Chemistry, West Bengal State University, Barasat, Kolkata 700126 (India); Das, Ranjan, E-mail: [email protected] [Department of Chemistry, West Bengal State University, Barasat, Kolkata 700126 (India)
2015-07-15
Photophysics of 5-(4′′-dimethylaminophenyl)-2-(4′-sulfophenyl)oxazole, sodium salt (DMO) which undergoes intramolecular charge transfer in the excited state was studied in micelles. In the cationic and the nonionic micelles, significantly higher fluorescence quantum yield is observed in comparison to the anionic micelles, due to much lower accessibility of DMO to the water molecules in the former micelles than the latter. Time-resolved fluorescence decays were characterized by a fast (τ{sub 1}) and a slow (τ{sub 2}) component of decay in all the micelles. The fast decay component (τ{sub 1}) increases significantly in going from the anionic micelles to the cationic micelles, because of the poorly hydrated headgroup region of the latter micelles compared to the former. Furthermore, much higher value of the slow component of decay (τ{sub 2}) is observed for the cationic and the neutral micelles than the anionic micelles. This is attributed to the increased penetration of water molecules into the micellar core of the anionic micelles compared to the cationic and the neutral micelles. - Highlights: • Photophysics of the fluorophore are remarkably different in the cationic and the anionic micelles. • Differential hydration of the surfactant headgroups gives rise to significantly different fluorescence quantum yield and lifetime in oppositely charged micelles. • Electrostatic interactions fine tune location of the fluorophore in the micelle–water interface of ionic micelles.
5. A charge transfer complex nematic liquid crystalline gel with high electrical conductivity
International Nuclear Information System (INIS)
Bhargavi, R.; Nair, Geetha G.; Krishna Prasad, S.; Majumdar, R.; Bag, Braja G.
2014-01-01
We describe the rheological, dielectric and elastic properties of a nematic liquid crystal gel created using an anthrylidene derivative of arjunolic acid, a chiral triterpenoid, obtained from the extracts of the wood of Terminalia arjuna. In this novel gel, having the electron-donor and acceptor components as minority constituents, the gelation and strengthening of charge-transfer complex (CTC) formation are seen to be occurring concomitantly. In addition to being mechanically strong with a large storage modulus, the gel with the maximized CTC exhibits Frank bend elastic constant values that approach nanonewton levels. The highlight of the study is the observation of 4–5 orders of magnitude increase in electrical conductivity for this gel, a value that is higher than even in the CT complexes of 2-d ordered columnar structures. A further important advantage of the present system over the columnar complex is that the high conductivity is seen for ac probing also, and owing to the nematic nature can be switched between its anisotropic limits. Some of these features are ascribed to a specific molecular packing architecture, which reduces the trapping of the charge carriers.
6. A charge transfer complex nematic liquid crystalline gel with high electrical conductivity
Science.gov (United States)
Bhargavi, R.; Nair, Geetha G.; Krishna Prasad, S.; Majumdar, R.; Bag, Braja G.
2014-10-01
We describe the rheological, dielectric and elastic properties of a nematic liquid crystal gel created using an anthrylidene derivative of arjunolic acid, a chiral triterpenoid, obtained from the extracts of the wood of Terminalia arjuna. In this novel gel, having the electron-donor and acceptor components as minority constituents, the gelation and strengthening of charge-transfer complex (CTC) formation are seen to be occurring concomitantly. In addition to being mechanically strong with a large storage modulus, the gel with the maximized CTC exhibits Frank bend elastic constant values that approach nanonewton levels. The highlight of the study is the observation of 4-5 orders of magnitude increase in electrical conductivity for this gel, a value that is higher than even in the CT complexes of 2-d ordered columnar structures. A further important advantage of the present system over the columnar complex is that the high conductivity is seen for ac probing also, and owing to the nematic nature can be switched between its anisotropic limits. Some of these features are ascribed to a specific molecular packing architecture, which reduces the trapping of the charge carriers.
7. Frequency dependent magneto-transport in charge transfer Co(II) complex
Energy Technology Data Exchange (ETDEWEB)
Shaw, Bikash Kumar; Saha, Shyamal K., E-mail: [email protected]
2014-09-01
A charge transfer chelated system containing ferromagnetic metal centers is the ideal system to investigate the magneto-transport and magneto-dielectric effects due to the presence of both electronic as well as magnetic properties and their coupling. Magneto-transport properties in materials are usually studied through dc charge transport under magnetic field. As frequency dependent conductivity is an essential tool to understand the nature of carrier wave, its spatial extension and their mutual interaction, in the present work, we have investigated frequency dependent magneto-transport along with magnetization behavior in [Co{sub 2}(II)-(5-(4-PhMe)-1,3,4-oxadiazole-H{sup +}-2-thiolate){sub 5}](OAc){sub 4} metal complex to elucidate the nature of above quantities and their response under magnetic field in the transport property. We have used the existing model for ac conduction incorporating the field dependence to explain the frequency dependent magneto-transport. It is seen that the frequency dependent magneto-transport could be well explained using the existing model for ac conduction. -Highlights: • Chelated Co(II) complex is synthesized for magneto-transport applications. • Frequency dependent magneto-transport and magnetization behavior are studied. • Nature of carrier wave, its spatial extension is investigated under magnetic field. • Existing model for ac conduction is used with magnetic field dependence.
8. The charge transfer induced by Cr doping in MgB2
International Nuclear Information System (INIS)
Zhang Huarong; Zhao Jiyin; Shi Lei
2005-01-01
Mg 1-x Cr x B 2 polycrystal bulk samples with 0 x 5% have been synthesized by a solid-state reaction and studied by X-ray diffraction, SEM and Raman spectrum. It is found that the c-axis of the lattice decreases as the Cr content increases, while the a-axis remains unchanged. Moreover, crystal grain size increases apparently with Cr doping concentration increase. The normal-state resistivity increases and the superconducting transition temperature (T c ) decreases from 38.2 K (x = 0) to 35.1 K (x 0.03) with the increase of Cr content. It is suggested that the charge transfer between the Mg-layer and the B-layer causes the decrease of the charge carrier concentration and induces the changes of T c and normal-state resistivity. On the other hand, by the Raman scattering study, it is found that the linewidth of Raman spectrum increases with the increase of Cr content, which is resulted by the competition between the electron-phonon interaction and substitution-induced disorder. The Raman peak has no evident shift due to the countervailing between the effects of the electron-phonon coupling and the grain size
9. Engineering Interfacial Charge Transfer in CsPbBr3 Perovskite Nanocrystals by Heterovalent Doping.
Science.gov (United States)
Begum, Raihana; Parida, Manas R; Abdelhady, Ahmed L; Murali, Banavoth; Alyami, Noktan M; Ahmed, Ghada H; Hedhili, Mohamed Nejib; Bakr, Osman M; Mohammed, Omar F
2017-01-18
Since compelling device efficiencies of perovskite solar cells have been achieved, investigative efforts have turned to understand other key challenges in these systems, such as engineering interfacial energy-level alignment and charge transfer (CT). However, these types of studies on perovskite thin-film devices are impeded by the morphological and compositional heterogeneity of the films and their ill-defined surfaces. Here, we use well-defined ligand-protected perovskite nanocrystals (NCs) as model systems to elucidate the role of heterovalent doping on charge-carrier dynamics and energy level alignment at the interface of perovskite NCs with molecular acceptors. More specifically, we develop an in situ doping approach for colloidal CsPbBr 3 perovskite NCs with heterovalent Bi 3+ ions by hot injection to precisely tune their band structure and excited-state dynamics. This synthetic method allowed us to map the impact of doping on CT from the NCs to different molecular acceptors. Using time-resolved spectroscopy with broadband capability, we clearly demonstrate that CT at the interface of NCs can be tuned and promoted by metal ion doping. We found that doping increases the energy difference between states of the molecular acceptor and the donor moieties, subsequently facilitating the interfacial CT process. This work highlights the key variable components not only for promoting interfacial CT in perovskites, but also for establishing a higher degree of precision and control over the surface and the interface of perovskite molecular acceptors.
10. Engineering Interfacial Charge Transfer in CsPbBr3 Perovskite Nanocrystals by Heterovalent Doping
KAUST Repository
Begum, Raihana
2016-12-17
Since compelling device efficiencies of perovskite solar cells have been achieved, investigative efforts have turned to understand other key challenges in these systems, such as engineering interfacial energy-level alignment and charge transfer (CT). However, these types of studies on perovskite thin-film devices are impeded by the morphological and compositional heterogeneity of the films and their ill-defined surfaces. Here, we use well-defined ligand-protected perovskite nanocrystals (NCs) as model systems to elucidate the role of heterovalent doping on charge-carrier dynamics and energy level alignment at the interface of perovskite NCs with molecular acceptors. More specifically, we develop an in situ doping approach for colloidal CsPbBr3 perovskite NCs with heterovalent Bi3+ ions by hot injection to precisely tune their band structure and excited-state dynamics. This synthetic method allowed us to map the impact of doping on CT from the NCs to different molecular acceptors. Using time-resolved spectroscopy with broadband capability, we clearly demonstrate that CT at the interface of NCs can be tuned and promoted by metal ion doping. We found that doping increases the energy difference between states of the molecular acceptor and the donor moieties, subsequently facilitating the interfacial CT process. This work highlights the key variable components not only for promoting interfacial CT in perovskites, but also for establishing a higher degree of precision and control over the surface and the interface of perovskite molecular acceptors.
11. A how-to approach for a 3D simulation of charge transfer characteristics in a gas electron multiplier (GEM)
CERN Document Server
Sharma, A
1999-01-01
In this paper a detailed description of how to simulate charge transfer processes in a gaseous device is presented, taking the gas electron multiplier (GEM) as an example. A 3-dimensional simulation of the electric field and avalanche is performed. Results on charge transport are compared to experiment and agree within experimental errors; the avalanche mechanism and positive ion feedback are studied. The procedures used in the simulation are described in detail, and program scripts are appended. (15 refs).
12. Solvent control of charge transfer excited state relaxation pathways in [Fe(2,2 '-bipyridine)(CN)4]2-
DEFF Research Database (Denmark)
Kjær, Kasper Skov; Kunnus, Kristjan; Harlang, Tobias C. B.
2018-01-01
The excited state dynamics of solvated [Fe(bpy)(CN)4]2-, where bpy = 2,2'-bipyridine, show significant sensitivity to the solvent Lewis acidity. Using a combination of optical absorption and X-ray emission transient spectroscopies, we have previously shown that the metal to ligand charge transfer...... the MLCT excited state relaxation dynamics of [Fe(bpy)(CN)4]2- in water, a strong Lewis acid solvent. The charge-transfer excited state is now found to decay in less than 100 femtoseconds, forming a quasi-stable metal centered excited state with a 13 picosecond lifetime. We find that this MC excited state...... developed for solar applications....
13. Charge transfer processes in hybrid solar cells composed of amorphous silicon and organic materials
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Sebastian; Neher, Dieter [Universitaet Potsdam, Inst. Physik u. Astronomie, Karl-Liebknecht-Strasse 24/25, 14467 Potsdam-Golm (Germany); Schulze, Tim; Korte, Lars [Helmholtz Zentrum Berlin, Inst. fuer Silizium Photovoltaik, Kekulestrasse 5, 12489 Berlin (Germany)
2011-07-01
The efficiency of hybrid solar cells composed of organic materials and amorphous hydrogenated silicon (a-Si:H) strongly depends upon the efficiency of charge transfer processes at the inorganic-organic interface. We investigated the performance of devices comprising an ITO/a-Si:H(n-type)/a-Si:H(intrinsic)/organic/metal multilayer structure and using two different organic components: zinc phthalocyanine (ZnPc) and poly(3-hexylthiophene) (P3HT). The results show higher power conversion- and quantum efficiencies for the P3HT based cells, compared to ZnPc. This can be explained by larger energy-level offset at the interface between the organic layer and a-Si:H, which facilitates hole transfer from occupied states in the valence band tail to the HOMO of the organic material and additionally promotes exciton splitting. The performance of the a-Si:H/P3HT cells can be further improved by treatment of the amorphous silicon surface with hydrofluoric acid (HF) and p-type doping of P3HT with F4TCNQ. The improved cells reached maximum power conversion efficiencies of 1%.
14. Direct evidence of charge separation in a metal-organic framework: efficient and selective photocatalytic oxidative coupling of amines via charge and energy transfer.
Science.gov (United States)
Xu, Caiyun; Liu, Hang; Li, Dandan; Su, Ji-Hu; Jiang, Hai-Long
2018-03-28
The selective aerobic oxidative coupling of amines under mild conditions is an important laboratory and commercial procedure yet a great challenge. In this work, a porphyrinic metal-organic framework, PCN-222, was employed to catalyze the reaction. Upon visible light irradiation, the semiconductor-like behavior of PCN-222 initiates charge separation, evidently generating oxygen-centered active sites in Zr-oxo clusters indicated by enhanced porphyrin π-cation radical signals. The photogenerated electrons and holes further activate oxygen and amines, respectively, to give the corresponding redox products, both of which have been detected for the first time. The porphyrin motifs generate singlet oxygen based on energy transfer to further promote the reaction. As a result, PCN-222 exhibits excellent photocatalytic activity, selectivity and recyclability, far superior to its organic counterpart, for the reaction under ambient conditions via combined energy and charge transfer.
15. DFT and TD-DFT computation of charge transfer complex between o-phenylenediamine and 3,5-dinitrosalicylic acid
International Nuclear Information System (INIS)
2016-01-01
DFT and TD-DFT studies of o-phenylenediamine (PDA), 3,5-dinitrosalicylic acid (DNSA) and their charge transfer complex have been carried out at B3LYP/6-311G(d,p) level of theory. Molecular geometry and various other molecular properties like natural atomic charges, ionization potential, electron affinity, band gap, natural bond orbital (NBO) and frontier molecular analysis have been presented at same level of theory. Frontier molecular orbital and natural bond orbital analysis show the charge delocalization from PDA to DNSA.
16. Hydrogen-transfer and charge-transfer in photochemical and radiation induced reactions. Progress report, November 1, 1975--October 31, 1976
International Nuclear Information System (INIS)
Cohen, S.G.
1976-10-01
The relative importance of light absorption, quenching of triplet, and hydrogen transfer repair has been examined in retardation by mercaptans of photoreduction of aromatic ketones by alcohols. In the reduction of benzophenone by 2-propanol, retardation is efficient and, after correction for the first two effects, is due entirely to hydrogen-transfer repair, as indicated by deuterium labeling. In reduction of acetophenone by α-methylbenzyl alcohol, repair by hydrogen transfer is also operative. In reduction of benzophenone by benzhydrol, retardation is less efficient and is due to quenching, as the ketyl radical does not abstract hydrogen from mercaptan rapidly in competition with coupling. Deuterium isotope effects are discussed in terms of competitive reactions. Photoreduction of benzophenone by 2-butylamine and by triethylamine is retarded by aromatic mercaptans and disulfides. Of the retardation not due to light absorption and triplet quenching by the sulfur compounds, half is due to hydrogen-transfer repair, as indicated by racemization and deuterium labeling. The remainder is attributed to quenching by the sulfur compound of the charge-transfer-complex intermediate. Photoreduction by primary and secondary amines, but not by tertiary amines, is accelerated by aliphatic mercaptans. The acceleration is attributed to catalysis of hydrogen transfer by the mercaptan in the charge-transfer complex. The effect is large in hydrocarbon solvent, less in polar organic solvents and absent in water
17. Laboratory estimation of net trophic transfer efficiencies of PCB congeners to lake trout (Salvelinus namaycush) from its prey
Science.gov (United States)
Madenjian, Charles P.; Rediske, Richard R.; O'Keefe, James P.; David, Solomon R.
2014-01-01
A technique for laboratory estimation of net trophic transfer efficiency (γ) of polychlorinated biphenyl (PCB) congeners to piscivorous fish from their prey is described herein. During a 135-day laboratory experiment, we fed bloater (Coregonus hoyi) that had been caught in Lake Michigan to lake trout (Salvelinus namaycush) kept in eight laboratory tanks. Bloater is a natural prey for lake trout. In four of the tanks, a relatively high flow rate was used to ensure relatively high activity by the lake trout, whereas a low flow rate was used in the other four tanks, allowing for low lake trout activity. On a tank-by-tank basis, the amount of food eaten by the lake trout on each day of the experiment was recorded. Each lake trout was weighed at the start and end of the experiment. Four to nine lake trout from each of the eight tanks were sacrificed at the start of the experiment, and all 10 lake trout remaining in each of the tanks were euthanized at the end of the experiment. We determined concentrations of 75 PCB congeners in the lake trout at the start of the experiment, in the lake trout at the end of the experiment, and in bloaters fed to the lake trout during the experiment. Based on these measurements, γ was calculated for each of 75 PCB congeners in each of the eight tanks. Mean γ was calculated for each of the 75 PCB congeners for both active and inactive lake trout. Because the experiment was replicated in eight tanks, the standard error about mean γ could be estimated. Results from this type of experiment are useful in risk assessment models to predict future risk to humans and wildlife eating contaminated fish under various scenarios of environmental contamination.
18. Through space and through bridge channels of charge transfer at p-n nano-junctions: A DFT study
Energy Technology Data Exchange (ETDEWEB)
Dandu, Naveen [Department of Chemistry and Biochemistry, NDSU, Fargo, ND 58108 (United States); Tretiak, Sergei [Theoretical Division, Center for Nonlinear Studies (CNLS) and Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, 57069, NM 87454 (United States); Kilina, Svetlana [Department of Chemistry and Biochemistry, NDSU, Fargo, ND 58108 (United States); Kilin, Dmitri, E-mail: [email protected] [Department of Chemistry and Biochemistry, NDSU, Fargo, ND 58108 (United States)
2016-12-20
Highlights: • Properties of interacting QDs depend on the fashion of interaction: through-bond or through-space. • The disconnected and undoped dimer models shows FÓ§rster band formation. • Dimer models with some doping exhibit degenerate charge-transfer excitons. • p- and n-doped qds shows polarization at the interface. • A photoexcitation polarizes p-n interface, in relation to phototovoltaic effect. - Abstract: Details of charge density distribution at p-n nano interface are analyzed with density functional theory techniques using model system of dimers of doped silicon quantum dots interacting through bond and through space. Spatial distributions of transition densities between the ground and excited states suggest the character of essential electronic excitations, which have a FÓ§rster, bound, unbound, or charge transfer character. A redistribution of electronic density from n-impurities to p-impurities results in a ground state polarization and creates an offset of energies of the bands localized on p-doped quantum dot and the bands localized on n-doped quantum dot. Although impurities contribute very few orbitals to the total density, a ground state charge redistribution and polarization are both responsible for the presence of a large number of charge transfer excitations involving solely silicon orbitals.
19. Charge transfer effects, thermo and photochromism in single crystal CVD synthetic diamond.
Science.gov (United States)
Khan, R U A; Martineau, P M; Cann, B L; Newton, M E; Twitchen, D J
2009-09-09
We report on the effects of thermal treatment and ultraviolet irradiation on the point defect concentrations and optical absorption profiles of single crystal CVD synthetic diamond. All thermal treatments were below 850 K, which is lower than the growth temperature and unlikely to result in any structural change. UV-visible absorption spectroscopy measurements showed that upon thermal treatment (823 K), various broad absorption features diminished: an absorption band at 270 nm (used to deduce neutral single substitutional nitrogen (N(S)(0)) concentrations) and also two broad features centred at approximately 360 and 520 nm. Point defect centre concentrations as a function of temperature were also deduced using electron paramagnetic resonance (EPR) spectroscopy. Above ∼500 K, we observed a decrease in the concentration of N(S)(0) centres and a concomitant increase in the negatively charged nitrogen-vacancy-hydrogen (NVH) complex (NVH(-)) concentration. Both transitions exhibited an activation energy between 0.6 and 1.2 eV, which is lower than that for the N(S)(0) donor (∼1.7 eV). Finally, it was found that illuminating samples with intense short-wave ultraviolet light recovered the N(S)(0) concentration and also the 270, 360 and 520 nm absorption features. From these results, we postulate a valence band mediated charge transfer process between NVH and single nitrogen centres with an acceptor trap depth for NVH of 0.6-1.2 eV. Because the loss of N(S)(0) concentration is greater than the increase in NVH(-) concentration we also suggest the presence of another unknown acceptor existing at a similar energy to NVH. The extent to which the colour in CVD synthetic diamond is dependent on prior history is discussed.
20. Synthesis, growth, structural modeling and physio-chemical properties of a charge transfer molecule: Guanidinium tosylate
Science.gov (United States)
Era, Paavai; Jauhar, RO. MU.; Vinitha, G.; Murugakoothan, P.
2018-05-01
An organic nonlinear optical material, guanidinium tosylate was synthesized adopting slow evaporation method and the crystals were harvested from aqueous methanolic medium with dimensions 13 × 9 × 3 mm3. Constitution of crystalline material was confirmed by single crystal X-ray diffraction study. The title compound crystallizes in the monoclinic crystal system with space group P21/c. The UV-vis-NIR spectral study of the grown crystal exhibits high transparency of 80% in the entire visible region with lower cut-off wavelength at 282 nm. Optimized molecular geometry of the grown crystal was obtained using density functional theory (DFT) and the frontier energy gaps calculated from the DFT aids to understand the charge transfer taking place in the molecule. The dielectric properties were studied as a function of temperature and frequency to find the charge distribution within the crystal. The titular compound is thermally stable up to 230 °C assessed by thermogravimetric and differential thermal analysis. Anisotropy in the mechanical behavior was observed while measuring for individual planes. The laser induced surface damage threshold of the grown crystal was measured to be 0.344 GW/cm2 for 1064 nm Nd:YAG laser radiation. Z-scan technique confirms the third-order nonlinear optical property with the ascertained nonlinear refractive index (n2), nonlinear absorption coefficient (β) and third order nonlinear susceptibility (χ(3)). Optical limiting study divulges that the transmitted output power step-up linearly with the increase of the input power at lower power realms and saturates from the threshold 24.95 mW/cm2 and amplitude 0.23 mW/cm2.
1. Evidence for excited state intramolecular charge transfer in benzazole-based pseudo-stilbenes.
Science.gov (United States)
Santos, Fabiano da Silveira; Descalzo, Rodrigo Roceti; Gonçalves, Paulo Fernando Bruno; Benvenutti, Edilson Valmir; Rodembusch, Fabiano Severo
2012-08-21
Two azo compounds were obtained through the diazotization reaction of aminobenzazole derivatives and N,N-dimethylaniline using clay montmorillonite KSF as catalyst. The synthesized dyes were characterized using elemental analysis, Fourier transform infrared spectroscopy, and (13)C and (1)H NMR spectroscopy in solution. Their photophysical behavior was studied using UV-vis and steady-state fluorescence in solution. These dyes present intense absorption in the blue region. The spectral features of the azo compounds can be related to the pseudo-stilbene type as well as the E isomer of the dyes. Excitation at the absorption maxima does not produce emissive species in the excited state. However, excitation around 350 nm allowed dual emission of fluorescence, from both a locally excited (LE, short wavelength) and an intramolecular charge transfer (ICT, long wavelength) state, which was corroborated by a linear relation of the fluorescence maximum (ν(max)) versus the solvent polarity function (Δf) from the Lippert-Mataga correlation. Evidence of TICT in these dyes was discussed from the viscosity dependence of the fluorescence intensity in the ICT emission band. Theoretical calculations were also performed in order to study the geometry and charge distribution of the dyes in their ground and excited electronic states. Using DFT methods at the theoretical levels BLYP/Aug-cc-pVDZ, for geometry optimizations and frequency calculations, and B3LYP/6-311+G(2d), for single-point energy evaluations, the calculations revealed that the least energetic and most intense photon absorption leads to a very polar excited state that relaxes non-radioactively, which can be associated with photochemical isomerization.
2. Organic charge transfer phase formation in thin films of the BEDT-TTF/TCNQ donor-acceptor system
DEFF Research Database (Denmark)
Solovyeva, Vita; Keller, K.; Huth, M.
2009-01-01
We have performed charge transfer phase formation studies on the donor/acceptor system bis-(ethylendithio)tetrathiafulvalene (BEDT-TTF)/tetracyanoquinodimethane,(TCNQ) by means of physical vapor deposition. We prepared donor/acceptor bilayer structures on glass and Si(100)/SiO substrates held...
3. Impact of exact exchange in the description of the electronic structure of organic charge-transfer molecular crystals
KAUST Repository
Fonari, Alexandr; Sutton, Christopher; Bredas, Jean-Luc; Coropceanu, Veaceslav
2014-01-01
in high-mobility organic crystals. We consider both crystals based on a single molecule, such as pentacene, and crystals based on mixed-stack charge-transfer systems, such as dibenzo-TTF–TCNQ. In the pentacene crystal, the band gap decreases
4. Determination of charge transfer resistance and capacitance of microbial fuel cell through a transient response analysis of cell voltage.
Science.gov (United States)
Ha, Phuc Thi; Moon, Hyunsoo; Kim, Byung Hong; Ng, How Yong; Chang, In Seop
2010-03-15
An alternative method for determining the charge transfer resistance and double-layer capacitance of microbial fuel cells (MFCs), easily implemented without a potentiostat, was developed. A dynamic model with two parameters, the charge transfer resistance and double-layer capacitance of electrodes, was derived from a linear differential equation to depict the current generation with respect to activation overvoltage. This model was then used to fit the transient cell voltage response to the current step change during the continuous operation of a flat-plate type MFC fed with acetate. Variations of the charge transfer resistance and the capacitance value with respect to the MFC design conditions (biocatalyst existence and electrode area) and operating parameters (acetate concentration and buffer strength in the catholyte) were then determined to elucidate the validity of the proposed method. This model was able to describe the dynamic behavior of the MFC during current change in the activation loss region; having an R(2) value of over 0.99 in most tests. Variations of the charge transfer resistance value (thousands of Omega) according to the change of the design factors and operational factors were well-correlated with the corresponding MFC performances. However, though the capacitance values (approximately 0.02 F) reflected the expected trend according to the electrode area change and catalyst property, they did not show significant variation with changes in either the acetate concentration or buffer strength. (c) 2009 Elsevier B.V. All rights reserved.
5. Theoretical and experimental study of charge transfer through DNA: Impact of mercury mediated T-Hg-T base pair
Czech Academy of Sciences Publication Activity Database
Kratochvílová, Irena; Vala, M.; Weiter, M.; Páv, Ondřej; Šebera, Jakub; Sychrovský, Vladimír
2015-01-01
Roč. 22, č. 1 (2015), s. 20 ISSN 1211-5894. [Discussions in Structural Molecular Biology. Annual Meeting of the Czech Society for Structural Biology /13./. 19.03.2015-21.03.2015, Nové Hrady] Institutional support: RVO:61388963 ; RVO:68378271 Keywords : charge transfer * T-Hg-T * steady-state fluorescence Subject RIV: CF - Physical ; Theoretical Chemistry
6. Quasi-four-body treatment of charge transfer in the collision of protons with atomic helium: I. Thomas related mechanisms
Science.gov (United States)
2018-04-01
The scattering of a completely bare ion by atoms larger than hydrogen is at least a four-body interaction, and the charge transfer channel involves a two-step process. Amongst the two-step interactions of the high-velocity single charge transfer in an anion-atom collision, there is one whose amplitude demonstrates a peak in the angular distribution of the cross sections. This peak, the so-called Thomas peak, was predicted by Thomas in a two-step interaction, classically, which could also be described through three-body quantum mechanical models. This work discusses a four-body quantum treatment of the charge transfer in ion-atom collisions, where two-step interactions illustrating a Thomas peak are emphasized. In addition, the Pauli exclusion principle is taken into account for the initial and final states as well as the operators. It will be demonstrated that there is a momentum condition for each two-step interaction to occur in a single charge transfer channel, where new classical interactions lead to the Thomas mechanism.
7. Charge transfer incollisions of Li3+ and Be4+ ions with atomic hydrogen at low impact energy
International Nuclear Information System (INIS)
Ohyama, T.; Itikawa, Y.
1981-08-01
Total charge transfer cross sections are calculated for the collisions of Li 3+ and Be 4+ ions with H(1s) atoms in the low energy region (E 3+ -H system, a reasonable agreement is found between the present calculation and the recent experiment. (author)
8. Turn-on fluorescence probes based on pyranine/viologen charge-transfer complexes for the determination of nucleotides
Energy Technology Data Exchange (ETDEWEB)
Schäferling, Michael, E-mail: [email protected]; Lang, Thomas; Schnettelker, Annette
2014-10-15
The formation of ground state charge-transfer complexes between pyranine (8-hydroxypyrene-1,3,6-trisulfonic acid) and viologen (paraquat) derivatives is utilized for the design of novel fluoroionophores for the determination of phosphate species, particularly of nucleotides. The strong quenching of the pyranine fluorescence by viologen-type charge transfer acceptors can be countermanded if these are functionalized with triethylammonium groups that serve as recognition elements for phosphate anions. We report on the fluorogenic responses of these water-soluble molecular probes in presence of different phosphates. Absorbance measurements give additional information on the charge transfer complex formation and the interaction with nucleotides. The experimental data show that these aggregates form attractive, simple and versatile fluorescence turn-on probes for nucleoside triphosphates. The reversibility of the fluorescence response is demonstrated by means of an enzymatic model assay using ATPase for the decomposition of adenosine triphosphate. - Highlights: • Pyranine/viologen charge-transfer complexes as molecular probe for ATP recognition. • Fluorescence turn on mechanism. • Selective compared to other nucleotides and phosphate anions. • Fast and reversible response applicable to monitor enzymatic reactions.
9. Density functional calculations of potential energy surface and charge transfer integrals in molecular triphenylene derivative HAT6
NARCIS (Netherlands)
Zbiri, M.; Johnson, M.R.; Kearley, G.J.; Mulder, F.M.
2009-01-01
We investigate the effect of structural fluctuations on charge transfer integrals, overlap integrals, and site energies in a system of two stacked molecular 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT6), which is a model system for conducting devices in organic photocell applications. A density
10. Detection of Intramolecular Charge Transfer and Dynamic Solvation in Eosin B by Femtosecond Two-Dimensional Electronic Spectroscopy
Science.gov (United States)
Ghosh, Soumen; Roscioli, Jerome D.; Beck, Warren F.
2014-06-01
We have employed 2D electronic photon echo spectroscopy to study intramolecular charge-transfer dynamics in eosin B. After preparation of the first excited singlet state (S_1) with 40-fs excitation pulses at 520 nm, the nitro group (--NO_2) in eosin B undergoes excited state torsional motion towards a twisted intramolecular charge transfer (TICT) state. As the viscosity of the surrounding solvent increases, the charge-transfer rate decreases because the twisting of the --NO_2 group is hindered. These conclusions are supported by the time evolution of the 2D spectrum, which provides a direct measure of the the ground-to-excited-state energy gap time-correlation function, M(t). In comparison to the inertial and diffusive solvation time scales exhibited by eosin Y, which lacks the nitro group, the M(t) function for eosin B exhibits under the same conditions an additional component on the 150-fs timescale that arises from quenching of the S_1 state by crossing to the TICT state. These results indicate that 2D electronic spectroscopy can be used as a sensitive probe of the rate of charge transfer in a molecular system and of the coupling to the motions of the surrounding solvent. (Supported by grant DE-SC0010847 from the Department of Energy, Office of Basic Energy Sciences, Photosynthetic Systems program.)
11. Impact of exact exchange in the description of the electronic structure of organic charge-transfer molecular crystals
KAUST Repository
Fonari, Alexandr
2014-10-21
We evaluate the impact that the amount of nonlocal Hartree-Fock (%HF) exchange included in a hybrid density functional has on the microscopic parameters (transfer integrals, band gaps, bandwidths, and effective masses) describing charge transport in high-mobility organic crystals. We consider both crystals based on a single molecule, such as pentacene, and crystals based on mixed-stack charge-transfer systems, such as dibenzo-TTF–TCNQ. In the pentacene crystal, the band gap decreases and the effective masses increase linearly with an increase in the amount of %HF exchange. In contrast, in the charge-transfer crystals, while the band gap increases linearly, the effective masses vary only slightly with an increase in %HF exchange. We show that the superexchange nature of the electronic couplings in charge-transfer systems is responsible for this peculiar evolution of the effective masses. We compare the density functional theory results with results obtained within the G0W0 approximation as a way of benchmarking the optimal amount of %HF exchange needed in a given functional.
12. Identification of the site where the electron transfer chain of plant mitochondria is stimulated by electrostatic charge screening.
NARCIS (Netherlands)
Krab, K.; Wagner, M.J.; Wagner, A.M.; Moller, I.M.
2000-01-01
Modular kinetic analysis was used to determine the sites in plant mitochondria where charge-screening stimulates the rate of electron transfer from external NAD(P)H to oxygen. In mitochondria isolated from potato (Solanum tuberosum L.) tuber callus, stimulation of the rate of oxygen uptake was
13. 41 CFR 102-36.285 - May we charge for personal property transferred to another federal agency?
Science.gov (United States)
2010-07-01
... Property Management Federal Property Management Regulations System (Continued) FEDERAL MANAGEMENT... general fund of the Treasury or appropriated therefrom but by law reimbursable from assessment, tax, or... corporation. (b) You may charge for direct costs you incurred incident to the transfer, such as packing...
14. An intramolecular charge transfer state of carbonyl carotenoids: implications for excited state dynamics of apo-carotenals and retinal
Czech Academy of Sciences Publication Activity Database
Polívka, Tomáš; Kaligotla, S.; Chábera, P.; Frank, H.A.
2011-01-01
Roč. 13, č. 22 (2011), s. 1463-9076 ISSN 1463-9076 Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoid * retinal * excited-state dynamics * charge-transfer state Subject RIV: BO - Biophysics Impact factor: 3.573, year: 2011
15. Strong isotope effects on the charge transfer in slow collisions of He2+ with atomic hydrogen, deuterium, and tritium
NARCIS (Netherlands)
Stolterfoht, N.; Cabrera-Trujillo, R.; Oehrn, Y.; Deumens, E.; Hoekstra, R.; Sabin, J. R.
2007-01-01
Probabilities and cross sections for charge transfer by He2+ impact on atomic hydrogen (H), deuterium (D), and tritium (T) at low collision energies are calculated. The results are obtained using an ab initio theory, which solves the time-dependent Schrodinger equation. For the H target, excellent
16. Coherence, energy and charge transfers in de-excitation pathways of electronic excited state of biomolecules in photosynthesis
DEFF Research Database (Denmark)
Bohr, Henrik; Malik, F. Bary
2013-01-01
The observed multiple de-excitation pathways of photo-absorbed electronic excited state in the peridinin–chlorophyll complex, involving both energy and charge transfers among its constituents, are analyzed using the bio-Auger (B-A) theory. It is also shown that the usually used F¨orster–Dexter...
17. Charge versus Energy Transfer Effects in High-Performance Perylene Diimide Photovoltaic Blend Films.
Science.gov (United States)
Singh, Ranbir; Shivanna, Ravichandran; Iosifidis, Agathaggelos; Butt, Hans-Jürgen; Floudas, George; Narayan, K S; Keivanidis, Panagiotis E
2015-11-11
Perylene diimide (PDI)-based organic photovoltaic devices can potentially deliver high power conversion efficiency values provided the photon energy absorbed is utilized efficiently in charge transfer (CT) reactions instead of being consumed in nonradiative energy transfer (ET) steps. Hitherto, it remains unclear whether ET or CT primarily drives the photoluminescence (PL) quenching of the PDI excimer state in PDI-based blend films. Here, we affirm the key role of the thermally assisted PDI excimer diffusion and subsequent CT reaction in the process of PDI excimer PL deactivation. For our study we perform PL quenching experiments in the model PDI-based composite made of poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b;4,5-b']dithiophene-2,6-diyl-alt-(4-(2-ethylhexanoyl)-thieno[3,4-b]thiophene)-2-6-diyl] (PBDTTT-CT) polymeric donor mixed with the N,N'-bis(1-ethylpropyl)-perylene-3,4,9,10-tetracarboxylic diimide (PDI) acceptor. Despite the strong spectral overlap between the PDI excimer PL emission and UV-vis absorption of PBDTTT-CT, two main observations indicate that no significant ET component operates in the overall PL quenching: the PL intensity of the PDI excimer (i) increases with decreasing temperature and (ii) remains unaffected even in the presence of 10 wt % content of the PBDTTT-CT quencher. Temperature-dependent wide-angle X-ray scattering experiments further indicate that nonradiative resonance ET is highly improbable due to the large size of PDI domains. The dominance of the CT over the ET process is verified by the high performance of devices with an optimum composition of 30:70 PBDTTT-CT:PDI. By adding 0.4 vol % of 1,8-diiodooctane we verify the plasticization of the polymer side chains that balances the charge transport properties of the PBDTTT-CT:PDI composite and results in additional improvement in the device efficiency. The temperature-dependent spectral width of the PDI excimer PL band suggests the presence of energetic disorder in the
18. Accurate determination of the charge transfer efficiency of photoanodes for solar water splitting.
Science.gov (United States)
Klotz, Dino; Grave, Daniel A; Rothschild, Avner
2017-08-09
The oxygen evolution reaction (OER) at the surface of semiconductor photoanodes is critical for photoelectrochemical water splitting. This reaction involves photo-generated holes that oxidize water via charge transfer at the photoanode/electrolyte interface. However, a certain fraction of the holes that reach the surface recombine with electrons from the conduction band, giving rise to the surface recombination loss. The charge transfer efficiency, η t , defined as the ratio between the flux of holes that contribute to the water oxidation reaction and the total flux of holes that reach the surface, is an important parameter that helps to distinguish between bulk and surface recombination losses. However, accurate determination of η t by conventional voltammetry measurements is complicated because only the total current is measured and it is difficult to discern between different contributions to the current. Chopped light measurement (CLM) and hole scavenger measurement (HSM) techniques are widely employed to determine η t , but they often lead to errors resulting from instrumental as well as fundamental limitations. Intensity modulated photocurrent spectroscopy (IMPS) is better suited for accurate determination of η t because it provides direct information on both the total photocurrent and the surface recombination current. However, careful analysis of IMPS measurements at different light intensities is required to account for nonlinear effects. This work compares the η t values obtained by these methods using heteroepitaxial thin-film hematite photoanodes as a case study. We show that a wide spread of η t values is obtained by different analysis methods, and even within the same method different values may be obtained depending on instrumental and experimental conditions such as the light source and light intensity. Statistical analysis of the results obtained for our model hematite photoanode show good correlation between different methods for
19. CoPc and CoPcF16 on gold: Site-specific charge-transfer processes
Directory of Open Access Journals (Sweden)
Fotini Petraki
2014-04-01
Full Text Available Interface properties of cobalt(II phthalocyanine (CoPc and cobalt(II hexadecafluoro-phthalocyanine (CoPcF16 to gold are investigated by photo-excited electron spectroscopies (X-ray photoemission spectroscopy (XPS, ultraviolet photoemission spectroscopy (UPS and X-ray excited Auger electron spectroscopy (XAES. It is shown that a bidirectional charge transfer determines the interface energetics for CoPc and CoPcF16 on Au. Combined XPS and XAES measurements allow for the separation of chemical shifts based on different local charges at the considered atom caused by polarization effects. This facilitates a detailed discussion of energetic shifts of core level spectra. The data allow the discussion of site-specific charge-transfer processes.
20. Influence of Coherent Tunneling and Incoherent Hopping on the Charge Transfer Mechanism in Linear Donor-Bridge-Acceptor Systems.
Science.gov (United States)
Li, Guangqi; Govind, Niranjan; Ratner, Mark A; Cramer, Christopher J; Gagliardi, Laura
2015-12-17
The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.
1. A model for the chain-to-plane charge transfer in YBa2Cu3O6+x
International Nuclear Information System (INIS)
Matic, V. M.; Lazarov, N. Dj.; Milic, M.
2012-01-01
A model for the chain-to-plane charge transfer is proposed to account for the two plateaus, at 60 K and at 90 K, of the T c (x) characteristics of the YBa 2 Cu 3 O 6+x high-T c superconductor. It is assumed that the number of holes transferred from a CuO chain of length l to two nearby CuO 2 sheets is proportional to l (that is, to the number of oxygen atoms in the chain), if the chain length is greater than, or equal to, a certain critical chain length, l cr , that is required to trigger the charge transfer process. No holes are assumed to have been transferred from chains of length l cr . The calculated T c (x) dependence is found to be in excellent agreement with the experimentally reported T c (x). The critical chain length parameter is estimated to be equal to l cr = 11 (eleven oxygen atoms in a chain), which is a greater value than that obtained in the previously proposed model for the chain-to-plane charge transfer (l cr = 4). The results obtained out of the proposed model are briefly discussed
2. Neutralized ion beam modification of cellulose membranes for study of ion charge effect on ion-beam-induced DNA transfer
Science.gov (United States)
Prakrajang, K.; Sangwijit, K.; Anuntalabhochai, S.; Wanichapichart, P.; Yu, L. D.
2012-02-01
Low-energy ion beam biotechnology (IBBT) has recently been rapidly developed worldwide. Ion-beam-induced DNA transfer is one of the important applications of IBBT. However, mechanisms involved in this application are not yet well understood. In this study plasma-neutralized ion beam was applied to investigate ion charge effect on induction of DNA transfer. Argon ion beam at 7.5 keV was neutralized by RF-driven plasma in the beam path and then bombarded cellulose membranes which were used as the mimetic plant cell envelope. Electrical properties such as impedance and capacitance of the membranes were measured after the bombardment. An in vitro experiment on plasmid DNA transfer through the cellulose membrane was followed up. The results showed that the ion charge input played an important role in the impedance and capacitance changes which would affect DNA transfer. Generally speaking, neutral particle beam bombardment of biologic cells was more effective in inducing DNA transfer than charged ion beam bombardment.
3. Four- and six-charge transfer reactions induced by 52Cr, 56Fe, 63Cu in rare-earths
International Nuclear Information System (INIS)
Mouchaty, G.
1977-01-01
The cross sections for transfer reactions in which 4 and 6 charges are gained by Sm and Nd targets have been measured, the projectiles being 52 Cr and 56 Fe at 343 and 377 MeV. These energies correspond to 1.5B, B being the interaction barrier. The results obtained indicate that the cross section increases when the number of charges transferred and the mass of the projectile are increased. The angular distributions and recoil ranges at each angle of 151 Dy produced through 52 Cr+ 148 Sm, 52 Cr+ 144 Nd, 56 Fe+ 144 Nd, 63 Cu+ 144 Nd reactions were determined for incident energies equivalent to 1.5B. After transformation into the c.m. system, the angular distributions exhibit a maximum close to 155 0 and a tail at small angles. The position of the maximum is independent of the incident ion and of the number of transferred charges. The analysis of the energy distributions indicate that the observed reactions can be explained by a two-step process: a transfer of nucleons followed by an evaporation step. The number of nucleons transferred in the 1st step and the associated excitation energies are higher for the events corresponding to the tail than for those corresponding to the maximum [fr
4. Effect of Conjugation Length on Photoinduced Charge-Transfer in π-Conjugated Oligomer-Acceptor Dyads
KAUST Repository
Jiang, Junlin
2017-05-25
A series of -conjugated oligomer-acceptor dyads were synthesized that feature oligo(phenylene ethynylene) (OPE) conjugated backbones end-capped with a naphthalene diimide (NDI) acceptor. The OPE segments vary in length from 4 to 8 phenylene ethynene units (PEn-NDI, where n = 4, 6 and 8). Fluorescence and transient absorption spectroscopy reveals that intramolecular OPE NDI charge transfer dominates the deactivation of excited states of the PEn-NDI oligomers. Both charge separation (CS) and charge recombination (CR) are strongly exothermic (G0CS ~ -1.1 and G0CR ~ -2.0 eV), and the driving forces do not vary much across the series because the oxidation and reduction potentials and singlet energies of the OPEs do not vary much with their length. Bimolecular photoinduced charge transfer between model OPEs that do not contain the NDI acceptors with methyl viologen was studied, and the results reveal that the absorption of the cation radical state (OPE+•) remains approximately constant ( ~ 575 nm) regardless of oligomer length. This finding suggests that the cation radical (polaron) of the OPE is relatively localized, effectively occupying a confined segment of n 4 repeat units in the longer oligomers. Photoinduced intramolecular electron transfer dynamics in the PEn-NDI series was investigated by UV-visible femtosecond transient absorption spectroscopy with visible and mid-infrared probes. Charge separation occurs on the 1 – 10 ps timescale, with the rates decreasing slightly with increased oligomer length (βCS ~ 0.15 Å-1). The rate for charge-recombination decreases in the sequence PE4-NDI > PE6-NDI ~ PE8-NDI. The discontinuous distance dependence in the rate for charge recombination may be related to the spatial localization of the positive polaron state in the longer oligomers.
5. Effect of Conjugation Length on Photoinduced Charge-Transfer in π-Conjugated Oligomer-Acceptor Dyads
KAUST Repository
Jiang, Junlin; Alsam, Amani Abdu; Wang, Shanshan; Aly, Shawkat Mohammede; Pan, Zhenxing; Mohammed, Omar F.; Schanze, Kirk S.
2017-01-01
A series of -conjugated oligomer-acceptor dyads were synthesized that feature oligo(phenylene ethynylene) (OPE) conjugated backbones end-capped with a naphthalene diimide (NDI) acceptor. The OPE segments vary in length from 4 to 8 phenylene ethynene units (PEn-NDI, where n = 4, 6 and 8). Fluorescence and transient absorption spectroscopy reveals that intramolecular OPE NDI charge transfer dominates the deactivation of excited states of the PEn-NDI oligomers. Both charge separation (CS) and charge recombination (CR) are strongly exothermic (G0CS ~ -1.1 and G0CR ~ -2.0 eV), and the driving forces do not vary much across the series because the oxidation and reduction potentials and singlet energies of the OPEs do not vary much with their length. Bimolecular photoinduced charge transfer between model OPEs that do not contain the NDI acceptors with methyl viologen was studied, and the results reveal that the absorption of the cation radical state (OPE+•) remains approximately constant ( ~ 575 nm) regardless of oligomer length. This finding suggests that the cation radical (polaron) of the OPE is relatively localized, effectively occupying a confined segment of n 4 repeat units in the longer oligomers. Photoinduced intramolecular electron transfer dynamics in the PEn-NDI series was investigated by UV-visible femtosecond transient absorption spectroscopy with visible and mid-infrared probes. Charge separation occurs on the 1 – 10 ps timescale, with the rates decreasing slightly with increased oligomer length (βCS ~ 0.15 Å-1). The rate for charge-recombination decreases in the sequence PE4-NDI > PE6-NDI ~ PE8-NDI. The discontinuous distance dependence in the rate for charge recombination may be related to the spatial localization of the positive polaron state in the longer oligomers.
6. Coupled quantum-classical method for long range charge transfer: relevance of the nuclear motion to the quantum electron dynamics
International Nuclear Information System (INIS)
Da Silva, Robson; Hoff, Diego A; Rego, Luis G C
2015-01-01
Charge and excitonic-energy transfer phenomena are fundamental for energy conversion in solar cells as well as artificial photosynthesis. Currently, much interest is being paid to light-harvesting and energy transduction processes in supramolecular structures, where nuclear dynamics has a major influence on electronic quantum dynamics. For this reason, the simulation of long range electron transfer in supramolecular structures, under environmental conditions described within an atomistic framework, has been a difficult problem to study. This work describes a coupled quantum mechanics/molecular mechanics method that aims at describing long range charge transfer processes in supramolecular systems, taking into account the atomistic details of large molecular structures, the underlying nuclear motion, and environmental effects. The method is applied to investigate the relevance of electron–nuclei interaction on the mechanisms for photo-induced electron–hole pair separation in dye-sensitized interfaces as well as electronic dynamics in molecular structures. (paper)
7. Influence of the zero point oscillation on the charge transfer in the heavy-ion deep inelastic collisions
Energy Technology Data Exchange (ETDEWEB)
Lin-xiao, Ge; Wen-qing, Shen; Chao-fan, Yu
1982-01-01
We discuss the variance of the charge distribution in the heavy ion deep inelastic collision on the basis of the Langevin equation. In order to explain the difference of the inital slope (early stage) of the charge distribution for the different reaction systems and different bombarding energy, an initial condition of the charge drift in the early stage of Dic is introduced. It is given by the harmonic or inhamonic motion around the zero point and closely depends on the nuclear structure and incident energy. The difference of the inertial mass and stiffness parameter may be the one of the reasons for the difference of charge transfer. In addition we also analyse the characterstic of the inertial mass parameter.
8. Crystalline structure of the marketed form of Rifampicin: a case of conformational and charge transfer polymorphism
Science.gov (United States)
de Pinho Pessoa Nogueira, Luciana; de Oliveira, Yara S.; de C. Fonseca, Jéssica; Costa, Wendell S.; Raffin, Fernanda N.; Ellena, Javier; Ayala, Alejandro Pedro
2018-03-01
Rifampicin is a semi-synthetic drug derived from rifamycin B, and currently integrates the fixed dose combination tablet formulations used in the treatment of tuberculosis. It is also used in the leprosy polychemotherapy and prophylaxis, which are diseases classified as neglected according to the World Health Organization. Rifampicin is a polymorphic drug and its desirable polymorphic form is labeled as II, being the main goal of this study the elucidation of its crystalline structure. Polymorph II is characterized by two molecules with different conformations in the asymmetric unit and the following lattice parameters: a = 14.0760 (10) Å, b = 17.5450 (10) Å, c = 17.5270 (10) Å, β = 92.15°. Differently to the previously reported structures, a charge transference from the hydroxyl group of the naphthoquinone of one conformer to the nitrogen of the piperazine group of the second conformer was observed. The relevance of the knowledge of this crystalline structure, which is the preferred polymorph for pharmaceutical formulations, was evidenced by analyzing raw materials with polymorphic mixtures. Thus, the results presented in this contribution close an old information gap allowing the complete solid-state characterization of rifampicin.
9. Electronic coupling effects and charge transfer between organic molecules and metal surfaces
Energy Technology Data Exchange (ETDEWEB)
Forker, Roman
2010-07-01
We employ a variant of optical absorption spectroscopy, namely in situ differential reflectance spectroscopy (DRS), for an analysis of the structure-properties relations of thin epitaxial organic films. Clear correlations between the spectra and the differently intense coupling to the respective substrates are found. While rather broad and almost structureless spectra are obtained for a quaterrylene (QT) monolayer on Au(111), the spectral shape resembles that of isolated molecules when QT is grown on graphite. We even achieve an efficient electronic decoupling from the subjacent Au(111) by inserting an atomically thin organic spacer layer consisting of hexa-peri-hexabenzocoronene (HBC) with a noticeably dissimilar electronic behavior. These observations are further consolidated by a systematic variation of the metal substrate (Au, Ag, and Al), ranging from inert to rather reactive. For this purpose, 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) is chosen to ensure comparability of the molecular film structures on the different metals, and also because its electronic alignment on various metal surfaces has previously been studied with great intensity. We present evidence for ionized PTCDA at several interfaces and propose the charge transfer to be related to the electronic level alignment governed by interface dipole formation on the respective metals. (orig.)
10. Protein-induced geometric constraints and charge transfer in bacteriochlorophyll-histidine complexes in LH2.
Science.gov (United States)
Wawrzyniak, Piotr K; Alia, A; Schaap, Roland G; Heemskerk, Mattijs M; de Groot, Huub J M; Buda, Francesco
2008-12-14
Bacteriochlorophyll-histidine complexes are ubiquitous in nature and are essential structural motifs supporting the conversion of solar energy into chemically useful compounds in a wide range of photosynthesis processes. A systematic density functional theory study of the NMR chemical shifts for histidine and for bacteriochlorophyll-a-histidine complexes in the light-harvesting complex II (LH2) is performed using the BLYP functional in combination with the 6-311++G(d,p) basis set. The computed chemical shift patterns are consistent with available experimental data for positive and neutral(tau) (N(tau) protonated) crystalline histidines. The results for the bacteriochlorophyll-a-histidine complexes in LH2 provide evidence that the protein environment is stabilizing the histidine close to the Mg ion, thereby inducing a large charge transfer of approximately 0.5 electronic equivalent. Due to this protein-induced geometric constraint, the Mg-coordinated histidine in LH2 appears to be in a frustrated state very different from the formal neutral(pi) (N(pi) protonated) form. This finding could be important for the understanding of basic functional mechanisms involved in tuning the electronic properties and exciton coupling in LH2.
11. Charge transfer and ionization in collisions of Si3+ with H from low to high energy
Science.gov (United States)
Wang, J. G.; He, B.; Ning, Y.; Liu, C. L.; Yan, J.; Stancil, P. C.; Schultz, D. R.
2006-11-01
Charge transfer processes due to collisions of ground state Si3+(3sS1) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from 0.01eV/u to 1MeV/u . Total and state-selective rate coefficients are also presented for temperatures from 2×103K to 107K . Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies.
12. Charge transfer and ionization in collisions of Si3+ with H from low to high energy
International Nuclear Information System (INIS)
Wang, J. G.; He, B.; Ning, Y.; Liu, C. L.; Yan, J.; Stancil, P. C.; Schultz, D. R.
2006-01-01
Charge transfer processes due to collisions of ground state Si 3+ (3s 1 S) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero et al. [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from 0.01 eV/u to 1 MeV/u. Total and state-selective rate coefficients are also presented for temperatures from 2x10 3 K to 10 7 K. Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies
13. Controllable Charge Transfer in Ag-TiO2 Composite Structure for SERS Application
Directory of Open Access Journals (Sweden)
Yaxin Wang
2017-06-01
Full Text Available The nanocaps array of TiO2/Ag bilayer with different Ag thicknesses and co-sputtering TiO2-Ag monolayer with different TiO2 contents were fabricated on a two-dimensional colloidal array substrate for the investigation of Surface enhanced Raman scattering (SERS properties. For the TiO2/Ag bilayer, when the Ag thickness increased, SERS intensity decreased. Meanwhile, a significant enhancement was observed when the sublayer Ag was 10 nm compared to the pure Ag monolayer, which was ascribed to the metal-semiconductor synergistic effect that electromagnetic mechanism (EM provided by roughness surface and charge-transfer (CT enhancement mechanism from TiO2-Ag composite components. In comparison to the TiO2/Ag bilayer, the co-sputtered TiO2-Ag monolayer decreased the aggregation of Ag particles and led to the formation of small Ag particles, which showed that TiO2 could effectively inhibit the aggregation and growth of Ag nanoparticles.
14. Temperature-dependent vibrational spectroscopy to study order-disorder transitions in charge transfer complexes
Directory of Open Access Journals (Sweden)
Rohan Isaac
2018-02-01
Full Text Available Charge-transfer (CT complexes are a promising class of materials for the semiconductor industry because of their versatile properties. This class of compounds shows a variety of phase transitions, which are of interest because of their potential impact on the electronic characteristics. Here temperature-dependent vibrational spectroscopy is used to study structural phase transitions in a set of organic CT complexes. Splitting and broadening of infrared-active phonons in the complex formed between pyrene and pyromellitic dianhydride (PMDA confirm the structural transition is of the order-disorder type and complement previous x-ray diffraction (XRD results. We show that this technique is a powerful tool to characterize transitions, and apply it to a range of binary CT complexes composed of polyaromatic hyrdocarbons (anthracene, perylene, phenanthrene, pyrene, and stilbene and PMDA. We extend the understanding of transitions in perylene-PMDA and pyrene-PMDA, and show that there are no order-disorder transitions present in anthracene-PMDA, stilbene-PMDA and phenanthrene-PMDA in the temperature range investigated here.
15. Temperature-dependent vibrational spectroscopy to study order-disorder transitions in charge transfer complexes
Science.gov (United States)
Isaac, Rohan; Goetz, Katelyn P.; Roberts, Drew; Jurchescu, Oana D.; McNeil, L. E.
2018-02-01
Charge-transfer (CT) complexes are a promising class of materials for the semiconductor industry because of their versatile properties. This class of compounds shows a variety of phase transitions, which are of interest because of their potential impact on the electronic characteristics. Here temperature-dependent vibrational spectroscopy is used to study structural phase transitions in a set of organic CT complexes. Splitting and broadening of infrared-active phonons in the complex formed between pyrene and pyromellitic dianhydride (PMDA) confirm the structural transition is of the order-disorder type and complement previous x-ray diffraction (XRD) results. We show that this technique is a powerful tool to characterize transitions, and apply it to a range of binary CT complexes composed of polyaromatic hyrdocarbons (anthracene, perylene, phenanthrene, pyrene, and stilbene) and PMDA. We extend the understanding of transitions in perylene-PMDA and pyrene-PMDA, and show that there are no order-disorder transitions present in anthracene-PMDA, stilbene-PMDA and phenanthrene-PMDA in the temperature range investigated here.
16. Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study
International Nuclear Information System (INIS)
Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.
2011-01-01
In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.
17. Charge-transfer-based terbium MOF nanoparticles as fluorescent pH sensor for extreme acidity.
Science.gov (United States)
Qi, Zewan; Chen, Yang
2017-01-15
Newly emerged metal organic frameworks (MOFs) have aroused the great interest in designing functional materials by means of its flexible structure and component. In this study, we used lanthanide Tb 3+ ions and small molecular ligands to design and assemble a kind of pH-sensitive MOF nanoparticle based on intramolecular-charge-transfer effect. This kind of made-to-order MOF nanoparticle for H + is highly specific and sensitive and could be used to fluorescently indicate pH value of strong acidic solution via preset mechanism through luminescence of Tb 3+ . The long luminescence lifetime of Tb 3+ allows eliminating concomitant non-specific fluorescence by time-revised fluorescence techniques, processing an advantage in sensing H + in biological media with strong autofluorescence. Our method showed a great potential of MOF structures in designing and constructing sensitive sensing materials for specific analytes directly via the assembly of functional ions/ligands. Copyright © 2016 Elsevier B.V. All rights reserved.
18. Analysis of Charge Transfer for in Situ Li Intercalated Carbon Nanotubes
KAUST Repository
Rana, Kuldeep
2012-05-24
Vertically aligned carbon nanotube (VA-CNT) arrays have been synthesized with lithium (Li) intercalation through an alcohol-catalyzed chemical vapor deposition technique by using a Li-containing catalyst. Scanning electron microscopy images display that synthesized carbon nanotubes (CNTs) are dense and vertically aligned. The effect of the Li-containing catalyst on VA-CNTs has been studied by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and electron energy loss spectroscopy (EELS). XPS results show the change in binding energy of Li 1s and C 1s peaks, which indicates that Li is inserted in VA-CNTs during growth. Analysis of Raman spectra reveals that the G-band profile of CNTs synthesized with the Li-containing catalyst is shifted, suggesting an electronic interaction between Li and neighboring C atoms of the CNTs. The EELS spectra of the C K edge and Li K edge from CNTs also confirmed that Li is inserted into CNTs during synthesis. We have performed ab inito calculations based on density functional theory for a further understanding of the structural and electronic properties of Li intercalated CNTs, especially addressing the controversial charge-transfer state between Li and C. © 2012 American Chemical Society.
19. Graphene oxide based photoinduced charge transfer label-free near-infrared fluorescent biosensor for dopamine.
Science.gov (United States)
Chen, Jin-Long; Yan, Xiu-Ping; Meng, Kang; Wang, Shu-Feng
2011-11-15
While the super fluorescence quenching capacity of graphene and graphene oxide (GO) has been extensively employed to develop fluorescent sensors, their own unique fluorescence and its potential for chemo-/biosensing have seldom been explored. Here we report a GO-based photoinduced charge transfer (PCT) label-free near-infrared (near-IR) fluorescent biosensor for dopamine (DA). The multiple noncovalent interactions between GO and DA and the ultrafast decay at the picosecond range of the near-IR fluorescence of GO resulted in effective self-assembly of DA molecules on the surface of GO, and significant fluorescence quenching, allowing development of a PCT-based biosensor with direct readout of the near-IR fluorescence of GO for selective and sensitive detection of DA. The developed method gave a detection limit of 94 nM and a relative standard deviation of 2.0% for 11 replicate detections of 2.0 μM DA and was successfully applied to the determination of DA in biological fluids with quantitative recovery (98-115%).
20. Spectroscopy and dynamics of charge transfer excitons in type-II band aligned quantum confined heterostructures
Energy Technology Data Exchange (ETDEWEB)
Kushavah, Dushyant [Centre for Research in Nanotechnology and Science, IIT Bombay-400076, Mumbai (India); Mohapatra, P. K.; Vasa, P.; Singh, B. P., E-mail: [email protected] [Department of physics, IIT Bombay, Mumbai-400076 (India); Rustagi, K. C. [Indian Institute of Science Education and Research Bhopal-462066, Bhopal (India); Bahadur, D. [Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai-400076 (India)
2015-05-15
We illustrate effect of charge transfer (CT) in type-II quantum confined heterostructure by comparing CdSe quantum dots (QDs), CdSe/CdTe heterostructure quantum dots (HQDs) and CdSe/CdTe/CdSe quantum well-quantum dots (QWQDs) heterostructures. CdSe core QDs were synthesized using a kinetic growth method where QD size depends on reaction time. For shell coating we used modified version of successive ionic layer adsorption and reaction (SILAR). Size of different QDs ∼5 to 7 nm were measured by transmission electron microscopy (TEM). Strong red shift from ∼597 to ∼746 nm in photoluminescence (PL) spectra from QDs to QWQDs shows high tunability which is not possible with single constituent semiconductor QDs. PL spectra have been recorded at different temperatures (10K-300K). Room temperature time correlated single photon counting (TCSPC) measurements for QDs to QWQDs show three exponential radiative decay. The slowest component decay constant in QWQDs comes around eight fold to ∼51 ns as compared to ∼6.5 ns in HQD suggesting new opportunities to tailor the radiative carrier recombination rate of CT excitons.
1. Spectrophotometric determination and thermodynamic studies of the charge transfer complexes of azelastine-HCl
Directory of Open Access Journals (Sweden)
Nahla N. Salama
2011-06-01
Full Text Available Three charge transfer complexes of azelastine as n-donor with π acceptors, dichloro-dicyanobenzoquinone (DDQ, chloranilic acid (CA and tetracyanoquinodimethane (TCNQ were prepared in acetonitrile. They yield a radical anions measured at 456, 520 and 841 nm within concentration ranges of 8.0–72, 40–320 and 1.6–14.4 μg mL−1 with good correlation coefficients (r = 0.9996–0.9998. The molar absorptivities and association constants for the colored products were evaluated using the Benesi–Hildebrand equation. The free energy change (ΔG0 and the enthalpy of formation (ΔH0 as well as the entropy (ΔS0 were determined for the reaction product with TCNQ. The methods were successfully applied to the analysis of azelastine in its pharmaceutical preparations, where no interferences could be observed from the additives commonly present in the eye drops or nasal spray as proved by good mean recoveries of 98.89 ± 1.06–99.54 ± 1.84%. The results were compared, favorably with the manufacturer method and validated according to ICH guidelines.
2. Charge transfer interaction using quasiatomic minimal-basis orbitals in the effective fragment potential method
International Nuclear Information System (INIS)
Xu, Peng; Gordon, Mark S.
2013-01-01
The charge transfer (CT) interaction, the most time-consuming term in the general effective fragment potential method, is made much more computationally efficient. This is accomplished by the projection of the quasiatomic minimal-basis-set orbitals (QUAMBOs) as the atomic basis onto the self-consistent field virtual molecular orbital (MO) space to select a subspace of the full virtual space called the valence virtual space. The diagonalization of the Fock matrix in terms of QUAMBOs recovers the canonical occupied orbitals and, more importantly, gives rise to the valence virtual orbitals (VVOs). The CT energies obtained using VVOs are generally as accurate as those obtained with the full virtual space canonical MOs because the QUAMBOs span the valence part of the virtual space, which can generally be regarded as “chemically important.” The number of QUAMBOs is the same as the number of minimal-basis MOs of a molecule. Therefore, the number of VVOs is significantly smaller than the number of canonical virtual MOs, especially for large atomic basis sets. This leads to a dramatic decrease in the computational cost
3. Photosynthesis Revisited: Optimization of Charge and Energy Transfer in Quantum Materials
Science.gov (United States)
Gabor, Nathaniel
2014-03-01
The integration of new nano- and molecular-scale quantum materials into ultra-efficient energy harvesting devices presents significant scientific challenges. Of the many challenges, the most difficult is achieving high photon-to-electron conversion efficiency while maintaining broadband absorption. Due to exciton effects, devices composed of quantum materials may allow near-unity optical absorption efficiency yet require the choice of precisely one fundamental energy (HOMO-LUMO gap). To maximize absorption, the simplest device would absorb at the peak of the solar spectrum, which spans the visible wavelengths. If the peak of the solar spectrum spans the visible wavelengths, then why are terrestrial plants green? Here, I discuss a physical model of photosynthetic absorption and photoprotection in which the cell utilizes active feedback to optimize charge and energy transfer, thus maximizing stored energy rather than absorption. This model, which addresses the question of terrestrial greenness, is supported by several recent results that have begun to unravel the details of photoprotection in higher plants. More importantly, this model indicates a novel route for the design of next-generation energy harvesting systems based on nano- and molecular-scale quantum materials.
4. Selective contacts drive charge extraction in quantum dot solids via asymmetry in carrier transfer kinetics
KAUST Repository
Mora-Sero, Ivan; Bertoluzzi, Luca; Gonzalez-Pedro, Victoria; Gimenez, Sixto; Fabregat-Santiago, Francisco; Kemp, Kyle W.; Sargent, Edward H.; Bisquert, Juan
2013-01-01
Colloidal quantum dot solar cells achieve spectrally selective optical absorption in a thin layer of solution-processed, size-effect tuned, nanoparticles. The best devices built to date have relied heavily on drift-based transport due to the action of an electric field in a depletion region that extends throughout the thickness of the quantum dot layer. Here we study for the first time the behaviour of the best-performing class of colloidal quantum dot films in the absence of an electric field, by screening using an electrolyte. We find that the action of selective contacts on photovoltage sign and amplitude can be retained, implying that the contacts operate by kinetic preferences of charge transfer for either electrons or holes. We develop a theoretical model to explain these experimental findings. The work is the first to present a switch in the photovoltage in colloidal quantum dot solar cells by purposefully formed selective contacts, opening the way to new strategies in the engineering of colloidal quantum dot solar cells. © 2013 Macmillan Publishers Limited. All rights reserved.
5. Optically active charge transfer in hybrids of Alq3 nanoparticles and MoS2 monolayer
Science.gov (United States)
Ghimire, Ganesh; Dhakal, Krishna P.; Neupane, Guru P.; Jo, Seong Gi; Kim, Hyun; Seo, Changwon; Lee, Young Hee; Joo, Jinsoo; Kim, Jeongyong
2017-05-01
Organic/inorganic hybrid structures have been widely studied because of their enhanced physical and chemical properties. Monolayers of transition metal dichalcogenides (1L-TMDs) and organic nanoparticles can provide a hybridization configuration between zero- and two-dimensional systems with the advantages of convenient preparation and strong interface interaction. Here, we present such a hybrid system made by dispersing π-conjugated organic (tris (8-hydroxyquinoline) aluminum(III)) (Alq3) nanoparticles (NPs) on 1L-MoS2. Hybrids of Alq3 NP/1L-MoS2 exhibited a two-fold increase in the photoluminescence of Alq3 NPs on 1L-MoS2 and the n-doping effect of 1L-MoS2, and these spectral and electronic modifications were attributed to the charge transfer between Alq3 NPs and 1L-MoS2. Our results suggested that a hybrid of organic NPs/1L-TMD can offer a convenient platform to study the interface interactions between organic and inorganic nano objects and to engineer optoelectronic devices with enhanced performance.
6. Simultaneous spectrophotometric determination of trimethoprim and sulphamethoxazole following charge-transfer complexation with chloranilic acid
Directory of Open Access Journals (Sweden)
2017-05-01
Full Text Available A simple, accurate and precise simultaneous spectrophotometric method has been developed for the analysis of trimethoprim–sulphamethoxazole combination in pure and tablet dosage forms. The method involves direct charge transfer complexation of trimethoprim (TMP with chloranilic acid (CAA in acetonitrile–dioxane solvent mixture and complexation of sulphamethoxazole (SMZ after its hydrolysis in dilute H2SO4. Optimization of temperature and time revealed the superiority of room temperature and 20 and 30 min respectively for TMP and SMZ. Optimal detector responses were obtained at 520 and 440 nm and were therefore selected as working wavelength maxima for SMZ and TMP respectively. TMP and hydrolysed SMZ were combined with CAA at mole ratios of 1:1 and 1:3 respectively. Accuracies were generally less than 4% (estimated as degree of inaccuracy or error with a precision of the order of less than 2% on a three-day assessment. Physicochemical factors responsible for complex stability were estimated and related to the observed data. The method was successfully applied to the determination of TMP and SMZ in tablet dosage forms with accuracies comparable to the official BP method. There were no interferences from common tablet excipients and TMP complex did not interfere with the assay of SMZ. The developed method could find application in routine quality control of TMP–SMZ combination. It is the first reported full simultaneous colorimetric assay of TMP and SMZ using the same analytical reagent.
7. Strategies for Efficient Charge Separation and Transfer in Artificial Photosynthesis of Solar Fuels.
Science.gov (United States)
Xu, Yuxing; Li, Ailong; Yao, Tingting; Ma, Changtong; Zhang, Xianwen; Shah, Jafar Hussain; Han, Hongxian
2017-11-23
Converting sunlight to solar fuels by artificial photosynthesis is an innovative science and technology for renewable energy. Light harvesting, photogenerated charge separation and transfer (CST), and catalytic reactions are the three primary steps in the processes involved in the conversion of solar energy to chemical energy (SE-CE). Among the processes, CST is the key "energy pump and delivery" step in determining the overall solar-energy conversion efficiency. Efficient CST is always high priority in designing and assembling artificial photosynthesis systems for solar-fuel production. This Review not only introduces the fundamental strategies for CST but also the combinatory application of these strategies to five types of the most-investigated semiconductor-based artificial photosynthesis systems: particulate, Z-scheme, hybrid, photoelectrochemical, and photovoltaics-assisted systems. We show that artificial photosynthesis systems with high SE-CE efficiency can be rationally designed and constructed through combinatory application of these strategies, setting a promising blueprint for the future of solar fuels. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
8. Antibacterial activity of large-area monolayer graphene film manipulated by charge transfer.
Science.gov (United States)
Li, Jinhua; Wang, Gang; Zhu, Hongqin; Zhang, Miao; Zheng, Xiaohu; Di, Zengfeng; Liu, Xuanyong; Wang, Xi
2014-03-12
Graphene has attracted increasing attention for potential applications in biotechnology due to its excellent electronic property and biocompatibility. Here we use both Gram-positive Staphylococcus aureus (S. aureus) and Gram-negative Escherichia coli (E. coli) to investigate the antibacterial actions of large-area monolayer graphene film on conductor Cu, semiconductor Ge and insulator SiO2. The results show that the graphene films on Cu and Ge can surprisingly inhibit the growth of both bacteria, especially the former. However, the proliferation of both bacteria cannot be significantly restricted by the graphene film on SiO2. The morphology of S. aureus and E. coli on graphene films further confirms that the direct contact of both bacteria with graphene on Cu and Ge can cause membrane damage and destroy membrane integrity, while no evident membrane destruction is induced by graphene on SiO2. From the viewpoint of charge transfer, a plausible mechanism is proposed here to explain this phenomenon. This study may provide new insights for the better understanding of antibacterial actions of graphene film and for the better designing of graphene-based antibiotics or other biomedical applications.
9. Absence of Intramolecular Singlet Fission in Pentacene-Perylenediimide Heterodimers: The Role of Charge Transfer State.
Science.gov (United States)
Wang, Long; Wu, Yishi; Chen, Jianwei; Wang, Lanfen; Liu, Yanping; Yu, Zhenyi; Yao, Jiannian; Fu, Hongbing
2017-11-16
A new class of donor-acceptor heterodimers based on two singlet fission (SF)-active chromophores, i.e., pentacene (Pc) and perylenediimide (PDI), was developed to investigate the role of charge transfer (CT) state on the excitonic dynamics. The CT state is efficiently generated upon photoexcitation. However, the resulting CT state decays to different energy states depending on the energy levels of the CT state. It undergoes extremely rapid deactivation to the ground state in polar CH 2 Cl 2 , whereas it undergoes transformation to a Pc triplet in nonpolar toluene. The efficient triplet generation in toluene is not due to SF but CT-mediated intersystem crossing. In light of the energy landscape, it is suggested that the deep energy level of the CT state relative to that of the triplet pair state makes the CT state actually serve as a trap state that cannot undergoes an intramolecular singlet fission process. These results provide guidance for the design of SF materials and highlight the requisite for more widely applicable design principles.
10. Selective contacts drive charge extraction in quantum dot solids via asymmetry in carrier transfer kinetics
KAUST Repository
Mora-Sero, Ivan
2013-08-12
Colloidal quantum dot solar cells achieve spectrally selective optical absorption in a thin layer of solution-processed, size-effect tuned, nanoparticles. The best devices built to date have relied heavily on drift-based transport due to the action of an electric field in a depletion region that extends throughout the thickness of the quantum dot layer. Here we study for the first time the behaviour of the best-performing class of colloidal quantum dot films in the absence of an electric field, by screening using an electrolyte. We find that the action of selective contacts on photovoltage sign and amplitude can be retained, implying that the contacts operate by kinetic preferences of charge transfer for either electrons or holes. We develop a theoretical model to explain these experimental findings. The work is the first to present a switch in the photovoltage in colloidal quantum dot solar cells by purposefully formed selective contacts, opening the way to new strategies in the engineering of colloidal quantum dot solar cells. © 2013 Macmillan Publishers Limited. All rights reserved.
11. The thermochromic behavior of aromatic amine-SO2 charge transfer complexes
Science.gov (United States)
Monezi, Natália M.; Borin, Antonio C.; Santos, Paulo S.; Ando, Rômulo A.
2017-02-01
The distinct thermochromism observed in solutions containing N,N-dimethylaniline (DMA) and N,N-diethylaniline (DEA) and SO2 was investigated by resonance Raman spectroscopy in a wide range of temperatures. The results indicate in addition to the charge transfer (CT) complexes DMA-SO2 and DEA-SO2, the presence of collision complexes involving the CT complexes and excess DMA and DEA molecules. The latter in fact is the chromophore responsible for the long wavelength absorption originating the color. The Raman signature of the collision complex was attributed to the distinct enhancement of a band at 1140 cm- 1 assigned to νs(SO2), in contrast to the same mode in the 1:1 complex at 1115 cm- 1. The intensity of such band, assigned to the collision complex is favored at high temperatures and depends on the steric hindrance associated to amines, as well as the SO2 molar fraction. Quantum chemical calculations based on time-dependent density functional theory (TDDFT) support the proposed interpretation.
12. Analysis of Charge Transfer for in Situ Li Intercalated Carbon Nanotubes
KAUST Repository
Rana, Kuldeep; Kucukayan-Dogu, Gokce; Sen, H. Sener; Boothroyd, Chris; Gulseren, Oguz; Bengu, Erman
2012-01-01
Vertically aligned carbon nanotube (VA-CNT) arrays have been synthesized with lithium (Li) intercalation through an alcohol-catalyzed chemical vapor deposition technique by using a Li-containing catalyst. Scanning electron microscopy images display that synthesized carbon nanotubes (CNTs) are dense and vertically aligned. The effect of the Li-containing catalyst on VA-CNTs has been studied by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and electron energy loss spectroscopy (EELS). XPS results show the change in binding energy of Li 1s and C 1s peaks, which indicates that Li is inserted in VA-CNTs during growth. Analysis of Raman spectra reveals that the G-band profile of CNTs synthesized with the Li-containing catalyst is shifted, suggesting an electronic interaction between Li and neighboring C atoms of the CNTs. The EELS spectra of the C K edge and Li K edge from CNTs also confirmed that Li is inserted into CNTs during synthesis. We have performed ab inito calculations based on density functional theory for a further understanding of the structural and electronic properties of Li intercalated CNTs, especially addressing the controversial charge-transfer state between Li and C. © 2012 American Chemical Society.
13. High pressure study of high temperatures superconductors: Material base, universal Tc-behavior, and charge transfer
International Nuclear Information System (INIS)
Chu, C.W.; Hor, P.H.; Lin, J.G.; Xiong, Q.; Huang, Z.J.; Meng, R.L.; Xue, Y.Y.; Jean, Y.C.
1991-01-01
The superconducting transition temperature (T c ) has been measured in YBa 2 Cu 3 O 6.7 , YBa 2 Cu 3 O 7 , Y 2 Ba 4 Cu 7 O 15 , YBa 2 Cu 4 O 8 , Tl 2 Ba 2 Ca n-1 Cu n O n+4-δ , La 2-x Sr x CuO 4 , and La 2-x Ba x CuO 4 under high pressures. The pressure effect on the positron lifetime (τ) has also been determined in the first four compounds. Based on these and other high pressure data, the authors suggest that (1) all known cuprate high temperature superconductors (HTS's) may be no more than mere modifications of either 214-T, 214-T', 123, or a combination of 214-T' and 123, (2) a nonmonotonic T c -behavior may govern the T c -variation of all hole cuprate HTS's and (3) pressure can induce charge transfer leading to a T c -change. The implications of these suggestions will also be discussed
14. Multiple Electron Charge Transfer Chemistries for Electrochemical Energy Storage Systems: The Metal Boride and Metal Air Battery
Science.gov (United States)
Stuart, Jessica F.
The primary focus of this work has been to develop high-energy capacity batteries capable of undergoing multiple electron charge transfer redox reactions to address the growing demand for improved electrical energy storage systems that can be applied to a range of applications. As the levels of carbon dioxide (CO2) increase in the Earth's atmosphere, the effects on climate change become increasingly apparent. According to the Energy Information Administration (EIA), the U.S. electric power sector is responsible for the release of 2,039 million metric tons of CO2 annually, equating to 39% of total U.S. energy-related CO2 emissions. Both nationally and abroad, there are numerous issues associated with the generation and use of electricity aside from the overwhelming dependence on fossil fuels and the subsequent carbon emissions, including reliability of the grid and the utilization of renewable energies. Renewable energy makes up a relatively small portion of total energy contributions worldwide, accounting for only 13% of the 3,955 billion kilowatt-hours of electricity produced each year, as reported by the EIA. As the demand to reduce our dependence on fossils fuels and transition to renewable energy sources increases, cost effective large-scale electrical energy storage must be established for renewable energy to become a sustainable option for the future. A high capacity energy storage system capable of leveling the intermittent nature of energy sources such as solar, wind, and water into the electric grid and provide electricity at times of high demand will facilitate this transition. In 2008, the Licht Group presented the highest volumetric energy capacity battery, the vanadium diboride (VB2) air battery, exceedingly proficient in transferring eleven electrons per molecule. This body of work focuses on new developments to this early battery such as fundamentally understanding the net discharge mechanism of the system, evaluation of the properties and
15. Strategies to enhance the excitation energy-transfer efficiency in a light-harvesting system using the intra-molecular charge transfer character of carotenoids
Energy Technology Data Exchange (ETDEWEB)
Yukihira, Nao [Department of Applied Chemistry for Environment; School of Science and Technology; Kwansei Gakuin University; Sanda; Japan; Sugai, Yuko [Department of Applied Chemistry for Environment; School of Science and Technology; Kwansei Gakuin University; Sanda; Japan; Fujiwara, Masazumi [Department of Applied Chemistry for Environment; School of Science and Technology; Kwansei Gakuin University; Sanda; Japan; Kosumi, Daisuke [Institute of Pulsed Power Science; Kumamoto University; Kumamoto; Japan; Iha, Masahiko [South Product Co. Ltd.; Uruma-shi; Japan; Sakaguchi, Kazuhiko [Department of Chemistry; Graduate School of Science; Osaka City University; Osaka 558-8585; Japan; Katsumura, Shigeo [Department of Chemistry; Graduate School of Science; Osaka City University; Osaka 558-8585; Japan; Gardiner, Alastair T. [Glasgow Biomedical Research Centre; University of Glasgow; 126 University Place; Glasgow, G12 8QQ; UK; Cogdell, Richard J. [Glasgow Biomedical Research Centre; University of Glasgow; 126 University Place; Glasgow, G12 8QQ; UK; Hashimoto, Hideki [Department of Applied Chemistry for Environment; School of Science and Technology; Kwansei Gakuin University; Sanda; Japan
2017-01-01
Fucoxanthin is a carotenoid that is mainly found in light-harvesting complexes from brown algae and diatoms. Due to the presence of a carbonyl group attached to polyene chains in polar environments, excitation produces an excited intra-molecular charge transfer. This intra-molecular charge transfer state plays a key role in the highly efficient (~95%) energy-transfer from fucoxanthin to chlorophyllain the light-harvesting complexes from brown algae. In purple bacterial light-harvesting systems the efficiency of excitation energy-transfer from carotenoids to bacteriochlorophylls depends on the extent of conjugation of the carotenoids. In this study we were successful, for the first time, in incorporating fucoxanthin into a light-harvesting complex 1 from the purple photosynthetic bacterium,Rhodospirillum rubrumG9+ (a carotenoidless strain). Femtosecond pump-probe spectroscopy was applied to this reconstituted light-harvesting complex in order to determine the efficiency of excitation energy-transfer from fucoxanthin to bacteriochlorophyllawhen they are bound to the light-harvesting 1 apo-proteins.
16. Frenkel and Charge-Transfer Excitations in Donor-acceptor Complexes from Many-Body Green's Functions Theory.
Science.gov (United States)
Baumeier, Björn; Andrienko, Denis; Rohlfing, Michael
2012-08-14
Excited states of donor-acceptor dimers are studied using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. For a series of prototypical small-molecule based pairs, this method predicts energies of local Frenkel and intermolecular charge-transfer excitations with the accuracy of tens of meV. Application to larger systems is possible and allowed us to analyze energy levels and binding energies of excitons in representative dimers of dicyanovinyl-substituted quarterthiophene and fullerene, a donor-acceptor pair used in state of the art organic solar cells. In these dimers, the transition from Frenkel to charge transfer excitons is endothermic and the binding energy of charge transfer excitons is still of the order of 1.5-2 eV. Hence, even such an accurate dimer-based description does not yield internal energetics favorable for the generation of free charges either by thermal energy or an external electric field. These results confirm that, for qualitative predictions of solar cell functionality, accounting for the explicit molecular environment is as important as the accurate knowledge of internal dimer energies.
17. An insight into the mechanism of charge-transfer of hybrid polymer:ternary/quaternary chalcopyrite colloidal nanocrystals
Directory of Open Access Journals (Sweden)
Parul Chawla
2014-08-01
Full Text Available In this work, we have demonstrated the structural and optoelectronic properties of the surface of ternary/quaternary (CISe/CIGSe/CZTSe chalcopyrite nanocrystallites passivated by tri-n-octylphosphine-oxide (TOPO and tri-n-octylphosphine (TOP and compared their charge transfer characteristics in the respective polymer: chalcopyrite nanocomposites by dispersing them in poly(3-hexylthiophene polymer. It has been found that CZTSe nanocrystallites due to their high crystallinity and well-ordered 3-dimensional network in its pristine form exhibit a higher steric- and photo-stability, resistance against coagulation and homogeneity compared to the CISe and CIGSe counterparts. Moreover, CZTSe nanocrystallites display efficient photoluminescence quenching as evident from the high value of the Stern–Volmer quenching constant (KSV and eventually higher charge transfer efficiency in their respective polymer P3HT:CZTSe composites. We modelled the dependency of the charge transfer from the donor and the charge separation mechanism across the donor–acceptor interface from the extent of crystallinity of the chalcopyrite semiconductors (CISe/CIGSe/CZTSe. Quaternary CZTSe chalcopyrites with their high crystallinity and controlled morphology in conjunction with regioregular P3HT polymer is an attractive candidate for hybrid solar cells applications.
18. The simplest equivalent circuit of a pulsed dielectric barrier discharge and the determination of the gas gap charge transfer
Science.gov (United States)
Pipa, A. V.; Koskulics, J.; Brandenburg, R.; Hoder, T.
2012-11-01
The concept of the simplest equivalent circuit for a dielectric barrier discharge (DBD) is critically reviewed. It is shown that the approach is consistent with experimental data measured either in large-scale sinusoidal-voltage driven or miniature pulse-voltage driven DBDs. An expression for the charge transferred through the gas gap q(t) is obtained with an accurate account for the displacement current and the values of DBD reactor capacitance. This enables (i) the significant reduction of experimental error in the determination of q(t) in pulsed DBDs, (ii) the verification of the classical electrical theory of ozonizers about maximal transferred charge qmax, and (iii) the development of a graphical method for the determination of qmax from charge-voltage characteristics (Q-V plots, often referred as Lissajous figures) measured under pulsed excitation. The method of graphical presentation of qmax is demonstrated with an example of a Q-V plot measured under pulsed excitation. The relations between the discharge current jR(t), the transferred charge q(t), and the measurable parameters are presented in new forms, which enable the qualitative interpretation of the measured current and voltage waveforms without the knowledge about the value of the dielectric barrier capacitance Cd. Whereas for quantitative evaluation of electrical measurements, the accurate estimation of the Cd is important.
19. Modeling the effect of shunt current on the charge transfer efficiency of an all-vanadium redox flow battery
Science.gov (United States)
Chen, Yong-Song; Ho, Sze-Yuan; Chou, Han-Wen; Wei, Hwa-Jou
2018-06-01
In an all-vanadium redox flow battery (VRFB), a shunt current is inevitable owing to the electrically conductive electrolyte that fills the flow channels and manifolds connecting cells. The shunt current decreases the performance of a VRFB stack as well as the energy conversion efficiency of a VRFB system. To understand the shunt-current loss in a VRFB stack with various designs and operating conditions, a mathematical model is developed to investigate the effects of the shunt current on battery performance. The model is calibrated with experimental data under the same operating conditions. The effects of the battery design, including the number of cells, state of charge (SOC), operating current, and equivalent resistance of the electrolytes in the flow channels and manifolds, on the shunt current are analyzed and discussed. The charge-transfer efficiency is calculated to investigate the effects of the battery design parameters on the shunt current. When the cell number is increased from 5 to 40, the charge transfer efficiency is decreased from 0.99 to a range between 0.76 and 0.88, depending on operating current density. The charge transfer efficiency can be maintained at higher than 0.9 by limiting the cell number to less than 20.
20. An insight into the mechanism of charge-transfer of hybrid polymer:ternary/quaternary chalcopyrite colloidal nanocrystals.
Science.gov (United States)
Chawla, Parul; Singh, Son; Sharma, Shailesh Narain
2014-01-01
In this work, we have demonstrated the structural and optoelectronic properties of the surface of ternary/quaternary (CISe/CIGSe/CZTSe) chalcopyrite nanocrystallites passivated by tri-n-octylphosphine-oxide (TOPO) and tri-n-octylphosphine (TOP) and compared their charge transfer characteristics in the respective polymer: chalcopyrite nanocomposites by dispersing them in poly(3-hexylthiophene) polymer. It has been found that CZTSe nanocrystallites due to their high crystallinity and well-ordered 3-dimensional network in its pristine form exhibit a higher steric- and photo-stability, resistance against coagulation and homogeneity compared to the CISe and CIGSe counterparts. Moreover, CZTSe nanocrystallites display efficient photoluminescence quenching as evident from the high value of the Stern-Volmer quenching constant (K SV) and eventually higher charge transfer efficiency in their respective polymer P3HT:CZTSe composites. We modelled the dependency of the charge transfer from the donor and the charge separation mechanism across the donor-acceptor interface from the extent of crystallinity of the chalcopyrite semiconductors (CISe/CIGSe/CZTSe). Quaternary CZTSe chalcopyrites with their high crystallinity and controlled morphology in conjunction with regioregular P3HT polymer is an attractive candidate for hybrid solar cells applications.
1. Charge transfer in low-energy collisions of H with He+ and H+ with He in excited states
Science.gov (United States)
Loreau, J.; Ryabchenko, S.; Muñoz Burgos, J. M.; Vaeck, N.
2018-04-01
The charge transfer process in collisions of excited (n = 2, 3) hydrogen atoms with He+ and in collisions of excited helium atoms with H+ is studied theoretically. A combination of a fully quantum-mechanical method and a semi-classical approach is employed to calculate the charge-exchange cross sections at collision energies from 0.1 eV u‑1 up to 1 keV u‑1. These methods are based on accurate ab initio potential energy curves and non-adiabatic couplings for the molecular ion HeH+. Charge transfer can occur either in singlet or in triplet states, and the differences between the singlet and triplet spin manifolds are discussed. The dependence of the cross section on the quantum numbers n and l of the initial state is demonstrated. The isotope effect on the charge transfer cross sections, arising at low collision energy when H is substituted by D or T, is investigated. Rate coefficients are calculated for all isotopes up to 106 K. Finally, the impact of the present calculations on models of laboratory plasmas is discussed.
2. The simplest equivalent circuit of a pulsed dielectric barrier discharge and the determination of the gas gap charge transfer
International Nuclear Information System (INIS)
Pipa, A. V.; Brandenburg, R.; Hoder, T.; Koskulics, J.
2012-01-01
The concept of the simplest equivalent circuit for a dielectric barrier discharge (DBD) is critically reviewed. It is shown that the approach is consistent with experimental data measured either in large-scale sinusoidal-voltage driven or miniature pulse-voltage driven DBDs. An expression for the charge transferred through the gas gap q(t) is obtained with an accurate account for the displacement current and the values of DBD reactor capacitance. This enables (i) the significant reduction of experimental error in the determination of q(t) in pulsed DBDs, (ii) the verification of the classical electrical theory of ozonizers about maximal transferred charge q max , and (iii) the development of a graphical method for the determination of q max from charge-voltage characteristics (Q-V plots, often referred as Lissajous figures) measured under pulsed excitation. The method of graphical presentation of q max is demonstrated with an example of a Q-V plot measured under pulsed excitation. The relations between the discharge current j R (t), the transferred charge q(t), and the measurable parameters are presented in new forms, which enable the qualitative interpretation of the measured current and voltage waveforms without the knowledge about the value of the dielectric barrier capacitance C d . Whereas for quantitative evaluation of electrical measurements, the accurate estimation of the C d is important.
3. Charge separation and transfer in hybrid type II tunneling structures of CdTe and CdSe nanocrystals
International Nuclear Information System (INIS)
2013-01-01
Closely packed nanocrystal systems have been investigated in this thesis with respect to charge separation by charge carrier tunneling. Clustered and layered samples have been analyzed using PL-measurements and SPV-methods. The most important findings are reviewed in the following. A short outlook is also provided for potential further aspects and application of the presented results. The main purpose of this thesis was to find and quantify electronic tunneling transfer in closely packed self-assembled nanocrystal structures presenting quantum mechanical barriers of about 1 nm width. We successfully used hybrid assemblies of CdTe and CdSe nanocrystals where the expected type II alignment between CdTe and CdSe typically leads to a concentration of electrons in CdSe and holes in CdTe nanocrystals. We were able to prove the charge selectivity of the CdTe-CdSe nanocrystal interface which induces charge separation. We mainly investigated the effects related to the electron transfer from CdTe to CdSe nanocrystals. Closely packing was achieved by two independent methods: the disordered colloidal clustering in solution and the layered assembly on dry glass substrates. Both methods lead to an inter-particle distance of about 1 nm of mainly organic material which acts as a tunneling barrier. PL-spectroscopy was applied. The PL-quenching of the CdTe nanocrystals in hybrid assemblies indicates charge separation by electron transfer from CdTe to CdSe nanocrystals. A maximum quenching rate of up to 1/100 ps was measured leading to a significant global PL-quenching of up to about 70 % for the CdTe nanocrystals. It was shown that charge separation dynamics compete with energy transfer dynamics and that charge separation typically dominates. The quantum confinement effect was used to tune the energetic offset between the CdTe and CdSe nanocrystals. We thus observe a correlation of PL-quenching and offset of the energy states for the electron transfer. The investigated PL
4. Charge separation and transfer in hybrid type II tunneling structures of CdTe and CdSe nanocrystals
Energy Technology Data Exchange (ETDEWEB)
2013-11-08
Closely packed nanocrystal systems have been investigated in this thesis with respect to charge separation by charge carrier tunneling. Clustered and layered samples have been analyzed using PL-measurements and SPV-methods. The most important findings are reviewed in the following. A short outlook is also provided for potential further aspects and application of the presented results. The main purpose of this thesis was to find and quantify electronic tunneling transfer in closely packed self-assembled nanocrystal structures presenting quantum mechanical barriers of about 1 nm width. We successfully used hybrid assemblies of CdTe and CdSe nanocrystals where the expected type II alignment between CdTe and CdSe typically leads to a concentration of electrons in CdSe and holes in CdTe nanocrystals. We were able to prove the charge selectivity of the CdTe-CdSe nanocrystal interface which induces charge separation. We mainly investigated the effects related to the electron transfer from CdTe to CdSe nanocrystals. Closely packing was achieved by two independent methods: the disordered colloidal clustering in solution and the layered assembly on dry glass substrates. Both methods lead to an inter-particle distance of about 1 nm of mainly organic material which acts as a tunneling barrier. PL-spectroscopy was applied. The PL-quenching of the CdTe nanocrystals in hybrid assemblies indicates charge separation by electron transfer from CdTe to CdSe nanocrystals. A maximum quenching rate of up to 1/100 ps was measured leading to a significant global PL-quenching of up to about 70 % for the CdTe nanocrystals. It was shown that charge separation dynamics compete with energy transfer dynamics and that charge separation typically dominates. The quantum confinement effect was used to tune the energetic offset between the CdTe and CdSe nanocrystals. We thus observe a correlation of PL-quenching and offset of the energy states for the electron transfer. The investigated PL
5. Electrosynthesis of Copper-Tetracyanoquinodimethane Based on the Coupling Charge Transfer across Water/1,2-Dichloroethane Interface
International Nuclear Information System (INIS)
Huang, Li; Li, Pei; Pamphile, Ndagijimana; Tian, Zhong-Qun; Zhan, Dongping
2014-01-01
Graphical abstract: - Highlights: • Organic semiconductor CuTCNQ is synthesized through electrochemistry of liquid/liquid interface. • A coupling charge transfer (CCT) mechanism is proposed for organic electrosynthesis. • The obtained CuTCNQ has good electrochemical and electronic properties. - Abstract: The organic salt Copper-Tetracyanoquinodimethane (CuTCNQ) is an important semiconductor used in electronics for field-effect transistors, switches and memory devices. Here we present a novel electrosynthetic method of CuTCNQ microneedles based on the coupling charge transfer across water/1,2-dichloroethane (W/1,2-DCE) interface. A HOPG electrode is covered by a small volume of 1,2-DCE solution, which is further covered by an aqueous solution to construct the W/1,2-DCE interface. When TCNQ in 1,2-DCE phase is reduced on HOPG, Cu 2+ in the aqueous solution will transfer across the W/1,2-DCE interface in order to maintain the electric neutrality. Therein CuTCNQ microneedles are formed which have good solid-state electrochemical and electronic properties. This coupling charge transfer mechanism is valuable and broadens the applications of liquid/liquid interface in organic electrosynthesis
6. Intense charge transfer surface based on graphene and thymine-Hg(II)-thymine base pairs for detection of Hg(2.).
Science.gov (United States)
Li, Jiao; Lu, Liping; Kang, Tianfang; Cheng, Shuiyuan
2016-03-15
In this article, we developed an electrochemiluminescence (ECL) sensor with a high-intensity charge transfer interface for Hg(2+) detection based on Hg(II)-induced DNA hybridization. The sensor was fabricated by the following simple method. First, graphene oxide (GO) was electrochemically reduced onto a glassy carbon electrode through cyclic voltammetry. Then, amino-labeled double-stranded (ds)DNA was assembled on the electrode surface using 1-pyrenebutyric acid N-hydroxysuccinimide as a linker between GO and DNA. The other terminal of dsDNA, which was labeled with biotin, was linked to CdSe quantum dots via biotin-avidin interactions. Reduced graphene oxide has excellent electrical conductivity. dsDNA with T-Hg(II)-T base pairs exhibited more facile charge transfer. They both accelerate the electron transfer performance and sensitivity of the sensor. The increased ECL signals were logarithmically linear with the concentration of Hg(II) when Hg(2+) was present in the detection solution. The linear range of the sensor was 10(-11) to 10(-8)mol/L (R=0.9819) with a detection limit of 10(-11)mol/L. This biosensor exhibited satisfactory results when it was used to detect Hg(II) in real water samples. The biosensor with high-intense charge transfer performance is a prospect avenue to pursue more and more sensitive detection method. Copyright © 2015 Elsevier B.V. All rights reserved.
7. Moessbauer effect study of charge and spin transfer in Fe-Cr
International Nuclear Information System (INIS)
Dubiel, S.M.; Zukrowski, J.
1981-01-01
The influence of temperature and time of annealing on hyperfine fields and isomer shifts has been studied for a range of Fe-Cr alloys containing 1-45 at% Cr. It has been revealed that up to 15 at% Cr neither time or temperature of annealing practically does affect the hyperfine parameters. For more concentrated samples, however, both temperature and time of annealing are important. In particular, the Moessbauer spectrum of Fe-45.5 at% Cr annealed at 700 0 C for 5 h was a single-line indicating that the sample was paramagnetic. The observed changes of the hyperfine fields and the isomer shifts have been interpreted in terms of a spin and charge transfer, respectively. Strong linear correlations between the following quantities have been revealed: the hyperfine field H(0,0) and the isomer shift IS(0,0); the average hyperfine field anti H and the average isomer shift anti Ianti S; the average hyperfine field anti H and the average number of Cr atoms in the first two coordination spheres, anti N. It has been calculated from the first two correlations that a) a change of polarization of itinerant s-like electrons of one electron is equivalent to a change of the hyperfine field of 1602 kOe, and b) on average, a unit change of s-like electron polarization is equivalent to 3277 kOe. The two constants are very close to theoretical estimations, which can be found in literature. Correlation between the hyperfine field and the isomer shift led to a conclusion that the substitution of Fe atoms by Cr ones decreases the density of spin-up electrons on average by 0.026 electrons per one Cr atom in a unit cell. These electrons are most likely trapped by Cr atoms, because the hyperfine field at neighbouring Fe nuclei decreases and the density of charge at those nuclei increases at the rate of 0.029 electrons per one Cr atom in a unit cell. (orig./BHO)
8. CNDO/2-SCF and PCILO (MO) calculations on the 1-butene/NA/and (charge-transfer) complex
Energy Technology Data Exchange (ETDEWEB)
Lochmann, R; Meiler, W
1977-01-01
CNDO/2-SCF and PCILO (MO) calculations on the 1-Butene/Na/sup +/ (charge-transfer) complex involving the olefinic m electrons were made in connection with butene adsorption in zeolites, including the effect of the cation on the conformation of the butene in the zeolite cavity. Calculations were made of rotational energy barriers, preferred cation arrangements with respect to the butene molecule, and charge distributions by both methods. Taking into account systematic errors with the two methods, it is concluded that the PCILO method, which predicts a stabilization of the skew over the cis conformation by the cation, gives closer agreement with experiment. Graph, tables, diagrams, and 19 references.
9. Charge transfer and rapidity gap analysis in p(π+)n interactions at 195 GeV/c
International Nuclear Information System (INIS)
Eisenberg, Y.; Haber, B.; Hochmann, D.; Karshon, U.; Ronat, E.E.; Shapira, A.; Yekutieli, G.
1980-01-01
We present charge transfer probabilities between CM hemispheres in pn and π + n interactions at 195 GeV/c. The relative probabilities for charge exchanges ΔQ > 1 as a function of rapidity gap length, r, are given. Both results are compared with those of π - p interactions at 200 GeV/c. The average of r, viz. , is given as a function of the gap number and of ΔQ for various multiplicities, and the reduced average gap lengths /ysub(max) for pn interactions are compared with data at a lower energy. (orig.)
10. Twisted intra-molecular charge transfer investigations of semiorganic triglycine phosphate single crystal for non linear optical applications
Science.gov (United States)
Meera, M. R.; Joselin Beaula, T.; Rayar, S. L.; Bena Jothy, V.
2017-09-01
NLO materials are gaining importance in technologies such as optical communication, optical computing and dynamic image processing. Many NLO crystals grown by mixing amino acids with various organic and inorganic acids have been reported in the literature. Hence, glycine mixed semi-organic material will be of special interest as a fundamental building block to develop many complex crystals with improved NLO properties. A semi organic Single crystal of Triglycine Phosphate (TGP) which was grown and spectral analysis have been using FTIR and Raman spectral analysis. Natural Bond Orbital Analysis and the atomic natural charges are also predicted. HOMO LUMO energy gap value suggests the possibility of charge transfer within the molecule.
11. Charge transfer and band bending at Au/Pb(Zr0.2Ti0.8)O3 interfaces investigated by photoelectron spectroscopy
International Nuclear Information System (INIS)
Apostol, Nicoleta G.; Stoflea, Laura E.; Lungu, George A.; Chirila, Cristina; Trupina, Lucian; Negrea, Raluca F.; Ghica, Corneliu; Pintilie, Lucian; Teodorescu, Cristian M.
2013-01-01
The growth of gold layers on Pb(Zr,Ti)O 3 (PZT) deposited on SrTiO 3 is investigated by X-ray photoelectron spectroscopy in the Au thickness range 2–100 Å. Two phases are identified, with compositions close to nominal PZT. The ‘standard’ phase is represented by all binding energies (Pb 4f, Ti 2p, Zr 3d, O 1s) sensibly equal to the nominal values for PZT, whereas the ‘charged’ phase exhibits all core levels are shifted by ∼1 eV toward higher binding energies. By taking into account also scanning probe microscopy images together with recent photoemission results, the ‘charged’ phase belongs to P (+) regions of PZT, whereas the ‘normal’ phase corresponds to regions with no net ferroelectric polarization perpendicular to the surface. Au deposition proceeds in a band bending of Φ PZT − Φ Au ∼ 0.4–0.5 eV for both phases, identified as similar shifts toward higher binding energies of all Pb, Ti, Zr, O core levels with Au deposition. The Au 4f core level exhibits also an unusually low binding energy component 1 eV below the ‘nominal’ Au 4f binding energy position (metal Au). This implies the existence of negatively charged gold, or electron transfer from PZT to Au, although the ‘normal’ PZT phase have a higher work function, as it is derived from the band bending. Most probably this charge transfer occurs toward Au nanoparticles, which have even higher ionization energies. High resolution transmission electron microscopy evidenced the formation of such isolated nanoparticles.
12. Wireless Energy Transfer Using Resonant Magnetic Induction for Electric Vehicle Charging Application
Science.gov (United States)
Dahal, Neelima
The research work for this thesis is based on utilizing resonant magnetic induction for wirelessly charging electric vehicles. The background theory for electromagnetic induction between two conducting loops is given and it is shown that an RLCequivalent circuit can be used to model the loops. An analysis of the equivalent circuit is used to show how two loosely coupled loops can be made to exchange energy efficiently by operating them at a frequency which is the same as the resonant frequency of both. Furthermore, it is shown that the efficiency is the maximum for critical coupling (determined by the quality factors of the loops), and increasing the coupling beyond critical coupling causes double humps to appear in the transmission efficiency versus frequency spectrum. In the experiment, as the loops are brought closer together which increases the coupling between them, doubles humps, as expected from the equivalent circuit analysis is seen. Two models for wireless energy transfer are identified: basic model and array model. The basic model consists of the two loosely coupled loops, the transmitter and the receiver. The array model consists of a 2 x 2 array of the transmitter and three parasites, and the receiver. It is shown that the array model allows more freedom for receiver placement at the cost of degraded transmission efficiency compared to the basic model. Another important part of the thesis is software validation. HFSS-IE and 4NEC2 are the software tools used and the simulation results for wire antennas are compared against references obtained from a textbook and a PhD dissertation. It is shown that the simulations agree well with the references and also with each other.
13. Electronic structure, charge transfer, and intrinsic luminescence of gadolinium oxide nanoparticles: Experiment and theory
Science.gov (United States)
Zatsepin, D. A.; Boukhvalov, D. W.; Zatsepin, A. F.; Kuznetsova, Yu. A.; Mashkovtsev, M. A.; Rychkov, V. N.; Shur, V. Ya.; Esin, A. A.; Kurmaev, E. Z.
2018-04-01
The cubic (c) and monoclinic (m) polymorphs of Gd2O3 were studied using the combined analysis of several materials science techniques - X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and photoluminescence (PL) spectroscopy. Density functional theory (DFT) based calculations for the samples under study were performed as well. The cubic phase of gadolinium oxide (c-Gd2O3) synthesized using a precipitation method exhibits spheroidal-like nanoclusters with well-defined edges assembled from primary nanoparticles with an average size of 50 nm, whereas the monoclinic phase of gadolinium oxide (m-Gd2O3) deposited using explosive pyrolysis has a denser structure compared with natural gadolinia. This phase also has a structure composed of three-dimensional complex agglomerates without clear-edged boundaries that are ∼21 nm in size plus a cubic phase admixture of only 2 at.% composed of primary edge-boundary nanoparticles ∼15 nm in size. These atomic features appear in the electronic structure as different defects ([Gd…Osbnd OH] and [Gd…Osbnd O]) and have dissimilar contributions to the charge-transfer processes among the appropriate electronic states with ambiguous contributions in the Gd 5р - O 2s core-like levels in the valence band structures. The origin of [Gd…Osbnd OH] defects found by XPS was well-supported by PL analysis. The electronic and atomic structures of the synthesized gadolinias calculated using DFT were compared and discussed on the basis of the well-known joint OKT-van der Laan model, and good agreement was established.
14. Ab initio study of charge transfer between lithium and aromatic hydrocarbons. Can the results be directly transferred to the lithium-graphene interaction?
Science.gov (United States)
2014-08-28
We have used electronic density calculations to study neutral complexes of Li with aromatic hydrocarbons. The charge transferred between a Li atom and benzene, coronene, circumcoronene, and circumcircumcoronene has been studied by ab initio methods (at the HF and MP2 level). Toward this aim, the method of integrating electron density in two cuboid fragments of space was applied. One of the fragments was constructed so that it enclosed the bulk of the electron density of lithium; the second, the bulk of the electron density of hydrocarbon. It was found that for each complex two conformations were identified: the most stable with a greater vertical Li-hydrocarbon distance, on the order of 2.5 Å, and another of higher energy with a corresponding distance less than 2 Å. In all cases the transfer of a fractional number, 0.1-0.3 electrons, between Li and hydrocarbon was found; however, the direction of the transfer was not the same in all complexes investigated. The structures of complexes of the first configuration could be represented as Li(σ-)···AH(σ+), whereas the opposite direction of charge transfer was found for complexes of the second configuration, with higher energy. The directions of the dipole moments in the complexes supported these conclusions because they directly measure the redistribution of electron density in a complex with respect to substrates.
15. Design and characteristic investigations of superconducting wireless power transfer for electric vehicle charging system via resonance coupling method
Energy Technology Data Exchange (ETDEWEB)
Chung, Y. D. [Suwon Science College, Suwon (Korea, Republic of); Yim, Seung Woo [Dept. of Korea Electric Power Corporation Research Institute, Daejeon (Korea, Republic of)
2014-09-15
As wireless power transfer (WPT) technology using strongly coupled electromagnetic resonators is a recently explored technique to realize the large power delivery and storage without any cable or wire, this technique is required for diffusion of electric vehicles (EVs) since it makes possible a convenient charging system. Typically, since the normal conducting coils are used as a transmitting coil in the CPT system, there is limited to deliver the large power promptly in the contactless EV charging system. From this reason, we proposed the combination CPT technology with HTS transmitting antenna, it is called as, superconducting contactless power transfer for EV (SUWPT4EV) system. As the HTS coil has an enough current density, it can deliver a mass amount of electric energy in spite of a small scale antenna. The SUCPT4EV system has been expected as a noble option to improve the transfer efficiency of large electric power. Such a system consists of two resonator coils; HTS transmitting antenna (Tx) coil and normal conducting receiver (Rx) coil. Especially, the impedance matching for each resonator is a sensitive and plays an important role to improve transfer efficiency as well as delivery distance. In this study, we examined the improvement of transmission efficiency and properties for HTS and copper antennas, respectively, within 45 cm distance. Thus, we obtained improved transfer efficiency with HTS antenna over 15% compared with copper antenna. In addition, we achieved effective impedance matching conditions between HTS antenna and copper receiver at radio frequency (RF) power of 370 kHz.
16. Design and characteristic investigations of superconducting wireless power transfer for electric vehicle charging system via resonance coupling method
International Nuclear Information System (INIS)
Chung, Y. D.; Yim, Seung Woo
2014-01-01
As wireless power transfer (WPT) technology using strongly coupled electromagnetic resonators is a recently explored technique to realize the large power delivery and storage without any cable or wire, this technique is required for diffusion of electric vehicles (EVs) since it makes possible a convenient charging system. Typically, since the normal conducting coils are used as a transmitting coil in the CPT system, there is limited to deliver the large power promptly in the contactless EV charging system. From this reason, we proposed the combination CPT technology with HTS transmitting antenna, it is called as, superconducting contactless power transfer for EV (SUWPT4EV) system. As the HTS coil has an enough current density, it can deliver a mass amount of electric energy in spite of a small scale antenna. The SUCPT4EV system has been expected as a noble option to improve the transfer efficiency of large electric power. Such a system consists of two resonator coils; HTS transmitting antenna (Tx) coil and normal conducting receiver (Rx) coil. Especially, the impedance matching for each resonator is a sensitive and plays an important role to improve transfer efficiency as well as delivery distance. In this study, we examined the improvement of transmission efficiency and properties for HTS and copper antennas, respectively, within 45 cm distance. Thus, we obtained improved transfer efficiency with HTS antenna over 15% compared with copper antenna. In addition, we achieved effective impedance matching conditions between HTS antenna and copper receiver at radio frequency (RF) power of 370 kHz
17. Degree of phase separation effects on the charge transfer properties of P3HT:Graphene nanocomposites
International Nuclear Information System (INIS)
Bkakri, R.; Kusmartseva, O.E.; Kusmartsev, F.V.; Song, M.; Bouazizi, A.
2015-01-01
Graphene layers were introduced into the matrix of regioregular poly (3-hexylthiophene-2, 5-diyl) (RR-P3HT) via solution processing in the perspective of the development of organic nanocomposites with high P3HT/Graphene interfaces areas for efficient charge transfer process. P3HT and graphene act as electrons donor and electrons acceptor materials, respectively. Spatial Fourier Transforms (FFT) and power spectral density (PSD) analysis of the AFM images show that the phase separation decreases with increasing the graphene weight ratio in the P3HT matrix. The Raman spectra of the P3HT:Graphene nanocomposites shows that the G-band of graphene shifts to low frequencies with progressive addition of graphene which proves that there is an interaction between the nanowires of P3HT and the graphene layers. We suggest that the shift of the G-band is due to electrons transfer from P3HT to graphene. The quenching of the photoluminescence (PL) intensity of P3HT with addition of graphene proves also that an electrons transfer process occurred at the P3HT/Graphene interfaces. - Highlights: • Graphene layers are elaborated from expandable graphite oxide. • The effects of the graphene doping level on the charge transfer process were studied. • The phase separation process decreases with increasing the graphene content in the P3HT matrix. • Quenching of the PL intensity is due to electrons transfer from P3HT to graphene
18. Charge-Transfer Dynamics in the Lowest Excited State of a Pentacene–Fullerene Complex: Implications for Organic Solar Cells
KAUST Repository
Joseph, Saju
2017-10-02
We characterize the dynamic nature of the lowest excited state in a pentacene/C60 complex on the femtosecond time scale, via a combination of ab initio molecular dynamics and time-dependent density functional theory. We analyze the correlations between the molecular vibrations of the complex and the oscillations in the electron-transfer character of its lowest excited state, which point to vibration-induced coherences between the (pentacene-based) local-excitation (LE) state and the complex charge-transfer (CT) state. We discuss the implications of our results on this model system for the exciton-dissociation process in organic solar cells.
19. Altering intra- to inter-molecular hydrogen bonding by dimethylsulfoxide: A TDDFT study of charge transfer for coumarin 343
Science.gov (United States)
Liu, Xiaochun; Yin, Hang; Li, Hui; Shi, Ying
2017-04-01
DFT and TDDFT methods were carried out to investigate the influences of intramolecular and intermolecular hydrogen bonding on excited state charge transfer for coumarin 343 (C343). Intramolecular hydrogen bonding is formed between carboxylic acid group and carbonyl group in C343 monomer. However, in dimethylsulfoxide (DMSO) solution, DMSO 'opens up' the intramolecular hydrogen bonding and forms solute-solvent intermolecular hydrogen bonded C343-DMSO complex. Analysis of frontier molecular orbitals reveals that intramolecular charge transfer (ICT) occurs in the first excited state both for C343 monomer and complex. The results of optimized geometric structures indicate that the intramolecular hydrogen bonding interaction is strengthened while the intermolecular hydrogen bonding is weakened in excited state, which is confirmed again by monitoring the shifts of characteristic peaks of infrared spectra. We demonstrated that DMSO solvent can not only break the intramolecular hydrogen bonding to form intermolecular hydrogen bonding with C343 but also alter the mechanism of excited state hydrogen bonding strengthening.
20. Charge transfer effects on the Fermi surface of Ba0.5K 0.5Fe2As2
KAUST Repository
Nazir, Safdar
2011-01-31
Ab-initio calculations within density functional theory are performed to obtain a more systematic understanding of the electronic structure of iron pnictides. As a prototypical compound we study Ba0.5K 0.5Fe2As2 and analyze the changes of its electronic structure when the interaction between the Fe2As 2 layers and their surrounding is modified. We find strong effects on the density of states near the Fermi energy as well as the Fermi surface. The role of the electron donor atoms in iron pnictides thus cannot be understood in a rigid band picture. Instead, the bonding within the Fe2As 2 layers reacts to a modified charge transfer from the donor atoms by adapting the intra-layer Fe-As hybridization and charge transfer in order to maintain an As3- valence state. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8518101572990417, "perplexity": 4638.066521374741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156460.64/warc/CC-MAIN-20180920101233-20180920121633-00470.warc.gz"} |
https://www.zora.uzh.ch/id/eprint/28847/ | # Growth-dependent phenotypic variation of molluscan shells: implications for allometric data interpretation
Urdy, S; Goudemand, N; Bucher, H; Chirat, R (2010). Growth-dependent phenotypic variation of molluscan shells: implications for allometric data interpretation. Journal of Experimental Zoology. Part B: Molecular and Developmental Evolution:303-326.
## Abstract
In recent years, developmental plasticity has received increasing attention. Specifically, some studies highlighted a possible association between shell shape and growth rates in intertidal gastropods. We use a growth vector model to study how hypothetical growth processes could underlie developmental plasticity in molluscs. It illustrates that variation in instantaneous shell growth rate can induce variability in allometric curves. Consequently, morphological variation is time-dependent. Basing our model parameters on a study documenting the results of transplants experiments of three gastropods ecomorphs, we reproduce the main aspects of the variation in size, shape, and growth rates among populations when bred in their own habitat or transplanted to another ecotype habitat. In agreement with empirical results, our simulation shows that a flatter growth profile corresponds to conditions of rapid growth. The model also allows the comparison of allometric slopes using different subdata sets that correspond to static and ontogenetic allometry. Our model highlights that depending on subdata sets, the main effects could be attributed to source population or environment. In addition, convergence or divergence of allometric slopes is observed depending on the subdata sets. Although there is evidence that shell shape in gastropods is to some extent growth rate dependent, gaining a general overview of the issue is challenging, in particular because of the scarcity of studies referring to allometry. We argue that the dynamics of development at the phenotypic level constitute a non-reducible level of investigation if one seeks to relate the observed amount of phenotypic variation to variability in the underlying factors.
## Abstract
In recent years, developmental plasticity has received increasing attention. Specifically, some studies highlighted a possible association between shell shape and growth rates in intertidal gastropods. We use a growth vector model to study how hypothetical growth processes could underlie developmental plasticity in molluscs. It illustrates that variation in instantaneous shell growth rate can induce variability in allometric curves. Consequently, morphological variation is time-dependent. Basing our model parameters on a study documenting the results of transplants experiments of three gastropods ecomorphs, we reproduce the main aspects of the variation in size, shape, and growth rates among populations when bred in their own habitat or transplanted to another ecotype habitat. In agreement with empirical results, our simulation shows that a flatter growth profile corresponds to conditions of rapid growth. The model also allows the comparison of allometric slopes using different subdata sets that correspond to static and ontogenetic allometry. Our model highlights that depending on subdata sets, the main effects could be attributed to source population or environment. In addition, convergence or divergence of allometric slopes is observed depending on the subdata sets. Although there is evidence that shell shape in gastropods is to some extent growth rate dependent, gaining a general overview of the issue is challenging, in particular because of the scarcity of studies referring to allometry. We argue that the dynamics of development at the phenotypic level constitute a non-reducible level of investigation if one seeks to relate the observed amount of phenotypic variation to variability in the underlying factors.
## Statistics
### Citations
Dimensions.ai Metrics
37 citations in Web of Science®
30 citations in Scopus® | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8780739903450012, "perplexity": 3585.0930187671684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742253.21/warc/CC-MAIN-20181114170648-20181114192648-00409.warc.gz"} |
http://mathhelpforum.com/differential-geometry/191451-analytic-function-unit-disk.html | # Math Help - Analytic Function in the Unit Disk
1. ## Analytic Function in the Unit Disk
Dear Colleagues,
Let $f$ be analytic function in the unit disk $D=\{z \in C:|z|<1\}$ with $|f(z)|<1$, for any $z \in D$. If $f(z_{1})=z_{1}, f(z_{2})=z_{2}$ where $z_{1}$ and $z_{2}$ are distinct, show that $f(z)=z$ for any $z \in D$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9863070249557495, "perplexity": 140.67365275755702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1433195035761.14/warc/CC-MAIN-20150601214355-00062-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/derivatives-and-sa.5745/ | # Derivatives and SA
• Start date
• #1
Gale
676
2
in my calc class, someone noticed that when you take the derivative of the formula for volume of a circle, it becomes the formula for the surface area. anyone know why? and what other shapes is this also true for?
• #2
Staff Emeritus
Gold Member
10,275
40
It's because the volume of a sphere can be found by integrating the surface area of spherical shells from the center to the surface.
Integrate[4 Pi r^2, {r, 0, R}] = 4/3 Pi R^3
It works for any shape. An area integrated over a third dimension is a volume.
For a cube, the integral looks like:
Integrate[6 Sqrt[2] s^2, {s, 0, (Sqrt[2]/2) R}] = R^3
- Warren
• #3
Homework Helper
43,021
970
It is also true that the derivative of the Area of a circle:
[pi]r2 (with respect to r) is the circumference (2[pi]r).
That's basically because, as Chroot said, that you can find the volume a sphere by integrating the surface area of "nested" spheres or the area of a circle by integrating the circumference of "nested" circles.
• #4
Gale
676
2
damn well, too bad i don't know what integrating is... i'm not that far into calc, but i guess i can tell my teacher that at any rate. also, what other shapes, aside from circles. i think he said something about cones... or conics... or something, i missed it.
• #5
Staff Emeritus
Gold Member
14,967
19
Any surface that, when applying a coating of paint with uniform thickness, is (sufficiently close to) the same kind of surface.
• #6
Gale
676
2
Any surface that, when applying a coating of paint with uniform thickness, is (sufficiently close to) the same kind of surface.
umm... i have no clue what that means...
and since we're on the subject of my having no clue... what is this 'nesting of spherical shells'
• #7
Staff Emeritus
Gold Member
Dearly Missed
6,881
10
Like layers of an onion. There is an outside sphere, just a thin shell, and inside that is another shell whose outside surface exactly coincides with the inside surface of the first one. And ... so on... one shell inside another till you get to the center. These shells all have the same finite thickness. And then you think of having twices as many shells, each half as thick. And ... so on ... till in the limit of the thickness going to zero you recover the volume of the solid ball .
• #8
lethe
653
0
this result also follows from stoke s theorem, one of my favorite theorems.
• #9
893
3
Originally posted by Gale17
umm... i have no clue what that means...
and since we're on the subject of my having no clue... what is this 'nesting of spherical shells'
Here's the connection: If you paint a sphere, then the volume of paint used is the surface area times the thickness of the paint layer. Or, another way to put it is that the surface area is the volume of paint (dV) divided by the thickness of paint (dr); S=dV/dr.
This works because for a sphere, the thickness of paint is an increment in radius. It wouldn't work for, say, a cube when its volume is epressed in terms of the length of a side: V=a^3, but S is not 3a^2. However, if you write the volume of a cube in terms of _half_ a side's length h=a/2, then V=8h^3 and S is indeed 24h^2.
• #10
phoenixthoth
1,605
2
"Like layers of an onion. There is an outside sphere, just a thin shell, and inside that is another shell whose outside surface exactly coincides with the inside surface of the first one. And ... so on... one shell inside another till you get to the center. These shells all have the same finite thickness. And then you think of having twices as many shells, each half as thick. And ... so on ... till in the limit of the thickness going to zero you recover the volume of the solid ball ."
these layers have infinitesimal thickness, right?
cheers,
phoenix
• #11
Staff Emeritus
Gold Member
14,967
19
An example of something with which this will not work is in order...
ellipses and other conic sections are good example; if you paint an ellipse (with an even thickness), the result is not an ellipse.
• #12
137
0
Damn you all, thats all I can ever think about when I'm painting!
• #13
Gale
676
2
thanks, i understand now i think. i'll double check in class tomorrow. whats is stokes theorem?
• #14
Gale
676
2
ok, i didn't understand your answers well enough to explain to my teacher, who by the way, is a wicked pain in the ass, and won't just tell me. so, could some one either explain this a different way or tell me where i could find out or something.
also: i just realized i worded my first question wrong, i said circle, i meant sphere. when you take the derative from the formula for the volume of a shere, you get the formula for it's surface area. i need to know why this is, and what shapes it holds true for, and also why?
• #15
Staff Emeritus
Gold Member
10,275
40
Since a circle doesn't have a volume, I automatically assumed you actually meant sphere. All our responses are appropriate to the sphere.
Did you not read the responses? Or did you just not understand them?
Let's say you start with a tiny little ball bearing -- one so small that its volume is negligible.
You then paint a very thin layer of paint around the ball bearing. Then you add another layer, and another layer, and so on, until you have a baseball sized sphere. The volume is made up of many layered spherical shells of paint. You can imagine that the thickness of each of the layers is so small that they are essentially two-dimensional surfaces.
The volume of the sphere can be easily imagined to be composed of an infinite number of infinitely thin layers of paint. The surface area of each layer is 4 pi r^2. The integral (sum) of the layers is a volume, 4/3 pi R^3. (r is an internal radius, R is the radius of the outermost surface.)
If the integral of 4 pi r^2 (dr) from 0 to R (from the center to the outside of the sphere) is 4/3 pi R^3, then the converse is also true: the derivative of 4/3 pi R^3 is 4 pi r^2.
As has been mentioned, this method works for any volumes that can be built out of such layers of paint.
- Warren
• #16
Gale
676
2
ah thanks, i was only sort of half understanding your answers. i read them, and understood what they said, but not how they related to the math i guess. would you believe that the little peice of understanding i kept missing was that the "layers of paint" were '2 dimensional' or individual sort of surface areas. i get it now though, i was just dense.
• #17
lethe
653
0
Originally posted by Gale17
whats is stokes theorem?
stokes theorem says that for any space, of any dimension, the integral of some object on the boundary of that object equals the integral of the derivative of that object.
this breaks down into many familiar special cases, the fundamental theorem of calculus, the divergence theorem, the curl theorem for line integrals, the gradient theorem, and many higher dimensional generalizations.
the boundary of a filled ball is the sphere, so stokes theorem makes this relationship trivial to prove, along with many generalizations of it.
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308 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8585806488990784, "perplexity": 803.5409667648249}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337428.0/warc/CC-MAIN-20221003164901-20221003194901-00371.warc.gz"} |
http://libros.duhnnae.com/2017/jul7/150090974054-One-dimensional-model-of-streaking-experiment-in-solids-Condensed-Matter-Other-Condensed-Matter.php | # One-dimensional model of streaking experiment in solids - Condensed Matter > Other Condensed Matter
One-dimensional model of streaking experiment in solids - Condensed Matter > Other Condensed Matter - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: One-dimensional model for study of sub-femtosecond experiment with metalsurface is put forward. The important features of the system, such as thepseudopotential for electron motion in the metal bulk, abrupt decrease of thenormal to the surface external electromagnetic field in the bulk, finite valueof the mean free path for electrons in the metal, and action on the ejectedelectron by the stationary screened positive hole in the metal are includedin the model. The results obtained reveal dependence of the streaking effect onthe final energy of the ejected electron. Meanwhile, the dependence of thestreaking on the character of the initial state localized or delocalizedappears to be more pronounced. This result may provide an additional mechanismfor interpretation of the results of very recent experiment Cavalieri\emph{et.al}, NATURE \textbf{449} 1029-1032 2007 .
Autor: A.K. Kazansky, P.M. Echenique
Fuente: https://arxiv.org/ | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9191958904266357, "perplexity": 4189.988620351601}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741016.16/warc/CC-MAIN-20181112172845-20181112194845-00145.warc.gz"} |
http://mathoverflow.net/questions/115803/the-pde-u-t-u-xx-u-yy-the-simplest-linear-second-order-pde-that-isnt-ell | # The PDE $u_t=u_{xx}-u_{yy}$: The simplest linear second-order PDE that isn't elliptic, parabolic, or hyperbolic.
I know that there have been several questions on here and stackexchange about linear PDE's which don't fall into the standard classification, but I had a more focused question which I haven't seen answered. The PDE $u_t=u_{xx}-u_{yy}$ (or, equivalently, $u_t=u_{xy}$), is the simplest linear second-order PDE that is not elliptic, parabolic, or hyperbolic. Its time-invariant solutions are solutions to the one-dimensional wave equation.
My question is,
How does this PDE compare to the standard parabolic and hyperbolic PDE's in the following categories:
• Fundamental solution: is there an integral solution which is a convolution with a fundamental solution?
• Smoothness: are solutions infinitely smooth or does the smoothness depend on boundary conditions?
• Propagation speed: infinite or finite?
I only recently read Evan's PDE book, and the only question I really took a crack at was the first. I looked for a solution involving exponentials in t, but I couldn't find one. I am interested in this question purely from a classification standpoint. Thanks!
Edit: As the comments below indicate, there can be no general solution with arbitrary initial conditions analogous to that for parabolic or hyperbolic equations. Also, solutions need not be infinitely smooth. Since this answer was pieced together from the comments, I'm making this community wiki, in case anyone would like to add to it later.
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I don't know if this particular equation has been studied before, but there was a lot of work on linear constant coefficient PDE's, notably by Leon Ehrenpreis, back in the 60's and maybe 70's. You might want to dig through those to see what was done back then. Also, the most obvious way to try to analyze your questions is via separation of variables. – Deane Yang Dec 8 '12 at 16:34
If one specialises to solutions independent of x, one obtains the backwards heat equations $u_t = -u_{yy}$, which has basically no good solvability properties forward in time. So I doubt that there is any meaningful way to solve the initial value problem. – Terry Tao Dec 8 '12 at 17:54
Solutions need not be infinitely smooth. A nonsmooth solution $u(x,y)$ to the equation $u_{xx}-u_{yy}=0$ (and these certainly exist) will be a solution to your equation. – Robert Bryant Dec 8 '12 at 19:46
As the comments by Terry Tao and Robert Bryant indicate, the understanding of a broad class of solutions to a PDE usually requires both identifying what boundary or initial value conditions to impose and in what function space to look for solutions. Standard PDE's come from physical models or variational problems that tell you what these should be. With a PDE that is not based on any such model or variational problem, it is much less clear what to do. – Deane Yang Dec 8 '12 at 20:44
Exponential solutions are easy to find. Just plug $\exp(ax+by+ct)$, and you will see that every $(a,b,c)$ that satisfies $c=a^2-b^2$ gives you a solution. This polynomial is called the symbol of the differential operator. For the general theory of linear PDE with constant coefficients, the best source is the first two volumes of Hormander, Analysis of Linear Differential Operators. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9044260382652283, "perplexity": 287.2629748820031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049274324.89/warc/CC-MAIN-20160524002114-00078-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/circular-launch.42552/ | # Circular Launch
1. Sep 10, 2004
### EaGlE
A ball is launched up a semicircular chute in such a way that at the top of the chute, just before it goes into free fall, the ball has a centripetal acceleration of magnitude 2g.
1.)How far from the bottom of the chute does the ball land? Your answer for the distance the ball travels from the end of the chute should contain R.
D=__________
can someone help me start this? i really dont know where to start this problem from.
#### Attached Files:
• ###### M2K.ca.7.jpg
File size:
6.3 KB
Views:
74
2. Sep 10, 2004
### Sirus
Use what you know to find the velocity of the ball at the top of the chute, then treat it as a projectiles question, where you know the initial velocity, the initial height (2R), and the acceleration due to gravity: how much time does it take for the ball to reach the ground when considering only its accelerated vertical motion, and how far will it have travelled horizontally during this time?
3. Sep 10, 2004
### Pyrrhus
Remember:
$$A_{c} = \frac{V^2}{R}$$
where $$A_{c}$$ is Centripetal Acceleration.
4. Sep 10, 2004
### EaGlE
i dont remeber us doing this in class at all, so i read the chapter relating to this subject many times, and it's confusing for me.
ok i know that a = 9.8m/s^2, initial velocity = 0, initial height = 2r
so...
x(t) = 2r + 0 + 1/2(-9.8)t^2
2r = -4.9t^2
sorry but i have no clue on what to do...
$$A_{c} = \frac{V^2}{R}$$
we dont know velocity right? .....
5. Sep 11, 2004
### Pyrrhus
Well the Problem gives you the $$A_{c}$$ and in the graphic you can see the radius is R, how can you use the equation i gave you, in order to find the speed at the top? and then use that speed for the projectile motion part.
Similar Discussions: Circular Launch | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.897546648979187, "perplexity": 647.3964604223063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608765.79/warc/CC-MAIN-20170527021224-20170527041224-00152.warc.gz"} |
http://mathhelpforum.com/pre-calculus/147684-solve-non-linear-system-equations.html | # Math Help - solve - Non-linear System of equations
1. ## solve - Non-linear System of equations
solve
2. Originally Posted by dapore
solve
From equation 1:
$x^3 = 3xy^2 + 11$
$x^3 - 11 = 3xy^2$
$\frac{x^3 - 11}{3x} = y^2$
$y = \sqrt{\frac{x^3 - 11}{3x}}$.
Substituting into equation 2:
$y^3 = 3x^2y + 2$
$\left(\sqrt{\frac{x^3 - 11}{3x}}\right)^3 = 3x^2\sqrt{\frac{x^3 - 11}{3x}} + 2$
Now try to solve for $x$.
3. $(1) + i(2)$ and $(1) - i(2)$ we have
$(x-iy)^3 = 11+2i ~~ (x+iy)^3 = 11-2i$
$x-iy = \sqrt[3]{11+2i} ~~ x+iy = \sqrt[3]{11-2i}$
$x = Re(\sqrt[3]{11+2i}) ~~ , ~~ y = - Im(\sqrt[3]{11+2i})$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9625028371810913, "perplexity": 3961.388246778887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657124771.92/warc/CC-MAIN-20140914011204-00293-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
http://math.stackexchange.com/questions/3388/pq%c2%b2-rsp-where-p-q-r-s-are-distinct-single-digit-natural-numbers-then-r | # (PQ)²=RSP, where P,Q,R,S are distinct single digit natural numbers, then R=?
I have a problem I tried to solve, but couldn't because I don't know the method to solve it and I've never come across such problem.
Here's the problem.
$(PQ)²=RSP$
Where $P, Q, R, S$ are distinct single digit natural numbers, then $R=$?
We need to find out the value of $R$, and given option are
a) $1$
b) $2$
c) $3$
d) $4$
e) $5$
I've tried solving it by option with newly created equation as $Q^2=\frac{RS}{P}$ and taking values of $R$ from above options and other variables as distinct single digit numbers other than $R$, I've gone to a level after which I've got myself a lot confused and didn't know what to do. I think there is easier method to solve it which I don't know.
I'd appreciate if someone could give me a hand with this. Thanks in advance. :)
PS: The answer is c) $3$
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Do PQ and RSP indicate concatenation? You should say this. – Qiaochu Yuan Aug 26 '10 at 16:37
I'm not sure. They haven't given any more information about it. But I'm presuming they mean multiplication. Like this - (PQ)²=RS*P I could be wrong though. :\ – Electrifyings Aug 26 '10 at 16:42
Oh. You don't seem to have realized this! PQ does not mean P times Q, it means the number with first digit P and second digit Q. – Qiaochu Yuan Aug 26 '10 at 16:43
Qiaochu: You're right, but it can be seen why he'd think multiplication is happening; joining two variables as concatenation is something you don't see very frequently. – Ｊ. Ｍ. Aug 26 '10 at 16:47
Retagged from "numerical-methods" (which this definitely isn't) to "arithmetic." – whuber Aug 26 '10 at 18:30
The steps are as follows.
• A square number can only end in $1, 4, 5, 6, 9$. To prove this one uses modular arithmetic. So $P = 1, 4, 5, 6, 9$.
• $40^2 > 999$, so $P = 1$.
• Since $(PQ)^2$ ends in $1$, it follows that $Q = 1, 9$.
• Since $P \neq Q$, it follows that $Q = 9$.
• So the digits are $19^2 = 361$.
-
OMG, thanks for clearing this up. Yeah, I figured this by trial and error and by going with options. LOL, all this time I was thinking its a multiplication and never had a single strike in my mind about concatenation. Thanks man for clearing it up! You made my day! :D – Electrifyings Aug 26 '10 at 16:50
Generalizing from decimal to arbitrary radix, a quick computer search seems to indicate that there are only a handful of radices with such a unique solution. This leads to a proof of the following
THEOREM $\;$ If in radix $\rm M$ notation we have $\rm (PQ)^2 = RSP$ with $\rm P,Q,R,S$ distinct digits and this solution is unique in radix $\:\rm M \:$ then it is one of the following, where $\;\rm A = 10,\; B = 11, \:\ldots,\: I = 18 \;$.
$$\begin{array}{|r|r|r|} \hline \rm M & \rm PQ & \rm RSP \\ \hline 6 & 15 & 321 \\ 7 & 23 & 562 \\ 8 & 17 & 341 \\ 9 & 18 & 351 \\ 10 & 19 & 361 \\ 11 & \rm 1A & 371 \\ 18 & \rm 1H & \rm 3E1 \\ 19 & \rm 1\:I & \rm 3F1 \\ \end{array}$$
Proof: $\;$ The two general solutions listed below prove that all radices $\;\rm M > 26 \;$ have nonunique solution (except possibly $\rm M = 44\:$). The remaining small number of exceptional cases were verified by computer.
$\quad\quad\rm (1\: M + M-1)^2 \;=\; \;\;\: 3\: M^2 + (M\;-\;\:4) M + 1, \quad\quad M > 7$
$\quad\quad\rm (4\: M + M-2)^2 \;=\; 24\: M^2 + (M-20) M + 4, \quad\quad M>26,\;\; M \ne 44$
-
Nice conjecture. But when M > 81 you can check that 93^2 = (9M+3)^2 = 81M^2 + 54M + 9 = (81)(54)9; i.e., (M,P,Q,R,S) = (M,9,3,81,54) is a solution for all M >= 82. – whuber Aug 27 '10 at 20:50
@whuber: The conjecture is true - see the above proof. – Bill Dubuque Jan 12 '11 at 23:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9232916235923767, "perplexity": 517.244489902126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802766267.61/warc/CC-MAIN-20141217075246-00092-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/186307/hopf-algebra-identity-under-convolution | # Hopf algebra: Identity under convolution
In Hopf algebra texts, it is usually stated that $1=\eta\epsilon\in$Hom($H^C,H^A$) is the identity under convolution.
$\eta$ is the unit, $\epsilon$ is the counit.
My question is, is that a definition, or can it be proved?
Sincere thanks for any help.
(Do let me know if you need any clarification on the above notations.)
-
Let $\mathbb K$ be a field. Let $(A,m)$ be a associative $\mathbb K$-algebra with unit $\eta: \mathbb K \to A$ and let $(C,\Delta)$ be a coassociative $\mathbb K$-coalgebra with counit $\varepsilon: C \to \mathbb K$. The convolution $\star: \operatorname{Hom}(C,A) \times \operatorname{Hom}(C,A) \to \operatorname{Hom}(C,A)$ is defined by $$f \star g := m \circ (f \otimes g) \circ \Delta.$$ Let $\mathbf 1 := \eta(1_{\mathbb K})$, then from the definition of the unit follows $$m(\mathbf 1 \otimes a) = a \quad \text{for all } a\in A.$$ Furthermore, $$(\varepsilon \otimes \operatorname{id}) \circ \Delta = 1_{\mathbb K} \otimes \operatorname{id},$$ by definition of counit. Using this we show $$\eta \varepsilon \star f = f \star \eta\varepsilon = f \quad \text{for all } f \in\operatorname{Hom}(C,A).$$ For all $c \in C$ we have \begin{align*} (\eta\varepsilon \star f)(c) &= (m \circ (\eta \varepsilon \otimes f) \circ \Delta)(c)\\ &=(m \circ (\eta \otimes f) \circ (\varepsilon \otimes \operatorname{id}) \circ \Delta)(c)\\ &= (m \circ (\eta \otimes f))(1_{\mathbb K} \otimes c)\\ &= m(\mathbf 1 \otimes f(c))\\ &= f(c), \end{align*} hence $\eta\varepsilon \star f = f$. Similarly one shows $f \star \eta\varepsilon = f$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000044107437134, "perplexity": 649.4772339392777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065954.23/warc/CC-MAIN-20150827025425-00157-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://cs.stackexchange.com/questions/37818/language-consisting-of-all-turing-machine-encodings?noredirect=1 | # Language consisting of all Turing machine encodings [closed]
$A=${$⟨M⟩$:$M$ $is$ $a$ $Turing$ $Machine$ }
What can be said about $A$ ? Specifically, is $A$ decidable,regular,CFL,CSL?
I would say $A$ is decidable since we can write an algorithm to check whether a string is a valid encoding of a Turing machine .
But, is $A$ Regular[or CFL or CSL] ?
Edit : Someone argued that he could make an encoding where all the possible strings(What would be the alphabet here?-same as the encoding I suppose) are valid encoding of a TM(since there is a one-to-one correspondence between two countable infinite sets), hence making $A$ regular .
• Under any reasonable encoding, $A$ is decidable, but in order to say anything more, you need to fix an encoding. – Yuval Filmus Jan 31 '15 at 22:41
• Under one encoding, all strings are encodings of Turing machines. Under others, the encoding is so complicated that it is not even context-free. It depends on the encoding. If the question doesn't specify the encoding, the answer is: "it depends on the encoding". – Yuval Filmus Jan 31 '15 at 22:51
• Enumerate all Turing machines. As the encoding of an arbitrary Turing machine, use the number of the machine denoted in unary. Every unary number is now the encoding of a Turing machine, by definition. So the language of the encodings is $1^*$ (or $1^+$). – reinierpost Jan 31 '15 at 22:58
• The question does have an answer – it depends on the encoding. – Yuval Filmus Jan 31 '15 at 23:13
• Well, may be you could add it as an answer. – PleaseHelp Jan 31 '15 at 23:19
The complexity of $A$ depends on the encoding used for Turing machines. It is easy to come up with an encoding in which every string encodes some Turing machine (there are lots of ways). In contrast, it is easy to come up with artificially "hard" encodings, say the $k$th Turing machine being encoded by $1^kb$, where $b=1$ iff the $k$th Turing machine halts on the empty input; under this encoding, $A$ is not decidable. Nevertheless, it seems intuitively clear that any reasonable encoding makes $A$ decidable, though it's hard to say anything more without knowing the exact encoding. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9408840537071228, "perplexity": 422.7252266556905}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373095.44/warc/CC-MAIN-20210305152710-20210305182710-00116.warc.gz"} |
https://socratic.org/questions/why-chelate-compounds-are-stable-than-nonchelated-compounds | Chemistry
Topics
# Why chelate compounds are stable than nonchelated compounds?
Dec 3, 2016
Well, to compare them on equal footing, we would be considering the same bonds being made with each kind of compound.
Consider the following reaction:
["M"("NH"_3)_6]^(z+) + 3(en) rightleftharpoons ["M"(en)_3]^(z+) + 6"NH"_3
where $e n$ is ethylenediamine:
Visually, at first glance, the only difference between $e n$ and ${\text{NH}}_{3}$ is that $e n$ has a $- {\text{CH"_2-"CH}}_{2} -$ bridge connecting the two nitrogens, and that both "teeth" on $\boldsymbol{e n}$ bind to the same metal.
(They both have the same atoms that bind, and they both contribute zero charge.)
This will therefore have a net zero enthalpy for the breaking and formation of the six $\text{M"-"N}$ interactions, because each of the six ${\text{NH}}_{3}$'s would form one $\text{M"-"N}$ interaction, but each of the three $e n$'s would form two $\text{M"-"N}$ interactions.
All that means is that enthalpy is not a significant stabilizing factor.
The main difference we're looking for is that $e n$ is fixed to a cis configuration, so by binding via two "teeth", it is going to restrict its own mobility.
Entropy is smaller with more restricted motion.
Therefore, its entropy of bond formation is less positive, and the decrease in entropy due to the interaction corresponds to favoring $e n$ over ${\text{NH}}_{3}$ (since $\Delta {S}_{\text{rxn" = sum DeltaS_"bonds broken" - sum DeltaS_"bonds formed}}$).
We call this the chelate effect, where the binding of a chelating ligand like $e n$ in comparison to $N {H}_{3}$ is entropically favorable. Hence, a chelating ligand creates a more entropically stable compound.
##### Impact of this question
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http://math.stackexchange.com/questions/441719/defining-the-coboundary-map-delta-on-the-sheaf-cech-cohomology-groups/441770 | # Defining the coboundary map $\delta_*$ on the Sheaf Cech Cohomology groups
I'm having trouble understanding the definitions I've been reading, of what has been called an 'induced coboundary operator' or a 'connecting homomorphism' depending on what source you're reading.
Firstly, the what I've been working with is the Cech Homology groups are induced by the coboundary operator.
$$\check{H}^p(\mathcal{U},\mathscr{E}) = \frac{\ker(\delta:C^p(\mathcal{U},\mathscr{E}) \xrightarrow{} C^{p+1}(\mathcal{U},\mathscr{E}))}{\delta C^{p-1}(\mathcal{U},\mathscr{E})}$$
Where $\mathcal{U} = \{U_\alpha\}$ is a locally finite open cover of our manifold $M$.
Initially we start with a short exact sequence of Sheaves $$0 \xrightarrow{} \mathscr{E} \xrightarrow{\alpha} \mathscr{F} \xrightarrow{\beta} \mathscr{G}\xrightarrow{} 0$$
This induces a map on the Cech cochain complexes
$$C^p(\mathcal{U},\mathscr{E}) \xrightarrow{\alpha} C^p(\mathcal{U},\mathscr{F}) \xrightarrow{\beta} C^p(\mathcal{U},\mathscr{G})$$
Which consequently induces maps on the cohomology groups
$$\check{H}^p(\mathcal{U},\mathscr{E}) \xrightarrow{\alpha_*} \check{H}^p(\mathcal{U},\mathscr{F}) \xrightarrow{\beta_*} \check{H}^p(\mathcal{U},\mathscr{G})$$
All these definitions are fine so far, the problem I encounter is the source I'm reading: "Griffiths & Harris - Principles of Algebraic Geometry", gives a very loose definition of the induced coboundary map
$$\delta_*:\check{H}^p(\mathcal{U},\mathscr{G}) \xrightarrow{} \check{H}^{p+1}(\mathcal{U},\mathscr{E})$$
The definition is contained within a proof of another theorem, it involves diagram chasing, yet is rather difficult to interpret.
-
I managed to adapt a proof I found in here involving relative homology groups.
I will append a subscript $p$ to denote the maps from the respective cochain complexes and cohomology groups.
We can define the map $\delta_{*p}: \check{H}^{p}(\mathcal{U},\mathscr{G})\xrightarrow{} \check{H}^{p+1}(\mathcal{U},\mathscr{E})$ by taking $\sigma \in C^{p}(\mathcal{U},\mathscr{G})$ with $\delta_p \sigma = 0$, thus representing a cohomology class $[\sigma] \in \check{H}^{p}(\mathcal{U},\mathscr{G})$.
Since the map $\beta_p$ is surjective, there is a $\tau \in C^{p}(\mathcal{U},\mathscr{F})$ such that $\beta_p(\tau) = \sigma$.
Now $\delta_p(\tau) \in \ker(\beta_{p+1})$, since the diagram is commutative and $$\beta_{p+1} \delta_p \tau = \delta_p \beta_p(\tau) = \delta_p \sigma = 0$$ Using the exactness of the rows and injectivity of $\alpha$, we can say that there exists a unique $\lambda \in C^{p+1}(\mathcal{U},\mathscr{E})$ such that $\alpha_{p+1} (\lambda) = \delta_p(\tau)$ and again using commutivity, we can see that $$\alpha_{p+2} \delta_{p+1} \lambda = \delta_{p+1} \alpha_{p+1} \lambda = \delta_{p+1} \delta_p \tau = 0$$ Again, given $\alpha$ is injective, this implies $\delta_{p+1} \lambda = 0$ and $[\lambda] \in \check{H}^{p+1}(\mathcal{U},\mathscr{E})$.
We define $\delta_{*p} [\sigma] = [\lambda] \in \check{H}^{p+1}(\mathcal{U},\mathscr{E})$ $\square$
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9919447898864746, "perplexity": 224.44430028507665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00336-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-geometry/105552-epsilon-delta-proof.html | # Math Help - Epsilon-Delta Proof
1. ## Epsilon-Delta Proof
Q. Xa is a convergent sequence in R^n where Xa->X as a-> infinity. Use epsilon-delta proof to prove that, in two possibly cases, BXa -> BX as a-> infinity (where B is in R).
I tried using the Squeeze Theorem. (Since Xa-X -> 0 as a -> infinity,
B(Xa-X) -> 0 as a -> infinity). But don't know how there are two cases and whether this proof can be expressed as epsilon-delta proof.
Any help would be greatly appreciated.
Thanks.
2. Originally Posted by 6DOM
Q. Xa is a convergent sequence in R^n where Xa->X as a-> infinity. Use epsilon-delta proof to prove that, in two possibly cases, BXa -> BX as a-> infinity (where B is in R).
I tried using the Squeeze Theorem. (Since Xa-X -> 0 as a -> infinity,
B(Xa-X) -> 0 as a -> infinity). But don't know how there are two cases and whether this proof can be expressed as epsilon-delta proof.
Any help would be greatly appreciated.
Thanks.
Since $x_a \to x$ as $a \to \infty$
This means that for every $\epsilon > 0$ there is a $N \in \mathbb{N}$ such that for all $a > N$
$|x_a-x| < \epsilon$
Since this is true for every epsilon set $\epsilon ' =\frac{\epsilon}{B}$ and pick a new $N_1 \in \mathbb{N}$ such that when $a > N_1 \implies$ $|x_a-x|< \epsilon '$
Now for any $a> N_1$
$|Bx_a-Bx|=|B||x_a-x|<|B|\epsilon ' =|B|\frac{\epsilon}{B}=\epsilon$
3. Thanks!
So would the other case be when B is 0?
4. I suppose the cases are when $B=0$ and when $B \neq 0$. The first one is trivial for the second, let $\epsilon$ and $\delta$ be such that if $a> \delta$ then $\Vert x_a - x \Vert < \frac{ \epsilon }{ \vert B \vert }$ (this can be done since $x_a$ converges and $B$ is a constant) then if $a> \delta$ $\Vert Bx_a - Bx \Vert < \epsilon$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9820438027381897, "perplexity": 527.3929885284253}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447548525.16/warc/CC-MAIN-20141224185908-00070-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.pcb-3d.com/tutorials/dc-motors-voltage-current-speed-power-losses-and-torque-relationships/ | # DC Motors – current, voltage, speed, power, losses and torque relationships
This article presents basic physical sizes of DC motor with permanent magnet on the stator. This type of motor is very suitable for driving autonomous robots. A main power of the robot is a battery (DC voltage), as well as the power of these engines. In this article, a RE 35 motor with a GP 32 C reducer with a transmission ratio of 1: 14 and a 1: 33 designed and manufactured by MAXON was used as an example.
# How is torque related to current?
Image 1. Relationship between torque and armature current for the MAXON RE35
Image 1. shows dependence of the armature current from the engine torque for the MAXON RE35 when the armature winding voltage is 12V. The increase in the torque on the motor shaft results in the linear increase in the armature current. It is also shown in the equation (8) from the previous tutorial. The current function I, depending on the torque M, shows that more current flowing through the motor will produce a higher torque. Part of the diagram that is painted in yellow is the area in which the engine is not allowed to operate for a long time (short term operation).
# How is torque related to speed?
Image 2. Relationship between speed and torque for a MAXON RE35
For each DC motor, a function of speed n can be plotted, depending on the torque M (mechanical engine characteristics). Image 2 shows the dependence of the speed n on the torque M at a constant voltage of 12V. It can be noted that the speed decreases linearly when the torque increases.
To draw the curve, two endpoints are used. The first point is when the torque is zero. The second point is when the speed is zero. The image shows that the armature speed is 405 rpm (rotation per minute) when the torque is zero. The torque is 7050 mNm when the speed is zero. This is not presented in the Image 2. If the armature motor voltage is changed, speed and torque also proportionally change. The relation between the speed without load (n0) and armature voltage (U) is given in the following equation:
The mechanical power at the output is derived from the input electrical power and power losses (Joule losses) in the motor according to the equation (12). If we use the equations (8) (9) from our previous tutorial and (11) we can calculate output mechanical power with equation (12).
Legend:
Pel – input electrical power
Pj – Power losses in motor
Pmeh – output mechanical power
n – speed
R – armature resistance
I – armature current
Using the equation (8) and integrating the values for input electrical power and power losses into equation (12), we obtain velocity expressed via the torque:
The mechanical output power is calculated over the speed n and torque M according to the following equation (14):
# How is mechanical output power related to the torque?
Figure 3 shows how the mechanical output power depends on the torque for the MAXON RE35 DC motor. The curve is plotted when applied voltage is 12V and ambient temperature is 25 Celsius degrees.
Figure 3. Relation between the mechanical output power and the torque for the MAXON RE35
# How is coefficient of efficiency related to the torque?
The coefficient of efficiency describes the relationship between the mechanical power obtained at the output and the electric power applied to the motor input connections. Dependence of the coefficient of efficiency on the torque for the MAXON RE35 is given in Figure 4.
Figure 4. Relation between the coefficient of efficiency and the torque for the MAXON RE35
The expression for the coefficient of efficiency is given in the following formula (15):
# How is armature resistance related to torque?
Figure 5. Relation between the armature resistance and the torque for the MAXON RE35
Dependence of the armature resistance on the torque for the DC motor MAXON RE35 is given in Figure 5.
# How is winding temperature related to torque?
Figure 6. Relation between the coil temperature and the torque for the MAXON RE35
Dependence of the armature winding temperature on the torque for the MAXON RE35 is given in Figure 6.
Usually, encoder is used for measuring speed and position of motor shaft. More about basic operation principle of an encoder, you can find in our tutorial “Optical digital incremental encoder“. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8752362728118896, "perplexity": 1109.5196204372062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141184870.26/warc/CC-MAIN-20201125213038-20201126003038-00279.warc.gz"} |
https://blog.metatheorem.org/2018/07/24/Linear-Categories-A-Folklore-Simplification.html | ## Linear Categories: A Folklore Simplification
Published: 24 July 2018
Recently, I read this paper. The authors use a simplified definition of a linear category, but without proof that their definition is really the same. So I emailed them about it, and started a nice conversion with Damiano Mazza, Marco Gaboardi, and Flavien Breuvart. Then at FLOC 2018 this year I got the opportunity to meet Damiano Mazza, Marco Gaboardi, and a few others for lunch. I learned from Damiano that that their simplification to the definition of linear categories is correct, but this simplification seems to be folklore. So in this post I am going to write out this simplification, and prove that it is equivalent to the original definition of a linear category.
## Linear Categories
Linear categories are one of the first sound and complete categorical models of intuitionistic linear logic proposed in Gavin Bierman’s thesis. He shows that the linear exponential, $!A$, can be modeled as a symmetric monoidal comonad. His original definition (Definition 35 on p. 140) is as follows.
A linear category, $\cat{C}$, consists of the following structure:
1. A symmetric monoidal category, $\cat{C}$, with finite products and coproducts,
2. A symmetric monoidal comonad $(!,\varepsilon, \delta, \m_{A,B}, \m_I)$ such that
a. For every free $!$-coalgebra $(!A,\delta_A)$ there are two distinguished monoidal natural transformations with components:
• (Weakening) $\w_A : !A \mto I$
• (Contraction) $\c_A : !A \to !A \otimes !A$
which form a commutative comonad and are coalgebra morphisms.
b. Whenever $f : (!A,\delta_A) \mto (!B,\delta_B)$ is a coalgebra morphism between free coalgebras, then it is also a comonoid morphism.
There is a lot packed into this definition, but we will expanded it in the next section.
## Linear Categories Simplified
Essentially, the simplification amounts to realizing that part b can be proven from the previous parts of the definition of a linear category, but with an additional assumption that is simpler than part b. The expanded simplified definition is as follows.
A linear category, $\cat{A}$, consists of the following structure:
1. A is a symmetric monoidal category $(\mathcal{A},\otimes,I,\lambda,\rho,\alpha,\beta)$,
2. A linear exponential comonad, $(!_{-},\delta,\varepsilon)$, which has the following structure:
• The endofunctor $! : \mathcal{A} \mto \mathcal{A}$ forms comonad on $\cat{A}$. That is, there are two natural transformations $\delta : ! A \mto !! A$ and $\varepsilon : !A \mto A$ that make the following diagrams commute:
• Four natural transformations:
• (Monoidal Map) $\m_{A,B} : ! A \otimes ! B \mto ! (A \otimes B)$
• (Monoidal Unit Map) $\m_I : I \mto ! I$
• (Contraction) $\c : !A \mto !A \otimes !A$
• (Weakening) $\w : ! A \mto I$
• The functor $! : \mathcal{A} \mto \mathcal{A}$ is symmetric monoidal. That is, the following diagrams must commute:
• The functor $! : \cat{A} \mto \cat{A}$ is a symmetric monoidal comonad. That is, the following diagrams must commute:
• Weakening must satisfy the following diagrams:
• Contraction must satisfy the following diagrams:
• Weakening and contraction form a commutative comonoid. That is, the following diagrams commute:
• Weakening and contraction are coalgebra morphisms. That is, the following diagrams must commute:
• $\delta_A : !A \mto !!A$ is a comonoid morphism between the comonoids $(!A,\w,\c)$ and $(!!A,\w,\c)$. That is, the following diagrams must commute:
All of the structure in the previous definition except for the last bullet corresponds to part 1 and part 2.a of the original definition of a linear category. The last bullet is a simplification of part 2.b. We now show that we can prove part 2.b from the assumptions in this simplified definition.
Whenever $f : (!A,\delta_A) \mto (!B,\delta_B)$ is a coalgebra morphism between free coalgebras, then it is also a comonoid morphism.
Suppose $f : (!A,\delta_A) \mto (!B,\delta_B)$ is a coalgebra morphism between free coalgebras. This assumption amounts to assuming the following diagram commutes:
It suffices to show that $f : (!A,\delta_A) \mto (!B,\delta_B)$ is also a comonoid morphism. Hence, we must show that the following diagrams commute:
The left diagram commutes, because the following expanded one does:
Diagrams $(1)$ and $(4)$ commute because $\delta$ is a comonoid morphism, diagram $(2)$ commutes because $f$ is assumed to be a coalgebra morphism, and diagram $(3)$ commutes by naturality of $\w$. Note that we have numbered the previous diagram in the order of the necessary replacements needed when doing the same proof equationally, and we do the same for the next diagram. This should make it easier to reconstruct the proof.
The diagram for contraction commutes (the diagram on the right above), because the following expanded one does:
Diagram $(3)$ commutes because $f$ is assumed to be a coalgebra morphism, diagram $(4)$ commutes by naturality of $\c$, diagram $(5)$ commutes by naturality of $\m$, and diagram $(6)$ commutes by naturality of $\varepsilon$.
Diagrams $(1)$ and $(8)$ commute, because the following one does:
The left triangle commutes, because $! : \cat{A} \mto \cat{A}$ is a comonad, and the bottom diagram commutes by naturality of $\varepsilon$.
Finally, diagrams $(2)$ and $(7)$ do not actually commute, but are parallel morphisms whose cofork is $\delta$. That is, the following diagram commutes:
The left diagram commutes because $\delta : !X \mto !!X$ is a comonoid morphism, and the right diagram commutes because weakening and contraction are coalgebra morphisms.
Therefore, the original diagram above corresponds to the following equational proof:
## Conclusion
This was a really fun proof, but not at all obvious. Folklore results hinder scientific progress, and hinder new comers from progressing in our field. We need to be writing down these types of results so others do not have to! This is the point of research after all.
If anyone knows of a paper that writes this proof down, then I would like to know about it so I can cite it in future work. I will update this post with any citations I can find.
Updates: Jean-Simon Lemay has communicated to Damiano that this first appeared in a paper by Cocket, Seely, and Blute, but I have not had time to dig through their papers to get the precise citation yet. | {"extraction_info": {"found_math": true, "script_math_tex": 51, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9748095273971558, "perplexity": 542.4931693519567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510969.31/warc/CC-MAIN-20181017023458-20181017044958-00405.warc.gz"} |
https://crypto.stackexchange.com/questions/34601/how-to-prove-hardness-of-approximate-gcd-problem | # How to prove hardness of approximate-GCD problem?
I am trying to prove the security of my system using the hardness assumption of the approximate-GCD problem using contradiction, i.e. If the attacker is able to break in our scheme, then attacker would be able to solve the approximate-GCD problem. I am stuck at the point where I proved that the complexity is O(2^rho) using brute-force approach. How shall I proceed? Is there any concrete complexity measure which can be used as to prove the contradiction?
• Assume there is a crack for your scheme, and now show that by inputting careful values to this crack program, you obtain a solution to AGCD, or at least get something easily converted into a solution. This is the formula for a reductionist security proof. You just show that you can actually use any crack to compute the hard problem easily. Even if the crack works in an unexpected way. – MickLH Jan 25 '17 at 20:57
I am stuck at the point where I proved that the complexity is $O(2^\rho)$ using brute-force approach. How shall I proceed? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9459689855575562, "perplexity": 329.28393101887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251705142.94/warc/CC-MAIN-20200127174507-20200127204507-00409.warc.gz"} |
https://physics.stackexchange.com/questions/133610/what-is-supersymmetry | # What is supersymmetry?
1. What is supersymmetry?
2. How is it useful in unifying physics? I have heard that supersymmetry states that every fermion is associated with a boson and vice versa. But I don't get hope this can help resolving problems in unifying physics.
What is supersymmetry (in a big nutshell)?
To explain supersymmetry, let us consider the simplest supersymmetric model which is the Wess-Zumino model with an action,
$$S=-\int d^4x \left( \frac{1}{2}\partial^\mu \phi^\star \partial_\mu \phi + i\psi^\dagger \bar{\sigma}^\mu \partial_\mu \psi + |F|^2 \right)$$
where $\phi$ is a scalar field, $\psi$ a Majorana spinor field and $F$ is known as an auxiliary field, a pseudo-scalar, which arises due to a subtlety explained later. A supersymmetry is a continuous symmetry relating bosons to fermions and vice versa. Most importantly, for it to be a symmetry of the system, we must require that the Lagrangian changes only up to a total derivative. Naively, we might propose:
$$\delta\phi = \epsilon_\alpha \psi^\alpha$$ $$\delta\psi^\alpha = \epsilon^\alpha\phi$$
where we have introduced an infinitesimal parameter $\epsilon^\alpha$ which is required in order to balance the indices on both sides of the transformation. The parameter is fermionic; to deduce the dimensionality, we can do some dimensional analysis.
$$[\partial_\mu\phi^\star\partial_\mu\phi] = 4,\; [\partial_\mu] = 1$$
hence $[\phi] = 1$. Similar reasoning for the fermionic field shows $[\psi] = 3/2$, as expected. Now from the transformation, we may deduce the dimension of the arbitrary parameter:
$$[\epsilon^\alpha] = [\psi]-[\phi] = 1/2$$
and $[\epsilon_\alpha] = -1/2$. Plugging the transformation in, and deducing $\delta\mathcal{L}$, we will find it does not quite cancel to leave only a total derivative left. After some manipulation, we can find:
$$\delta\psi_\alpha = -i(\sigma^\nu\epsilon^\dagger)_\alpha \partial_\nu \phi$$
Now to address the auxiliary field, $F$. If we compute the equations of motion, we find
$$\frac{\partial \mathcal{L}}{\partial F} \sim F \quad \frac{\partial \mathcal{L}}{\partial (\partial F)} = 0$$
which implies $F=0$. Although it may seem adding the field has no effect, remember that $F=0$ is only true on-shell. The purpose of $F$ then is actually off-shell, which you will notice balances the required degrees of freedom of the system for consistency.
A Historical Note
In 1967, Coleman and Mandula published a paper, All Possible Symmetry of the S-Matrix, which aptly presented a theorem restricting S-matrix symmetries. However, a key assumption was
A symmetry transformation is said to be an internal symmetry transformation if it commutes with P. This implies that it acts only on particle-type indices, and has no matrix elements between particles of different four-momentum or different spin. A group composed of such transformations is called an internal symmetry group.
In other words, the symmetries were bosonic; notice that supersymmetry is in fact fermionic, and hence not subject to the Coleman-Mandula theorem. In some ways, one may attribute the initial development of supersymmetry to a desire to find a loophole in the Coleman-Mandula theorem.
Resources
• For a simple introduction, see the Beyond the Standard Model course by Professor Veronica Sanz, available here: http://www.perimeterscholars.org/338.html, which includes videos.
• For a modern introduction, complete with superfields, supermanifolds and more, see the text String Theory and M-Theory: A Modern Introduction, by Becker, Becker and Schwarz where it is presented in the context of string theory. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9113717079162598, "perplexity": 211.38571522560886}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00396.warc.gz"} |
https://sciencesprings.wordpress.com/2022/09/20/from-alice-at-cernch-alice-pins-down-hypermatter-properties/ | ## From ALICE at CERN(CH): “ALICE pins down hypermatter properties”
9.20.22
The collaboration’s latest study of a “strange” and unstable nucleus known as the hypertriton offers new insight into the particle interactions that may take place at the hearts of neutron stars.
The international ALICE collaboration at the Large Hadron Collider (LHC) has just released the most precise measurements to date of two properties of a hypernucleus that may exist in the cores of neutron stars.
Atomic nuclei and their antimatter counterparts, known as antinuclei, are frequently produced at the LHC in high-energy collisions between heavy ions or protons. On a less frequent but still regular basis, unstable nuclei called hypernuclei are also formed. In contrast to normal nuclei, which comprise just protons and neutrons (that is, nucleons), hypernuclei are also made up of hyperons – unstable particles containing quarks of the strange type.
Almost 70 years since they were first observed in cosmic rays, hypernuclei continue to fascinate physicists because they are rarely produced in the natural world and, although they are traditionally made and studied in low-energy nuclear-physics experiments, it’s extremely challenging to measure their properties.
At the LHC, hypernuclei are created in significant quantities in heavy-ion collisions, but the only hypernucleus observed at the collider so far is the lightest hypernucleus, the hypertriton, which is composed of a proton, a neutron and a Lambda – a hyperon containing one strange quark.
In their new study, the ALICE team examined a sample of about one thousand hypertritons produced in lead–lead collisions that occurred in the LHC during its second run. Once formed in these collisions, the hypertritons fly for a few centimetres inside the ALICE experiment before decaying into two particles, a helium-3 nucleus and a charged pion, which the ALICE detectors can catch and identify. The ALICE team investigated these daughter particles and the tracks they leave in the detectors.
By analysing this sample of hypertritons, one of the largest available for these “strange” nuclei, the ALICE researchers were able to obtain the most precise measurements yet of two of the hypertriton’s properties: its lifetime (how long it takes to decay) and the energy required to separate its hyperon, the Lambda, from the remaining constituents.
These two properties are fundamental to understanding the internal structure of this hypernucleus and, as a consequence, the nature of the strong force that binds nucleons and hyperons together. The study of this force is not only interesting in its own right but can also offer valuable insight into the particle interactions that may take place in the inner cores of neutron stars. These cores, which are very dense, are predicted to favour the creation of hyperons over purely nucleonic matter.
Measurements of the hypertriton’s lifetime performed with different techniques over time, including ALICE’s new measurement (red). The horizontal lines and boxes denote the statistical and systematic uncertainties, respectively. The dashed-dotted lines represent different theoretical predictions. (Image: ALICE collaboration)
The new ALICE measurements indicate that the interaction between the hypertriton’s hyperon and its two nucleons is extremely weak: the Lambda separation energy is just a few tens of kiloelectronvolts, similar to the energy of X-rays used in medical imaging, and the hypertriton’s lifetime is compatible with that of the free Lambda.
In addition, since matter and antimatter are produced in nearly equal amounts at the LHC, the ALICE collaboration was also able to study antihypertritons and determine their lifetime. The team found that, within the experimental uncertainty of the measurements, antihypertriton and hypertriton have the same lifetime. Finding even a slight difference between the two lifetimes could signal the breaking of a fundamental symmetry of nature, CPT symmetry.
With data from the third run of the LHC, which started in earnest this July, ALICE will not only further investigate the properties of the hypetriton but will also extend its studies to include heavier hypernuclei. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473496437072754, "perplexity": 1422.213430193264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943750.71/warc/CC-MAIN-20230322051607-20230322081607-00720.warc.gz"} |
http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-2 | PL EN
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## Studia Mathematica
2009 | 195 | 2 | 113-125
Tytuł artykułu
### Dimensions of non-differentiability points of Cantor functions
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For a probability vector (p₀,p₁) there exists a corresponding self-similar Borel probability measure μ supported on the Cantor set C (with the strong separation property) in ℝ generated by a contractive similitude $h_{i}(x) = a_{i}x + b_{i}$, i = 0,1. Let S denote the set of points of C at which the probability distribution function F(x) of μ has no derivative, finite or infinite. The Hausdorff and packing dimensions of S have been found by several authors for the case that $p_{i} > a_{i}$, i = 0,1. However, when p₀ < a₀ (or equivalently p₁ < a₁) the structure of S changes significantly and the previous approaches fail to be effective any more. The present paper is devoted to determining the Hausdorff and packing dimensions of S for the case p₀ < a₀.
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Tom
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113-125
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wydano
2009
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autor
• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China
autor
• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China
autor
• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China
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Bibliografia
Identyfikatory | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8174346685409546, "perplexity": 874.6764955756105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488507640.82/warc/CC-MAIN-20210622033023-20210622063023-00001.warc.gz"} |
https://www.arxiv-vanity.com/papers/cond-mat/0111022/ | # 25Mg NMR study of the MgB2 superconductor
M. Mali J. Roos, A. Shengelaya and H. Keller Physik–Institut, Universität Zürich, CH–8057 Zürich, Switzerland K. Conder Laboratory for Neutron Scattering, ETH Zürich and PSI Villigen, CH–5232 Villigen PSI, Switzerland
###### Abstract
NMR spectra and nuclear spin-lattice relaxation time, , have been measured in polycrystalline with a superconducting transition temperature = 39 K in zero magnetic field. From the first order and second order quadrupole perturbed NMR spectrum a quadrupole coupling frequency = 222.0(1.5) kHz is obtained. sK and Knight shift ppm are temperature independent in the normal conducting phase. The Korringa ratio equals to 0.95 which is very close to the ideal value of unity for s-electrons. The comparison of the experimental , , and with the corresponding values obtained by LDA calculations shows an excellent agreement for all three quantities.
###### pacs:
The recent discovery of superconductivity in with remarkably high = 39 K Nagamatsu has attracted much attention. In particular the observation of a sizeable boron Budko isotope effect strongly suggests that this simple layered intermetallic compound belongs to the conventional family of phonon mediated BCS superconductors. The relevant electron-phonon coupling constant is proportional to the density of states (DOS) at the Fermi level. So it is important to have experimental data of this quantity in .
Nuclear magnetic resonance (NMR) in metals probes the DOS at the Fermi level. The measured quantities, the spin lattice relaxation rate, 1/, and the Knight shift, , are related to the electron spin susceptibility () of electrons close to the Fermi level, specifically , and . In case the atomic site symmetry in the crystal structure is less than cubic and the atom has a nuclear quadrupole moment as it applies for Mg and B in , quadrupolar disturbed NMR delivers in addition valuable information on the electric field gradient (EFG) at the specific nuclear site. Unlike 1/ and the EFG is determined by the distribution of all charges. Up to date only measurements of 1/, , and of the quadrupole coupling to the EFG, expressed by quadrupole coupling frequency , of were performed Kotegawa ; Gerashenko ; Jung ; Tou . While there is reasonable agreement among ’s and relaxation rates, there is a considerable controversy concerning the Knight shifts. While some authors Gerashenko report in the normal conducting state a small temperature independent isotropic shift of 175 ppm, others Jung report a smaller and even temperature dependent shift of approximately 60 ppm, which they attribute to the Fermi-contact interaction. Finally there is also a report Tou of a negative shift of mere 5 ppm attributed to the core polarization. These large discrepancies most likely come from the choice of different materials as references for the Knight shift, as well as from difficulties to measure the small Knight shift of a broad and in addition quadrupolarly shifted central line powder spectrum.
As far as we know, there are no experimental data concerning the NMR quantities at the Mg site in , although theoretical predictions based on ab initio local density approximation (LDA) calculations exist for Mg Knight shift, 1/ and EFG Pavarini ; Tsvyashchenko . To some degree the lack of experimental Mg NMR data is understandable considering the fact that the only NMR active isotope has a small magnetic moment and low natural abundance. Consequently the NMR signals are weak even in high magnetic fields. Their detection often demands prohibitively long signal accumulation times. Despite this handicap we were able to measure NMR of the naturally abundant in . Here we report the temperature dependence of Knight shift, spin-lattice relaxation time, and quadrupole coupling frequency of in . We compare the experimental results with the theoretical predictions and we find for all three Mg NMR quantities an excellent agreement. Since all calculations were done by state of the art LDA methods the good agreement between calculated and measured NMR quantities confirms the LDA as a good approximation for .
The sample was prepared using stoichiometric amounts of magnesium and boron (99 and 99.99, respectively) in a form of powder. Both components were thoroughly mixed and pressed into pellets. These were placed in a tantalum crucible equipped with a non-vacuum tight cover. The crucible was then sealed under vacuum in a quartz ampoule. The sample was synthesized during heating at 600, 800 and 900 C for one hour at each temperature. X-ray diffraction (XRD) has revealed only small amount of as an impurity phase. DC magnetization measurements (Fig. 1) in a magnetic field of 1 mT (ZFC) yield a transition temperature of 39 K.
Before we proceed let us first present a few NMR relevant characteristics of the isotope. The isotope’s natural abundance is 10.0 and its nucleus has spin 5/2, a gyromagnetic ratio , and a quadrupole moment web elements . NMR measurements were performed on a polycrystalline powder sample with a pulsed Fourier-transform spectrometer at an external magnetic field T. Fig. 2 presents the central line powder spectrum gained by Fourier transform of the free induction decay signal induced by a -pulse.
The spectrum shows the typical powder pattern of the central transition line of a spin 5/2 system whose levels are disturbed in second order by quadrupole coupling to an axially symmetric EFG. There are two peaks in the spectrum with an indication of a washed out step left and close to the minimum between the peaks. The three features from left to right (see Fig. 2) are the extrema singularities that occur at three powder grain orientations having either , or . Here represents the angle between the largest principal component, , of the EFG tensor and the magnetic field direction. Due to the site symmetry the EFG tensor at Mg and B sites is axially symmetric along the c-axis. Therefore its points into the c-axis direction. From the distance between the two peaks in the spectrum and by help of the second order quadrupole effect expression Abragam
Δν=25[I(I+1)−3/4]ν2Q144νL=25ν2Q18νL,
we can calculate , defined as
νQ≡3eQVzz2I(2I−1)h=3eQVzz20h.
Having kHz and Larmor frequency MHz, as determined by NMR from in water solution, one gets kHz. In addition we were able to see the singularities of the first satellites in the satellite powder spectrum presented in the insert of Fig. 2. From the separation of the two first satellite singularities, that are positioned symmetrically with respect to the central line , one gets immediately . For an axially symmetric EFG is simply equal to this separation. The gained kHz agrees very well with the above result. The second result, however, is always more reliable especially in case when the additional Knight shift of the spectrum is anisotropic. Since for there is no quadrupole shift of the central line the step in the spectrum can be used to determine the Knight shift, , of the crystallites whose c-axis is parallel to the magnetic field. From the shift of the step with respect to we get then ppm. Further we noticed that the ratio of the distances of the and singularities with respect to the step is somewhat less than the value 16/9 theoretically expected for an isotropic magnetic shift of the central line powder spectrum. This allows the conclusion that the Knight shift has to be slightly anisotropic. The Knight shift, , for crystallites whose c-axis is perpendicular to must be a bit larger than . We estimate the difference between and to be about +10 ppm. In the normal conducting phase from 294 K down to 19 K we observe that the Knight shift (see Fig. 3) and = 222.0(1.5) kHz remain in error bar limits constant.
Such a behavior was also observed for Knight shift Gerashenko and Gerashenko ; Jung . At 19 K the shape of the Mg central line spectrum changes drastically . The peak of the singularity starts to diminish and disappears quickly by cooling below 19 K. In Fig. 4 we exhibit two central line spectra one measured at 6 K and the other one at 294 K that have their intensities scaled to equal height for easier comparison. The peak of the singularity seen in the high temperature spectrum obviously is missing in the 6 K spectrum. We explain this by the appearance of superconductivity in the grains with their c-axis close to the direction perpendicular to the external magnetic field. Nevertheless, a substantial part of the spectrum coming from crystallites with a smaller remains unchanged down to 6 K. This indicates that in a magnetic field of 9 T at 6 K a substantial part of the powder sample still remains normal conducting. In view of the large anisotropy quoted in the literature (2 – 9) LimaPatnaikSimon this comes not as a surprise.
However, this has consequences for the determination of NMR quantities and their temperature dependence in the superconducting phase. Necessarily one has to take into account the anisotropy and avoid to average over the NMR signals coming from crystallites with different orientations in the magnetic field. For reliable NMR measurements in the superconducting state large enough single crystals or aligned crystallites of are most desirable.
The measurements of the NMR quantity were done by the method of selective inversion of the central line and a subsequent monitoring of the nuclear magnetization recovery at variable delay times t. The relaxation rate defined as , where W represents the spectral density of the fluctuating internal magnetic fields, was extracted by fitting the data to the recovery law
M(t)M(∞)=1−Γ[135e−2Wt+845e−12Wt+5063e−30Wt],
obtained from the solution of the master equation for a spin 5/2 system in case of magnetic relaxation and selective excitation of the central line AndrewSuter . The constant , also a fit parameter, depends on the inversion ratio of the central line. We measured only in the normal conducting phase at three temperatures 30, 80 and 294 K. The results are presented in Table 1. As expected for a metal the product remains constant. The weighted average of the three values is sK.
What is the dominant mechanism of magnetic relaxation and Knight shift of Mg and B in ? In most metals it is the Fermi-contact interaction of the nucleus with the s-electrons at the Fermi level. However, in case of the states near the Fermi level are mainly boron p-electron states with a very small contribution of the s-electrons. Pavarini et al. Pavarini making ab initio LDA calculations of 1/ and at and sites in show that the dominant relaxation mechanism at the nucleus is the interaction with the electronic orbital moment. For the nucleus, however, they predict that the dominant relaxation mechanism is the Fermi-contact interaction, which also dominates the Mg Knight shift. They get for sK, ppm, and ppm which is in excellent agreement with our experimental values sK, ppm, and ppm. Forming the Korringa ratio Carter we get experimentally , where sK for , with and the gyromagnetic ratios for electron and nucleus, respectively. The observed experimental Korringa ratio of 0.95 is very close to the ideal value of unity for s-electrons. This result is another confirmation that the Fermi-contact interaction is indeed the dominant mechanism responsible for relaxation and Knight shift at the Mg site.
As next we compare the experimentally determined major principal component, , of the EFG tensor at the Mg site with calculated ab initio within the density functional theory by Tsvyashchenko et al. Tsvyashchenko using the full-potential linearized augmented plane wave method. From the experimentally determined and by use of the quadrupole moment we extract the absolute value V/m . The quadrupole coupling to the EFG and therefore do not depend on the sign of . The gained experimental has then to be compared to the absolute value of the calculated V/m Tsvyashchenko . We note that the agreement of both absolute values is excellent. Tsvashchenko et al. Tsvyashchenko also calculated at the boron site where they get V/m which again is in good agreement with the experimental value V/m Gerashenko ; Jung . The ability to reproduce the experimental NMR quantities at both Mg and B sites by LDA calculations certainly strengthens the confidence into the LDA approach to calculate other material parameters.
The authors acknowledge useful discussions with M. Angst. The work was supported in part by the Swiss National Science Foundation. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8724038004875183, "perplexity": 1038.528518159162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00483.warc.gz"} |