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https://www.physicsforums.com/threads/help-finding-the-initial-speed.260972/

# Help finding the initial speed 1. Oct 1, 2008 ### 1234567890 Help finding the initial speed plz !!! 1. The problem statement, all variables and given/known data An archer shoots an arrow horizontally at a target 12 m away. The arrow is aimed directly at the center of the target, but it hits 52 cm lower. What was the initial speed of the arrow? (Neglect air resistance.) 2. Relevant equations the equation i was given is : y= h - .5at^2 and x=vo*t so we then know t= x/vo second part of the equation is y=h -.5 a(x/vo)^2 then vox* the square root of (a/2)*(x^2/h-y) 3. The attempt at a solution the problem im having is finding all the right data to complete the problem. We know x = distance which then = 12 and h(height) = 52cm or .52m so in the first equation when it says y=h-.5at^2 and x=vo*t we need to find t so we can subsitute it for t^2 in the 1st equation. so the equation is t=x/vo and we get t=12/vo i dont need the answer to the problem i just need help finding what t is so i can solve it for myself. can you please explain how to find vo or whatever i need to find to start this problem. ive been working on it for a while now and i cant seem to come up with any answers. Thanks alot to anyone who can be a hand 2. Oct 1, 2008 ### Sakha Re: Help finding the initial speed plz !!! You know that the arrow accelerate downwards 9.8m/s2 (g), so using your distance formula, you could get the time it takes to the arrow to travel 52cm downwards. That same time is the time that the arrow, with speed v travels 12m in direction to the target. 3. Oct 1, 2008 ### 1234567890 Re: Help finding the initial speed plz !!! thanks man i got it Similar Discussions: Help finding the initial speed

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https://deepai.org/publication/ear-slicing-for-matchings-in-hypergraphs

# Ear-Slicing for Matchings in Hypergraphs We study when a given edge of a factor-critical graph is contained in a matching avoiding exactly one, pregiven vertex of the graph. We then apply the results to always partition the vertex-set of a 3-regular, 3-uniform hypergraph into at most one triangle (hyperedge of size 3) and edges (subsets of size 2 of hyperedges), corresponding to the intuition, and providing new insight to triangle and edge packings of Cornuéjols' and Pulleyblank's. The existence of such a packing can be considered to be a hypergraph variant of Petersen's theorem on perfect matchings, and leads to a simple proof for a sharpening of Lu's theorem on antifactors of graphs. ## Authors • 4 publications • ### A generalization of the Kővári-Sós-Turán theorem We present a new proof of the Kővári-Sós-Turán theorem that ex(n, K_s,t)... 02/13/2020 ∙ by Jesse Geneson, et al. ∙ 0 • ### Color-critical Graphs and Hereditary Hypergraphs A quick proof of Gallai's celebrated theorem on color-critical graphs is... 10/24/2019 ∙ by András Sebő, et al. ∙ 0 • ### Sufficient Conditions for Tuza's Conjecture on Packing and Covering Triangles Given a simple graph G=(V,E), a subset of E is called a triangle cover i... 05/06/2016 ∙ by Xujin Chen, et al. ∙ 0 • ### On the connectivity threshold for colorings of random graphs and hypergraphs Let Ω_q=Ω_q(H) denote the set of proper [q]-colorings of the hypergraph ... 03/14/2018 ∙ by Michael Anastos, et al. ∙ 0 • ### On S-packing edge-colorings of cubic graphs Given a non-decreasing sequence S = (s 1,s 2,. .. ,s k) of positive inte... 11/29/2017 ∙ by Nicolas Gastineau, et al. ∙ 0 • ### Linear Programming complementation and its application to fractional graph theory In this paper, we introduce a new kind of duality for Linear Programming... 07/30/2019 ∙ by Maximilien Gadouleau, et al. ∙ 0 • ### The complete set of minimal simple graphs that support unsatisfiable 2-CNFs A propositional logic sentence in conjunctive normal form that has claus... 12/28/2018 ∙ by Vaibhav Karve, et al. ∙ 0 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction Given a hypergraph , where is the power-set of we will call the elements of vertices, and those of hyperedges, . We say that a hypergraph is -uniform if all of its hyperedges have elements, and it is -regular if all of its vertices are contained in hyperedges. Hyperedges may be present with multiplicicities, for instance the hypergraph with consisting of the hyperedge with multiplicity is a -uniform, -regular hypergraph. The hereditary closure of the hypergraph is where , and is hereditary, if . For the new edges of the hereditary closure we do not need to define multiplicities we will consider them all to be one. Hyperedges of cardinality will be called singletons, those of cardinality and are called edges and triangles respectively. Deleting a vertex of the hypergraph results in the hypergraph . For hereditary hypergraphs this is the same as deleting from all hyperedges. The degree of in is the number of hyperedges containing . Given a hypergraph , denote by the set of edges (of size two) in , . We do not need parallel edges in , we suppose is a graph without parallel edges or loops. The (connected) components of are defined as those of . These form a partition of , and correspond to the usual hypergraph components: is connected if is connected. Abusing terminology, the vertex-set of a component is also called component. We define a graph as a hypergraph with , that is, a -uniform hypergraph without loops or parallel edges. A matching in a graph is a set of pairwise vertex-disjoint edges. A matching is perfect if it partitions the vertex-set of the graph. A graph is called factor-critical if has a perfect matching (also called a -factor) for all . In this note we prove two lemmas, possibly interesting for their own sake, on when a given edge of a factor-critical graph is contained in a matching avoiding exactly one, pregiven vertex of the graph, leading to a result on -uniform hypergraphs (Section 2). We then prove that a -regular and -uniform hypergraph is perfectly matchable in some sense (a generalization of Petersen’s theorem [6] on -uniform hypergraphs), sharpening a result of Lu’s [5] (Section 3). ## 2 Ears and Triangles An ear-decomposition consists of a circuit , and paths sharing its (one or two) endpoints with ; are called ears. An ear is called trivial, if it consists of one edge. An ear is called odd if it has an odd number of edges. Lovász [3], [4] proved that a graph is factor-critical if and only if it has an ear-decomposition with all ears odd. For , denote by ear the index of the first ear when vertex occurs. (It may occur later only as an endpoint of an ear.) Given an ear-decomposition, we call an edge odd, if earear, and if we also require that is joined to an endpoint of by an odd subpath of not containing , and that the same holds interchanging the role of and . We will call an odd ear-decomposition maximal if for every odd edge , earear, we have . Clearly, there exists a maximal odd ear-decomposition, since while there are odd edges with endpoints on , we can obviously replace the ears and , where is necessarily a trivial ear, with two odd ears. In particular, an odd ear-decomposition with a maximum number of nontrivial ears (equivalently, with a minimum number of trivial ears) is maximal. We need the following lemmas that may also have some self-interest and other applications: for , , it provides a sufficient condition for to have a perfect matching containing . ###### Lemma 2.1. Let be a factor-critical graph given with an odd ear-decomposition, and let be an odd edge in a nontrivial ear. For any vertex with earearear, there exists a perfect matching of containing . Proof : Let be the ear-decomposition. We can suppose without loss of generality (since by the easy direction of Lovász’s theorem [3], a graph having an odd ear-decomposition is factor-critical) that is on the last ear . Since is in , and is factor-critical (again by the easy direction of Lovász’s theorem), has a perfect matching . Adding the odd edges of to , we get the matching of the assertion. Cornuéjols, Hartvigsen and Pulleyblank [1], [2] (see also [4]) need to check when a factor-critical graph is partitionable into triangles and edges, and for this they try out all triangles. The following lemma improves this for the unions of triangles by showing that they always have such a partition: ###### Lemma 2.2. If is a -uniform hypergraph and is factor-critical, then has a partition into one triangle and a perfect matching in . Proof : Consider a maximal odd ear-decomposition, let be an odd edge on its last nontrivial ear and let be a triangle containing . If ear, we are done by Lemma 2.1: a matching , of and the triangle do partition . Suppose now ear. If choose a vertex on at odd distance from both and , and let both and denote this same vertex. The following proof holds then for both or . We can suppose without loss of generality that the endpoint of the ear , , , and the other endpoint of (possibly ) follow one another in this order on the ear. The path between and is even, because if it were odd, the edge would be odd - the path between and being odd by the assumption that the edge is odd -, contradicting the maximality of the ear-decomposition. But then a perfect matching of and every second edge of the subpath of between and , covering but not covering , and the odd edges of the rest of including , form a perfect matching in containing . Replacing in this perfect matching by finishes the proof. ## 3 Regular Hypergraphs ###### Theorem 3.1. If is a -uniform, -regular hypergraph, then has either a perfect matching (if is even), or it is factor-critical (if is odd) and in the latter case can be partitioned into one triangle and a perfect matching of . Proof : If has a perfect matching we have nothing to prove. Suppose it has not. Claim. is factor-critical. We prove more: for , , the number of components of satisfies . (Then by Tutte’s theorem [7], see also [4], has a perfect matching for all .) For each component , by -regularity, . In this sum, divisible by , every hyperedge is counted as many times as it has vertices in . Since is connected, and , we have that the sum of for all hyperedges that meet , itself divisible by by -uniformity, is strictly larger than . Therefore, the sum of for these edges is nonzero and also divisible by , so it is at least . The vertices not in of the edges that meet are in , hence , so summing for all edges, the sum is at least : 3k≤∑e∈E|e∩X|≤∑x∈XdH(x)=3|X|, so , finishing the proof of the claim. Now Lemma 2.2 can be readily applied. The intuition that at most one triangle may be enough is highly influenced by Cornuéjols, Hartvigsen and Pulleyblank’s work [1], [2], even if these are not explicitly used. The heart of the proof is encoded in the two lemmas that show: we can either increase the number of nontrivial ears or find the wanted partition, and for this, -uniformity is not needed. The proof is clearly algorithmic, providing a low degree polynomial algorithm. Finally, we prove a sharpening of Lu’s theorem [5], which considered a question in [4]. A simple proof of Lu’s theorem has been the initial target of this work. ###### Corollary 3.1. Let be a -regular bipartite graph with bipartition and . Then has a subgraph with all degrees of vertices in equal to , all degrees of vertices in equal to or , except possibly at most one vertex of which is of degree . Proof : Delete pairwise disjoint perfect matchings one by one (they are well-known to exist in bipartite regular graphs  [4] by Hall’s theorem, actually a -edge-coloring also exists by Kőnig’s edge-coloring theorem). Define then the hypergraph with , and to have one hyperedge for each consisting of the set of neighbors of . Since there are no loops or parallel edges in (see Section 1), the defined hypergraph is -uniform and -regular. Apply now Theorem 3.1. As the proof shows, the essential case is , when the theorem can be considered to be a generalization of Petersen’s theorem [6] about perfect matchings in graphs. Let us also state the reformulation to hypergraphs by the inverse of the correspondence in the proof: ###### Corollary 3.2. If is a -uniform, -regular hypergraph, , then can be partitioned into hyperedges of of size and at most one hyperedge of size . Acknowledgment: Many thanks to Zoltán Szigeti and Louis Esperet for precious suggestions! ## References • [1] G. Cornuéjols, W. R. Pulleyblank, Critical Graphs, Matchings and Tours or a Hierarchy of Relaxations for the Travelling Salesman Problem, Combinatorica, 3(1) (1983), 36–52. • [2] G. Cornuéjols, D. Hartvigsen, W.  R .Pulleyblank, Packing Subgraphs in a Graph, Operations Research letters, Volume 1, Number 4 (1982) • [3] L. Lovász, A note on factor-critical graphs, Studia Sci. Math. Hungar., 7, 1972, 279–280. • [4] L. Lovász, M. D. Plummer, Matching theory, Ann. Discrete Math., 29 North Holland, Amsterdam, 1986. • [5] H. Lu, Antifactor of regular bipartite graphs, https://arxiv.org/pdf/1511.09277v1.pdf • [6] J. Petersen, Die Theorie der regulären Graphen, Acta Math,, 15, 1891, 193–220, Jbuch. 23-115. • [7] W. T. Tutte, The factorization of linear graphs, J. of the London Mathematical Society, 22, 107-111.

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https://www.muchen.ca/documents/ASTR200/asn1.html

Muchen He 44638154 [email protected] muchen.ca ASTR 200 # W19 Assignment 1 Updated 2019-09-11 ## 1. Angles Big and Small (a) Imagine that you are at the centre of the Earth, which you can assume to be transparent. Consider two points on the Earth’s surface that are separated by 10 arcseconds. What is the physical distance between the two points? The physical distance we’re looking for between the two points is the arclength we’re trying to find, where the angle is 10 arcseconds. First, we convert the angle from arcsec to radians: $\theta=10{\small\text{arcsec}}\times\frac{1{\small\text{arcmin}}}{60{\small\text{arcsec}}}\times\frac{1{\small\deg}}{60{\small\text{arcmin}}}\times\frac{\pi}{180{\small\deg}}=4.85\times10^{-5}$ Then to find the arc length, we use the radius of Earth, which is $R_\oplus$=6371 km. \begin{aligned} d&=\theta r\\ &=\theta R_\oplus\\ &=(4.85\times10^{-5})(6371\text{ km})\\ &=\boxed{0.309\text{ km}} \end{aligned} Therefore the distance between the two points is 0.309 km or 308.8 m. (b) How many square degrees are on the full celestial sphere? The full celestial sphere is a whole sphere with surface area $A=4\pi r^2$. The square angle of a full celestial sphere is simply the area divided by $r^2$ which gives us $\Omega=4\pi$ steradians. To convert to square degrees, we use the conversion factor to convert from radians to degrees except we need to square the conversion factor because we’re working with two-dimensional units. $\Omega_{\deg}=\Omega\times\left(\frac{180\deg}{\pi}\right)^2$ Plugging in the numbers: $\Omega_{\deg}={4\pi\cdot180\over\pi}=\boxed{720\deg^2}$ The solid degrees that covers the full celestial sphere is 720 square degrees. (c) You have a telescope with a CCD detector that has a square field of view of 4 square arcminutes. How many pointings of the telescope will be needed to cover an area of 6 degrees by 10 degrees? Assume that we’re looking at the celestial sphere. Assume that our CCD detector is a square sensor such that the field of view of 4 square arcminutes is 2 arcminutes for horizontal and vertical field of view. Then we convert 2 arcminutes to degrees: $2\small{\text{arcmin}}\times\frac{1\deg}{60\small{\text{arcmin}}}=0.0\bar 3 \deg$ That means we for each frame, we can cover 0.03 degrees by 0.03 degrees. Which means: $\frac{6\deg}{0.0333\deg}=180\\ \frac{10\deg}{0.0333\deg}=300$ It takes 180 and 300 pointings respectively to cover 6 degrees by 10 degrees area. Therefore, the total number of pointings required is $180\times300=\boxed{54,000}$ We need 54,000 pointings to cover an area of 6 degrees by 10 degrees. ## 2. Solar System Basics (a) The observed orbital synodic periods of Venus and Mars and 583.9 days and 779.9 days, respectively. Calculate their sidereal periods. Assume 1 year is exactly 365.25 days. Then Venus has an orbital synodic period of 1.5986 years, and Mars has an orbital synodic period of 2.1338 years. Synodic means that this is the time interval for the planet to repeat a configuration with respect to Earth. To calculate the sidereal period, we use the relationship $\frac{1}{P_\text{syn}}=\frac{1}{P_\text{inner}}-\frac{1}{P_\text{outer}}$ Venus is an inferior planet. So we’re solving for the “inner” sidereal period; the “outer” sidereal period is Earth’s so it’s simply 1. \begin{aligned} \frac{1}{1.5986\text{ yr}}&=\frac{1}{P_\text{inner}}-1\\ P_\text{inner}&=\left(\frac{1}{1.5986\text{ yr}}+1\right)^{-1}\\ &=\boxed{0.6255 \text{ yr}} \end{aligned} Mars is a superior planet. So we are solving for the “outer” sidereal period. Identical procedure: \begin{aligned} \frac{1}{2.1338\text{ yr}}&=1-\frac{1}{P_\text{outer}}\\ P_\text{outer}&=\left(1-\frac{1}{2.1338\text{ yr}}\right)^{-1}\\ &=\boxed{1.882 \text{ yr}} \end{aligned} The sidereal orbital period of Venus and Mars respectively is 0.6255 years or 228.5 days, and 1.882 years or 687.4 days. (b) Which of the superior planets has the shortest synodic period, and why? Using the relationship between sidereal and synodic period from above, and simplifying for superior planets, we get $P_{\text{syn}_\text{superior}}=\frac{P_\text{outer}}{P_\text{outer}-1}$ To obtain the shortest synodic period, There must be a great difference in sidereal period of Earth and the superior planet. In other words, in this case, we’re look for a planet with the longest sidereal period, or the planet that orbits farthest away from center. At the time of writing, the superior planet that has the shortest synodic period is Neptune. (c) A certain asteroid is 1 au from the Sun at perihelion and 5 au from the Sun at aphelion. Find the semi-major axis, eccentricity, and semi-minor axis of its orbit. Include a sketch of the geometry. First, the sketch of the geometry: The perihelion and aphelion (as seen from the drawing) makes up the major axis. Therefore the semimajor axis is given by: $a=\frac{1\text{AU}+5\text{AU}}{2}=\boxed{3\text{AU}}$ The geometric center is therefore 3AU from both perihelion and aphelion. The distance from one of the foci to the geometric center is given by $ae=2$AU. This distance is determined by subtraction of perihelion as seen in the drawing. Therefore the eccentricity is: $e=\frac{2\text{AU}}{3\text{AU}}=\boxed{2/3}$ Now we assume a point on the ellipse such that the distance to one focus is the same as to the other focus ($r=r’$). Then we can make a right-angle triangle and apply the Pythagoras theorem to find the semi-minor axis $b$. In particular, we know that $r=r’$ and that the definition of the ellipse is $r+r’=2a$ which leads to $r=r’=a$. Applying the Pythagorean theorem with the right triangle: $b^2+(ae)^2=r^2$ Substitute the variables and then rearrange we can calculate the semi-minor axis $b$: \begin{aligned} b^2&=a^2(1-e^2)\\ b&=\sqrt{a^2(1-e^2)}\\ &=\sqrt{(3)^2\left(1-\left(\frac{2}{3}\right)^2\right)}\\ &=\sqrt{5}\\ &=\boxed{2.236\text{AU}} \end{aligned} The geometry of the asteroid’s orbit has semimajor axis of 3AU, eccentricity of ⅔ or 0.667, and semi-minor axis of 2.236AU. ## 3. Calculus Refresher A simple model of a planetary atmosphere has the number density $n$ decreasing roughly exponentially with height $z$ above the planet’s surface: $n(z)=n_0e^{-z/H_p}$, where $n_0$ is the number density at the surface of the planet, and $H_p$ is is the pressure scale height. At the surface of the Earth, the number density for nitrogen is $n_0=2\times 10^{25} \text{m}^{-3}$ and the scale height for is about $H_p=8.7$ km. The model is valid up to about 90 km. Compute the number of nitrogen molecules in the Earth’s atmosphere. You will have to make at least one important approximation in order to do this; explain clearly what you have done. First, let’s graph the density function of Nitrogen from sea level (z=0) to z=90 km: ### Approximation #1 Notice that even though the exponential decay of number of particles is significant at the altitude of 90 km, there is still a significant number of nitrogen particles in magnitude of 6.43×1020 per meter cubed. We can make an approximation that the function $n(z)$ is piecewise such that for $z>90$ km, $n(z)=0$. ### Approximation #2 We approximate that the planet is a completely smooth sphere such that the density is uniform everywhere. ### Integration Function The function for total number of particles is an integration of a multiplication of density function and volume. $\int_0^{90,000}n(z)A(z)\mathrm dz$ Where $n(z)$ is the density function of Nitrogen as previously defined. Function $A(z)$ is surface area of the atmosphere for a specific $z$ height. Both $A(z)\mathrm dz$ will give us the volume of infinitesimal slice of the atmosphere. The area function is given by the formula of the surface area of a sphere plus the altitude $z$: $A(z)=4\pi (R_\oplus+z)^2$ ### Computing the Integral \begin{aligned} N&=\int n(z)A(z)\mathrm dz\\ &=4\pi n_0 \int e^\frac{-z}{H_p}(R_\oplus+z)^2 \mathrm dz \end{aligned} This is a very complicated function to integrate. So let’s do some digging into whether if this is necessary (See next section). ### Approximation #3 The lower bound of the surface area is at sea-level, where z=0, then $A(0)$=5.10×108 km2. The upper bound is at z=90km, and $A(90\text{km})$=5.24×108 km2, which is less than 3% difference. Knowing that because Earth’s radius is so large compared to the thickness of the atmosphere we’re considering, we can approximate Earth’s atmosphere as a flat sheet, by “unwrapping” the spherical shell into a flat disk with top area of $4\pi R_\oplus^2$ and 90km thick. Now the modified function to integrate is as follows. The two equations are for lower and upper bound of number of nitrogen particles, respectively. $N_\text{lower bound}=4\pi R_\oplus^2 n_0 \int e^{-\frac{z}{H_p}} \mathrm dz\\ N_\text{upper bound}=4\pi (R_\oplus+90,000)^2 n_0 \int e^{-\frac{z}{H_p}} \mathrm dz$ But because of the exponential falloff of the number of particles as we move away from Earth’s surface, the lower bound approximation is more accurate. Ergo we will just calculate the lower bound. ### Computing the Definite Integral Let’s do the integration first. \begin{aligned} \int_0^{90,000} e^{-\frac{z}{H_p}}\mathrm dz &=\left[-H_p e^{-\frac{z}{H_p}}\right]^{z=90,000}_{z=0}\\ &=H_p \left( 1-e^{-\frac{90,000}{H_p}} \right)\\ &=8,700 \left( 1-e^{-\frac{90,000}{8,700}} \right)\\ &=8,699.72\text{m} \end{aligned} Now we multiply the rest: \begin{aligned} 4\pi R_\oplus^2 n_0 \int e^{-\frac{z}{H_p}} \mathrm dz &=4\pi R_\oplus^2 n_0(8699.72)\\ &=\boxed{8.875\times10^{43}} \end{aligned} Using meter as standard unit for all calculations, we get the final answer of 8.875×1043 particles.

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http://mathoverflow.net/questions/47835/when-can-you-reverse-the-orientation-of-a-complex-manifold-and-still-get-a-compl?sort=oldest

# When can you reverse the orientation of a complex manifold and still get a complex manifold? I'm told that $\overline{\mathbb{C}P^2}$, i.e. $\mathbb{C}P^2$ with reverse orientation, is not a complex manifold. But for example, $\overline{\mathbb{C}}$ is still a complex manifold and biholomorphic to $\mathbb{C}$. This makes me wonder, if $X$ is complex manifold is there a general criterion for when $\overline{X}$ also has a complex structure? For example, it seems that if $X$ is an affine variety than simply replacing $i$ with $-i$ gives $\overline{X}$ a complex structure and $X, \overline{X}$ are biholomorphic. EDIT: the last claim is wrong; see BCnrd's comments below and Dmitri's example. Also, as explained by Dmitri and BCnrd, $X$ should be taken to have even complex dimension. Another question: if $X$ and $\overline{X}$ both have complex structures, are they necessarily biholomorphic? Edit: No per Dmitri's answer below. - Is there a simple reason for why $\overline{\mathbb{CP}^2}$ is not a complex manifold? – J.C. Ottem Nov 30 '10 at 22:31 @J.C. Ottern: Any almost complex structure compatible with the orientation on a closed 4-manifold $X$ satisfies $c_1^2[X]=2\chi+3\sigma$ ($\chi$=Euler char, $\sigma$=signature). This is by Hirzebruch's signature theorem. – Tim Perutz Nov 30 '10 at 22:40 Fix an alg. closure $\mathbf{C}$ of $\mathbf{R}$, equipped with unique abs. value extending the one on $\mathbf{R}$, complex analysis is developed without needing a preferred $\sqrt{-1}$. The complex structure has no reliance on any orientation. The so-called canonical orientation on complex manifolds is just the functorial one arising from a choice of $\sqrt{-1}$; can make either choice, complex structure can't tell! Likewise, the analytification functor on locally finite type $\mathbf{C}$-scheme has nothing to do with any such choice. Note $p$-adic analysis goes the same way. – BCnrd Nov 30 '10 at 22:48 What is canonical is that even-dim'l C-manifolds have an intrinsic orientation determined by C-structure: an orientation of $\mathbf{C}$ endows all C-manifolds with functorial orientation, and changing initial choice affects the orientation on $n$-dimensional C-manifolds by $(-1)^n$. So for even $n$ the question is well-posed. This has nothing to do with changing $i$ and $-i$, and your impression in the affine case is wrong. In any dim., can "twist" structure sheaf by C-conj. to get a new C-manifold (modelled on $\overline{f}(\overline{z})$), but that's a different beast. – BCnrd Nov 30 '10 at 23:13 If you take an odd dimensional complex manifold $X$ with holomorphic structure $J$ then $-J$ defines on $X$ a holomorphic structure as well. And, of course, $J$ and $-J$ induce on $X$ opposite orientations. In general it is not true that these two complex manifolds are biholomprphic. Indeed, if $X$ is a complex curve, then $(X,J)$ is biholomorphic to $(X,-J)$ only if $X$ admits and anti-holomorphic involution (this will be the case for example if $X$ is given by an equation with real coefficients). Starting from this example on can construct a (singular) affine variety $Y$ of dimension $3$, such that $(Y,J)$ is not byholomorphic to $(Y,-J)$. Namely, let $C$ be a compact complex curve that does not admit an anti-holomorphic involution say of genus $g=2$. Consider the rank two bundle over it, equal to the sum $TC\oplus TC$ ($TC$ is the tangent bundle to $C$). Contract the zero section of the total space of this bundle, this gives you desired singular $Y$. - Nice example but I wonder -and this is not so important, just curious if there's a nice answer- if $C$ is a genus 2 curve and I describe it as a degree 2 cover of $\mathbb{P}^1$: $y^2 = (x - a_1)\cdots (x - a_6)$, is there simple condition on the $a_i$ that guarantees that it does not have an antiholomorphic involution? – solbap Dec 1 '10 at 16:23 Yes, there should be a relatively simple criterion, one should check when the configuration of points $a_1,...,a_6$ is (not) invariant under any anti-holomorphic involution of $\mathbb CP^1$. For example, in the case of elliptic curve $y^2=(x-a_1)...(x-a_4)$ the necessary and sufficient condition for having anti-holomorphic involution is that the double ratio of $\frac{a_1-a_2}{a_3-a_4}$ is real. If all double ratios of $a_1,...,a_6$ are real, then again we have an anti-holomorphic involution. But this is not necessary there are two more cases (like $(x^2+a)(x^2+b)(x^2+c)$ $a,b,c>0$)... – Dmitri Dec 1 '10 at 17:51 It seems to me that you could be interested in the following (I haven't checked the paper in detail, but I think theorems of this "style" could be helpful for you): Theorem Let $X$ be a compact complex surface admitting a complex structure for $\bar{X}$. Then $X$ (and $\bar{X}$) satisfies one of the following: (1) $X$ is geometrically ruled, or (2) the Chern numbers $c_1^2$ and $c_2$ of $X$ vanish, or (3) $X$ is uniformised by the polydisk. In particular, the signature of $X$ vanishes. Other material that could be helpful is: -

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http://math.stackexchange.com/questions/149491/linear-algebra-norm-notation

# Linear algebra norm notation I was reading a paper where the authors used the following notation: $||b - \mathbf{A}x||^2_D = (b - \mathbf{A}x)^t \mathbf{D} (b - \mathbf{A}x)$, where $\mathbf{D}$ is a diagonal matrix I was curious about the subscript $D$ when taking the norm-2. Does this notation represent something special or is it just the author's way of expressing the quantity in the right hand side? Have you guys encountered this notation before? Thanks! - Yes, this is fairly standard notation with 'variable metric' methods of optimization. The expression above is the definition, except that $D$ is positive definite (otherwise it doesn't define a norm). –  copper.hat May 25 '12 at 5:37 I hope I understood the question correctly. I think the superscript $2$ is just supposed to mean "squared", it has nothing to do with the $2$-norm, and is just the author's way of expressing the right hand side. The reason the notation is natural is the following: given a diagonal matrix $D$ with positive entries, we can define an inner product by $$\langle x,y\rangle_D = x^TDy$$ Now every inner product $\langle \cdot, \cdot \rangle$ induces a norm by $$\|x\| = \sqrt{\langle x, x \rangle }$$ or, in other words, $$\|x\|^2 = \langle x, x \rangle$$ So what the author means is that the norm $\|x\|_D$ is defined by $$\|x\|_D = \sqrt{\langle x,y\rangle_D} = \sqrt{x^TDx}$$ or, to avoid the square root notation, $$\|x\|_D^2 = x^TDx$$ I guess the only correlation to the $2$-norm is that both are induced by an inner product. - Ok. I understand that the superscript 2 means "squared." I can also see why this expressions is natural. My only question was about the subscript $D$. I think your answer makes sense i.e the author defined the $||x||_D$ as $x^T D x$. I was just wondering if this operation had a particular name. Thanks! –  Damian May 25 '12 at 4:35 @Damian OK. I'm not aware of any particular name for this. Maybe someone else knows though. –  user12014 May 25 '12 at 4:46 One might extend this notation to any positive definite symmetric matrix in place of $\mathbf D$, which (for a finite dimensional real vector space) will give you an arbitrary inner product, and norm defined by such an inner product. Although it is not mentioned, I suppose $\mathbf D$ has only positive diagonal entries (so is positive definite), otherwhise it does not define an inner product or norm. –  Marc van Leeuwen May 25 '12 at 4:47 Yes, you are right. The paper does mention that the elements of $\mathbf{D}$ are positive. So you are saying that $\mathbf{D}$ does not have to be diagonal, right? –  Damian May 25 '12 at 4:49

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https://worldwidescience.org/topicpages/l/l3+experimental+hall.html

#### Sample records for l3 experimental hall 1. Rock support of the L3 experimental hall complex International Nuclear Information System (INIS) Laughton, C. 1990-06-01 The methods of excavation and support selected for the LEP works are discussed in this paper. The excavation of the halls and chambers in discrete passes, from the roof down, and their temporary support by patterned fully bonded rock bolts and shotcrete ensured that mass deformations were contained. When working in soft rock materials where discontinuity, elastic and possibly plastic deformations may each play an important role in the overall rock structure stability, it is of paramount importance to systematically monitor the behavior of the rock in-situ. The use of instrumentation to indicate location, direction, levels, and rate of movement is essential to ensure that a safe, efficient and economical mining operation can be undertaken, and that any remedial action will be taken at the appropriate time. The use of the New Austrian Tunneling support mechanisms allowed the engineer greater flexibility in handling local reinforcement of the rock structure if superficial or relatively deep-seated instability was encountered. However, in the case where second linings are to be accommodated and flexible support mechanisms used, care should be taken to foresee over-excavation in weaker zones to allow for larger displacements prior to the attainment of confinement-convergence equilibria. 4 refs., 7 figs 2. Experimental halls workshop summary International Nuclear Information System (INIS) Thorndike, A. 1976-01-01 At the experimental halls workshop, discussions were held on: (1) open areas as compared with enclosed halls; (2) the needs of ep, anti pp, and other options; (3) the hall for the lepton detector; and (4) the hall for the hadron spectrometer. The value of different possibilities for the future experimental program was explored. A number of suggestions emerged which will be used as the design of the experimental halls progresses 3. Experimental halls workshop summary International Nuclear Information System (INIS) Thorndike, A. 1976-01-01 On May 26 and 27, 1976, approximately 50 people met for an informal workshop on plans for experimental halls for ISABELLE. Plans as they exist in the May 1976 version of the ISABELLE proposal were presented. Discussions were held on the following four general topics by separate working groups: (1) pros and cons of open areas as compared with enclosed halls; (2) experimental hall needs of ep, anti pp, and other options; (3) hall for the lepton detector; and (4) hall for the hadron spectrometer. The planning for experimental halls at PEP, the hall for the lepton detector, the hadron spectrometer, and open areas are discussed 4. Experimental halls workshop summary International Nuclear Information System (INIS) Thorndike, A. 1976-01-01 A brief discussion is given of: (1) pros and cons of open areas as compared with enclosed halls; (2) experimental hall needs of ep, anti p p, and other options; (3) hall for the lepton detector; and, (4) hall for the hadron spectrometer 5. The Isolde experimental hall CERN Multimedia Laurent Guiraud 2000-01-01 General view of the Isotope-Separator On-Line (ISOLDE) hall. ISOLDE is dedicated to the production of a large variety of radioactive ion beams for many different experiments. Rare isotopes can be produced allowing the study of spectra for neutrino beam production. 6. General vibration monitoring: Experimental hall International Nuclear Information System (INIS) Jendrzejczyk, J.A.; Wambsganss, M.W.; Smith, R.K. 1993-01-01 The reported vibration data were generated from measurements made on the experimental hall floor on December 2, 1992. At the time of the measurements, the ESRF hydrolevel was set-up in the Early Assembly Area (EAA) of the experimental hall and was being used to measure static displacement (settlement) of the floor. The vibration measurement area was on and adjacent to the EAA, in the vicinity of the ESRF hydrolevel test which was in progress. This report summarizes the objectives, instrumentation, measurement locations, observations, and conclusions, and provides selected results in the form of RMS vs. time plots, and power spectral densities from which frequency information can be derived. Measured response amplitudes were within the vibration criteria established for the APS 7. Report of experimental hall subworking group International Nuclear Information System (INIS) Miyake, K.; Ohama, T.; Takahashi, K. 1982-01-01 The general plan of constructing the TRISTAN e + e - colliding beam experimental halls may be divided into two parts. The first step is to construct two test-experimental halls associated with the 6.5 GeV x 6.5 GeV e + e - accumulator ring, and the second step is to build four experimental halls at the 30 GeV x 30 GeV e + e - TRISTAN main ring. At this workshop, extensive discussions on the detailed design of the four main ring experimental halls have been made. Four experimental areas will be built at the main ring, and two test-experimental halls at the accumulating ring. Among the four areas at the main ring, two will be used for electron-proton possible as well as electron-positron colliding beam experiment. The other two will be used exclusively for e + e - colliding experiments. Only a preliminary design has been made for these four experimental areas. A tentative plan of a larger experimental hall includes a counting and data processing room, a utility room, and a radiation safety control room. Two smaller halls have simpler structure. The figures of the experimental halls are presented. The two test-experimental halls at the accumulator ring will be used to test the detectors for e + e - colliding experiments before the final installation. The utility rooms designed for the halls are used to supply coolant and electric power of superconducting magnets. At the workshop, various ideas concerning the preliminary plan are presented. (Kato, T.) 8. Shielding consideration for the SSCL experimental halls International Nuclear Information System (INIS) Bull, J.; Coyne, J.; Mokhov, N.; Stapleton, G. 1994-03-01 The Superconducting Super Collider which is being designed and built in Waxahachie, Texas consists Of series of proton accelerators, culminating in a 20 Te proton on proton collider. The collider will be in a tunnel which will be 87 km in circumference and. on average about 30 meters underground. The present design calls for two large interaction halls on the east side of the ring. The shielding for these halls is being designed for an interaction rate of 10 9 Hz or 10 16 interactions per year, based on 10 7 seconds per operational year. SSC guidelines require that the shielding be designed to meet the criterion of 1mSv per year for open areas off site 2mSv per year for open areas on site, and 2mSv per year for controlled areas. Only radiation workers will be routinely allowed to work in controlled areas. It should be pointed that there is a potential for an accidental full beam loss in either of the experimental halls, and this event would consist of the loss of the full circulating beam up to 4 x 10 14 protons. With the present design. the calculated dose equivalent for this event is about 10% of the annual dose equivalent for the normal p-p interactions, so that die accident condition does not control the shielding. If, for instance, local shielding within the experimental hall is introduced into the calculations, this could change. The shielding requirements presented here are controlled by the normal p-p interactions. Three important questions were addressed in the present calculations. They are (1) the thickness of the roof over the experimental halls, (2) the configuration of the shafts and adits which give access to the halls, and (3) the problem of ground water and air activation 9. Experimental test of 200 W Hall thruster with titanium wall Science.gov (United States) Ding, Yongjie; Sun, Hezhi; Peng, Wuji; Xu, Yu; Wei, Liqiu; Li, Hong; Li, Peng; Su, Hongbo; Yu, Daren 2017-05-01 We designed a 200 W Hall thruster based on the technology of pushing down a magnetic field with two permanent magnetic rings. Boron nitride (BN) is an important insulating wall material for Hall thrusters. The discharge characteristics of the designed Hall thruster were studied by replacing BN with titanium (Ti). Experimental results show that the designed Hall thruster can discharge stably for a long time under a Ti channel. Experiments were performed to determine whether the channel and cathode are electrically connected. When the channel wall and cathode are insulated, the divergence angle of the plume increases, but the performance of the Hall thruster is improved in terms of thrust, specific impulse, anode efficiency, and thrust-to-power ratio. Ti exhibits a powerful antisputtering capability, a low emanation rate of gas, and a large structural strength, making it a potential candidate wall material in the design of low-power Hall thrusters. 10. Experimental and theoretical studies of cylindrical Hall thrusters International Nuclear Information System (INIS) Smirnov, Artem; Raitses, Yegeny; Fisch, Nathaniel J. 2007-01-01 The Hall thruster is a mature electric propulsion device that holds considerable promise in terms of the propellant saving potential. The annular design of the conventional Hall thruster, however, does not naturally scale to low power. The efficiency tends to be lower and the lifetime issues are more aggravated. Cylindrical geometry Hall thrusters have lower surface-to-volume ratio than conventional thrusters and, thus, seem to be more promising for scaling down. The cylindrical Hall thruster (CHT) is fundamentally different from the conventional design in the way the electrons are confined and the ion space charge is neutralized. The performances of both the large (9-cm channel diameter, 600-1000 W) and miniaturized (2.6-cm channel diameter, 50-300 W) CHTs are comparable with those of the state-of-the-art conventional (annular) design Hall thrusters of similar sizes. A comprehensive experimental and theoretical study of the CHT physics has been conducted, addressing the questions of electron cross-field transport, propellant ionization, plasma-wall interaction, and formation of the electron distribution function. Probe measurements in the harsh plasma environment of the microthruster were performed. Several interesting effects, such as the unusually high ionization efficiency and enhanced electron transport, were observed. Kinetic simulations suggest the existence of the strong fluctuation-enhanced electron diffusion and predict the non-Maxwellian shape of the electron distribution function. Through the acquired understanding of the new physics, ways for further optimization of this means for low-power space propulsion are suggested. Substantial flexibility in the magnetic field configuration of the CHT is the key tool in achieving the high-efficiency operation 11. Experimental probes of emergent symmetries in the quantum Hall system CERN Document Server Lutken, C A 2011-01-01 Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Gamma(0)(2). We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille level with the prediction from Gamma(0)(2). We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle hole duality leads to an extensive web of dualities related to those in plateau insulator transitions, and we derive a formula relating dual pairs (B, B(d)) of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out... 12. Quantum Hall effects recent theoretical and experimental developments CERN Document Server Ezawa, Zyun Francis 2013-01-01 Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. Tremendous theoretical and experimental developments are still being made in this sphere. Composite bosons, composite fermions and anyons were among distinguishing ideas in the original edition. In the 2nd edition, fantastic phenomena associated with the interlayer phase coherence in the bilayer system were extensively described. The microscopic theory of the QHE was formulated based on the noncommutative geometry. Furthermore, the unconventional QHE in graphene was reviewed, where the electron dynamics can be treated as relativistic Dirac fermions and even the supersymmetric quantum mechanics plays a key role. In this 3rd edition, all chapters are carefully reexamined and updated. A highlight is the new chapter on topological insulators. Indeed, the concept of topological insulator stems from the QHE. Other new topics are recent prominent experime... 13. Experimental Evaluation of MHD Generators Operating at High Hall Coefficients International Nuclear Information System (INIS) Barthelemy, R.R.; Stephan, B.G.; Cooper, R.F. 1966-01-01 The experimental evaluation of such open-cycle MHD generator operation, particularly at large values of the Hall parameter and Mach number, is scarce. A flexible combustion-driven MHD generator test facility is being constructed to investigate various generator-operating parameters, generator configurations and designs, and component materials. The plasma source is a combustion chamber in which toluene, or another suitable fuel, is burned with gaseous oxygen diluted with nitrogen. Potassium hydroxide seed is injected with the fuel to produce the necessary plasma conductivity. The gas stream is accelerated in a supersonic nozzle and then flows through the channel. The Hall channel is constructed of water-cooled Inconel rings suitably grooved for the zirconia electrode material. The rings are insulated from each other with Teflon spacers which are shielded from the high temperature gas by a layer of alumina refractory. The channel consists of 54 water-cooled rings assembled in three independent sections. Provisions for instrumentation consist of 15 points for static pressure measurement along the nozzle, channel and diffuser; 20 thermocouple measurements; 3 split rings for transverse current measurements; a voltmeter panel for all 54 electrodes; and all necessary fluid and electrical monitoring instruments. The channel is followed by a diffuser in which some of the dynamic pressure of the gas stream is recovered. The magnet is an iron core design with coils wound of hollow conductor to permit of water-cooling for high power operation. The magnet can operate at field strengths of up to 23 kG. Details of the test programme planned for the generator (commissioning at the end of 1966) are given. (author) 14. A high intensity beam handling system at the KEK-PS new experimental hall International Nuclear Information System (INIS) Tanaka, K.H.; Minakawa, M.; Yamanoi, Y. 1991-01-01 We would like to summarize newly developed technology for handling high-intensity beams. This was practically employed in the beam-handling system of primary protons at the KEK-PS new experimental hall. (author) 15. Theoretical and Experimental Investigation of Force Estimation Errors Using Active Magnetic Bearings with Embedded Hall Sensors DEFF Research Database (Denmark) Voigt, Andreas Jauernik; Santos, Ilmar 2012-01-01 to ∼ 20% of the nominal air gap the force estimation error is found to be reduced by the linearized force equation as compared to the quadratic force equation, which is supported by experimental results. Additionally the FE model is employed in a comparative study of the force estimation error behavior...... of AMBs by embedding Hall sensors instead of mounting these directly on the pole surfaces, force estimation errors are investigated both numerically and experimentally. A linearized version of the conventionally applied quadratic correspondence between measured Hall voltage and applied AMB force... 16. L3 + Cosmics Experiment CERN Multimedia 2002-01-01 %RE4 %title\\\\ \\\\The L3+C experiment takes advantage of the unique properties of the L3 muon spectrometer to get an accurate measurement of cosmic ray muons 30 m underground. A new muon trigger, readout and DAQ system have been installed, as well as a scintillator array covering the upper surfaces of the L3 magnet for timing purposes. The acceptance amounts to 200 $m^2 sr$. The data are collected independently in parallel with L3 running. In spring 2000 a scintillator array will be installed on the roof of the SX hall in order to estimate the primary energy of air showers associated with events observed in L3+C.\\\\ \\\\The cosmic ray muon momentum spectrum, the zenith angular dependence and the charge ratio are measured with high accuracy between 20 and 2000 GeV/c. The results will provide new information about the primary composition, the shower development in the atmosphere, and the inclusive pion and kaon (production-) cross sections (specifically the "$\\pi$/K ratio") at high energies. These data will also hel... 17. Laser Safety for the Experimental Halls at SLAC_s Linac Coherent Light Source (LCLS) Energy Technology Data Exchange (ETDEWEB) Woods, Michael; Anthony, Perry; /SLAC; Barat, Ken; /LBL, Berkeley; Gilevich, Sasha; Hays, Greg; White, William E.; /SLAC 2009-01-15 The LCLS at the SLAC National Accelerator Laboratory will be the world's first source of an intense hard x-ray laser beam, generating x-rays with wavelengths of 1nm and pulse durations less than 100fs. The ultrafast x-ray pulses will be used in pump-probe experiments to take stop-motion pictures of atoms and molecules in motion, with pulses powerful enough to take diffraction images of single molecules, enabling scientists to elucidate fundamental processes of chemistry and biology. Ultrafast conventional lasers will be used as the pump. In 2009, LCLS will deliver beam to the Atomic Molecular and Optical (AMO) Experiment, located in one of 3 x-ray Hutches in the Near Experimental Hall (NEH). The NEH includes a centralized Laser Hall, containing up to three Class 4 laser systems, three x-ray Hutches for experiments and vacuum transport tubes for delivering laser beams to the Hutches. The main components of the NEH laser systems are a Ti:sapphire oscillator, a regen amplifier, green pump lasers for the oscillator and regen, a pulse compressor and a harmonics conversion unit. Laser safety considerations and controls for the ultrafast laser beams, multiple laser controlled areas, and user facility issues are discussed. 18. Optical design of beam lines at the KEK-PS new experimental hall International Nuclear Information System (INIS) Tanaka, K.H.; Ieiri, M.; Noumi, H.; Minakawa, M.; Yamanoi, Y.; Kato, Y.; Ishii, H.; Suzuki, Y.; Takasaki, M. 1995-01-01 A new counter experimental hall [K.H. Tanaka et al., IEEE Trans. Magn. 28 (1992) 697] was designed and constructed at the KEK 12-GeV Proton Synchrotron (KEK-PS). The extracted proton beam from the KEK-PS is introduced to the new hall through the newly-prepared primary beam line, EP1, and hits two production targets in cascade. The upstream target provides secondary particles to the low momentum (0.4-0.6 GeV/c) separated beam line, K5, and the downstream target is connected to the medium momentum (0.6-2.0 GeV/c) separated beam line, K6. Several new ideas were employed in the beam optical designs of EP1, K5 and K6 in order to increase the number and the purity of the short-lived secondary particles, such as kaons and pions, under the limited energy and intensity of the primary protons provided by the KEK-PS. These new ideas are described in this paper as well as the first commissioning results. (orig.) 19. Quantum Hall resistance standard in graphene devices under relaxed experimental conditions Science.gov (United States) Schopfer, F.; Ribeiro-Palau, R.; Lafont, F.; Brun-Picard, J.; Kazazis, D.; Michon, A.; Cheynis, F.; Couturaud, O.; Consejo, C.; Jouault, B.; Poirier, W. Large-area and high-quality graphene devices synthesized by CVD on SiC are used to develop reliable electrical resistance standards, based on the quantum Hall effect (QHE), with state-of-the-art accuracy of 1x10-9 and under an extended range of experimental conditions of magnetic field (down to 3.5 T), temperature (up to 10 K) or current (up to 0.5 mA). These conditions are much relaxed as compared to what is required by GaAs/AlGaAs standards and will enable to broaden the use of the primary quantum electrical standards to the benefit of Science and Industry for electrical measurements. Furthermore, by comparison of these graphene devices with GaAs/AlGaAs standards, we demonstrate the universality of the QHE within an ultimate uncertainty of 8.2x10-11. This suggests the exact relation of the quantized Hall resistance with the Planck constant and the electron charge, which is crucial for the new SI to be based on fixing such fundamental constants. These results show that graphene realizes its promises and demonstrates its superiority over other materials for a demanding application. Nature Nanotech. 10, 965-971, 2015, Nature Commun. 6, 6806, 2015 20. High Accuracy Beam Current Monitor System for CEBAF'S Experimental Hall A International Nuclear Information System (INIS) J. Denard; A. Saha; G. Lavessiere 2001-01-01 CEBAF accelerator delivers continuous wave (CW) electron beams to three experimental Halls. In Hall A, all experiments require continuous, non-invasive current measurements and a few experiments require an absolute accuracy of 0.2 % in the current range from 1 to 180 (micro)A. A Parametric Current Transformer (PCT), manufactured by Bergoz, has an accurate and stable sensitivity of 4 (micro)A/V but its offset drifts at the muA level over time preclude its direct use for continuous measurements. Two cavity monitors are calibrated against the PCT with at least 50 (micro)A of beam current. The calibration procedure suppresses the error due to PCT's offset drifts by turning the beam on and off, which is invasive to the experiment. One of the goals of the system is to minimize the calibration time without compromising the measurement's accuracy. The linearity of the cavity monitors is a critical parameter for transferring the accurate calibration done at high currents over the whole dynamic range. The method for measuring accurately the linearity is described 1. Development of an access control system for the LHD experimental hall International Nuclear Information System (INIS) Kawano, T.; Inoue, N.; Sakuma, Y.; Uda, T.; Yamanishi, H.; Miyake, H.; Tanahashi, S.; Motozima, O. 2000-01-01 An access control system for the LHD (Large Helical Device) experimental hall had been constructed and its practical operation started in March 1998. Continuously, the system has been improved. The present system keeps watch on involved entrance and exit for the use of persons at four entrances by using five turnstile gates while watching on eight shielding doors at eight positions (four entrances, three carriage entrances and a hall overview) and a stairway connecting the LHD main hall with the LHD basement. Besides, for the security of safety operation of the LHD, fifteen kinds of interlock signals are exchanged between the access control system and the LHD control system. Seven of the interlock signals are properly sent as the occasional demands from the access control system to the LHD control system, in which three staple signals are B Personnel Access to Controlled Area, D Shielding Door Closed, and E No Entrance. It is important that any plasma experiments of the LHD are not permitted while the signal B being sent or D being not sent. The signal E is sent to inform the LHD control system that the turnstile gates are locked. All the plasma experiments should not be done unless the lock procedure of the turnstile is confirmed. When the turnstile gates are locked, any persons cannot enter into the LHD controlled area, but are permissible to exit only. Six of the interlock signals are used to send the information of the working at that time in the LHD controlled area to the access control system. When one signal of the operation mode is sent to the access control system from the LHD, the access control system sets the turnstile gate in situation corresponding to the operation mode, A Equipment Operation, B Vacuum Pumping, C Coil Cooling, D Coil Excitation, and E Plasma Experiment. If the access control system receives, for example, the signal B, this system sets the turnstile gate in the condition of control such that only persons assigned to the work of vacuum 2. Development of apparatus for high-intensity beam lines at the KEK-PS new experimental hall International Nuclear Information System (INIS) Yamanoi, Yutaka; Tanaka, Kazuhiro; Minakawa, Michifumi 1992-01-01 The new counter experimental hall was constructed at the KEK 12 GeV Proton Synchrotron (the KEK-PS) in order to handle high-intensity primary proton beams of up to 1 x 10 13 pps (protons per second), which is one order of magnitude greater than the present beam intensity of the KEK-PS, 1 x 10 12 pps. New technologies for handling high-intensity beams have, then, been developed and employed in the new hall construction. A part of our R/D work on handling high intensity beam is briefly reported. (author) 3. The parasitic model of L2 and L3 vocabulary acquisition: evidence from naturalistic and experimental studies Directory of Open Access Journals (Sweden) Peter Ecke 2014-09-01 Full Text Available This paper reviews evidence for the Parasitic Model of Vocabulary Acquisition for second and third language learners/developing multilinguals. It first describes the model’s predictions about default processes based on the detection and use of similarity at the three stages involved in the development of individual lexical items: (1 the establishing of a form representation, (2 the building of connections to syntactic frame and concept representations, and (3 the strengthening and automatization of representations and access routes. The paper then summarizes both naturalistic and experimental evidence for processes involved at these three stages. Finally it discusses open issues and potential areas for future investigation. 4. Experimental demonstration of programmable multi-functional spin logic cell based on spin Hall effect Energy Technology Data Exchange (ETDEWEB) Zhang, X.; Wan, C.H., E-mail: [email protected]; Yuan, Z.H.; Fang, C.; Kong, W.J.; Wu, H.; Zhang, Q.T.; Tao, B.S.; Han, X.F., E-mail: [email protected] 2017-04-15 Confronting with the gigantic volume of data produced every day, raising integration density by reducing the size of devices becomes harder and harder to meet the ever-increasing demand for high-performance computers. One feasible path is to actualize more logic functions in one cell. In this respect, we experimentally demonstrate a prototype spin-orbit torque based spin logic cell integrated with five frequently used logic functions (AND, OR, NOT, NAND and NOR). The cell can be easily programmed and reprogrammed to perform desired function. Furthermore, the information stored in cells is symmetry-protected, making it possible to expand into logic gate array where the cell can be manipulated one by one without changing the information of other undesired cells. This work provides a prospective example of multi-functional spin logic cell with reprogrammability and nonvolatility, which will advance the application of spin logic devices. - Highlights: • Experimental demonstration of spin logic cell based on spin Hall effect. • Five logic functions are realized in a single logic cell. • The logic cell is reprogrammable. • Information in the cell is symmetry-protected. • The logic cell can be easily expanded to logic gate array. 5. Experimental Verification of the Hall Effect during Magnetic Reconnection in a Laboratory Plasma International Nuclear Information System (INIS) Yang Ren; Masaaki Yamada; Stefan Gerhardt; Hantao Ji; Russell Kulsrud; Aleksey Kuritsyn 2005-01-01 In this letter we report a clear and unambiguous observation of the out-of-plane quadrupole magnetic field suggested by numerical simulations in the reconnecting current sheet in the Magnetic Reconnection Experiment (MRX). Measurements show that the Hall effect is large in collisionless regime and becomes small as the collisionality increases, indicating that the Hall effect plays an important role in collisionless reconnection 6. Experimental Studies of Anode Sheath Phenomena in a Hall Thruster Discharge International Nuclear Information System (INIS) Dorf, L.; Raitses, Y.; Fisch, N.J. 2004-01-01 Both electron-repelling and electron-attracting anode sheaths in a Hall thruster were characterized by measuring the plasma potential with biased and emissive probes [L. Dorf, Y. Raitses, V. Semenov, and N.J. Fisch, Appl. Phys. Let. 84 (2004) 1070]. In the present work, two-dimensional structures of the plasma potential, electron temperature, and plasma density in the near-anode region of a Hall thruster with clean and dielectrically coated anodes are identified. Possible mechanisms of anode sheath formation in a Hall thruster are analyzed. The path for current closure to the anode appears to be the determining factor in the anode sheath formation process. The main conclusion of this work is that the anode sheath formation in Hall thrusters differs essentially from that in the other gas discharge devices, like a glow discharge or a hollow anode, because the Hall thruster utilizes long electron residence times to ionize rather than high neutral pressures 7. Experimental approach of plasma supersonic expansion physics and of Hall effect propulsion systems International Nuclear Information System (INIS) Mazouffre, Stephane 2009-01-01 This report for accreditation to supervise research (HDR) proposes a synthesis of scientific and research works performed by the author during about ten years. Thus, a first part addresses studies on plasma rarefied supersonic flows: expansion through a sonic hole and through a Laval nozzle. The next part addresses the study of plasma propulsion for spacecraft, and more particularly electric propulsion based on the Hall effect: phenomena of ionic and atomic transport, characteristics of the electric field, energy deposition on walls, basic scale laws, related works, hybrid Hall-RF propulsion systems. The third part presents perspectives and projects related to propulsion by Hall effect (research topics, planned researches, a European project on high power, hybrid Hall-RF propulsion) and to ions-ions plasma (the PEGASES concept, the NExET test installation, RF source of negative ions and magnetic trap) 8. Prevention and reversal of experimental autoimmune thyroiditis (EAT) in mice by administration of anti-L3T4 monoclonal antibody at different stages of disease development. Science.gov (United States) Stull, S J; Kyriakos, M; Sharp, G C; Braley-Mullen, H 1988-11-01 Experimental autoimmune thyroiditis (EAT) can be induced in CBA/J mice following the transfer of spleen cells from mouse thyroglobulin (MTg)-sensitized donors that have been activated in vitro with MTg. Since L3T4+ T cells are required to transfer EAT in this model, the present study was undertaken to assess the effectiveness of the anti-L3T4 monoclonal antibody (mAb) GK1.5 in preventing or arresting the development of EAT. Spleen cells from mice given mAb GK1.5 prior to sensitization with MTg and adjuvant could not transfer EAT to normal recipients and cells from these mice did not proliferate in vitro to MTg. Donor mice given GK1.5 before immunization did not develop anti-MTg autoantibody and recipients of cells from such mice also produced little anti-MTg. GK1.5 could also prevent the proliferation and activation of sensitized effector cell precursors when added to in vitro cultures. When a single injection of mAb GK1.5 was given to recipients of in vitro-activated spleen cells, EAT was reduced whether the mAb was given prior to cell transfer or as late as 19 days after cell transfer. Whereas the incidence and severity of EAT was consistently reduced by injecting recipient mice with GK1.5, the same mice generally had no reduction in anti-MTg autoantibody. Since EAT is consistently induced in control recipients by 14-19 days after cell transfer, the ability of mAb GK1.5 to inhibit EAT when injected 14 or 19 days after cell transfer indicates that a single injection of the mAb GK1.5 can cause reversal of the histopathologic lesions of EAT in mice. These studies further establish the important role of L3T4+ T cells in the pathogenesis of EAT in mice and also suggest that therapy with an appropriate mAb may be an effective treatment for certain autoimmune diseases even when the therapy is initiated late in the course of the disease. 9. An experimental investigation of the internal magnetic field topography of an operating Hall thruster International Nuclear Information System (INIS) Peterson, Peter Y.; Gallimore, Alec D.; Haas, James M. 2002-01-01 Magnetic field measurements were made in the discharge channel of the 5 kW-class P5 laboratory-model Hall thruster to investigate what effect the Hall current has on the static, applied magnetic field topography. The P5 was operated at 1.6 and 3.0 kW with a discharge voltage of 300 V. A miniature inductive loop probe (B-Dot probe) was employed to measure the radial magnetic field profile inside the discharge channel of the P5 with and without the plasma discharge. These measurements are accomplished with minimal disturbance to thruster operation with the High-speed Axial Reciprocating Probe system. The results of the B-Dot probe measurements indicate a change in the magnetic field topography from that of the vacuum field measurements. The measured magnetic field profiles are then examined to determine the possible nature and source of the difference between the vacuum and plasma magnetic field profiles 10. Radiation protection design of the APPA experimental hall at the FAIR facility; Strahlenschutzplanung fuer die APPA-Experimentierhalle bei FAIR Energy Technology Data Exchange (ETDEWEB) Kissel, R.; Braeuning-Demian, A.; Conrad, I.; Evdokimov, A.; Lang, R.; Radon, T.; Zieser, B. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Belousov, A. [NASA, Pasadena, CA (United States). Jet Propulsion Lab.; Fehrenbacher, G. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); FAIR - Facility for Antiproton and Ion Research in Europe GmbH, Darmstadt (Germany) 2016-07-01 The APPA-research program (Atomic, Plasma Physics and Applications) comprises experiments for fundamental research in atomic and plasma physics, biophysics and materials research. A dedicated building for the experimental areas including a technical supply annex is planned. In the hall are located four different experimental setups for the four APPA collaborations. Two beamlines for protons and heavy ions, both from the SIS18 and SIS100 synchrotrons are designed. The demands for beam energies, intensities and time structure differ significantly among the experiments. Consequently, different types of beams will be used, for example uranium beams with energies of 2 GeV/nucleon and an intensity of 3 x 10{sup 11} ions/pulse (pulse length of the order of hundred nanoseconds, repetition period 180 seconds). Another experiment requires a proton beam with energies of around 10 GeV and a primary intensity of 5 x 10{sup 10} protons/second. The highest interaction rate is expected by the plasma physics experiments with about 50 % of the primary intensity. The remaining beam will be stopped in a so called beam dump producing further radiation, especially neutron radiation which must be shielded. For the design of the shielding it is necessary to know the spatial distribution of the dose rate for uranium beams and for proton beams with different energies and intensities in the experimental hall. The aim for the shielding layout is to achieve a dose rate below 0,5 μSv/hour at the premises. 11. Experimental setup for deeply virtual Compton scattering (DVCS) experiment in hall A at Jefferson Laboratory International Nuclear Information System (INIS) Camsonne, A. 2005-11-01 The Hall A Deeply Virtual Compton Scattering (DVCS) experiment used the 5.757 GeV polarized electron beam available at Jefferson Laboratory and ran from september until december 2004. Using the standard Hall A left high resolution spectrometer three kinematical points were taken at a fixed x b (jorken) = 0.32 value for three Q 2 values: 1.5 GeV 2 , 1.91 GeV 2 , 2.32 GeV 2 . An electromagnetic Lead Fluoride calorimeter and a proton detector scintillator array designed to work at a luminosity of 10 37 cm -2 s -1 were added to ensure the exclusivity of the DVCS reaction. In addition to the new detectors new custom electronics was used: a calorimeter trigger module which determines if an electron photon coincidence has occurred and a sampling system allowing to deal with pile-up events during the offline analysis. Finally the data from the kinematic at Q 2 = 2.32 GeV 2 and s = 5.6 GeV 2 allowed to get a preliminary result for the exclusive π 0 electroproduction on the proton. (author) 12. Experimental study of effect of magnetic field on anode temperature distribution in an ATON-type Hall thruster Science.gov (United States) Liu, Jinwen; Li, Hong; Mao, Wei; Ding, Yongjie; Wei, Liqiu; Li, Jianzhi; Yu, Daren; Wang, Xiaogang 2018-05-01 The energy deposition caused by the absorption of electrons by the anode is an important cause of power loss in a Hall thruster. The resulting anode heating is dangerous, as it can potentially reduce the thruster lifetime. In this study, by considering the ring shape of the anode of an ATON-type Hall thruster, the effects of the magnetic field strength and gradient on the anode ring temperature distribution are studied via experimental measurement. The results show that the temperature distribution is not affected by changes in the magnetic field strength and that the position of the peak temperature is essentially unchanged; however, the overall temperature does not change monotonically with the increase of the magnetic field strength and is positively correlated with the change in the discharge current. Moreover, as the magnetic field gradient increases, the position of the peak temperature gradually moves toward the channel exit and the temperature tends to decrease as a whole, regardless of the discharge current magnitude; in any case, the position of the peak temperature corresponds exactly to the intersection of the magnetic field cusp with the anode ring. Further theoretical analysis shows that the electrons, coming from the ionization region, travel along two characteristic paths to reach the anode under the guidance of the cusped magnetic field configuration. The change of the magnetic field strength or gradient changes the transfer of momentum and energy of the electrons in these two paths, which is the main reason for the changes in the temperature and distribution. This study is instructive for matching the design of the ring-shaped anode and the cusp magnetic field of an ATON-type Hall thruster. 13. Skyrmions and Hall viscosity Science.gov (United States) Kim, Bom Soo 2018-05-01 We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems. 14. L3 detector Energy Technology Data Exchange (ETDEWEB) Anon. 1992-01-15 This is the final article in the CERN Courier series marking a decade of the four big experiments - Aleph, Delphi, L3 and Opal - at CERN's LEP electron-positron collider. Data-taking started soon after LEP became operational in July 1989, followed by substantial runs in 1990 and 1991. Because of the long lead times involved in today's major physics undertakings, preparations for these four experiments got underway in the early 1980s. 15. L3 detector International Nuclear Information System (INIS) Anon. 1992-01-01 This is the final article in the CERN Courier series marking a decade of the four big experiments - Aleph, Delphi, L3 and Opal - at CERN's LEP electron-positron collider. Data-taking started soon after LEP became operational in July 1989, followed by substantial runs in 1990 and 1991. Because of the long lead times involved in today's major physics undertakings, preparations for these four experiments got underway in the early 1980s 16. Hall effect in hopping regime International Nuclear Information System (INIS) Avdonin, A.; Skupiński, P.; Grasza, K. 2016-01-01 A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted. 17. Hall effect in hopping regime Energy Technology Data Exchange (ETDEWEB) Avdonin, A., E-mail: [email protected] [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Skupiński, P. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Grasza, K. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Institute of Electronic Materials Technology, ul. Wólczyńska 133, 01-919 Warszawa (Poland) 2016-02-15 A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted. 18. Theoretical and experimental study of resonant 3d X-ray photoemission and resonant L3M45M45 Auger transition of PdO International Nuclear Information System (INIS) Uozumi, Takayuki; Kotani, Akio 2000-01-01 The observed 3d X-ray photoemission spectra (XPS), resonant 3dXPS (RXPS) at the L 3 edge and resonant L 3 M 45 M 45 Auger electron spectra (RAES) of 4d transition metal oxide PdO are successfully analyzed by means of an impurity Anderson model. The importance of Pd 4d-O 2p hybridization effect is especially emphasized in the interpretation of observed spectra. It causes charge transfer satellites in 3dXPS and L 3 M 45 M 45 RAES and mainly determines the structure of resonance enhancements in 3dRXPS. From the analysis of spectra, 4d-2p charge transfer energy Δ, 4d correlation energy U dd and 4d-2p transfer integral pdσ are estimated to be 5.5 eV, 4.5 eV and 2.1 eV, respectively. The character of the insulating energy gap PdO is also theoretically investigated: PdO is classified as an intermediate-type insulator due to the strong 4d-2p hybridization. (author) 19. Experimental measurement of magnetic field null in the vacuum chamber of KTM tokamak based on matrix of 2D Hall sensors Energy Technology Data Exchange (ETDEWEB) Shapovalov, G.; Chektybayev, B., E-mail: [email protected]; Sadykov, A.; Skakov, M.; Kupishev, E. 2016-11-15 Experimental technique of measurement of magnetic field null region inside of the KTM tokamak vacuum chamber has been developed. Square matrix of 36 2D Hall sensors, which used in the technique, allows carrying out direct measurements of poloidal magnetic field dynamics in the vacuum chamber. To better measuring accuracy, Hall sensor’s matrix was calibrated with commercial Helmholtz coils and in situ measurement of defined magnetic field from poloidal and toroidal coils. Standard KTM Data-Acquisition System has been used to collect data from Hall sensors. Experimental results of measurement of magnetic field null in the vacuum chamber of KTM are shown in the paper. Additionally results of the magnetic field null reconstruction from signals of inductive total flux loops are shown in the paper. 20. Planar Hall effect bridge magnetic field sensors DEFF Research Database (Denmark) Henriksen, A.D.; Dalslet, Bjarke Thomas; Skieller, D.H. 2010-01-01 Until now, the planar Hall effect has been studied in samples with cross-shaped Hall geometry. We demonstrate theoretically and experimentally that the planar Hall effect can be observed for an exchange-biased ferromagnetic material in a Wheatstone bridge topology and that the sensor signal can...... Hall effect bridge sensors.... 1. Proposal for an Experimental Test of the Role of Confining Potentials in the Integral Quantum Hall Effect OpenAIRE Brueckner, Reinhold 2000-01-01 We propose an experiment using a three-gate quantum Hall device to probe the dependence of the integral quantum Hall effect (IQHE) on the shape of the lateral confining potential in edge regions. This shape can, in a certain configuration determine whether or not the IQHE occurs. 2. L3 Experiment CERN Multimedia Falagan bobillo, M A; Chen, E F A; Prokofiev, D; Prokofiev, D; Shvorab, A; Galaktionov, Y; Kopal, M; Cotorobai, F; Le goff, J; Tully, C; Van hoek, W; Nozik, V Z; Nessi-tedaldi, F; De la cruz, B; Wadhwa, M; Chtcheguelski, V; Anderhub, H B; Guo, Y; Garcia-abia, P; Piroue, P; Della marina, R; Cerrada, M; Gailloud, M; Xia, L; Chaturvedi, U K; Pistolesi, E; Zhang, S 2002-01-01 % L3 \\\\ \\\\ The detector consists of a large volume low field solenoid magnet, a small central tracking system with very high spatial resolution, a high resolution electromagnetic calorimeter encapsulating the central detector, a hadron calorimeter acting also as a muon filter, and high precision muon tracking chambers. \\\\ \\\\The detector is designed to measure energy and position of leptons with the highest obtainable precision allowing a mass resolution $\\Delta$m/m smaller than 2\\% in dilepton final states. Hadronic energy flux is detected by a fine-grained calorimeter, which also serves as muon filter and tracking device. \\\\ \\\\The outer boundary of the detector is given by the iron return-yoke of a conventional magnet, using aluminium plates for the coil. The field is 0.5~T over a length of 12~m. This large volume allows a high precision muon momentum measurement, performed by three sets of drift chambers in the central detector region. From the multiple measurement of the coordinate in the bending plane a m... 3. Scheme for generating and transporting THz radiation to the X-ray experimental hall at the European XFEL Energy Technology Data Exchange (ETDEWEB) Decking, Winfried; Kocharyan, Vitali; Saldin, Evgeni; Zagorodnov, Igor [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany) 2011-12-15 The design of a THz edge radiation source for the European XFEL is presented.We consider generation of THz radiation from the spent electron beam downstream of the SASE2 undulator in the electron beam dump area. In this way, the THz output must propagate at least for 250 meters through the photon beam tunnel to the experimental hall to reach the SASE2 X-ray hutches. We propose to use an open beam waveguide such as an iris guide as transmission line. In order to efficiently couple radiation into the iris transmission line, generation of the THz radiation pulse can be performed directly within the iris guide. The line transporting the THz radiation to the SASE2 X-ray hutches introduces a path delay of about 20 m. Since THz pump/X-ray probe experiments should be enabled, we propose to exploit the European XFEL baseline multi-bunch mode of operation, with 222 ns electron bunch separation, in order to cope with the delay between THz and X-ray pulses. We present start-to-end simulations for 1 nC bunch operation-parameters, optimized for THz pump/X-ray probe experiments.Detailed characterization of the THz and SASE X-ray radiation pulses is performed. Highly focused THz beams will approach the high field limit of 1 V/atomic size. (orig.) 4. Hall A Data.gov (United States) Federal Laboratory Consortium — The instrumentation in Hall A at the Thomas Jefferson National Accelerator Facility was designed to study electroand photo-induced reactions at very high luminosity... 5. Hall C Data.gov (United States) Federal Laboratory Consortium — Hall C's initial complement of equipment (shown in the figure), includes two general-purpose magnetic spectrometers. The High Momentum Spectrometer (HMS) has a large... 6. 12 April 2013 - The British Royal Academy of Engineering visiting the LHC superconducting magnet test hall with R. Veness and the ATLAS experimental cavern with Collaboration Spokesperson D. Charlton. CERN Multimedia 2013-01-01 12 April 2013 - The British Royal Academy of Engineering visiting the LHC superconducting magnet test hall with R. Veness and the ATLAS experimental cavern with Collaboration Spokesperson D. Charlton. 7. Experimental observation of the spin-Hall effect in a spin–orbit coupled two-dimensional hole gas Czech Academy of Sciences Publication Activity Database Kaestner, B.; Wunderlich, J.; Jungwirth, Tomáš; Sinova, J.; Nomura, K.; MacDonald, A. H. 2006-01-01 Roč. 34, - (2006), s. 47-52 ISSN 1386-9477 R&D Projects: GA ČR GA202/02/0912 Institutional research plan: CEZ:AV0Z10100521 Keywords : spin Hall effect * spintronics * spin-orbit interaction Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.084, year: 2006 8. The quantized Hall effect International Nuclear Information System (INIS) Klitzing von, K. 1989-01-01 The quantized Hall effect is theoretically explained in detail as are its basic properties. The explanation is completed with the pertinent mathematical relations and illustrative figures. Experimental data are critically assessed obtained by quantum transport measurement in a magnetic field on two-dimensional systems. The results are reported for a MOSFET silicon transistor and for GaAs-Al x Ga 1-x As heterostructures. The application is discussed of the quantized Hall effect in determining the fine structure constant or in implementing the resistance standard. (M.D.). 27 figs., 57 refs 9. Experimental setup for deeply virtual Compton scattering (DVCS) experiment in hall A at Jefferson Laboratory; Dispositif experimental pour la diffusion Compton virtuelle dans le regime profondement inelastique dans le hall A au Jefferson Laboratory Energy Technology Data Exchange (ETDEWEB) Camsonne, A 2005-11-15 The Hall A Deeply Virtual Compton Scattering (DVCS) experiment used the 5.757 GeV polarized electron beam available at Jefferson Laboratory and ran from september until december 2004. Using the standard Hall A left high resolution spectrometer three kinematical points were taken at a fixed x{sub b}(jorken) = 0.32 value for three Q{sup 2} values: 1.5 GeV{sup 2}, 1.91 GeV{sup 2}, 2.32 GeV{sup 2}. An electromagnetic Lead Fluoride calorimeter and a proton detector scintillator array designed to work at a luminosity of 10{sup 37} cm{sup -2}s{sup -1} were added to ensure the exclusivity of the DVCS reaction. In addition to the new detectors new custom electronics was used: a calorimeter trigger module which determines if an electron photon coincidence has occurred and a sampling system allowing to deal with pile-up events during the offline analysis. Finally the data from the kinematic at Q{sup 2} = 2.32 GeV{sup 2} and s = 5.6 GeV{sup 2} allowed to get a preliminary result for the exclusive {pi}{sup 0} electroproduction on the proton. (author) 10. An experimental study on Γ(2) modular symmetry in the quantum Hall system with a small spin splitting International Nuclear Information System (INIS) Huang, C F; Chang, Y H; Cheng, H H; Yang, Z P; Yeh, H D; Hsu, C H; Liang, C-T; Hang, D R; Lin, H H 2007-01-01 Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows features of the Γ(2) modular symmetry, which includes distorted flowlines and a shifted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quantization (Dolan 2000 Phys. Rev. B 62 10278). Universal scaling is found under the reduction of the modular symmetry. It is also shown that the Hall conductivity can still be governed by the scaling law when the semicircle law and the scaling on the longitudinal conductivity are invalid 11. Experimental Investigation of a Direct-drive Hall Thruster and Solar Array System at Power Levels up to 10 kW Science.gov (United States) Snyder, John S.; Brophy, John R.; Hofer, Richard R.; Goebel, Dan M.; Katz, Ira 2012-01-01 As NASA considers future exploration missions, high-power solar-electric propulsion (SEP) plays a prominent role in achieving many mission goals. Studies of high-power SEP systems (i.e. tens to hundreds of kilowatts) suggest that significant mass savings may be realized by implementing a direct-drive power system, so NASA recently established the National Direct-Drive Testbed to examine technical issues identified by previous investigations. The testbed includes a 12-kW solar array and power control station designed to power single and multiple Hall thrusters over a wide range of voltages and currents. In this paper, single Hall thruster operation directly from solar array output at discharge voltages of 200 to 450 V and discharge powers of 1 to 10 kW is reported. Hall thruster control and operation is shown to be simple and no different than for operation on conventional power supplies. Thruster and power system electrical oscillations were investigated over a large range of operating conditions and with different filter capacitances. Thruster oscillations were the same as for conventional power supplies, did not adversely affect solar array operation, and were independent of filter capacitance from 8 to 80 ?F. Solar array current and voltage oscillations were very small compared to their mean values and showed a modest dependence on capacitor size. No instabilities or anomalous behavior were observed in the thruster or power system at any operating condition investigated, including near and at the array peak power point. Thruster startup using the anode propellant flow as the power 'switch' was shown to be simple and reliable with system transients mitigated by the proper selection of filter capacitance size. Shutdown via cutoff of propellant flow was also demonstrated. A simple electrical circuit model was developed and is shown to have good agreement with the experimental data. 12. Laurance David Hall. Science.gov (United States) Coxon, Bruce 2011-01-01 An account is given of the life, scientific contributions, and passing of Laurance David Hall (1938-2009), including his early history and education at the University of Bristol, UK, and the synthesis and NMR spectroscopy of carbohydrates and other natural products during ∼20 years of research and teaching at the University of British Columbia in Vancouver, Canada. Lists of graduate students, post-doctoral fellows, and sabbatical visitors are provided for this period. Following a generous endowment by Dr. Herchel Smith, Professor Hall built a new Department of Medicinal Chemistry at Cambridge University, UK, and greatly expanded his researches into the technology and applications of magnetic resonance imaging (MRI) and zero quantum NMR. MRI technology was applied both to medical problems such as the characterization of cartilage degeneration in knee joints, the measurement of ventricular function, lipid localization in animal models of atherosclerosis, paramagnetic metal complexes of polysaccharides as contrast agents, and studies of many other anatomical features, but also to several aspects of materials analysis, including food analyses, process control, and the elucidation of such physical phenomena as the flow of liquids through porous media, defects in concrete, and the visualization of fungal damage to wood. Professor Hall's many publications, patents, lectures, and honors and awards are described, and also his successful effort to keep the Asilomar facility in Pacific Grove, California as the alternating venue for the annual Experimental NMR Conference. Two memorial services for Professor Hall are remembered. Copyright © 2011 Elsevier Inc. All rights reserved. 13. Experimental study of nonlinear interaction of plasma flow with charged thin current sheets: 2. Hall dynamics, mass and momentum transfer Directory of Open Access Journals (Sweden) S. Savin 2006-01-01 cyclotron one, in extended turbulent zones are a promising alternative in place of the usual parallel electric fields invoked in the macro-reconnection scenarios. Further cascading towards electron scales is supposed to be due to unstable parallel electron currents, which neutralize the potential differences, either resulted from the ion- burst interactions or from the inertial drift. The complicated MP shape suggests its systematic velocity departure from the local normal towards the average one, inferring domination for the MP movement of the non-local processes over the small-scale local ones. The measured Poynting vector indicates energy transmission from the MP into the upstream region with the waves triggering impulsive downstream flows, providing an input into the local flow balance and the outward movement of the MP. Equating the transverse electric field inside the MP TCS by the Hall term in the Ohm's law implies a separation of the different plasmas primarily by the Hall current, driven by the respective part of the TCS surface charge. The Hall dynamics of TCS can operate either without or as a part of a macro-reconnection with the magnetic field annihilation. 14. L3: Experiment for LEP International Nuclear Information System (INIS) Anon. 1985-01-01 The detector features a large magnetic hall enclosing an easily modifiable central detector, with physics objectives extending beyond those of the initial phase of LEP running (collision energies of around 100 GeV). The design places great emphasis on high precision (one per cent) measurement of photon, electron and muon momenta, together with good resolution of hadron jets and precise information from the interaction vertex. To be installed 50 m below ground, the detector will be enclosed in a 8000 ton solenoid, 15.6 m high and 13.6 m long, providing a central field of 0.5 t. At the centre of this magnetic 'cave' will be the vertex detector, a 'Time Expansion Chamber' (TEC) extending 50 cm radially from the interaction point and providing high spatial and track separation resolution. (orig./HSI). 15. Experimental study of the Hall effect and electron diffusion region during magnetic reconnection in a laboratory plasma International Nuclear Information System (INIS) Ren Yang; Yamada, Masaaki; Ji Hantao; Dorfman, Seth; Gerhardt, Stefan P.; Kulsrud, Russel 2008-01-01 The Hall effect during magnetic reconnection without an external guide field has been extensively studied in the laboratory plasma of the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)] by measuring its key signature, an out-of-plane quadrupole magnetic field, with magnetic probe arrays whose spatial resolution is on the order of the electron skin depth. The in-plane electron flow is deduced from out-of-plane magnetic field measurements. The measured in-plane electron flow and numerical results are in good agreement. The electron diffusion region is identified by measuring the electron outflow channel. The width of the electron diffusion region scales with the electron skin depth (∼5.5-7.5c/ω pe ) and the peak electron outflow velocity scales with the electron Alfven velocity (∼0.12-0.16V eA ), independent of ion mass. The measured width of the electron diffusion region is much wider and the observed electron outflow is much slower than those obtained in 2D numerical simulations. It is found that the classical and anomalous dissipation present in the experiment can broaden the electron diffusion region and slow the electron outflow. As a consequence, the electron outflow flux remains consistent with numerical simulations. The ions, as measured by a Mach probe, have a much wider outflow channel than the electrons, and their outflow is much slower than the electron outflow everywhere in the electron diffusion region 16. Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator Energy Technology Data Exchange (ETDEWEB) Feng, Yang; Feng, Xiao; Ou, Yunbo; Wang, Jing; Liu, Chang; Zhang, Liguo; Zhao, Dongyang; Jiang, Gaoyuan; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu 2015-09-16 We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau. 17. Spin Hall effects Science.gov (United States) Sinova, Jairo; Valenzuela, Sergio O.; Wunderlich, J.; Back, C. H.; Jungwirth, T. 2015-10-01 Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Despite being observed only a decade ago, these effects are already ubiquitous within spintronics, as standard spin-current generators and detectors. Here the theoretical and experimental results that have established this subfield of spintronics are reviewed. The focus is on the results that have converged to give us the current understanding of the phenomena, which has evolved from a qualitative to a more quantitative measurement of spin currents and their associated spin accumulation. Within the experimental framework, optical-, transport-, and magnetization-dynamics-based measurements are reviewed and linked to both phenomenological and microscopic theories of the effect. Within the theoretical framework, the basic mechanisms in both the extrinsic and intrinsic regimes are reviewed, which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. Also reviewed is the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regimes, as well as the spin-pumping theory of spin generation used in many measurements of the spin Hall angle. A further connection to the spin-current-generating spin Hall effect to the inverse spin galvanic effect is given, in which an electrical current induces a nonequilibrium spin polarization. This effect often accompanies the spin Hall effect since they share common microscopic origins. Both can exhibit the same symmetries when present in structures comprising ferromagnetic and nonmagnetic layers through their induced current-driven spin torques or induced voltages. Although a short chronological overview of the evolution of the spin Hall effect field and the resolution of some early controversies is given, the main body of this review is structured from a pedagogical 18. Quantum critical Hall exponents CERN Document Server Lütken, C A 2014-01-01 We investigate a finite size "double scaling" hypothesis using data from an experiment on a quantum Hall system with short range disorder [1-3]. For Hall bars of width w at temperature T the scaling form is w(-mu)T(-kappa), where the critical exponent mu approximate to 0.23 we extract from the data is comparable to the multi-fractal exponent alpha(0) - 2 obtained from the Chalker-Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal sigma-model with m matter fields [5]. The value nu(8) = 2.60513 ... of the localisation exponent obtained from the m = 8 model is in excellent agreement with the best available numerical value nu(num) = 2.607 +/- 0.004 derived from the CC-model [6]. Existing experimental data appear to favour the m = 9 model, suggesting that the quantum Hall system is not in the same universality class as th... 19. Implementation and integration in the L3 experimentation of a level-2 trigger with event building, based on C104 data driven cross-bar switches and on T9000 transputers International Nuclear Information System (INIS) Masserot, A. 1995-01-01 This thesis describes the new level-2 trigger system. It has been developed to fit the L3 requirements induced by the LEP phase 2 conditions. At each beam crossing, the system memorizes the trigger data, builds-up the events selected by the level-1 hard-wired processors and finally rejects on-line the background identified by algorithms coded in Fortran. Based on T9000 Transputers and on C104 data driven cross-bar switches, the system uses prototypes designed by INMOS/SGS THOMSON for parallel processing applications. Emphasis is set on a new event building technic, on its integration in L3 and on performance. (author). 38 refs., 68 figs., 36 tabs 20. Contribution of the study of the Hall Effect. Hall Effect of powder products International Nuclear Information System (INIS) Cherville, Jean 1961-01-01 This research thesis reports the development of an apparatus aimed at measuring the Hall Effect and the magneto-resistance of powders at room temperature and at the liquid nitrogen temperature. The author also proposes a theoretical contribution to the Hall Effect and reports the calculation of conditions to be met to obtain a correct value for the Hall constant. Results are experimentally verified. The method is then applied to the study of a set of powdered pre-graphitic graphites. The author shows that their Hall coefficient confirms the model already proposed by Mrozowski. The study of the Hall Effect of any kind of powders can thus be performed, and the Hall Effect can therefore be a mean to study mineral and organic compounds, and notably powdered biological molecules [fr 1. The fluctuation Hall conductivity and the Hall angle in type-II superconductor under magnetic field Energy Technology Data Exchange (ETDEWEB) Tinh, Bui Duc, E-mail: [email protected] [Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang (Viet Nam); Department of Physics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi (Viet Nam); Hoc, Nguyen Quang; Thu, Le Minh [Department of Physics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi (Viet Nam) 2016-02-15 Highlights: • The time-dependent Ginzburg–Landau was used to calculate fluctuation Hall conductivity and Hall angle in type-II superconductor in 2D and 3D. • We obtain analytical expressions for the fluctuation Hall conductivity and the Hall angle summing all Landau levels without need to cutoff higher Landau levels to treat arbitrary magnetic field. • The results were compared to the experimental data on YBCO. - Abstract: The fluctuation Hall conductivity and the Hall angle, describing the Hall effect, are calculated for arbitrary value of the imaginary part of the relaxation time in the frame of the time-dependent Ginzburg–Landau theory in type II-superconductor with thermal noise describing strong thermal fluctuations. The self-consistent Gaussian approximation is used to treat the nonlinear interaction term in dynamics. We obtain analytical expressions for the fluctuation Hall conductivity and the Hall angle summing all Landau levels without need to cutoff higher Landau levels to treat arbitrary magnetic field. The results are compared with experimental data on high-T{sub c} superconductor. 2. Cutting the L3 torque tube CERN Multimedia Laurent Guiraud 2001-01-01 Workers cut the torque tube, with a plasma-cutting device on the L3 experiment, which closed with the LEP accelerator in 2000. L3 was housed in a huge red solenoid, which will be taken over by the ALICE detector when the new LHC is completed. 3. The L3+C detector, a unique tool-set to study cosmic rays International Nuclear Information System (INIS) Adriani, O.; Akker, M. van den; Banerjee, S.; Baehr, J.; Betev, B.; Bourilkov, D.; Bottai, S.; Bobbink, G.; Cartacci, A.; Chemarin, M.; Chen, G.; Chen, H.S.; Chiarusi, T.; Dai, C.J.; Ding, L.K.; Duran, I.; Faber, G.; Fay, J.; Grabosch, H.J.; Groenstege, H.; Guo, Y.N.; Gupta, S.; Haller, Ch.; Hayashi, Y.; He, Z.X.; Hebbeker, T.; Hofer, H.; Hoferjun, H.; Huo, A.X.; Ito, N.; Jing, C.L.; Jones, L.; Kantserov, V.; Kawakami, S.; Kittel, W.; Koenig, A.C.; Kok, E.; Korn, A.; Kuang, H.H.; Kuijpers, J.; Ladron de Guevara, P.; Le Coultre, P.; Lei, Y.; Leich, H.; Leiste, R.; Li, D.; Li, L.; Li, Z.C.; Liu, Z.A.; Liu, H.T.; Lohmann, W.; Lu, Y.S.; Ma, X.H.; Ma, Y.Q.; Mil, A. van; Monteleoni, B.; Nahnhauer, R.; Pauss, F.; Parriaud, J.-F.; Petersen, B.; Pohl, M.; Qing, C.R.; Ramelli, R.; Ravindran, K.C.; Rewiersma, P.; Rojkov, A.; Saidi, R.; Schmitt, V.; Schoeneich, B.; Schotanus, D.J.; Shen, C.Q.; Sulanke, H.; Tang, X.W.; Timmermans, C.; Tonwar, S.; Trowitzsch, G.; Unger, M.; Verkooijen, H.; Wang, X.L.; Wang, X.W.; Wang, Z.M.; Wijk, R. van; Wijnen, Th.A.M.; Wilkens, H.; Xu, Y.P.; Xu, Z.Z.; Yang, C.G.; Yang, X.F.; Yao, Z.G.; Yu, Z.Q.; Zhang, S.; Zhu, G.Y.; Zhu, Q.Q.; Zhuang, H.L.; Zwart, A.N.M. 2002-01-01 The L3 detector at the CERN electron-positron collider, LEP, has been employed for the study of cosmic ray muons. The muon spectrometer of L3 consists of a set of high-precision drift chambers installed inside a magnet with a volume of about 1000 m 3 and a field of 0.5 T. Muon momenta are measured with a resolution of a few percent at 50 GeV. The detector is located under 30 m of overburden. A scintillator air shower array of 54 m by 30 m is installed on the roof of the surface hall above L3 in order to estimate the energy and the core position of the shower associated with a sample of detected muons. Thanks to the unique properties of the L3+C detector, muon research topics relevant to various current problems in cosmic ray and particle astrophysics can be studied 4. The L3+C detector, a unique tool-set to study cosmic rays CERN Document Server Adriani, O; Banerjee, S; Bähr, J; Betev, B L; Bourilkov, D; Bottai, S; Bobbink, Gerjan J; Cartacci, A M; Chemarin, M; Chen, G; Chen He Sheng; Chiarusi, T; Dai Chang Jiang; Ding, L K 2002-01-01 The L3 detector at the CERN electron-positron collider, LEP, has been employed for the study of cosmic ray muons. The muon spectrometer of L3 consists of a set of high-precision drift chambers installed inside a magnet with a volume of about 1000 m**3 and a field of 0.5 T. Muon momenta are measured with a resolution of a few percent at 50 GeV. The detector is located under 30 m of overburden. A scintillator air shower array of 54 m by 30 m is installed on the roof of the surface hall above L3 in order to estimate the energy and the core position of the shower associated with a sample of detected muons. Thanks to the unique properties of the L3+C detector, muon research topics relevant to various current problems in cosmic ray and particle astrophysics can be studied. 5. The quantum Hall effects: Philosophical approach Science.gov (United States) Lederer, P. 2015-05-01 The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as gauge invariance, strong interactions in Condensed Matter physics, emergence of new paradigms. This paper focuses on some related philosophical questions. Various brands of positivism or agnosticism are confronted with the physics of the Quantum Hall Effects. Hacking's views on Scientific Realism, Chalmers' on Non-Figurative Realism are discussed. It is argued that the difficulties with those versions of realism may be resolved within a dialectical materialist approach. The latter is argued to provide a rational approach to the phenomena, theory and ontology of the Quantum Hall Effects. 6. Cryogenic microsize Hall sensors International Nuclear Information System (INIS) Kvitkovic, J.; Polak, M. 1993-01-01 Hall sensors have a variety of applications in magnetic field measurements. The active area of the Hall sensor does not play an important role in measuring of homogeneous magnetic field. Actually Hall sensors are widely used to measure profiles of magnetic fields produced by magnetization currents in samples of HTC superconductors, as well as of LTC ones. Similar techniques are used to measure magnetization of both HTC and LTC superconductors. In these cases Hall sensor operates in highly inhomogeneous magnetic fields. Because of that, Hall sensors with very small active area are required. We developed and tested Hall sensors with active area 100 μm x 100 μm - type M and 50 μm x 50 μm - type V. Here we report on the most imporant parameters of these units, as well as on their properties as differential magnetometer. (orig.) 7. L3 experiment dismantling at LEP CERN Multimedia Laurent Guiraud 2001-01-01 The last muon chamber is removed from the L3 experiment at the LEP collider, which was in operation from 1989 to 2000. The large red magnet yoke will be reused by the ALICE experiment when the LHC is constructed. 8. Resistive Instabilities in Hall Current Plasma Discharge International Nuclear Information System (INIS) Litvak, Andrei A.; Fisch, Nathaniel J. 2000-01-01 Plasma perturbations in the acceleration channel of a Hall thruster are found to be unstable in the presence of collisions. Both electrostatic lower-hybrid waves and electromagnetic Alfven waves transverse to the applied electric and magnetic field are found to be unstable due to collisions in the E X B electron flow. These results are obtained assuming a two-fluid hydrodynamic model in slab geometry. The characteristic frequencies of these modes are consistent with experimental observations in Hall current plasma thrusters 9. Hall effect in organic layered conductors Directory of Open Access Journals (Sweden) R.A.Hasan 2006-01-01 Full Text Available The Hall effect in organic layered conductors with a multisheeted Fermi surfaces was considered. It is shown that the experimental study of Hall effect and magnetoresistance anisotropy at different orientations of current and a quantizing magnetic field relative to the layers makes it possible to determine the contribution of various charge carriers groups to the conductivity, and to find out the character of Fermi surface anisotropy in the plane of layers. 10. Anomalous Hall effect Science.gov (United States) Nagaosa, Naoto; Sinova, Jairo; Onoda, Shigeki; MacDonald, A. H.; Ong, N. P. 2010-04-01 The anomalous Hall effect (AHE) occurs in solids with broken time-reversal symmetry, typically in a ferromagnetic phase, as a consequence of spin-orbit coupling. Experimental and theoretical studies of the AHE are reviewed, focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical works, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of the Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established systematic trends. These two developments, in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of the Berry-phase curvatures and it is therefore an intrinsic quantum-mechanical property of a perfect crystal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. The full modern semiclassical treatment of the AHE is reviewed which incorporates an anomalous contribution to wave-packet group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew-scattering and side-jump) scattering-related mechanisms. In addition, more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms are reviewed, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, a 11. Recent results from the L3 Collaboration International Nuclear Information System (INIS) Ting, S.C.C. 1993-01-01 In this report we summarize the recent results from the L3 Collaboration. The L3 Collaboration is one of the largest international collaborations in high energy physics and consists of many universities from the United States including University of Michigan, M.I.T., Caltlech, Princeton and Harvard, and leading research centers from France, Germany, Switzerland, Holland, India, China, Korea, Russia and other nations 12. 27 Febuary 2012 - US DoE Associate Director of Science for High Energy Physics J. Siegrist visiting the LHC superconducting magnet test hall with adviser J.-P. Koutchouk and engineer M. Bajko; in CMS experimental cavern with Spokesperson J. Incadela;in ATLAS experimental cavern with Deputy Spokesperson A. Lankford; in ALICE experimental cavern with Spokesperson P. Giubellino; signing the guest book with Director for Accelerators and Technology S. Myers. CERN Multimedia Laurent Egli 2012-01-01 27 Febuary 2012 - US DoE Associate Director of Science for High Energy Physics J. Siegrist visiting the LHC superconducting magnet test hall with adviser J.-P. Koutchouk and engineer M. Bajko; in CMS experimental cavern with Spokesperson J. Incadela;in ATLAS experimental cavern with Deputy Spokesperson A. Lankford; in ALICE experimental cavern with Spokesperson P. Giubellino; signing the guest book with Director for Accelerators and Technology S. Myers. 13. The Forward Muon Detector of L3 CERN Document Server Adam, A; Alarcon, J; Alberdi, J; Alexandrov, V S; Aloisio, A; Alviggi, M G; Anderhub, H; Ariza, M; Azemoon, T; Aziz, T; Bakker, F; Banerjee, S; Banicz, K; Barcala, J M; Becker, U; Berdugo, J; Berges, P; Betev, B L; Biland, A; Bobbink, Gerjan J; Böck, R K; Böhm, A; Borisov, V S; Bosseler, K; Bouvier, P; Brambilla, Elena; Burger, J D; Burgos, C; Buskens, J; Carlier, J C; Carlino, G; Causaus, J; Cavallo, N; Cerjak, I; Cerrada-Canales, M; Chang, Y H; Chen, H S; Chendvankar, S R; Chvatchkine, V B; Daniel, M; De Asmundis, R; Decreuse, G; Deiters, K; Djambazov, L; Duraffourg, P; Erné, F C; Esser, H; Ezekiev, S; Faber, G; Fabre, M; Fernández, G; Freudenreich, Klaus; Fritschi, M; García-Abia, P; González, A; Gurtu, A; Gutay, L J; Haller, C; Herold, W D; Herrmann, J M; Hervé, A; Hofer, H; Höfer, M; Hofer, T; Homma, J; Horisberger, Urs; Horváth, I L; Ingenito, P; Innocente, Vincenzo; Ioudine, I; Jaspers, M; de Jong, P; Kästli, W; Kaspar, H; Kitov, V; König, A C; Koutsenko, V F; Lanzano, S; Lapoint, C; Lebedev, A; Lecomte, P; Lista, L; Lübelsmeyer, K; Lustermann, W; Ma, J M; Milesi, M; Molinero, A; Montero, A; Moore, R; Nahn, S; Navarrete, J J; Okle, M; Orlinov, I; Ostojic, R; Pandoulas, D; Paolucci, P; Parascandolo, P; Passeggio, G; Patricelli, S; Peach, D; Piccolo, D; Pigni, L; Postema, H; Puras, C; Ren, D; Rewiersma, P A M; Rietmeyer, A; Riles, K; Risco, J; Robohm, A; Rodin, J; Röser, U; Romero, L; Van Rossum, W; Rykaczewski, H; Sarakinos, M E; Sassowsky, M; Shchegelskii, V; Scholz, N; Schultze, K; Schuylenburg, H; Sciacca, C; Seiler, P G; Siedenburg, T; Siedling, R; Smith, B; Soulimov, V; Sadhakar, K; Syben, O; Tonutti, M; Udovcic, A; Ulbricht, J; Veillet, L; Vergain, M; Viertel, Gert M; Von Gunten, H P; Vorobyov, A A; Vrankovic, V; De Waard, A; Waldmeier-Wicki, S; Wallraff, W; Walter, H C; Wang, J C; Wei, Z L; Wetter, R; Willmott, C; Wittgenstein, F; Wu, R J; Yang, K S; Zhou, L; Zhou, Y; Zuang, H L 1996-01-01 The Forward-Backward muon detector of the L3 experiment is presented. Intended to be used for LEP 200 physics, it consists of 96 self-calibrating drift chambers of a new design enclosing the magnet pole pieces of the L3 solenoid. The pole pieces are toroidally magnetized to form two independent analyzing spectrometers. A novel trigger is provided by resistive plate counters attached to the drift chambers. Details about the design, construction and performance of the whole system are given together with results obtained during the 1995 running at LEP. 14. L3-forward-backward muon spectrometer International Nuclear Information System (INIS) Deiters, K. 1995-01-01 The performance of the distance sensors could be successfully tested in the L3 detector. One sensor of each type got installed together with a precision sensor. This sensor is based on a glass rod with optical marks which are scanned by a system of light diodes. It has a measurement accuracy of 1 μm. We proved, that the desired accuracy of 10 μm was reached and that the sensors work in the environment of the L3 detector. (author) 11 figs., 5 refs 15. Halls Lake 1990 Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Salt marsh habitats along the shoreline of Halls Lake are threatened by wave erosion, but the reconstruction of barrier islands to reduce this erosion will modify or... 16. Cognitive approaches to L3 acquisition Directory of Open Access Journals (Sweden) Maria del Pilar Garcia Mayo 2012-06-01 Full Text Available Multilingualism has established itself as an area of systematic research in linguistic studies over the last two decades. The multilingual phenomenon can be approached from different perspectives: educational, formal linguistic, neurolinguistic, psycholinguistic and sociolinguistic, among others. This article presents an overview of cognitive (psychological and formal linguistic approaches to third language (L3 acquisition where the assumption is that language acquisition is a complex multi-faceted process. After identifying what is meant by L3, the article briefly reviews the major issues addressed from both the psycholinguistic strand and the emerging L3 linguistic strand and concentrates on those aspects that are in need of further research in both.El plurilingüismo se ha ganado su propia área de investigación dentro de los estudios de lingüística en las últimas dos décadas. El fenómeno se puede abordar desde perspectivas diferentes: educativa, lingüística de carácter formal, neurolingüística, psicolingüística y sociolingüística, entre otras. Este artículo presenta una visión general de dos perspectivas cognitivas, la psicológica y la procedente de la lingüística formal, al tema de la adquisición de la tercera lengua (L3. Ambas perspectivas comparten la asunción de que la adquisición del lenguaje es un proceso complejo y con varias vertientes. Después de identificar lo que entendemos por L3, el artículo revisa de forma sucinta los principales temas que se han tratado tanto desde la perspectiva psicolingüística como desde la más emergente perspectiva lingüística en materia de L3 y se concentra en aquellos aspectos que consideramos que necesitan mayor investigación en ambas. 17. The quantum hall effect International Nuclear Information System (INIS) El-Arabi, N. M. 1993-01-01 Transport phenomena in two dimensional semiconductors have revealed unusual properties. In this thesis these systems are considered and discussed. The theories explain the Integral Quantum Hall Effect (IQHE) and the Fractional Quantum Hall Effect (FQHE). The thesis is composed of five chapters. The first and the second chapters lay down the theory of the IQHE, the third and fourth consider the theory of the FQHE. Chapter five deals with the statistics of particles in two dimension. (author). Refs 18. Hall viscosity of hierarchical quantum Hall states Science.gov (United States) Fremling, M.; Hansson, T. H.; Suorsa, J. 2014-03-01 Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter τ, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor ν =2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution. 19. Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations Energy Technology Data Exchange (ETDEWEB) Owerre, S. A., E-mail: [email protected] [African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5 (Canada) 2016-07-28 Quite recently, the magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. The thermal Hall conductivity κ{sup xy} changes sign as a function of magnetic field or temperature on the kagome lattice, and κ{sup xy} changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of the magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We find that κ{sup xy} has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome, and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a T{sup 2} law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in a honeycomb optical lattice. 20. The muon spectrometer of the L3 detector at LEP International Nuclear Information System (INIS) Peng, Y. 1988-01-01 In this thesis the construction of the muon spectrometer of the L3 detector is described, one of the four detectors presently being prepared for experimentation at LEP. This accelerator is built at CERN, Geneva, and is due to start operation in July 1989. One of the unique features of the L3 experiment is the measurement of the momentum of the muons produced in the e + e - collisions iwht an independent muon spectrometer. This makes it possible to study final states involving muons, with high accuracy (δP/P = 2% at 45 GeV). The muon spectrometer consists of 80 large drift chambers, arranged in 16 modules or 'octants', that fill a cylindrical volume of 12 m in length, 5 m inner diameter and 12 m outer diameter. The design of the drift chambers, the construction, the alignment procedure and the test results for the complete octants are described. 51 refs.; 57 figs.; 16 tabs 1. Tasks related to increase of RA reactor exploitation and experimental potential, 01. Designing the protection chamber in the RA reactor hall for handling the radioactive experimental equipment (I-II) Part II, Vol. II International Nuclear Information System (INIS) Pavicevic, M. 1963-07-01 This second volume of the project for construction of the protection chamber in the RA reactor hall for handling the radioactive devices includes the technical description of the chamber, calculation of the shielding wall thickness, bottom lead plate, horizontal stability of the chamber, cost estimation, and the engineering drawings 2. Kosmische Myonen im L3-Detektor CERN Document Server Saidi, Rachid 2000-01-01 Durch die Untersuchung des Mondschattens in der primaren kosmischen Strahlung konnen Informationen uber die Winkelau osung des L3-Detektors gewonnen werden, sowie mit ausreichender Statistik das Verhaltnis von Antiprotonen zu Protonen fur Protonenergien um 1 TeV abgeschatzt werden. Die Bahn der Protonen vom Mond zur Erde wird durch folgende Eekte beein ut: Das Magnetfeld zwischen Mond und Erde lenkt die geladenen Teilchen ab. Fur 1 TeV Protonenenergie wurde ein Wert von 1:70 abgeschatzt. Die Mehrfachstreuung in der 30 m dicken Erdschicht uber L3 verursacht eine Winkelverschmierung von 3.5 mrad fur 100 GeV Myonen. Der Winkel zwischen Proton und den sekundaren Myonen, die durch Wechselwirkung von primaren Kernen mit den oberen Schichten der Atmosphare entstehen, betragt 3 mrad fur 100 GeV Myonen. Die berechnete Winkelau osung dieser Untersuchung fur den L3-Detektor mit verschiedenen Energien betragt einen Wert von 0:170 0:030 fur das starkste Myonschattensignal bei 150 GeV Myonenenergie. Dabei wurde fur den Mon... 3. Spin Hall Effect in Doped Semiconductor Structures Science.gov (United States) Tse, Wang-Kong; Das Sarma, Sankar 2006-03-01 We present a microscopic theory of the extrinsic spin Hall effect based on the diagrammatic perturbation theory. Side-jump (SJ) and skew-scattering (SS) contributions are explicitly taken into account to calculate the spin Hall conductivity, and we show their effects scale as σxy^SJ/σxy^SS ˜(/τ)/ɛF, where τ being the transport relaxation time. Motivated by recent experimental work we apply our theory to n-doped and p-doped 3D and 2D GaAs structures, obtaining analytical formulas for the SJ and SS contributions. Moreover, the ratio of the spin Hall conductivity to longitudinal conductivity is found as σs/σc˜10-3-10-4, in reasonable agreement with the recent experimental results of Kato et al. [Science 306, 1910 (2004)] in n-doped 3D GaAs system. 4. Extrinsic spin Hall effect in graphene Science.gov (United States) Rappoport, Tatiana The intrinsic spin-orbit coupling in graphene is extremely weak, making it a promising spin conductor for spintronic devices. In addition, many applications also require the generation of spin currents in graphene. Theoretical predictions and recent experimental results suggest one can engineer the spin Hall effect in graphene by greatly enhancing the spin-orbit coupling in the vicinity of an impurity. The extrinsic spin Hall effect then results from the spin-dependent skew scattering of electrons by impurities in the presence of spin-orbit interaction. This effect can be used to efficiently convert charge currents into spin-polarized currents. I will discuss recent experimental results on spin Hall effect in graphene decorated with adatoms and metallic cluster and show that a large spin Hall effect can appear due to skew scattering. While this spin-orbit coupling is small if compared with what it is found in metals, the effect is strongly enhanced in the presence of resonant scattering, giving rise to robust spin Hall angles. I will present our single impurity scattering calculations done with exact partial-wave expansions and complement the analysis with numerical results from a novel real-space implementation of the Kubo formalism for tight-binding Hamiltonians. The author acknowledges the Brazilian agencies CNPq, CAPES, FAPERJ and INCT de Nanoestruturas de Carbono for financial support. 5. Experimental Infection of Sheep using Infective Lar- vae (L3 ... African Journals Online (AJOL) ²Previous: Ethiopian Wildlife Conservation Authority/Ethiopian Agricultural Research Organiza- .... coincidentally there was also a positive relationship, Regression statistics ..... Helminths, Arthropods and Protozoa of Domesticated Animals,. 6. Many-body calculation of the coincidence L3 photoelectron spectroscopy main line of Ni metal International Nuclear Information System (INIS) Ohno, Masahide 2008-01-01 The partial singles L 3 photoelectron spectroscopy (PES) main line of Ni metal correlated with Auger electrons emitted by the localized L 3 -VV Auger decay is calculated by a many-body theory. The partial singles L 3 PES main line of Ni metal almost coincides in both line shape and peak kinetic energy (KE) with the singles one. The former main line peak shows a KE shift of only 0.01 eV toward the lower KE and a very small asymmetric line shape change compared to the singles one. The asymmetric line shape change and the peak KE shift of the partial singles L 3 main line are very small. However, they are due to the variation with photoelectron KE in the branching ratio of the partial Auger decay width in the partial singles L 3 PES main line by the photoelectron KE dependent imaginary part of the shakeup self-energy. The L 3 PES main line of Ni metal measured in coincidence with the L 3 -VV ( 1 G) Auger electron spectroscopy (AES) main line peak is the partial singles one modulated by a spectral function R a of a fixed energy Auger electron analyzer so that it should show only a symmetric line narrowing by R a compared to the singles one. The L 3 PES main line peak of Ni metal measured in coincidence with the delocalized band-like L 3 -VV AES peak or not completely split-off (or not completely localized) L 3 -VV ( 3 F) AES peak, will show an asymmetric line narrowing and a KE shift compared to the singles one. Thus, the L 3 PES main line of Ni metal in coincidence with various parts of the L 3 -VV AES spectrum depends on which part of the L 3 -VV AES spectrum a fixed energy Auger electron analyzer is set. The experimental verification is in need 7. Quantum Hall conductivity in a Landau type model with a realistic geometry International Nuclear Information System (INIS) Chandelier, F.; Georgelin, Y.; Masson, T.; Wallet, J.-C. 2003-01-01 In this paper, we revisit some quantum mechanical aspects related to the quantum Hall effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of quantum Hall experiments. The resulting formalism is then used to compute explicitly the Hall conductivity from a Kubo formula 8. Inverse spin Hall effect by spin injection Science.gov (United States) Liu, S. Y.; Horing, Norman J. M.; Lei, X. L. 2007-09-01 Motivated by a recent experiment [S. O. Valenzuela and M. Tinkham, Nature (London) 442, 176 (2006)], the authors present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Their theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering. 9. Intrinsic superspin Hall current Science.gov (United States) Linder, Jacob; Amundsen, Morten; Risinggârd, Vetle 2017-09-01 We discover an intrinsic superspin Hall current: an injected charge supercurrent in a Josephson junction containing heavy normal metals and a ferromagnet generates a transverse spin supercurrent. There is no accompanying dissipation of energy, in contrast to the conventional spin Hall effect. The physical origin of the effect is an antisymmetric spin density induced among transverse modes ky near the interface of the superconductor arising due to the coexistence of p -wave and conventional s -wave superconducting correlations with a belonging phase mismatch. Our predictions can be tested in hybrid structures including thin heavy metal layers combined with strong ferromagnets and ordinary s -wave superconductors. 10. Composite fermions in the quantum Hall effect International Nuclear Information System (INIS) Johnson, B.L.; Kirczenow, G. 1997-01-01 The quantum Hall effect and associated quantum transport phenomena in low-dimensional systems have been the focus of much attention for more than a decade. Recent theoretical development of interesting quasiparticles - 'composite fermions' - has led to significant advances in understanding and predicting the behaviour of two-dimensional electron systems under high transverse magnetic fields. Composite fermions may be viewed as fermions carrying attached (fictitious) magnetic flux. Here we review models of the integer and fractional quantum Hall effects, including the development of a unified picture of the integer and fractional effects based upon composite fermions. The composite fermion picture predicts remarkable new physics: the formation of a Fermi surface at high magnetic fields, and anomalous ballistic transport, thermopower, and surface acoustic wave behaviour. The specific theoretical predictions of the model, as well as the body of experimental evidence for these phenomena are reviewed. We also review recent edge-state models for magnetotransport in low-dimensional devices based on the composite fermion picture. These models explain the fractional quantum Hall effect and transport phenomena in nanoscale devices in a unified framework that also includes edge state models of the integer quantum Hall effect. The features of the composite fermion edge-state model are compared and contrasted with those of other recent edge-state models of the fractional quantum Hall effect. (author) 11. Air temperature gradient in large industrial hall Science.gov (United States) Karpuk, Michał; Pełech, Aleksander; Przydróżny, Edward; Walaszczyk, Juliusz; Szczęśniak, Sylwia 2017-11-01 In the rooms with dominant sensible heat load, volume airflow depends on many factors incl. pre-established temperature difference between exhaust and supply airflow. As the temperature difference is getting higher, airflow volume drops down, consequently, the cost of AHU is reduced. In high industrial halls with air exhaust grids located under the ceiling additional temperature gradient above working zone should be taken into consideration. In this regard, experimental research of the vertical air temperature gradient in high industrial halls were carried out for the case of mixing ventilation system The paper presents the results of air temperature distribution measurements in high technological hall (mechanically ventilated) under significant sensible heat load conditions. The supply airflow was delivered to the hall with the help of the swirl diffusers while exhaust grids were located under the hall ceiling. Basing on the air temperature distribution measurements performed on the seven pre-established levels, air temperature gradient in the area between 2.0 and 7.0 m above the floor was calculated and analysed. 12. The Monty Hall Dilemma. Science.gov (United States) 1995-01-01 Examines people's behavior in the Monty Hall Dilemma (MHD), in which a person must make two decisions to win a prize. In a series of five studies, found that people misapprehend probabilities in the MHD. Discusses the MHD's relation to illusion of control, belief perseverance, and the status quo bias. (RJM) 13. Hall Sweet Home Science.gov (United States) Oguntoyinbo, Lekan 2011-01-01 Many urban and commuter universities have their sights set on students who are unlikely to connect with the college and likely to fail unless the right strategies are put in place to help them graduate. In efforts to improve retention rates, commuter colleges are looking to an unusual suspect: residence halls. The author discusses how these… 14. Anomalous Hall effect Czech Academy of Sciences Publication Activity Database Nagaosa, N.; Sinova, Jairo; Onoda, S.; MacDonald, A. H.; Ong, N. P. 2010-01-01 Roč. 82, č. 2 (2010), s. 1539-1592 ISSN 0034-6861 Institutional research plan: CEZ:AV0Z10100521 Keywords : anomalous Hall effect * spintronics Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 51.695, year: 2010 15. CERN News: Slow ejection efficiency at the PS; Vacuum tests on the ISR; Fire in the neutrino beam-line; Prototype r.f . cavity for the Booster; Crane-bridge in ISR experimental hall; Modifications to the r.f . system at the PS CERN Multimedia 1969-01-01 CERN News: Slow ejection efficiency at the PS; Vacuum tests on the ISR; Fire in the neutrino beam-line; Prototype r.f . cavity for the Booster; Crane-bridge in ISR experimental hall; Modifications to the r.f . system at the PS 16. 18 January 2011 - Ing. Vittorio Malacalza, ASG Superconductors S.p.A, Italy in the LHC superconducting magnet test hall with Deputy Department Head L. Rossi, in the LHC tunnel at Point 5 and CMS experimental area with Spokesperson G. Tonelli. CERN Multimedia Maximilien Brice 2011-01-01 18 January 2011 - Ing. Vittorio Malacalza, ASG Superconductors S.p.A, Italy in the LHC superconducting magnet test hall with Deputy Department Head L. Rossi, in the LHC tunnel at Point 5 and CMS experimental area with Spokesperson G. Tonelli. 17. 27 January 2012 - Mitglieder des Stiftungsrates Academia Engelberg und Gesellschaft zum Bettag Luzern Schweiz welcomed by Head of International Relations F. Pauss; visiting LHC tunnel at Point 5 and CMS experimental cavern; in the LHC superconducting magnet test hall SM18. CERN Multimedia Maximilien Brice 2012-01-01 27 January 2012 - Mitglieder des Stiftungsrates Academia Engelberg und Gesellschaft zum Bettag Luzern Schweiz welcomed by Head of International Relations F. Pauss; visiting LHC tunnel at Point 5 and CMS experimental cavern; in the LHC superconducting magnet test hall SM18. 18. Unconventional quantum Hall effect in Floquet topological insulators KAUST Repository Tahir, M. 2016-07-27 We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the lights polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity αyx = 0 at zero Fermi energy, to a Hall insulator state with αyx = e2/2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (±1/2,±3/2,±5/2, ...)e2/h. © 2016 IOP Publishing Ltd Printed in the UK. 19. Unconventional quantum Hall effect in Floquet topological insulators KAUST Repository Tahir, M.; Vasilopoulos, P.; Schwingenschlö gl, Udo 2016-01-01 We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the lights polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity αyx = 0 at zero Fermi energy, to a Hall insulator state with αyx = e2/2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (±1/2,±3/2,±5/2, ...)e2/h. © 2016 IOP Publishing Ltd Printed in the UK. 20. Spin Hall effect on a noncommutative space International Nuclear Information System (INIS) Ma Kai; Dulat, Sayipjamal 2011-01-01 We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V 1 (r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, σ=ρθ (ρ is the electron concentration, θ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space. 1. A luminosity measurement at LEP using the L3 detector Energy Technology Data Exchange (ETDEWEB) Koffeman, E.N. 1996-06-25 To perform high precision measurements at particle colliders it is crucial to know the exact intensity of the colliding beams. In particle physics this quantity is generally referred to as the luminosity. The determination of the luminosity in one of the experiments (L3) is the topic of this thesis. The implementation and the use of a silicon strip detector in L3, will be described in detail. In chapter one the most important parameters measured at LEP are discussed, preceded by a short introduction to the Standard Model. The process generally used for luminosity measurements in electron positron colliders is small angle Bhabha scattering. This process is discussed at the end of chapter one. In chapter two the characteristics of the collider and the L3 experiment are given. Together with the signature of the small angle Bhabha scattering, these experimental conditions determine the specifications for the design of the luminosity monitor. The general features of silicon strip detectors for their application in high energy physics are presented in chapter three. Some special attention is given to the behaviour of the sensors used for the tracking detector in the luminosity monitor. The more specific design details of the luminosity monitor are constricted to chapter four. In chapter five the conversion from detector signals into ccordinates relevant for the analysis is explained. The selection of the small angle Bhabha scattering events and the subsequent determination of the luminosity, are presented in chapter six. Systematic uncertainties are carefully studied. Important for a good understanding of the Bhabha selection are the events where a photon is produced in the scattering process. These events are separately studied. In chapter seven a comparison is presented between the radiative events observed in the data and their modelling in the Bhlumi Monte Carlo programme. (orig.). 2. A luminosity measurement at LEP using the L3 detector International Nuclear Information System (INIS) Koffeman, E.N. 1996-01-01 To perform high precision measurements at particle colliders it is crucial to know the exact intensity of the colliding beams. In particle physics this quantity is generally referred to as the luminosity. The determination of the luminosity in one of the experiments (L3) is the topic of this thesis. The implementation and the use of a silicon strip detector in L3, will be described in detail. In chapter one the most important parameters measured at LEP are discussed, preceded by a short introduction to the Standard Model. The process generally used for luminosity measurements in electron positron colliders is small angle Bhabha scattering. This process is discussed at the end of chapter one. In chapter two the characteristics of the collider and the L3 experiment are given. Together with the signature of the small angle Bhabha scattering, these experimental conditions determine the specifications for the design of the luminosity monitor. The general features of silicon strip detectors for their application in high energy physics are presented in chapter three. Some special attention is given to the behaviour of the sensors used for the tracking detector in the luminosity monitor. The more specific design details of the luminosity monitor are constricted to chapter four. In chapter five the conversion from detector signals into ccordinates relevant for the analysis is explained. The selection of the small angle Bhabha scattering events and the subsequent determination of the luminosity, are presented in chapter six. Systematic uncertainties are carefully studied. Important for a good understanding of the Bhabha selection are the events where a photon is produced in the scattering process. These events are separately studied. In chapter seven a comparison is presented between the radiative events observed in the data and their modelling in the Bhlumi Monte Carlo programme. (orig.) 3. Spin hall effect associated with SU(2) gauge field Science.gov (United States) Tao, Y. 2010-01-01 In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which, in two-dimensional system, is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and frac{3}{2} respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the expression for the spin force, and note that the most basic spin Hall effect indeed originate from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect , which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable. Here we have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics. 4. Paired Hall states International Nuclear Information System (INIS) Greiter, M. 1992-01-01 This dissertation contains a collection of individual articles on various topics. Their significance in the corresponding field as well as connections between them are emphasized in a general and comprehensive introduction. In the first article, the author explores the consequences for macroscopic effective Lagrangians of assuming that the momentum density is proportional to the flow of conserved current. The universal corrections obtained for the macroscopic Lagrangian of a superconductor describe the London Hall effect, and provide a fully consistent derivation of it. In the second article, a heuristic principle is proposed for quantized Hall states: the existence and incompressibility of fractionally quantized Hall states is explained by an argument based on an adiabatic localization of magnetic flux, the process of trading uniform flux for an equal amount of fictitious flux attached to the particles. This principle is exactly implemented in the third article. For a certain class of model Hamiltonians, the author obtains Laughlin's Jastrow type wave functions explicitly from a filled Landau level, by smooth extrapolation in quantum statistics. The generalization of this analysis to the torus geometry shows that theorems restricting the possibilities of quantum statistics on closed surfaces are circumvented in the presence of a magnetic field. In the last article, the existence is proposed of a novel incompressible quantum liquid, a paired Hall state, at a half filled Landau level. This state arises adiabatically from free fermions in zero magnetic field, and reduces to a state previously proposed by Halperin in the limit of tightly bound pairs. It supports unusual excitations, including neutral fermions and charge e/4 anyons with statistical parameter θ = π/8 5. Guild Hall retrofit Energy Technology Data Exchange (ETDEWEB) 1984-08-01 This report demonstrates the economic viability of an exterior rewrap retrofit performed on a public community facility for the performing arts. This facility originally consisted of two mess halls built by the American army. The exterior retrofit consisted of constructing a super-insulated passageway to link the two halls as well as completely wrapping the facility with six millimetre polyethylene to provide an airtight barrier. The roofs and walls were reinsulated and insulation levels were increased to RSI 10.5 in the ceilings and RSI 7.7 in the walls. The installation of a propane fuelled furnace was also included in the retrofit package. Prior to the renovations and retrofitting, the Guild Hall facility was almost unusable. The demonstration project transformed the cold, drafty buildings into an attractive, comfortable and functional centre for the performing arts. Heating requirements have been reduced to 500 MJ/m {sup 2} of floor space annually compared to a predicted 1,760 MJ/m{sup 2} of floor space based on HOTCAN analysis of the heating requirements without the energy conservation measures. 9 figs., 10 tabs. 6. Measurement of L3 subshell absorption jump ratios and jump factors for high Z elements using EDXRF technique International Nuclear Information System (INIS) Kaçal, M.R. 2014-01-01 Energy dispersive X-ray fluorescence technique (EDXRF) has been employed for measuring L 3 -subshell absorption jump ratios, r L 3 and jump factors, J L 3 for high Z elements. Jump factors and jump ratios for these elements have been determined by measuring L 3 subshell fluorescence parameters such as L 3 subshell X-ray production cross section σ L 3 , L 3 subshell fluorescence yield, ω L 3 , total L 3 subshell and higher subshells photoionization cross section σ L T . Measurements were performed using a Cd-109 radioactive point source and an Si(Li) detector in direct excitation experimental geometry. Measured values for jump factors and jump ratios have been compared with theoretically calculated and other experimental values. - Highlights: • This paper regards L 3 subshell absorption jump ratios and jump factors using the EDXRF method. • These parameters were measured using a new method. • This method is more useful than other methods which require much effort. • Results are in good agreement with theoretical and experimental values 7. The fractional quantum Hall effect International Nuclear Information System (INIS) Stormer, H.L. 1988-01-01 The fractional quantum Hall effect (FQHE), is the manifestation of a new, highly correlated, many-particle ground state that forms in a two-dimensional electron system at low temperatures and in high magnetic fields. It is an example of the new physics that has grown out of the tremendous recent advances in semiconductor material science, which has provided us with high-quality, lower-dimensional carrier systems. The novel electronic state exposes itself in transport experiments through quantization of the Hall resistance to an exact rational fraction of h/e, and concomitantly vanishing longitudinal resistivity. Its relevant energy scale is only a few degrees kelvin. The quantization is a consequence of the spontaneous formation of an energy gap separating the condensed ground state from its rather elusive quasiparticle excitations. The theoretical understanding of the novel quantum liquids which underlie the FQHE has predominantly emerged from an ingenious many-particle wave function strongly supported by numerous few-particle simulations. Theory has now constructed a complex model for ideal two-dimensional electron systems in the presence of high magnetic fields and makes definitive, often fascinating predictions. Experiments have successively uncovered odd-denominator fractional states reaching presently to 7/13. The application of new experimental tools to the FQHE, such as optics, microwaves, and phonon techniques promises the direct observation of such parameters as the gap energy and possibly even some of the more elusive quantities in the future. While theory and experiment in the FQHE appear to be converging, there remains considerable room for challenging surprises. This paper provides a concise overview of the FQHE. It focuses on the experimental aspects and states, but does not expand on the theoretical advances. 70 refs., 11 figs 8. Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures OpenAIRE N'diaye, P. B.; Akosa, C. A.; Manchon, A. 2016-01-01 We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-B\\"uttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic a... 9. The Effects of L2 Experience on L3 Perception Science.gov (United States) Onishi, Hiromi 2016-01-01 This study examines the influence of experience with a second language (L2) on the perception of phonological contrasts in a third language (L3). This study contributes to L3 phonology by examining the influence of L2 phonological perception abilities on the perception of an L3 at the beginner level. Participants were native speakers of Korean… 10. A hall for assembly and cryogenic tests International Nuclear Information System (INIS) Beaunier, J.; Buhler, S.; Caruette, A.; Chevrollier, R.; Junquera, T.; Le Scornet, J.C. 1999-01-01 Cryodrome, an assembly hall and the testing ground for cryogenic equipment and R and D experiments for the superconducting cavities is going to be transformed for its future missions. The cryogenic utilities, especially the He low pressure pumping capacity, was rearranged and extended to a new area. Space was provided to install CRYHOLAB, a new horizontal cryostat for cavity testing. Automatic control and supervision of the utilities and the experimental area are rebuilt and updated. (authors) 11. Quantum hall effect. A perspective International Nuclear Information System (INIS) Aoki, Hideo 2006-01-01 Novel concepts and phenomena are emerging recently in the physics of quantum Hall effect. This article gives an overview, which starts from the fractional quantum Hall system viewed as an extremely strongly correlated system, and move on to present various phenomena involving internal degrees of freedom (spin and layer), non-equilibrium and optical properties, and finally the spinoff to anomalous Hall effect and the rotating Bose-Einstein condensate. (author) 12. Magnesium Hall Thruster Science.gov (United States) Szabo, James J. 2015-01-01 This Phase II project is developing a magnesium (Mg) Hall effect thruster system that would open the door for in situ resource utilization (ISRU)-based solar system exploration. Magnesium is light and easy to ionize. For a Mars- Earth transfer, the propellant mass savings with respect to a xenon Hall effect thruster (HET) system are enormous. Magnesium also can be combusted in a rocket with carbon dioxide (CO2) or water (H2O), enabling a multimode propulsion system with propellant sharing and ISRU. In the near term, CO2 and H2O would be collected in situ on Mars or the moon. In the far term, Mg itself would be collected from Martian and lunar regolith. In Phase I, an integrated, medium-power (1- to 3-kW) Mg HET system was developed and tested. Controlled, steady operation at constant voltage and power was demonstrated. Preliminary measurements indicate a specific impulse (Isp) greater than 4,000 s was achieved at a discharge potential of 400 V. The feasibility of delivering fluidized Mg powder to a medium- or high-power thruster also was demonstrated. Phase II of the project evaluated the performance of an integrated, highpower Mg Hall thruster system in a relevant space environment. Researchers improved the medium power thruster system and characterized it in detail. Researchers also designed and built a high-power (8- to 20-kW) Mg HET. A fluidized powder feed system supporting the high-power thruster was built and delivered to Busek Company, Inc. 13. Spin Hall effect transistor Czech Academy of Sciences Publication Activity Database Wunderlich, Joerg; Park, B.G.; Irvine, A.C.; Zarbo, Liviu; Rozkotová, E.; Němec, P.; Novák, Vít; Sinova, Jairo; Jungwirth, Tomáš 2010-01-01 Roč. 330, č. 6012 (2010), s. 1801-1804 ISSN 0036-8075 R&D Projects: GA AV ČR KAN400100652; GA MŠk LC510 EU Projects: European Commission(XE) 215368 - SemiSpinNet Grant - others:AV ČR(CZ) AP0801 Program:Akademická prémie - Praemium Academiae Institutional research plan: CEZ:AV0Z10100521 Keywords : spin Hall effect * spintronics * spin transistor Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 31.364, year: 2010 14. Spontaneous Hall effect in a chiral p-wave superconductor Science.gov (United States) Furusaki, Akira; Matsumoto, Masashige; Sigrist, Manfred 2001-08-01 In a chiral superconductor with broken time-reversal symmetry a spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force due to spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, nonuniversal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov-de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order h/(ekFλ)2, where kF is the Fermi wave vector and λ is the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed. 15. Quantum Hall Electron Nematics Science.gov (United States) MacDonald, Allan In 2D electron systems hosted by crystals with hexagonal symmetry, electron nematic phases with spontaneously broken C3 symmetry are expected to occur in the quantum Hall regime when triplets of Landau levels associated with three different Fermi surface pockets are partially filled. The broken symmetry state is driven by intravalley Coulombic exchange interactions that favor spontaneously polarized valley occupations. I will discuss three different examples of 2D electron systems in which this type of broken symmetry state is expected to occur: i) the SnTe (111) surface, ii) the Bi (111) surface. and iii) unbalanced bilayer graphene. This type of quantum Hall electron nematic state has so far been confirmed only in the Bi (111) case, in which the anisotropic quasiparticle wavefunctions of the broken symmetry state were directly imaged. In the SnTe case the nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions and intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the three-fold Landau level degeneracy, yielding a ground state energy with 2 π/3 periodicity as a function of Zeeman-field orientation angle. I will comment on the possibility of observing similar states in the absence of a magnetic field. Supported by DOE Division of Materials Sciences and Engineering Grant DE-FG03-02ER45958. 16. The ISOLDE hall CERN Multimedia Maximilien Brice 2002-01-01 Since 1992, after its move from the 600 MeV SC, ISOLDE is a customer of the Booster (then 1 GeV, now 1.4 GeV). The intense Booster beam (some 3E13 protons per pulse) is directed onto a target, from which a mixture of isotopes emanates. After ionization and electrostatic acceleration to 60 keV, they enter one of the 2 spectrometers (General Purpose Separator: GPS, and High Resolution Separator: HRS) from which the selected ions are directed to the experiments. The photos show: the REX-ISOLDE post accelerator; the mini-ball experiment; an overview of the ISOLDE hall. In the picture (_12) of the hall, the separators are behind the wall. From either of them, beams can be directed into any of the many beamlines towards the experiments, some of which are visible in the foreground. The elevated cubicle at the left is EBIS (Electron Beam Ion Source), which acts as a charge-state multiplier for the REX facility. The ions are further mass analzyzed and passed on to the linac which accelerates them to higher energies. T... 17. Energy consumption of sport halls Energy Technology Data Exchange (ETDEWEB) 1983-01-01 The energy consumption of Finland's sports halls (ball games halls, ice hockey halls and swimming halls) represent approximately 1% of that of the country's whole building stock. In the light of the facts revealed by the energy study the potential energy saving rate in sports halls is 15-25%. The total savings would be something like FIM 30-40 million per annum, of which about a half would be achieved without energy-economic investments only by changing utilization habits and by automatic control measures. The energy-economic investments are for the most part connected with ventilation and their repayment period is from one to five years. On the basis of the energy study the following specific consumption are presented as target values: swimming halls: heat (kWh/m*H3/a)100, electricity (kWh/m*H3/a)35, water (l/m*H3/a)1000 icehockey halls (warm): heat (kWh/m*H3/a)25, electricity (kWh/m*H3/a)15, water (l/m*H3/a)200, ball games halls (multi-purpose halls): heat (kWh/m*H3/a)30, electricity (kWh/m*H3/a)25, water (l/m*H3/a)130. In the study the following points proved to be the central areas of energy saving in sports halls: 1. Flexible regulation of the temperature in sports spaces on the basis of the sport in question. 2. The ventilation of swimming halls should be adjusted in such a way that the humidity of the hall air would comply with the limit humidity curve determined by the quality of structures and the temperature of the outdoor air. 3. An ice skating hall is an establishment producing condensing energy from 8 to 9 months a year worth of approx. 100.000-150.000 Finnmarks. The development of the recovery of condensing energy has become more important. 4. The ventilation of ball games halls may account for over 50% of the energy consumption of the whole building. Therefore special attention should be paid to the optimatization of ventilation as a whole. 18. Analysis list: l(3)mbt [Chip-atlas[Archive Lifescience Database Archive (English) Full Text Available l(3)mbt Cell line,Larvae + dm3 http://dbarchive.biosciencedbc.jp/kyushu-u/dm3/target/l(3)mbt.1.tsv http:...//dbarchive.biosciencedbc.jp/kyushu-u/dm3/target/l(3)mbt.5.tsv http://dbarchive.bioscie...ncedbc.jp/kyushu-u/dm3/target/l(3)mbt.10.tsv http://dbarchive.biosciencedbc.jp/kyushu-u/dm3/colo/l(3)mbt.Cell_line.tsv,http:...//dbarchive.biosciencedbc.jp/kyushu-u/dm3/colo/l(3)mbt.Larvae.tsv http:...//dbarchive.biosciencedbc.jp/kyushu-u/dm3/colo/Cell_line.gml,http://dbarchive.biosciencedbc.jp/kyushu-u/dm3/colo/Larvae.gml ... 19. Scanning vector Hall probe microscopy International Nuclear Information System (INIS) Cambel, V.; Gregusova, D.; Fedor, J.; Kudela, R.; Bending, S.J. 2004-01-01 We have developed a scanning vector Hall probe microscope for mapping magnetic field vector over magnetic samples. The microscope is based on a micromachined Hall sensor and the cryostat with scanning system. The vector Hall sensor active area is ∼5x5 μm 2 . It is realized by patterning three Hall probes on the tilted faces of GaAs pyramids. Data from these 'tilted' Hall probes are used to reconstruct the full magnetic field vector. The scanning area of the microscope is 5x5 mm 2 , space resolution 2.5 μm, field resolution ∼1 μT Hz -1/2 at temperatures 10-300 K 20. Coulomb blockade in hierarchical quantum Hall droplets International Nuclear Information System (INIS) Cappelli, Andrea; Georgiev, Lachezar S; Zemba, Guillermo R 2009-01-01 The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, ν = m/(mp ± 1), and find a non-trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, which is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge. (fast track communication) 1. Observation of the anomalous Hall effect in GaAs International Nuclear Information System (INIS) Miah, M Idrish 2007-01-01 Devices for the direct detection of the spin current, based on the anomalous Hall effect (AHE), are fabricated on n-type GaAs bulk semiconductor materials. The AHE is observed in the device when the photoinduced spin-polarized electrons are injected into it, and it is found that the effect depends on the applied electric field. The origin of the field-dependent observed Hall effect is discussed based on the D'yakonov-Perel' (DP) spin relaxation mechanism. The spin-dependent Hall effect is also found to be enhanced with increasing doping concentration. The present experimental results might have potential applications in semiconductor spintronic devices since the effect is closely related to the spin Hall effect 2. Observation of the anomalous Hall effect in GaAs Energy Technology Data Exchange (ETDEWEB) Miah, M Idrish [Nanoscale Science and Technology Centre, School of Science, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Department of Physics, University of Chittagong, Chittagong, Chittagong - 4331 (Bangladesh) 2007-03-21 Devices for the direct detection of the spin current, based on the anomalous Hall effect (AHE), are fabricated on n-type GaAs bulk semiconductor materials. The AHE is observed in the device when the photoinduced spin-polarized electrons are injected into it, and it is found that the effect depends on the applied electric field. The origin of the field-dependent observed Hall effect is discussed based on the D'yakonov-Perel' (DP) spin relaxation mechanism. The spin-dependent Hall effect is also found to be enhanced with increasing doping concentration. The present experimental results might have potential applications in semiconductor spintronic devices since the effect is closely related to the spin Hall effect. 3. Recent results from L3+COSMICS at CERN L3 collaboration CERN Document Server Bertaina, M 2002-01-01 11x10 sup 9 cosmic ray muon events above 20 GeV have been collected with the L3+C detector at LEP, CERN, in 1999 and 2000. During the last year the energy, core position and direction of the air showers causing the observed muons could be derived for part of the data. Preliminary results for the vertical muon flux and charge ratio depending on the muon momentum are shown. The influence of the air shower energy on the muon properties is studied. A search for muon rate increase during the solar flare of the 14 sup t sup h July 2000 is performed. Meteorological effects on cosmic ray intensity measurements are discussed. 4. On Hall current fluid International Nuclear Information System (INIS) Shen, M.C.; Ebel, D. 1987-01-01 In this paper some new results concerning magnetohydrodynamic (MHD) equations with the Hall current (HC) term in the Ohm's law are presented. For the cylindrical pinch of a compressible HC fluid, it is found that for large time and long wave length the solution to the governing equations exhibits the behavior of solitons as in the case of an ideal MHD model. In some special cases, the HC model appears to be better posed. An open question is whether a simple toroidal equilibrium of an HC fluid with resistivity and viscosity exists. The answer to this question is affirmative if the prescribed velocity on the boundary has a small norm. Furthermore, the equilibrium is also linearly and nonlinearly stable 5. Farm Hall: The Play Science.gov (United States) Cassidy, David C. 2013-03-01 It's July 1945. Germany is in defeat and the atomic bombs are on their way to Japan. Under the direction of Samuel Goudsmit, the Allies are holding some of the top German nuclear scientists-among them Heisenberg, Hahn, and Gerlach-captive in Farm Hall, an English country manor near Cambridge, England. As secret microphones record their conversations, the scientists are unaware of why they are being held or for how long. Thinking themselves far ahead of the Allies, how will they react to the news of the atomic bombs? How will these famous scientists explain to themselves and to the world their failure to achieve even a chain reaction? How will they come to terms with the horror of the Third Reich, their work for such a regime, and their behavior during that period? This one-act play is based upon the transcripts of their conversations as well as the author's historical work on the subject. 6. Quantum Hall effect International Nuclear Information System (INIS) Joynt, R.J. 1982-01-01 A general investigation of the electronic structure of two dimensional systems is undertaken with a view towards understanding the quantum Hall effect. The work is limited to the case of a strong perpendicular magnetic field, with a disordered potential and an externally applied electric field. The electrons are treated as noninteracting. First, the scattering theory of the system is worked out. The surprising result is found that a wavepacket will reform after scattering from an isolated potential. Also it will tend to be accelerated in the neighborhood of the scatterer if the potential has bound states. Fredholm theory can then be used to show that the extended states carry an additional current which compensates for the zero current of the bound states. Together, these give the quantized conductance. The complementary case of a smooth random potential is treated by a path-integral approach which exploits the analogies to the classical equations of motion. The Green's function can be calculated approximately, which gives the general character of both the bound and extended states. Also the ratio of these two types of states can be computed for a given potential. The charge density is uniform in first approximation, and the Hall conductance is quantized. Higher-order corrections for more rapidly fluctuating potential are calculated. The most general conditions under which the conductance is quantized are discussed. Because of the peculiar scattering properties of the system, numerical solution of the Schroedinger equation is of interest, both to confirm the analytical results, and for pedagogical reasons. The stability and convergence problems inherent in the computer solution of the problem are analyzed. Results for some model scattering potentials are presented 7. Quantum energy teleportation in a quantum Hall system Energy Technology Data Exchange (ETDEWEB) Yusa, Go; Izumida, Wataru; Hotta, Masahiro [Department of Physics, Tohoku University, Sendai 980-8578 (Japan) 2011-09-15 We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters. 8. Hall Effect Gyrators and Circulators Science.gov (United States) Viola, Giovanni; DiVincenzo, David P. 2014-04-01 The electronic circulator and its close relative the gyrator are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative nonreciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an Ohmically contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90°. In this limit, we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the ac wavelength. An experiment is proposed to achieve GHz-band gyration in millimeter (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realizing a Hall gyrator is also analyzed. 9. Technicians dismantle the inner section of L3 CERN Multimedia Laurent Guiraud 2001-01-01 The technicians are dismantling the forward tracking chamber located at the heart of the L3 detector. This formed part of the hadronic calorimeter, which is used for measuring particle energies. L3 was an experiment at the LEP collider that ran from 1989 to 2000. 10. GLONASS CDMA L3 ambiguity resolution and positioning NARCIS (Netherlands) Zaminpardaz, Safoora; Teunissen, P.J.G.; Nadarajah, Nandakumaran 2016-01-01 A first assessment of GLONASS CDMA L3 ambiguity resolution and positioning performance is provided. Our analyses are based on GLONASS L3 data from the satellite pair SVNs 755-801, received by two JAVAD receivers at Curtin University, Perth, Australia. In our analyses, four different versions of 11. Topological Hall and spin Hall effects in disordered skyrmionic textures KAUST Repository Ndiaye, Papa Birame; Akosa, Collins Ashu; Manchon, Aurelien 2017-01-01 We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering. 12. Topological Hall and spin Hall effects in disordered skyrmionic textures KAUST Repository Ndiaye, Papa Birame 2017-02-24 We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering. 13. Tuning giant anomalous Hall resistance ratio in perpendicular Hall balance Energy Technology Data Exchange (ETDEWEB) Zhang, J. Y.; Yang, G. [Department of Materials Physics and Chemistry, University of Science and Technology Beijing, Beijing 100083 (China); State Key Laboratory of Magnetism, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Wang, S. G., E-mail: [email protected], E-mail: [email protected] [State Key Laboratory of Magnetism, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Liu, J. L. [State Key Laboratory of Magnetism, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Physics, Beijing University of Aeronautics and Astronautics, Beijing 100191 (China); Wang, R. M. [Department of Physics, Beijing University of Aeronautics and Astronautics, Beijing 100191 (China); Amsellem, E.; Kohn, A. [Department of Materials Engineering, Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Yu, G. H., E-mail: [email protected], E-mail: [email protected] [Department of Materials Physics and Chemistry, University of Science and Technology Beijing, Beijing 100083 (China) 2015-04-13 Anomalous Hall effect at room temperature in perpendicular Hall balance with a core structure of [Pt/Co]{sub 4}/NiO/[Co/Pt]{sub 4} has been tuned by functional CoO layers, where [Pt/Co]{sub 4} multilayers exhibit perpendicular magnetic anisotropy. A giant Hall resistance ratio up to 69 900% and saturation Hall resistance (R{sub S}{sup P}) up to 2590 mΩ were obtained in CoO/[Pt/Co]{sub 4}/NiO/[Co/Pt]{sub 4}/CoO system, which is 302% and 146% larger than that in the structure without CoO layers, respectively. Transmission electron microscopy shows highly textured [Co/Pt]{sub 4} multilayers and oxide layers with local epitaxial relations, indicating that the crystallographic structure has significant influence on spin dependent transport properties. 14. Anode Fall Formation in a Hall Thruster International Nuclear Information System (INIS) Dorf, Leonid A.; Raitses, Yevgeny F.; Smirnov, Artem N.; Fisch, Nathaniel J. 2004-01-01 As was reported in our previous work, accurate, nondisturbing near-anode measurements of the plasma density, electron temperature, and plasma potential performed with biased and emissive probes allowed the first experimental identification of both electron-repelling (negative anode fall) and electron-attracting (positive anode fall) anode sheaths in Hall thrusters. An interesting new phenomenon revealed by the probe measurements is that the anode fall changes from positive to negative upon removal of the dielectric coating, which appears on the anode surface during the course of Hall thruster operation. As reported in the present work, energy dispersion spectroscopy analysis of the chemical composition of the anode dielectric coating indicates that the coating layer consists essentially of an oxide of the anode material (stainless steel). However, it is still unclear how oxygen gets into the thruster channel. Most importantly, possible mechanisms of anode fall formation in a Hall thruster with a clean and a coated anodes are analyzed in this work; practical implication of understanding the general structure of the electron-attracting anode sheath in the case of a coated anode is also discussed 15. LOFT/L3-, Loss of Fluid Test, 7. NRC L3 Small Break LOCA Experiment International Nuclear Information System (INIS) 1992-01-01 1 - Description of test facility: The LOFT Integral Test Facility is a scale model of a LPWR. The intent of the facility is to model the nuclear, thermal-hydraulic phenomena which would take place in a LPWR during a LOCA. The general philosophy in scaling coolant volumes and flow areas in LOFT was to use the ratio of the LOFT core [50 MW(t)] to a typical LPWR core [3000 MW(t)]. For some components, this factor is not applied; however, it is used as extensively as practical. In general, components used in LOFT are similar in design to those of a LPWR. Because of scaling and component design, the LOFT LOCA is expected to closely model a LPWR LOCA. 2 - Description of test: This was the seventh in the NRC L3 Series of small-break LOCA experiments. A 2.5-cm (10-in.) cold-leg non-communicative-break LOCA was simulated. The experiment was conducted on 20 June 1980 16. Anisotropic intrinsic spin Hall effect in quantum wires International Nuclear Information System (INIS) Cummings, A W; Akis, R; Ferry, D K 2011-01-01 We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit couplings. In particular, at low densities, when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the [1-bar 10] axis, which is the opposite of what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications. (paper) 17. A holographic model for the fractional quantum Hall effect Energy Technology Data Exchange (ETDEWEB) Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium) 2015-01-08 Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions. 18. A holographic model for the fractional quantum Hall effect Science.gov (United States) Lippert, Matthew; Meyer, René; Taliotis, Anastasios 2015-01-01 Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions. 19. Gauge invariance and fractional quantized Hall effect International Nuclear Information System (INIS) Tao, R.; Wu, Y.S. 1984-01-01 It is shown that gauge invariance arguments imply the possibility of fractional quantized Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantized Hall effect must be degenerate; the non-degenerate ground state can only produce the integral quantized Hall effect. 12 references 20. "Hall mees" Linnateatris / Triin Sinissaar Index Scriptorium Estoniae Sinissaar, Triin 1999-01-01 Tallinn Linnateatri ja Raadioteatri ühislavastus "Hall mees" Gill Adamsi näidendi järgi, lavastaja Eero Spriit, osades Helene Vannari ja Väino Laes, kunstnik Kustav - Agu Püüman. Esietendus 22. okt 1. Sheldon-Hall syndrome Directory of Open Access Journals (Sweden) 2009-03-01 Full Text Available Abstract Sheldon-Hall syndrome (SHS is a rare multiple congenital contracture syndrome characterized by contractures of the distal joints of the limbs, triangular face, downslanting palpebral fissures, small mouth, and high arched palate. Epidemiological data for the prevalence of SHS are not available, but less than 100 cases have been reported in the literature. Other common clinical features of SHS include prominent nasolabial folds, high arched palate, attached earlobes, mild cervical webbing, short stature, severe camptodactyly, ulnar deviation, and vertical talus and/or talipes equinovarus. Typically, the contractures are most severe at birth and non-progressive. SHS is inherited in an autosomal dominant pattern but about half the cases are sporadic. Mutations in either MYH3, TNNI2, or TNNT3 have been found in about 50% of cases. These genes encode proteins of the contractile apparatus of fast twitch skeletal muscle fibers. The diagnosis of SHS is based on clinical criteria. Mutation analysis is useful to distinguish SHS from arthrogryposis syndromes with similar features (e.g. distal arthrogryposis 1 and Freeman-Sheldon syndrome. Prenatal diagnosis by ultrasonography is feasible at 18–24 weeks of gestation. If the family history is positive and the mutation is known in the family, prenatal molecular genetic diagnosis is possible. There is no specific therapy for SHS. However, patients benefit from early intervention with occupational and physical therapy, serial casting, and/or surgery. Life expectancy and cognitive abilities are normal. 2. Anode sheath in Hall thrusters International Nuclear Information System (INIS) Dorf, L.; Semenov, V.; Raitses, Y. 2003-01-01 A set of hydrodynamic equations is used to describe quasineutral plasma in ionization and acceleration regions of a Hall thruster. The electron distribution function and Poisson equation are invoked for description of a near-anode region. Numerical solutions suggest that steady-state operation of a Hall thruster can be achieved at different anode sheath regimes. It is shown that the anode sheath depends on the thruster operating conditions, namely the discharge voltage and the mass flow rate 3. Theory of spin Hall effect OpenAIRE Chudnovsky, Eugene M. 2007-01-01 An extension of Drude model is proposed that accounts for spin and spin-orbit interaction of charge carriers. Spin currents appear due to combined action of the external electric field, crystal field and scattering of charge carriers. The expression for spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, spin Hall conductivity $\\sigma_s$ and charge conductivity $\\sigma_c$ are related through $\\sigma_s = [2 \\pi \\hbar... 4. Optimization of Cylindrical Hall Thrusters International Nuclear Information System (INIS) Raitses, Yevgeny; Smirnov, Artem; Granstedt, Erik; Fisch, Nathaniel J. 2007-01-01 The cylindrical Hall thruster features high ionization efficiency, quiet operation, and ion acceleration in a large volume-to-surface ratio channel with performance comparable with the state-of-the-art annular Hall thrusters. These characteristics were demonstrated in low and medium power ranges. Optimization of miniaturized cylindrical thrusters led to performance improvements in the 50-200W input power range, including plume narrowing, increased thruster efficiency, reliable discharge initiation, and stable operation. 5. Optimization of Cylindrical Hall Thrusters International Nuclear Information System (INIS) Raitses, Yevgeny; Smirnov, Artem; Granstedt, Erik; Fi, Nathaniel J. 2007-01-01 The cylindrical Hall thruster features high ionization efficiency, quiet operation, and ion acceleration in a large volume-to-surface ratio channel with performance comparable with the state-of-the-art annular Hall thrusters. These characteristics were demonstrated in low and medium power ranges. Optimization of miniaturized cylindrical thrusters led to performance improvements in the 50-200W input power range, including plume narrowing, increased thruster efficiency, reliable discharge initiation, and stable operation 6. Not your grandfather's concert hall Science.gov (United States) Cooper, Russell; Malenka, Richard; Griffith, Charles; Friedlander, Steven 2004-05-01 The opening of Judy and Arthur Zankel Hall on 12 September 2003, restores Andrew Carnegie's original 1891 concept of having three outstanding auditoriums of different sizes under one roof, and creates a 21st-century venue for music performance and education. With concerts ranging from early music to avant-garde multimedia productions, from jazz to world music, and from solo recitals to chamber music, Zankel Hall expands the breadth and depth of Carnegie Hall's offerings. It allows for the integration of programming across three halls with minifestivals tailored both to the size and strengths of each hall and to the artists and music to be performed. The new flexible space also provides Carnegie Hall with an education center equipped with advanced communications technology. This paper discusses the unique program planned for this facility and how the architects, theatre consultants, and acousticians developed a design that fulfilled the client's expectations and coordinated the construction of the facility under the floor of the main Isaac Stern Auditorium without having to cancel a single performance. 7. Modular invariance, universality and crossover in the quantum Hall effect International Nuclear Information System (INIS) Dolan, Brian P. 1999-01-01 An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall states, a generalisation of the law of corresponding states from rational filling factors to complex conductivity, which has a mathematical expression in terms of an action of the modular group on the upper-half complex conductivity plane. This symmetry implies universality in quantum Hall crossovers. The assumption that the β-function for the complex conductivity is a complex analytic function, together with some experimental constraints, results in an analytic expression for the crossover, as a function of the external magnetic field 8. Admittance of multiterminal quantum Hall conductors at kilohertz frequencies International Nuclear Information System (INIS) Hernández, C.; Consejo, C.; Chaubet, C.; Degiovanni, P. 2014-01-01 We present an experimental study of the low frequency admittance of quantum Hall conductors in the [100 Hz, 1 MHz] frequency range. We show that the frequency dependence of the admittance of the sample strongly depends on the topology of the contacts connections. Our experimental results are well explained within the Christen and Büttiker approach for finite frequency transport in quantum Hall edge channels taking into account the influence of the coaxial cables capacitance. In the Hall bar geometry, we demonstrate that there exists a configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the sample and observe its dependence on the filling factor 9. Admittance of multiterminal quantum Hall conductors at kilohertz frequencies Energy Technology Data Exchange (ETDEWEB) Hernández, C. [Departamento de Física, Universidad Militar Nueva Granada, Carrera 11 101-80 Bogotá D.C. (Colombia); Consejo, C.; Chaubet, C., E-mail: [email protected] [Université Montpellier 2, Laboratoire Charles Coulomb UMR5221, F-34095 Montpellier, France and CNRS, Laboratoire Charles Coulomb UMR5221, F-34095 Montpellier (France); Degiovanni, P. [Université de Lyon, Fédération de Physique Andrée Marie Ampère, CNRS, Laboratoire de Physique de l' Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France) 2014-03-28 We present an experimental study of the low frequency admittance of quantum Hall conductors in the [100 Hz, 1 MHz] frequency range. We show that the frequency dependence of the admittance of the sample strongly depends on the topology of the contacts connections. Our experimental results are well explained within the Christen and Büttiker approach for finite frequency transport in quantum Hall edge channels taking into account the influence of the coaxial cables capacitance. In the Hall bar geometry, we demonstrate that there exists a configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the sample and observe its dependence on the filling factor. 10. Iodine Hall Thruster Science.gov (United States) Szabo, James 2015-01-01 Iodine enables dramatic mass and cost savings for lunar and Mars cargo missions, including Earth escape and near-Earth space maneuvers. The demonstrated throttling ability of iodine is important for a singular thruster that might be called upon to propel a spacecraft from Earth to Mars or Venus. The ability to throttle efficiently is even more important for missions beyond Mars. In the Phase I project, Busek Company, Inc., tested an existing Hall thruster, the BHT-8000, on iodine propellant. The thruster was fed by a high-flow iodine feed system and supported by an existing Busek hollow cathode flowing xenon gas. The Phase I propellant feed system was evolved from a previously demonstrated laboratory feed system. Throttling of the thruster between 2 and 11 kW at 200 to 600 V was demonstrated. Testing showed that the efficiency of iodine fueled BHT-8000 is the same as with xenon, with iodine delivering a slightly higher thrust-to-power (T/P) ratio. In Phase II, a complete iodine-fueled system was developed, including the thruster, hollow cathode, and iodine propellant feed system. The nominal power of the Phase II system is 8 kW; however, it can be deeply throttled as well as clustered to much higher power levels. The technology also can be scaled to greater than 100 kW per thruster to support megawatt-class missions. The target thruster efficiency for the full-scale system is 65 percent at high specific impulse (Isp) (approximately 3,000 s) and 60 percent at high thrust (Isp approximately 2,000 s). 11. L3 English acquisition in Denmark and Greenland DEFF Research Database (Denmark) Spellerberg, Stine Marie 2011-01-01 This paper presents findings of gender-related tendencies found in a study of factors influential in third language acquisition of English in Denmark and Greenland. A survey consisting of a questionnaire and an English test was carried out amongst pupils in their last year of compulsory schooling...... in Copenhagen, Denmark, and Nuuk, Greenland. In total, responses from 187 pupils were included, some of which were responses from pupils learning English as a second language; these respondents were included for comparisons (Copenhagen: L2 learners N =59, L3 learners N=32; Nuuk: L3 learners N=96; age: 14......' degree of English classroom anxiety. The results differentiate the view that L3 learners as a group do less well in English than L2 learner peers, warranting further research into gender-related tendencies and extra focus on the English acquisition of L3 learner boys in particular in the Danish context.... 12. IceBridge DMS L3 Photogrammetric DEM Data.gov (United States) National Aeronautics and Space Administration — The IceBridge DMS L3 Photogrammetric DEM (IODMS3) data set contains gridded digital elevation models and orthorectified images of Greenland derived from the Digital... 13. Curcumin analog L3 alleviates diabetic atherosclerosis by multiple effects. Science.gov (United States) Zheng, Bin; Yang, Liu; Wen, Caixia; Huang, Xiuwang; Xu, Chenxia; Lee, Kuan-Han; Xu, Jianhua 2016-03-15 L3, an analog of curcumin, is a compound isolated from a traditional Chinese medicine Turmeric. In this paper, we aims to explore the efficacy of L3 on diabetic atherosclerosis and the related mechanism. The effect of L3 was studied on glucose and lipid metabolism, antioxidant status, atherosclerosis-related indexes and pathological changes of main organs in the mice model of diabetes induced by streptozotocin and high-fat diet. The results showed that L3 treatment could meliorate dyslipidemia and hyperglycemia, reduce oxidative stress, enhance the activity of antioxidases, increase the nitric oxide level in plasma and aortic arch, decrease the production of reactive oxygen species in pancreas and lectin-like oxidized low-density lipoprotein receptor-1 expression in aortic arch, and meliorate the fatty and atherosclerotic degeneration in aortic arch, thereby preventing the development of diabetes and its complications. These results suggested that L3 can alleviate the diabetic atherosclerosis by multiple effects. This study provided scientific basis for the further research and clinical application of L3. Copyright © 2016 Elsevier B.V. All rights reserved. 14. Composite fermions a unified view of the quantum Hall regime CERN Document Server 1998-01-01 One of the most exciting recent developments to have emerged from the quantum Hall effect is the subject of composite fermions. This important volume gives a self-contained, comprehensive description of the subject, including fundamentals, more advanced theoretical work, and results from experimental observations of composite fermions. 15. ac spin-Hall effect International Nuclear Information System (INIS) Entin-Wohlman, O. 2005-01-01 Full Text:The spin-Hall effect is described. The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field E(ω) generates a spin-polarization current, normal to E, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to ω 2 . At non-zero temperatures the coupling to the phonons yields an imaginary term proportional to ω. The interference also yields persistent spin currents at thermal equilibrium, at E = 0. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other 16. Spin-Hall nano-oscillator: A micromagnetic study Energy Technology Data Exchange (ETDEWEB) Giordano, A.; Azzerboni, B.; Finocchio, G. [Department of Electronic Engineering, Industrial Chemistry and Engineering, University of Messina, C.da di Dio, I-98166 Messina (Italy); Carpentieri, M. [Department of Electrical and Information Engineering, Politecnico of Bari, via E. Orabona 4, I-70125 Bari (Italy); Laudani, A. [Department of Engineering, University of Roma Tre, via V. Volterra 62, I-00146 Roma (Italy); Gubbiotti, G. [Istituto Officina dei Materiali del CNR (CNR-IOM), Unità di Perugia c/o Dipartimento di Fisica e Geologia, Via A. Pascoli, 06123 Perugia (Italy) 2014-07-28 This Letter studies the dynamical behavior of spin-Hall nanoscillators from a micromagnetic point of view. The model parameters have been identified by reproducing recent experimental data quantitatively. Our results indicate that a strongly localized mode is observed for in-plane bias fields such as in the experiments, while predict the excitation of an asymmetric propagating mode for large enough out-of plane bias field similarly to what observed in spin-torque nanocontact oscillators. Our findings show that spin-Hall nanoscillators can find application as spin-wave emitters for magnonic applications where spin waves are used for transmission and processing information on nanoscale. 17. Hall measurements and grain-size effects in polycrystalline silicon International Nuclear Information System (INIS) Ghosh, A.K.; Rose, A.; Maruska, H.P.; Eustace, D.J.; Feng, T. 1980-01-01 The effects of grain size on Hall measurements in polycrystalline silicon are analyzed and interpreted, with some modifications, using the model proposed by Bube. This modified model predicts that the measured effective Hall voltage is composed of components originating from the bulk and space-charge regions. For materials with large grain sizes, the carrier concentration is independent of the intergrain boundary barrier, whereas the mobility is dependent on it. However, for small grains, both the carrier density and mobility depend on the barrier. These predictions are consistent with experimental results of mm-size Wacker and μm-size neutron-transmutation-doped polycrystalline silicon 18. Effect of Anode Dielectric Coating on Hall Thruster Operation International Nuclear Information System (INIS) Dorf, L.; Raitses, Y.; Fisch, N.J.; Semenov, V. 2003-01-01 An interesting phenomenon observed in the near-anode region of a Hall thruster is that the anode fall changes from positive to negative upon removal of the dielectric coating, which is produced on the anode surface during the normal course of Hall thruster operation. The anode fall might affect the thruster lifetime and acceleration efficiency. The effect of the anode coating on the anode fall is studied experimentally using both biased and emissive probes. Measurements of discharge current oscillations indicate that thruster operation is more stable with the coated anode 19. Magnetoresistance and Hall resistivity of semimetal WTe2 ultrathin flakes. Science.gov (United States) Luo, Xin; Fang, Chi; Wan, Caihua; Cai, Jialin; Liu, Yong; Han, Xiufeng; Lu, Zhihong; Shi, Wenhua; Xiong, Rui; Zeng, Zhongming 2017-04-07 This article reports the characterization of WTe 2 thin flake magnetoresistance and Hall resistivity. We found it does not exhibit magnetoresistance saturation when subject to high fields, in a manner similar to their bulk characteristics. The linearity of Hall resistivity in our devices confirms the compensation of electrons and holes. By relating experimental results to a classic two-band model, the lower magnetoresistance values in our samples is demonstrated to be caused by decreased carrier mobility. The dependence of mobility on temperature indicates the main role of optical phonon scattering at high temperatures. Our results provide more detailed information on carrier behavior and scattering mechanisms in WTe 2 thin films. 20. Analysis of Multi Muon Events in the L3 Detector CERN Document Server Schmitt, Volker 2000-01-01 The muon density distribution in air showers initiated by osmi parti les is sensitive to the hemi al omposition of osmi rays. The density an be measured via the multipli ity distribution in a nite size dete tor, as it is L3. With a shallow depth of 30 meters under ground, the dete tor provides an ex ellent fa ility to measure a high muon rate, but being shielded from the hadroni and ele troni shower omponent. Subje t of this thesis is the des ription of the L3 Cosmi s experiment (L3+C), whi h is taking data sin e May 1999 and the analysis of muon bundles in the large magneti spe trometer of L3. The new osmi trigger and readout system is brie y des ribed. The in uen e of dierent primaries on the multipli ity distribution has been investigated using Monte Carlo event samples, generated with the CORSIKA program. The simulation results showed that L3+C measures in the region of the \\knee" of the primary spe trum of osmi rays. A new pattern re ognition has been developed and added to the re onstru tion ode, whi h ... 1. Carl Gustav Jung and Granville Stanley Hall on Religious Experience. Science.gov (United States) Kim, Chae Young 2016-08-01 Granville Stanley Hall (1844-1924) with William James (1842-1910) is the key founder of psychology of religion movement and the first American experimental or genetic psychologist, and Carl Gustav Jung (1875-1961) is the founder of the analytical psychology concerned sympathetically about the religious dimension rooted in the human subject. Their fundamental works are mutually connected. Among other things, both Hall and Jung were deeply interested in how the study of religious experience is indispensable for the depth understanding of human subject. Nevertheless, except for the slight indication, this common interest between them has not yet been examined in academic research paper. So this paper aims to articulate preliminary evidence of affinities focusing on the locus and its function of the inner deep psychic dimension as the religious in the work of Hall and Jung. 2. Crossover between spin swapping and Hall effect in disordered systems KAUST Repository Saidaoui, Hamed Ben Mohamed 2015-07-16 We theoretically study the crossover between spin Hall effect and spin swapping, a recently predicted phenomenon that consists of the interchange between the current flow and its spin polarization directions [M. B. Lifshits and M. I. Dyakonov, Phys. Rev. Lett. 103, 186601 (2009)]. Using a tight-binding model with spin-orbit coupled disorder, spin Hall effect, spin relaxation, and spin swapping are treated on equal footing. We demonstrate that spin swapping and spin Hall effect present very different dependencies as a function of the spin-orbit coupling and disorder strengths and confirm that the former exceeds the latter in the parameter range considered. Three setups are proposed for the experimental observation of the spin swapping effect. 3. The quantum Hall effect in quantum dot systems International Nuclear Information System (INIS) Beltukov, Y M; Greshnov, A A 2014-01-01 It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given 4. Crossover between spin swapping and Hall effect in disordered systems KAUST Repository Saidaoui, Hamed Ben Mohamed; Otani, Y.; Manchon, Aurelien 2015-01-01 We theoretically study the crossover between spin Hall effect and spin swapping, a recently predicted phenomenon that consists of the interchange between the current flow and its spin polarization directions [M. B. Lifshits and M. I. Dyakonov, Phys. Rev. Lett. 103, 186601 (2009)]. Using a tight-binding model with spin-orbit coupled disorder, spin Hall effect, spin relaxation, and spin swapping are treated on equal footing. We demonstrate that spin swapping and spin Hall effect present very different dependencies as a function of the spin-orbit coupling and disorder strengths and confirm that the former exceeds the latter in the parameter range considered. Three setups are proposed for the experimental observation of the spin swapping effect. 5. Search on charginos and neutralinos with the L3 detector at LEP; Recherche de charginos et de neutralinos avec le detecteur L3 au LEP Energy Technology Data Exchange (ETDEWEB) Chereau, Xavier [Laboratoire dAnnecy-le-vieux de physique des particules, Grenoble-1 Univ., 74 Annecy (France) 1998-04-30 This work presents an experimental search for supersymmetric particles, the charginos and the neutralinos, at center of mass energies {radical} 161, 172 and 183 GeV, with the L3 detector at the e{sup +}e{sup -} collider LEP. Assuming R-parity conservation, SUSY events have a large missing energy, carried by the lightest supersymmetric particle (LSP), which allow us to distinguish them from standard events. Then, for all the studied final states and all the energies, we optimized the selections in order to have the best signal-to-noise ratio. No excess of events were observed with respect to the standard model predictions. We set upper limits on the chargino and neutralino production cross sections. In the frame of the constraint MSSM, these results were combined with the results from the L3 slepton analyses to set lower limits on the chargino and neutralino masses: particularly, we exclude a neutralino {chi}{sub 1}{sup 0} bar lighter than 25.9 GeV/c{sup 2} (95% C.L.). This result plays an important role for the interpretation of the dark matter in universe. The search for events with missing energy needs a detector with a good hermeticity. At the end of 1995, a new electromagnetic calorimeter was installed in the L3 experiment. Here we present the improvements of performances and the calibration of this detector composed of 48 bricks made with lead and scintillating fibers (SPACAL) 71 refs., 104 figs., 21 tabs. 6. ATLAS Assembly Hall Open Day CERN Multimedia Patrice Loiez 2004-01-01 To mark the 50th Anniversary of the founding of CERN, a day of tours, displays and presentations was held in October 2004. The assembly halls for the experiments that were waiting to be installed on the LHC, such as ATLAS shown here, were transformed into display areas and cafés. 7. Universal intrinsic spin Hall effect Czech Academy of Sciences Publication Activity Database Sinova, J.; Culcer, D.; Sinitsyn, N. A.; Niu, Q.; Jungwirth, Tomáš; MacDonald, A. H. 2004-01-01 Roč. 92, č. 12 (2004), 126603/1-126603/4 ISSN 0031-9007 R&D Projects: GA ČR GA202/02/0912 Institutional research plan: CEZ:AV0Z1010914 Keywords : semiconductor quantum wells * spin-orbit interaction * spin Hall effect Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.218, year: 2004 8. Spin Hall effect for anyons International Nuclear Information System (INIS) Dhar, S.; Basu, B.; Ghosh, Subir 2007-01-01 We explain the intrinsic spin Hall effect from generic anyon dynamics in the presence of external electromagnetic field. The free anyon is represented as a spinning particle with an underlying non-commutative configuration space. The Berry curvature plays a major role in the analysis 9. The Other Hall Effect: College Board Physics Science.gov (United States) Sheppard, Keith; Gunning, Amanda M. 2013-01-01 Edwin Herbert Hall (1855-1938), discoverer of the Hall effect, was one of the first winners of the AAPT Oersted Medal for his contributions to the teaching of physics. While Hall's role in establishing laboratory work in high schools is widely acknowledged, his position as chair of the physics section of the Committee on College Entrance… 10. The muon filter of the L3 detector International Nuclear Information System (INIS) Adriani, O.; Bocciolini, M.; Cartacci, A.M.; Civinini, C.; D'Alessandro, R.; Gallo, E.; Landi, G.; Marchionni, A.; Meschini, M.; Monteleoni, B.; Pieri, M.; Spillantini, P.; Wang, Y.F.; Florence Univ. 1991-01-01 In this article we describe the outer part (Muon Filter) of the Hadron Calorimeter of the L3 detector. Construction and performance of the brass chambers, which form the sensitive part of the detector, are reviewed. We also report the results from data taken on two beam tests, at CERN. (orig.) 11. Bilingual Education and L3 Learning: Metalinguistic Advantage or Not? Science.gov (United States) Rutgers, Dieuwerke; Evans, Michael 2017-01-01 Metalinguistic skills are highlighted in the literature as providing bilinguals with an advantage in additional language (L3) learning. The extent to which this may apply to bilingual education and content-and-language-integrated-learning settings, however, is as yet little understood. This article reports on a study exploring and comparing the… 12. Dismantling the silicon microstrip detector on L3 CERN Multimedia Laurent Guiraud 2001-01-01 The silicon microstrip detector is located at the heart of the detector and must be kept cool to prevent thermal noise. The work shown here is the removal of the cooling system. L3 was dismantled as part of the closure of the entire LEP accelerator in 2000 to make way for the new LHC. 13. Transit-time instability in Hall thrusters International Nuclear Information System (INIS) Barral, Serge; Makowski, Karol; Peradzynski, Zbigniew; Dudeck, Michel 2005-01-01 Longitudinal waves characterized by a phase velocity of the order of the velocity of ions have been recurrently observed in Hall thruster experiments and simulations. The origin of this so-called ion transit-time instability is investigated with a simple one-dimensional fluid model of a Hall thruster discharge in which cold ions are accelerated between two electrodes within a quasineutral plasma. A short-wave asymptotics applied to linearized equations shows that plasma perturbations in such a device consist of quasineutral ion acoustic waves superimposed on a background standing wave generated by discharge current oscillations. Under adequate circumstances and, in particular, at high ionization levels, acoustic waves are amplified as they propagate, inducing strong perturbation of the ion density and velocity. Responding to the subsequent perturbation of the column resistivity, the discharge current generates a standing wave, the reflection of which sustains the generation of acoustic waves at the inlet boundary. A calculation of the frequency and growth rate of this resonance mechanism for a supersonic ion flow is proposed, which illustrates the influence of the ionization degree on their onset and the approximate scaling of the frequency with the ion transit time. Consistent with experimental reports, the traveling wave can be observed on plasma density and velocity perturbations, while the plasma potential ostensibly oscillates in phase along the discharge 14. Hypernuclear Spectroscopy at JLab Hall C International Nuclear Information System (INIS) Hashimoto, Osamu; Chiba, Atsushi; Doi, Daisuke; Fujii, Yu; Toshiyuki, Gogami; Kanda, Hiroki; Kaneta, M.; Kawama, Daisuke; Maeda, Kazushige; Maruta, Tomofumi; Matsumura, Akihiko; Nagao, Sho; Nakamura, Satoshi; Shichijo, Ayako; Tamura, Hirokazu; Taniya, Naotaka; Yamamoto, Taku; Yokota, Kosuke; Kato, S.; Sato, Yoshinori; Takahashi, Toshiyuki; Noumi, Hiroyuki; Motoba, T.; Hiyama, E.; Albayrak, Ibrahim; Ates, Ozgur; Chen, Chunhua; Christy, Michael; Keppel, Cynthia; Kohl, Karl; Li, Ya; Liyanage, Anusha Habarakada; Tang, Liguang; Walton, T.; Ye, Zhihong; Yuan, Lulin; Zhu, Lingyan; Baturin, Pavlo; Boeglin, Werner; Dhamija, Seema; Markowitz, Pete; Raue, Brian; Reinhold, Joerg; Hungerford, Ed; Ent, Rolf; Fenker, Howard; Gaskell, David; Horn, Tanja; Jones, Mark; Smith, Gregory; Vulcan, William; Wood, Stephen; Johnston, C.; Simicevic, Neven; Wells, Stephen; Samanta, Chhanda; Hu, Bitao; Shen, Ji; Wang, W.; Zhang, Xiaozhuo; Zhang, Yi; Feng, Jing; Fu, Y.; Zhou, Jian; Zhou, S.; Jiang, Yi; Lu, H.; Yan, Xinhu; Ye, Yunxiu; Gan, Liping; Ahmidouch, Abdellah; Danagoulian, Samuel; Gasparian, Ashot; Elaasar, Mostafa; Wesselmann, Frank; Asaturyan, Arshak; Margaryan, Amur; Mkrtchyan, Arthur; Mkrtchyan, Hamlet; Tadevosyan, Vardan; Androic, Darko; Furic, Miroslav; Petkovic, Tomislav; Seva, Tomislav; Niculescu, Gabriel; Niculescu, Maria-Ioana; Rodriguez, Victor; Cisbani, Evaristo; Cusanno, Francesco; Garibaldi, Franco; Urciuoli, Guido; De Leo, Raffaele; Maronne, S.; Achenbach, Carsten; Pochodzalla, J. 2010-01-01 Since the 1st generation experiment, E89-009, which was successfully carried out as a pilot experiment of (e,e(prime)K + ) hypernuclear spectroscopy at JLab Hall C in 2000, precision hypernuclear spectroscopy by the (e,e(prime)K + ) reactions made considerable progress. It has evolved to the 2nd generation experiment, E01-011, in which a newly constructed high resolution kaon spectrometer (HKS) was installed and the 'Tilt method' was adopted in order to suppress large electromagnetic background and to run with high luminosity. Preliminary high-resolution spectra of 7 ΛHe and 28 ΛAl together with that of 12 ΛB that achieved resolution better than 500 keV(FWHM) were obtained. The third generation experiment, E05-115, has completed data taking with an experimental setup combining a new splitter magnet, high resolution electron spectrometer (HES) and the HKS used in the 2nd generation experiment. The data were accumulated with targets of 7 Li, 9 Be, 10 B, 12 C and 52 Cr as well as with those of CH 2 and H 2 O for calibration. The analysis is under way with particular emphasis of determining precision absolute hypernuclear masses. In this article, hypernuclear spectroscopy program in the wide mass range at JLab Hall C that has undergone three generation is described. 15. Observation of the fractional quantum Hall effect in graphene. Science.gov (United States) Bolotin, Kirill I; Ghahari, Fereshte; Shulman, Michael D; Stormer, Horst L; Kim, Philip 2009-11-12 When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. The experimental discovery of an anomalous integer quantum Hall effect in graphene has enabled the study of a correlated two-dimensional electronic system, in which the interacting electrons behave like massless chiral fermions. However, owing to the prevailing disorder, graphene has so far exhibited only weak signatures of correlated electron phenomena, despite intense experimental and theoretical efforts. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields. 16. Anomalous Hall effect scaling in ferromagnetic thin films KAUST Repository Grigoryan, Vahram L. 2017-10-23 We propose a scaling law for anomalous Hall effect in ferromagnetic thin films. Our approach distinguishes multiple scattering sources, namely, bulk impurity, phonon for Hall resistivity, and most importantly the rough surface contribution to longitudinal resistivity. In stark contrast to earlier laws that rely on temperature- and thickness-dependent fitting coefficients, this scaling law fits the recent experimental data excellently with constant parameters that are independent of temperature and film thickness, strongly indicating that this law captures the underlying physical processes. Based on a few data points, this scaling law can even fit all experimental data in full temperature and thickness range. We apply this law to interpret the experimental data for Fe, Co, and Ni and conclude that (i) the phonon-induced skew scattering is unimportant as expected; (ii) contribution from the impurity-induced skew scattering is negative; (iii) the intrinsic (extrinsic) mechanism dominates in Fe (Co), and both the extrinsic and intrinsic contributions are important in Ni. 17. Anomalous Hall effect scaling in ferromagnetic thin films KAUST Repository Grigoryan, Vahram L.; Xiao, Jiang; Wang, Xuhui; Xia, Ke 2017-01-01 We propose a scaling law for anomalous Hall effect in ferromagnetic thin films. Our approach distinguishes multiple scattering sources, namely, bulk impurity, phonon for Hall resistivity, and most importantly the rough surface contribution to longitudinal resistivity. In stark contrast to earlier laws that rely on temperature- and thickness-dependent fitting coefficients, this scaling law fits the recent experimental data excellently with constant parameters that are independent of temperature and film thickness, strongly indicating that this law captures the underlying physical processes. Based on a few data points, this scaling law can even fit all experimental data in full temperature and thickness range. We apply this law to interpret the experimental data for Fe, Co, and Ni and conclude that (i) the phonon-induced skew scattering is unimportant as expected; (ii) contribution from the impurity-induced skew scattering is negative; (iii) the intrinsic (extrinsic) mechanism dominates in Fe (Co), and both the extrinsic and intrinsic contributions are important in Ni. 18. Mutations in the bacterial ribosomal protein l3 and their association with antibiotic resistance DEFF Research Database (Denmark) Klitgaard, Rasmus N; Ntokou, Eleni; Nørgaard, Katrine 2015-01-01 -type genes with mutated L3 genes in a chromosomal L3 deletion strain. In this way, the essential L3 gene is available for the bacteria while allowing replacement of the wild type with mutated L3 genes. This enables investigation of the effect of single mutations in Escherichia coli without a wild-type L3... 19. Hall effect in noncommutative coordinates International Nuclear Information System (INIS) Dayi, Oemer F.; Jellal, Ahmed 2002-01-01 We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov-Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θ can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates 20. Revising the worksheet with L3: a language and environment foruser-script interaction Energy Technology Data Exchange (ETDEWEB) Hohn, Michael H. 2008-01-22 This paper describes a novel approach to the parameter anddata handling issues commonly found in experimental scientific computingand scripting in general. The approach is based on the familiarcombination of scripting language and user interface, but using alanguage expressly designed for user interaction and convenience. The L3language combines programming facilities of procedural and functionallanguages with the persistence and need-based evaluation of data flowlanguages. It is implemented in Python, has access to all Pythonlibraries, and retains almost complete source code compatibility to allowsimple movement of code between the languages. The worksheet interfaceuses metadata produced by L3 to provide selection of values through thescriptit self and allow users to dynamically evolve scripts withoutre-running the prior versions. Scripts can be edited via text editors ormanipulated as structures on a drawing canvas. Computed values are validscripts and can be used further in other scripts via simplecopy-and-paste operations. The implementation is freely available underan open-source license. 1. Local structural disorder in REFeAsO oxypnictides by RE L3 edge XANES International Nuclear Information System (INIS) Xu, W; Chu, W S; Wu, Z Y; Marcelli, A; Di Gioacchino, D; Joseph, B; Iadecola, A; Bianconi, A; Saini, N L 2010-01-01 The REFeAsO (RE = La, Pr, Nd and Sm) system has been studied by RE L 3 x-ray absorption near edge structure (XANES) spectroscopy to explore the contribution of the REO spacers between the electronically active FeAs slabs in these materials. The XANES spectra have been simulated by full multiple scattering calculations to describe the different experimental features and their evolution with the RE size. The near edge feature just above the L 3 white line is found to be sensitive to the ordering/disordering of oxygen atoms in the REO layers. In addition, shape resonance peaks due to As and O scattering change systematically, indicating local structural changes in the FeAs slabs and the REO spacers due to RE size. The results suggest that interlayer coupling and oxygen order/disorder in the REO spacers may have an important role in the superconductivity and itinerant magnetism of the oxypnictides. 2. Scanning vector Hall probe microscope Czech Academy of Sciences Publication Activity Database Fedor, J.; Cambel, V.; Gregušová, D.; Hanzelka, Pavel; Dérer, J.; Volko, J. 2003-01-01 Roč. 74, č. 12 (2003), s. 5105 - 5110 ISSN 0034-6748 Institutional research plan: CEZ:AV0Z2065902 Keywords : VHPM * Hall sensor * Helium cryostat Subject RIV: JB - Sensors, Measurment, Regulation Impact factor: 1.343, year: 2003 http://web. ebscohost .com/ehost/pdf?vid=8&hid=115&sid=a7c0555a-21f4-4932-b1c6-a308ac4dd50b%40sessionmgr2 3. Numerical investigation of a Hall thruster plasma International Nuclear Information System (INIS) Roy, Subrata; Pandey, B.P. 2002-01-01 The dynamics of the Hall thruster is investigated numerically in the framework of a one-dimensional, multifluid macroscopic description of a partially ionized xenon plasma using finite element formulation. The model includes neutral dynamics, inelastic processes, and plasma-wall interaction. Owing to disparate temporal scales, ions and neutrals have been described by set of time-dependent equations, while electrons are considered in steady state. Based on the experimental observations, a third order polynomial in electron temperature is used to calculate ionization rate. The results show that in the acceleration channel the increase in the ion number density is related to the decrease in the neutral number density. The electron and ion velocity profiles are consistent with the imposed electric field. The electron temperature remains uniform for nearly two-thirds of the channel; then sharply increases to a peak before dropping slightly at the exit. This is consistent with the predicted electron gyration velocity distribution 4. Determination of the Hall Thruster Operating Regimes International Nuclear Information System (INIS) L. Dorf; V. Semenov; Y. Raitses; N.J. Fisch 2002-04-01 A quasi one-dimensional (1-D) steady-state model of the Hall thruster is presented. For the same discharge voltage two operating regimes are possible -- with and without the anode sheath. For given mass flow rate, magnetic field profile and discharge voltage a unique solution can be constructed, assuming that the thruster operates in one of the regimes. However, we show that for a given temperature profile the applied discharge voltage uniquely determines the operating regime: for discharge voltages greater than a certain value, the sheath disappears. That result is obtained over a wide range of incoming neutral velocities, channel lengths and widths, and cathode plane locations. It is also shown that a good correlation between the quasi 1-D model and experimental results can be achieved by selecting an appropriate electron mobility and temperature profile 5. Spin Hall magnetoresistance at high temperatures International Nuclear Information System (INIS) Uchida, Ken-ichi; Qiu, Zhiyong; Kikkawa, Takashi; Iguchi, Ryo; Saitoh, Eiji 2015-01-01 The temperature dependence of spin Hall magnetoresistance (SMR) in Pt/Y 3 Fe 5 O 12 (YIG) bilayer films has been investigated in a high temperature range from room temperature to near the Curie temperature of YIG. The experimental results show that the magnitude of the magnetoresistance ratio induced by the SMR monotonically decreases with increasing the temperature and almost disappears near the Curie temperature. We found that, near the Curie temperature, the temperature dependence of the SMR in the Pt/YIG film is steeper than that of a magnetization curve of the YIG; the critical exponent of the magnetoresistance ratio is estimated to be 0.9. This critical behavior of the SMR is attributed mainly to the temperature dependence of the spin-mixing conductance at the Pt/YIG interface 6. 6 February 2012 - Supreme Audit Institutions from Norway, Poland, Spain and Switzerland visiting the LHC tunnel at Point 5, CMS underground experimental area, CERN Control Centre and LHC superconducting magnet test hall. Delegations are throughout accompanied by Swiss P. Jenni, Polish T. Kurtyka, Spanish J. Salicio, Norwegian S. Stapnes and International Relations Adviser R. Voss. (Riksrevisjonen, Oslo; Tribunal de Cuentas , Madrid; the Court of Audit of Switzerland and Najwyzsza Izba Kontroli, Varsaw) CERN Multimedia Jean-Claude Gadmer 2012-01-01 6 February 2012 - Supreme Audit Institutions from Norway, Poland, Spain and Switzerland visiting the LHC tunnel at Point 5, CMS underground experimental area, CERN Control Centre and LHC superconducting magnet test hall. Delegations are throughout accompanied by Swiss P. Jenni, Polish T. Kurtyka, Spanish J. Salicio, Norwegian S. Stapnes and International Relations Adviser R. Voss. (Riksrevisjonen, Oslo; Tribunal de Cuentas , Madrid; the Court of Audit of Switzerland and Najwyzsza Izba Kontroli, Varsaw) 7. Conceptual design report, CEBAF basic experimental equipment Energy Technology Data Exchange (ETDEWEB) NONE 1990-04-13 The Continuous Electron Beam Accelerator Facility (CEBAF) will be dedicated to basic research in Nuclear Physics using electrons and photons as projectiles. The accelerator configuration allows three nearly continuous beams to be delivered simultaneously in three experimental halls, which will be equipped with complementary sets of instruments: Hall A--two high resolution magnetic spectrometers; Hall B--a large acceptance magnetic spectrometer; Hall C--a high-momentum, moderate resolution, magnetic spectrometer and a variety of more dedicated instruments. This report contains a short description of the initial complement of experimental equipment to be installed in each of the three halls. 8. L'effet Hall Quantique Science.gov (United States) Samson, Thomas Nous proposons une methode permettant d'obtenir une expression pour la conductivite de Hall de structures electroniques bidimensionnelles et nous examinons celle -ci a la limite d'une temperature nulle dans le but de verifier l'effet Hall quantique. Nous allons nous interesser essentiellement a l'effet Hall quantique entier et aux effets fractionnaires inferieurs a un. Le systeme considere est forme d'un gaz d'electrons en interaction faible avec les impuretes de l'echantillon. Le modele du gaz d'electrons consiste en un gaz bidimensionnel d'electrons sans spin expose perpendiculairement a un champ magnetique uniforme. Ce dernier est decrit par le potentiel vecteur vec{rm A} defini dans la jauge de Dingle ou jauge symetrique. Conformement au formalisme de la seconde quantification, l'hamiltonien de ce gaz est represente dans la base des etats a un-corps de Dingle |n,m> et exprime ainsi en terme des operateurs de creation et d'annihilation correspondants a_sp{ rm n m}{dag} et a _{rm n m}. Nous supposons de plus que les electrons du niveau fondamental de Dingle interagissent entre eux via le potentiel coulombien. La methode utilisee fait appel a une equation mai tresse a N-corps, de nature quantique et statistique, et verifiant le second principe de la thermodynamique. A partir de celle-ci, nous obtenons un systeme d'equations differentielles appele hierarchie d'equations quantique dont la resolution nous permet de determiner une equation a un-corps, dite de Boltzmann quantique, et dictant l'evolution de la moyenne statistique de l'operateur non-diagonal a _sp{rm n m}{dag } a_{rm n}, _{rm m}, sous l'action du champ electrique applique vec{rm E}(t). C'est sa solution Tr(p(t) a _sp{rm n m}{dag} a_{rm n},_ {rm m}), qui definit la relation de convolution entre la densite courant de Hall vec{rm J}_{rm H }(t) et le champ electrique vec {rm E}(t) dont la transformee de Laplace-Fourier du noyau nous fournit l'expression de la conductivite de Hall desiree. Pour une valeur de 9. Quantum spin/valley Hall effect and topological insulator phase transitions in silicene KAUST Repository Tahir, M. 2013-04-26 We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments. 10. Quantum spin/valley Hall effect and topological insulator phase transitions in silicene KAUST Repository Tahir, M.; Manchon, Aurelien; Sabeeh, K.; Schwingenschlö gl, Udo 2013-01-01 We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments. 11. Main Parameters Characterization of Bulk CMOS Cross-Like Hall Structures Directory of Open Access Journals (Sweden) Maria-Alexandra Paun 2016-01-01 Full Text Available A detailed analysis of the cross-like Hall cells integrated in regular bulk CMOS technological process is performed. To this purpose their main parameters have been evaluated. A three-dimensional physical model was employed in order to evaluate the structures. On this occasion, numerical information on the input resistance, Hall voltage, conduction current, and electrical potential distribution has been obtained. Experimental results for the absolute sensitivity, offset, and offset temperature drift have also been provided. A quadratic behavior of the residual offset with the temperature was obtained and the temperature points leading to the minimum offset for the three Hall cells were identified. 12. Interaction Induced Quantum Valley Hall Effect in Graphene Directory of Open Access Journals (Sweden) E. C. Marino 2015-03-01 Full Text Available We use pseudo-quantum electrodynamics in order to describe the full electromagnetic interaction of the p electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the T→0 conductivity after a smooth zero-frequency limit is taken in Kubo’s formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous quantum valley Hall effect below an activation temperature of the order of 2 K. The transverse (Hall valley conductivity is evaluated exactly and shown to coincide with the one in the usual quantum Hall effect. Finally, by considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P- and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect. 13. Field theory of anyons and the fractional quantum Hall effect International Nuclear Information System (INIS) Viefers, S.F. 1997-11-01 The thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyons gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low-energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effects 14. Single particle detection: Phase control in submicron Hall sensors International Nuclear Information System (INIS) Di Michele, Lorenzo; Shelly, Connor; Gallop, John; Kazakova, Olga 2010-01-01 We present a phase-sensitive ac-dc Hall magnetometry method which allows a clear and reliable separation of real and parasitic magnetic signals of a very small magnitude. High-sensitivity semiconductor-based Hall crosses are generally accepted as a preferential solution for non-invasive detection of superparamagnetic nanobeads used in molecular biology, nanomedicine, and nanochemistry. However, detection of such small beads is often hindered by inductive pick-up and other spurious signals. The present work demonstrates an unambiguous experimental route for detection of small magnetic moments and provides a simple theoretical background for it. The reliability of the method has been tested for a variety of InSb Hall sensors in the range 600 nm-5 μm. Complete characterization of empty devices, involving Hall coefficients and noise measurements, has been performed and detection of a single FePt bead with diameter of 140 nm and magnetic moment of μ≅10 8 μ B has been achieved with a 600 nm-wide sensor. 15. Influence of energy bands on the Hall effect in degenerate semiconductors International Nuclear Information System (INIS) Wu, Chhi-Chong; Tsai, Jensan 1989-01-01 The influence of energy bands on the Hall effect and transverse magnetoresistance has been investigated according to the scattering processes of carriers in degenerate semiconductors such as InSb. Results show that the Hall angle, Hall coefficient, and transverse magnetoresistance depend on the dc magnetic field for both parabolic and nonparabolic band structures of semiconductors and also depend on the scattering processes of carriers in semiconductors due to the energy-dependent relaxation time. From their numerical analysis for the Hall effect, it is shown that the conduction electrons in degenerate semiconductors play a major role for the carrier transport phenomenon. By comparing with experimental data of the transverse magnetoresistance, it shows that the nonparabolic band model is better in agreement with the experimental work than the parabolic band model of semiconductors 16. Spin Hall effect by surface roughness KAUST Repository Zhou, Lingjun 2015-01-08 The spin Hall and its inverse effects, driven by the spin orbit interaction, provide an interconversion mechanism between spin and charge currents. Since the spin Hall effect generates and manipulates spin current electrically, to achieve a large effect is becoming an important topic in both academia and industries. So far, materials with heavy elements carrying a strong spin orbit interaction, provide the only option. We propose here a new mechanism, using the surface roughness in ultrathin films, to enhance the spin Hall effect without heavy elements. Our analysis based on Cu and Al thin films suggests that surface roughness is capable of driving a spin Hall angle that is comparable to that in bulk Au. We also demonstrate that the spin Hall effect induced by surface roughness subscribes only to the side-jump contribution but not the skew scattering. The paradigm proposed in this paper provides the second, not if only, alternative to generate a sizable spin Hall effect. 17. Tunneling Anomalous and Spin Hall Effects. Science.gov (United States) Matos-Abiague, A; Fabian, J 2015-07-31 We predict, theoretically, the existence of the anomalous Hall effect when a tunneling current flows through a tunnel junction in which only one of the electrodes is magnetic. The interfacial spin-orbit coupling present in the barrier region induces a spin-dependent momentum filtering in the directions perpendicular to the tunneling current, resulting in a skew tunneling even in the absence of impurities. This produces an anomalous Hall conductance and spin Hall currents in the nonmagnetic electrode when a bias voltage is applied across the tunneling heterojunction. If the barrier is composed of a noncentrosymmetric material, the anomalous Hall conductance and spin Hall currents become anisotropic with respect to both the magnetization and crystallographic directions, allowing us to separate this interfacial phenomenon from the bulk anomalous and spin Hall contributions. The proposed effect should be useful for proving and quantifying the interfacial spin-orbit fields in metallic and metal-semiconductor systems. 18. Search on charginos and neutralinos with the L3 detector at LEP International Nuclear Information System (INIS) Chereau, Xavier 1998-01-01 This work presents an experimental search for supersymmetric particles, the charginos and the neutralinos, at center of mass energies √ 161, 172 and 183 GeV, with the L3 detector at the e + e - collider LEP. Assuming R-parity conservation, SUSY events have a large missing energy, carried by the lightest supersymmetric particle (LSP), which allow us to distinguish them from standard events. Then, for all the studied final states and all the energies, we optimized the selections in order to have the best signal-to-noise ratio. No excess of events were observed with respect to the standard model predictions. We set upper limits on the chargino and neutralino production cross sections. In the frame of the constraint MSSM, these results were combined with the results from the L3 slepton analyses to set lower limits on the chargino and neutralino masses: particularly, we exclude a neutralino χ 1 0 bar lighter than 25.9 GeV/c 2 (95% C.L.). This result plays an important role for the interpretation of the dark matter in universe. The search for events with missing energy needs a detector with a good hermeticity. At the end of 1995, a new electromagnetic calorimeter was installed in the L3 experiment. Here we present the improvements of performances and the calibration of this detector composed of 48 bricks made with lead and scintillating fibers (SPACAL) 19. Focused ion beam patterned Hall nano-sensors International Nuclear Information System (INIS) Candini, A.; Gazzadi, G.C.; Di Bona, A.; Affronte, M.; Ercolani, D.; Biasiol, G.; Sorba, L. 2007-01-01 By means of focused ion beam milling, we fabricate Hall magnetometers with active areas as small as 100x100nm 2 . The constituent material can either be metallic (Au), semimetallic (Bi) or doped bulk semiconducting (Si doped GaAs). We experimentally show that Au nano-probes can work from room temperature down to liquid helium with magnetic flux sensitivity -1 Φ 0 20. Tunneling between edge states in a quantum spin Hall system. Science.gov (United States) Ström, Anders; Johannesson, Henrik 2009-03-06 We analyze a quantum spin Hall device with a point contact connecting two of its edges. The contact supports a net spin tunneling current that can be probed experimentally via a two-terminal resistance measurement. We find that the low-bias tunneling current and the differential conductance exhibit scaling with voltage and temperature that depend nonlinearly on the strength of the electron-electron interaction. 1. Nanoconstriction spin-Hall oscillator with perpendicular magnetic anisotropy Science.gov (United States) Divinskiy, B.; Demidov, V. E.; Kozhanov, A.; Rinkevich, A. B.; Demokritov, S. O.; Urazhdin, S. 2017-07-01 We experimentally study spin-Hall nano-oscillators based on [Co/Ni] multilayers with perpendicular magnetic anisotropy. We show that these devices exhibit single-frequency auto-oscillations at current densities comparable to those for in-plane magnetized oscillators. The demonstrated oscillators exhibit large magnetization precession amplitudes, and their oscillation frequency is highly tunable by the electric current. These features make them promising for applications in high-speed integrated microwave circuits. 2. Effet Hall quantique, liquides de Luttinger et charges fractionnaires Science.gov (United States) Roche, Patrice; Rodriguez, V.; Glattli, D. Christian We review some basic properties of the Fractional Quantum Hall Effect and particularly address the physics of the edge states. The chiral Luttinger liquid properties of the edges are discussed and probed experimentally using transport measurements. Shot noise measurements, which allow determination of the quasiparticle charge are also discussed. To cite this article: P. Roche et al., C. R. Physique 3 (2002) 717-732. 3. Hydrogen Learning for Local Leaders – H2L3 Energy Technology Data Exchange (ETDEWEB) Serfass, Patrick [Technology Transition Corporation, Washington, DC (United States) 2017-03-30 The Hydrogen Learning for Local Leaders program, H2L3, elevates the knowledge about hydrogen by local government officials across the United States. The program reaches local leaders directly through “Hydrogen 101” workshops and webinar sessions; the creation and dissemination of a unique report on the hydrogen and fuel cell market in the US, covering 57 different sectors; and support of the Hydrogen Student Design Contest, a competition for interdisciplinary teams of university students to design hydrogen and fuel cell systems based on technology that’s currently commercially available. 4. Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime OpenAIRE Song, Juntao; Prodan, Emil 2013-01-01 The conductivity$\\sigma$and resistivity$\\rho$tensors of the disordered Hofstadter model are mapped as functions of Fermi energy$E_F$and temperature$Tin the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors are eliminated by using the non-commutative Kubo-formula. The results reproduce all the key experimental characteristics of this transition in Integer Quantum Hall (IQHE) systems. In particular, the Quantized Hall Insulator (QHI) phase is det... 5. Anomalous Hall effect in polycrystalline Ni films KAUST Repository Guo, Zaibing 2012-02-01 We systematically studied the anomalous Hall effect in a series of polycrystalline Ni films with thickness ranging from 4 to 200 nm. It is found that both the longitudinal and anomalous Hall resistivity increased greatly as film thickness decreased. This enhancement should be related to the surface scattering. In the ultrathin films (46 nm thick), weak localization corrections to anomalous Hall conductivity were studied. The granular model, taking into account the dominated intergranular tunneling, has been employed to explain this phenomenon, which can explain the weak dependence of anomalous Hall resistivity on longitudinal resistivity as well. © 2011 Elsevier Ltd. All rights reserved. 6. Temperature Gradient in Hall Thrusters International Nuclear Information System (INIS) Staack, D.; Raitses, Y.; Fisch, N.J. 2003-01-01 Plasma potentials and electron temperatures were deduced from emissive and cold floating probe measurements in a 2 kW Hall thruster, operated in the discharge voltage range of 200-400 V. An almost linear dependence of the electron temperature on the plasma potential was observed in the acceleration region of the thruster both inside and outside the thruster. This result calls into question whether secondary electron emission from the ceramic channel walls plays a significant role in electron energy balance. The proportionality factor between the axial electron temperature gradient and the electric field is significantly smaller than might be expected by models employing Ohmic heating of electrons 7. Synthesis and aqueous phase behavior of thermoresponsive biodegradable poly(D,L-3-methylglycolide)-block-poly(ethyelene glycol)-block-poly(D,L-3-methylglycolide) triblock copolymers NARCIS (Netherlands) Zhong, Zhiyuan; Dijkstra, Pieter J.; Feijen, Jan; Kwon, Young-Min; Bae, You Han; Kim, Sung Wan 2002-01-01 Novel biodegradable thermosensitive triblock copolymers of poly(D,L-3-methylglycolide)-block-poly(ethylene glycol)-block-poly(D,L-3-methylglycolide) (PMG-PEG-PMG) have been synthesized. Ring-opening polymerization of D,L-3-methyl-glycolide (MG) initiated with poly(ethylene glycol) (PEG) and 8. Tasks related to increase of RA reactor exploitation and experimental potential, 01. Designing the protection chamber in the RA reactor hall for handling the radioactive experimental equipment (I-II) Part II, Vol. II; Radovi na povecanju eksploatacionih i eksperimentalnih mogucnosti reaktora RA, 01. Projektovanje zastitne komore u hali reaktora RA za rad sa aktivnim eksperimentalnim uredjajima (I-II), II Deo, Album II Energy Technology Data Exchange (ETDEWEB) Pavicevic, M [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Serbia and Montenegro) 1963-07-15 This second volume of the project for construction of the protection chamber in the RA reactor hall for handling the radioactive devices includes the technical description of the chamber, calculation of the shielding wall thickness, bottom lead plate, horizontal stability of the chamber, cost estimation, and the engineering drawings. 9. 75 FR 7467 - Gary E. Hall and Rita C. Hall; Notice of Application Accepted for Filing With the Commision... Science.gov (United States) 2010-02-19 ... Rita C. Hall; Notice of Application Accepted for Filing With the Commision, Soliciting Motions To.... Project No.: 13652-000. c. Date filed: January 11, 2010. d. Applicant: Gary E. Hall and Rita C. Hall. e... Policies Act of 1978, 16 U.S.C. 2705, 2708. h. Applicant Contact: Mr. Gary E. Hall and Ms. Rita C. Hall, P... 10. Nondestructive hall coefficient measurements using ACPD techniques Science.gov (United States) Velicheti, Dheeraj; Nagy, Peter B.; Hassan, Waled 2018-04-01 Hall coefficient measurements offer great opportunities as well as major challenges for nondestructive materials characterization. The Hall effect is produced by the magnetic Lorentz force acting on moving charge carriers in the presence of an applied magnetic field. The magnetic perturbation gives rise to a Hall current that is normal to the conduction current but does not directly perturb the electric potential distribution. Therefore, Hall coefficient measurements usually exploit the so-called transverse galvanomagnetic potential drop effect that arises when the Hall current is intercepted by the boundaries of the specimen and thereby produce a measurable potential drop. In contrast, no Hall potential is produced in a large plate in the presence of a uniform normal field at quasi-static low frequencies. In other words, conventional Hall coefficient measurements are inherently destructive since they require cutting the material under tests. This study investigated the feasibility of using alternating current potential drop (ACPD) techniques for nondestructive Hall coefficient measurements in plates. Specifically, the directional four-point square-electrode configuration is investigated with superimposed external magnetic field. Two methods are suggested to make Hall coefficient measurements in large plates without destructive machining. At low frequencies, constraining the bias magnetic field can replace constraining the dimensions of the specimen, which is inherently destructive. For example, when a cylindrical permanent magnet is used to provide the bias magnetic field, the peak Hall voltage is produced when the diameter of the magnet is equal to the diagonal of the square ACPD probe. Although this method is less effective than cutting the specimen to a finite size, the loss of sensitivity is less than one order of magnitude even at very low frequencies. In contrast, at sufficiently high inspection frequencies the magnetic field of the Hall current induces a 11. Hall magnetohydrodynamics of neutral layers International Nuclear Information System (INIS) Huba, J.D.; Rudakov, L.I. 2003-01-01 New analytical and numerical results of the dynamics of inhomogeneous, reversed field current layers in the Hall limit (i.e., characteristic length scales < or approx. the ion inertial length) are presented. Specifically, the two- and three-dimensional evolution of a current layer that supports a reversed field plasma configuration and has a density gradient along the current direction is studied. The two-dimensional study demonstrates that a density inhomogeneity along the current direction can dramatically redistribute the magnetic field and plasma via magnetic shock-like or rarefaction waves. The relative direction between the density gradient and current flow plays a critical role in the evolution of the current sheet. One important result is that the current sheet can become very thin rapidly when the density gradient is directed opposite to the current. The three-dimensional study uses the same plasma and field configuration as the two-dimensional study but is also initialized with a magnetic field perturbation localized along the current channel upstream of the plasma inhomogeneity. The perturbation induces a magnetic wave structure that propagates in the direction of the electron drift (i.e., opposite to the current). The propagating wave structure is a Hall phenomenon associated with magnetic field curvature. The interaction between the propagating wave structure and the evolving current layer can lead to rapid magnetic field line reconnection. The results are applied to laboratory and space plasma processes 12. Mesoscopic spin Hall effect in semiconductor nanostructures Science.gov (United States) Zarbo, Liviu , appeared in 1970s, it is only in the past few years that advances in optical detection of nonequilibrium magnetization in semiconductors have made possible the detection of such extrinsic SHE in groundbreaking experiments. The experimental pursuits of SHE have, in fact, been largely motivated by very recent theoretical speculations for several order of magnitude greater spin Hall currents driven by intrinsic SO mechanisms due to SO couplings existing not only around the impurity but also throughout the sample. The homogeneous intrinsic SO couplings are capable of spin-splitting the band structure and appear as momentum-dependent magnetic field within the sample which causes spin non-conservation due to precession of injected spins which are not in the eigenstates of the corresponding Zeeman term. Besides deepening our understanding of subtle relativistic effects in solids, SHE has attracted a lot of attention since it offers an all-electrical way of generating pure spin currents in semiconductors. (Abstract shortened by UMI.) 13. The soviet manned lunar program N1-L3 Science.gov (United States) Lardier, Christian 2018-01-01 The conquest of space was marked by the Moon race in which the two superpowers, the United States and the Soviet Union, were engaged in the 1960s. On the American side, the Apollo program culminated with the Man on the Moon in July 1969, 50 years ago. At the same time, the Soviet Union carried out a similar program which was kept secret for 20 years. This N1-L3 program was unveiled in August 1989. Its goal was to arrive on the Moon before the Americans. It included an original super-rocket, development of which began in June 1960. But this program became a national priority only in August 1964 and the super-rocket failed four times between 1969 and 1972. This article analyses the reasons for these failures, which led to the cancellation of the program in 1974. 14. Multilingual students' acquisition of English as their L3 DEFF Research Database (Denmark) Samal Jalal, Rawand with regard to English proficiency. The current study conducted in Denmark investigated multilingual students’ English proficiency compared to their monolingual peers’, and examined which learning strategies proficient L3 learners utilize. The sample was comprised of 9-graders who are monolinguals (N = 82......) and multilinguals with Turkish L1 (N = 134). The participants provided basic demographic information, and were tested in their general English proficiency. Out of the 70 multilinguals with Turkish L1, 12 participants were selected for further testing; i.e., the four participants who scored the lowest, four...... participants with intermediate scores, and the four who scored the highest, on a test of English proficiency. These participants were tested in their L1 (Turkish) and their L2 (Danish) in order to examine whether their proficiency in their L1 and L2 was associated with English proficiency. Furthermore, the 12... 15. Quantum Hall effect in quantum electrodynamics International Nuclear Information System (INIS) Penin, Alexander A. 2009-01-01 We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum-mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak dependence of the universal von Klitzing constant on the magnetic field strength, which can possibly be observed in a dedicated experiment, is predicted 16. Hall devices improve electric motor efficiency Science.gov (United States) Haeussermann, W. 1979-01-01 Efficiency of electric motors and generators is reduced by radial magnetic forces created by symmetric fields within device. Forces are sensed and counteracted by Hall devices on excitation or control windings. Hall generators directly measure and provide compensating control of anu asymmetry, eliminating additional measurements needed for calibration feedback control loop. 17. Higher fractions theory of fractional hall effect International Nuclear Information System (INIS) Kostadinov, I.Z.; Popov, V.N. 1985-07-01 A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author) 18. Sensitivity of resistive and Hall measurements to local inhomogeneities DEFF Research Database (Denmark) Koon, Daniel W.; Wang, Fei; Petersen, Dirch Hjorth 2014-01-01 We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. ...... simulations on both a linear four-point probe array on a large circular disc and a van der Pauw square geometry. Furthermore, the results also agree well with Náhlík et al. published experimental results for physical holes in a circular copper foil disc.......We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. We... 19. Fast micro Hall effect measurements on small pads DEFF Research Database (Denmark) Østerberg, Frederik Westergaard; Petersen, Dirch Hjorth; Nielsen, Peter F. 2011-01-01 Sheet resistance, carrier mobility, and sheet carrier density are important parameters in semiconductor production, and it is therefore important to be able to rapidly and accurately measure these parameters even on small samples or pads. The interpretation of four-point probe measurements on small...... pads is non-trivial. In this paper we discuss how conformal mapping can be used to evaluate theoretically expected measurement values on small pads. Theoretical values calculated from analytical mappings of simple geometries are compared to the values found from the numerical conformal mapping...... of a square onto the infinite half-plane, where well-established solutions are known. Hall effect measurements are performed to show, experimentally, that it is possible to measure Hall mobility in less than one minute on squares as small as 7070 lm2 with a deviation of 66.5% on a 1r level from accurate... 20. Quantum Hall effect in epitaxial graphene with permanent magnets. Science.gov (United States) Parmentier, F D; Cazimajou, T; Sekine, Y; Hibino, H; Irie, H; Glattli, D C; Kumada, N; Roulleau, P 2016-12-06 We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications. 1. Quantum Hall Valley Nematics: From Field Theories to Microscopic Models Science.gov (United States) Parameswaran, Siddharth The interplay between quantum Hall ordering and spontaneously broken internal'' symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. I will discuss a theory of broken-symmetry quantum Hall states, applicable to a class of multivalley systems, where the symmetry at issue is a point-group element that combines a spatial rotation with a permutation of valley indices. I will explore its ramifications for the phase diagram of a variety of experimental systems, such as AlAs and Si quantum wells and the surface states of bismuth. I will also discuss unconventional transport phenomena in these phases in the presence of quenched randomness, and the possible mechanisms of selection between degenerate broken-symmetry phases in clean systems. I acknowledge support from NSF DMR-1455366. 2. Quantum Hall effect in epitaxial graphene with permanent magnets Science.gov (United States) Parmentier, F. D.; Cazimajou, T.; Sekine, Y.; Hibino, H.; Irie, H.; Glattli, D. C.; Kumada, N.; Roulleau, P. 2016-12-01 We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications. 3. Anomalous Hall effect in ZrTe5 Science.gov (United States) Liang, Tian; Lin, Jingjing; Gibson, Quinn; Kushwaha, Satya; Liu, Minhao; Wang, Wudi; Xiong, Hongyu; Sobota, Jonathan A.; Hashimoto, Makoto; Kirchmann, Patrick S.; Shen, Zhi-Xun; Cava, R. J.; Ong, N. P. 2018-05-01 Research in topological matter has expanded to include the Dirac and Weyl semimetals1-10, which feature three-dimensional Dirac states protected by symmetry. Zirconium pentatelluride has been of recent interest as a potential Dirac or Weyl semimetal material. Here, we report the results of experiments performed by in situ three-dimensional double-axis rotation to extract the full 4π solid angular dependence of the transport properties. A clear anomalous Hall effect is detected in every sample studied, with no magnetic ordering observed in the system to the experimental sensitivity of torque magnetometry. Large anomalous Hall signals develop when the magnetic field is rotated in the plane of the stacked quasi-two-dimensional layers, with the values vanishing above about 60 K, where the negative longitudinal magnetoresistance also disappears. This suggests a close relation in their origins, which we attribute to the Berry curvature generated by the Weyl nodes. 4. Electron Cross-field Transport in a Miniaturized Cylindrical Hall Thruster International Nuclear Information System (INIS) Smirnov Artem; Raitses Yevgeny; Fisch Nathaniel J 2005-01-01 Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. The present paper gives a review of the experimental and numerical investigations of electron crossfield transport in the 2.6 cm miniaturized cylindrical Hall thruster (100 W power level). We show that, in order to explain the discharge current observed for the typical operating conditions, the electron anomalous collision frequency ν b has to be on the order of the Bohm value, ν B ∼ ω c /16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant. The optimal regimes of thruster operation at low background pressure (below 10 -5 Torr) in the vacuum tank appear to be different from those at higher pressure (∼ 10 -4 Torr) 5. Unconventional fractional quantum Hall effect in monolayer and bilayer graphene Science.gov (United States) Jacak, Janusz; Jacak, Lucjan 2016-01-01 The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition. PMID:27877866 6. The quantum Hall effect helicity Energy Technology Data Exchange (ETDEWEB) Shrivastava, Keshav N., E-mail: [email protected] [Department of Physics, University of Malaya, Kuala Lumpur 50603 (Malaysia); School of Physics, University of Hyderabad, Hyderabad 500046 (India) 2015-04-16 The quantum Hall effect in semiconductor heterostructures is explained by two signs in the angular momentum j=l±s and g=(2j+1)/(2l+1) along with the Landau factor (n+1/2). These modifications in the existing theories explain all of the fractional charges. The helicity which is the sign of the product of the linear momentum with the spin p.s plays an important role for the understanding of the data at high magnetic fields. In particular it is found that particles with positive sign in the spin move in one direction and those with negative sign move in another direction which explains the up and down stream motion of the particles. 7. Stuart Hall: An Organic Intellectual Directory of Open Access Journals (Sweden) Johanna Fernández Castro 2017-01-01 Full Text Available Stuart Hall (3 February 1932 – 10 February 2014 is acknowledged as one of the founding figures of British Cultural Studies. His extensive academic work on topics such as race, ethnicity and identity reflects his own position as a diasporic intellectual. His contribution to the study of popular culture is determined by the importance of his political character in every social act, his non-deterministic view of Marxism, and is especially determined by his insistence on playing an active role beyond academia in order to contribute to the transformation of hegemonic structures. The following biography aims to give a focused view of his personal history and its direct influence on his key theoretical reflections. 8. Hall effect mobility for SiC MOSFETs with increasing dose of nitrogen implantation into channel region Science.gov (United States) Noguchi, Munetaka; Iwamatsu, Toshiaki; Amishiro, Hiroyuki; Watanabe, Hiroshi; Kita, Koji; Yamakawa, Satoshi 2018-04-01 The Hall effect mobility (μHall) of the Si-face 4H-SiC metal–oxide–semiconductor field effect transistor (MOSFET) with a nitrogen (N)-implanted channel region was investigated by increasing the N dose. The μHall in the channel region was systematically examined regarding channel structures, that is, the surface and buried channels. It was experimentally demonstrated that increasing the N dose results in an improvement in μHall in the channel region due to the formation of the buried channel. However, further increase in N dose was found to decrease the μHall in the channel region, owing to the decrease in the electron mobility in the N-implanted bulk region. 9. Interplay of Rashba effect and spin Hall effect in perpendicular Pt/Co/MgO magnetic multilayers Institute of Scientific and Technical Information of China (English) 赵云驰; 杨光; 董博闻; 王守国; 王超; 孙阳; 张静言; 于广华 2016-01-01 The interplay of the Rashba effect and the spin Hall effect originating from current induced spin–orbit coupling was investigated in the as-deposited and annealed Pt/Co/MgO stacks with perpendicular magnetic anisotropy. The above two effects were analyzed based on Hall measurements under external magnetic fields longitudinal and vertical to dc current, respectively. The coercive field as a function of dc current in vertical mode with only the Rashba effect involved decreases due to thermal annealing. Meanwhile, spin orbit torques calculated from Hall resistance with only the spin Hall effect involved in the longitudinal mode decrease in the annealed sample. The experimental results prove that the bottom Pt/Co interface rather than the Co/MgO top one plays a more critical role in both Rashba effect and spin Hall effect. 10. High precision micro-scale Hall Effect characterization method using in-line micro four-point probes DEFF Research Database (Denmark) Petersen, Dirch Hjorth; Hansen, Ole; Lin, Rong 2008-01-01 Accurate characterization of ultra shallow junctions (USJ) is important in order to understand the principles of junction formation and to develop the appropriate implant and annealing technologies. We investigate the capabilities of a new micro-scale Hall effect measurement method where Hall...... effect is measured with collinear micro four-point probes (M4PP). We derive the sensitivity to electrode position errors and describe a position error suppression method to enable rapid reliable Hall effect measurements with just two measurement points. We show with both Monte Carlo simulations...... and experimental measurements, that the repeatability of a micro-scale Hall effect measurement is better than 1 %. We demonstrate the ability to spatially resolve Hall effect on micro-scale by characterization of an USJ with a single laser stripe anneal. The micro sheet resistance variations resulting from... 11. Quantized Hall conductance as a topological invariant International Nuclear Information System (INIS) Niu, Q.; Thouless, Ds.J.; Wu, Y.S. 1984-10-01 Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references 12. Piezo Voltage Controlled Planar Hall Effect Devices. Science.gov (United States) Zhang, Bao; Meng, Kang-Kang; Yang, Mei-Yin; Edmonds, K W; Zhang, Hao; Cai, Kai-Ming; Sheng, Yu; Zhang, Nan; Ji, Yang; Zhao, Jian-Hua; Zheng, Hou-Zhi; Wang, Kai-You 2016-06-22 The electrical control of the magnetization switching in ferromagnets is highly desired for future spintronic applications. Here we report on hybrid piezoelectric (PZT)/ferromagnetic (Co2FeAl) devices in which the planar Hall voltage in the ferromagnetic layer is tuned solely by piezo voltages. The change of planar Hall voltage is associated with magnetization switching through 90° in the plane under piezo voltages. Room temperature magnetic NOT and NOR gates are demonstrated based on the piezo voltage controlled Co2FeAl planar Hall effect devices without the external magnetic field. Our demonstration may lead to the realization of both information storage and processing using ferromagnetic materials. 13. Stability of the Hall sensors performance under neutron irradiation International Nuclear Information System (INIS) Duran, I.; Hron, M.; Stockel, J.; Viererbl, L.; Vsolak, R.; Cerva, V.; Bolshakova, I.; Holyaka, R.; Vayakis, G. 2004-01-01 A principally new diagnostic method must be developed for magnetic measurements in steady state regime of operation of fusion reactor. One of the options is the use of transducers based on Hall effect. The use of Hall sensors in ITER is presently limited by their questionable radiation and thermal stability. Issues of reliable operation in ITER like radiation and thermal environment are addressed in the paper. The results of irradiation tests of candidate Hall sensors in LVR-15 and IBR-2 experimental fission reactors are presented. Stable operation (deterioration of sensitivity below one percent) of the specially prepared sensors was demonstrated during irradiation by the total fluence of 3.10 16 n/cm 2 in IBR-2 reactor. Increasing the total neutron fluence up to 3.10 17 n/cm 2 resulted in deterioration of the best sensor's output still below 10% as demonstrated during irradiation in LVR-15 fission reactor. This level of neutron is already higher than the expected ITER life time neutron fluence for a sensor location just outside the ITER vessel. (authors) 14. Precision Electron Beam Polarimetry in Hall C at Jefferson Lab Science.gov (United States) Gaskell, David 2013-10-01 The electron beam polarization in experimental Hall C at Jefferson Lab is measured using two devices. The Hall-C/Basel Møller polarimeter measures the beam polarization via electron-electron scattering and utilizes a novel target system in which a pure iron foil is driven to magnetic saturation (out of plane) using a superconducting solenoid. A Compton polarimeter measures the polarization via electron-photon scattering, where the photons are provided by a high-power, CW laser coupled to a low gain Fabry-Perot cavity. In this case, both the Compton-scattered electrons and backscattered photons provide measurements of the beam polarization. Results from both polarimeters, acquired during the Q-Weak experiment in Hall C, will be presented. In particular, the results of a test in which the Møller and Compton polarimeters made interleaving measurements at identical beam currents will be shown. In addition, plans for operation of both devices after completion of the Jefferson Lab 12 GeV Upgrade will also be discussed. 15. Parametric studies of the Hall Thruster at Soreq International Nuclear Information System (INIS) Ashkenazy, J.; Rattses, Y.; Appelbaum, G. 1997-01-01 An electric propulsion program was initiated at Soreq a few years ago, aiming at the research and development of advanced Hall thrusters for various space applications. The Hall thruster accelerates a plasma jet by an axial electric field and an applied radial magnetic field in an annular ceramic channel. A relatively large current density (> 0.1 A/cm 2 ) can be obtained, since the acceleration mechanism is not limited by space charge effects. Such a device can be used as a small rocket engine onboard spacecraft with the advantage of a large jet velocity compared with conventional rocket engines (10,000-30,000 m/s vs. 2,000-4,800 m/s). An experimental Hall thruster was constructed at Soreq and operated under a broad range of operating conditions and under various configurational variations. Electrical, magnetic and plasma diagnostics, as well as accurate thrust and gas flow rate measurements, have been used to investigate the dependence of thruster behavior on the applied voltage, gas flow rate, magnetic field, channel geometry and wall material. Representative results highlighting the major findings of the studies conducted so far are presented 16. Properties of Nonabelian Quantum Hall States Science.gov (United States) Simon, Steven H. 2004-03-01 The quantum statistics of particles refers to the behavior of a multiparticle wavefunction under adiabatic interchange of two identical particles. While a three dimensional world affords the possibilities of Bosons or Fermions, the two dimensional world has more exotic possibilities such as Fractional and Nonabelian statistics (J. Frölich, in Nonperturbative Quantum Field Theory", ed, G. t'Hooft. 1988). The latter is perhaps the most interesting where the wavefunction obeys a nonabelian'' representation of the braid group - meaning that braiding A around B then B around C is not the same as braiding B around C then A around B. This property enables one to think about using these exotic systems for robust topological quantum computation (M. Freedman, A. Kitaev, et al, Bull Am Math Soc 40, 31 (2003)). Surprisingly, it is thought that quasiparticles excitations with such nonabelian statistics may actually exist in certain quantum Hall states that have already been observed. The most likely such candidate is the quantum Hall ν=5/2 state(R. L. Willett et al, Phys. Rev. Lett. 59, 1776-1779 (1987)), thought to be a so-called Moore-Read Pfaffian state(G. Moore and N. Read, Nucl Phys. B360 362 (1991)), which can be thought of as a p-wave paired superconducting state of composite fermions(M. Greiter, X. G. Wen, and F. Wilczek, PRL 66, 3205 (1991)). Using this superconducting analogy, we use a Chern-Simons field theory approach to make a number of predictions as to what experimental signatures one should expect for this state if it really is this Moore-Read state(K. Foster, N. Bonesteel, and S. H. Simon, PRL 91 046804 (2003)). We will then discuss how the nonabelian statistics can be explored in detail using a quantum monte-carlo approach (Y. Tserkovnyak and S. H. Simon, PRL 90 106802 (2003)), (I. Finkler, Y. Tserkovnyak, and S. H. Simon, work in progress.) that allows one to explicitly drag one particle around another and observe the change in the wavefunctions 17. The infrared Hall effect in YBCO: Temperature and frequency dependence of Hall scattering International Nuclear Information System (INIS) Grayson, M.; Cerne, J.; Drew, H.D.; Schmadel, D.C.; Hughes, R.; Preston, J.S.; Kung, P.J.; Vale, L. 1999-01-01 The authors measure the Hall angle, θ H , in YBCO films in the far- and mid-infrared to determine the temperature and frequency dependence of the Hall scattering. Using novel modulation techniques they measure both the Faraday rotation and ellipticity induced by these films in high magnetic fields to deduce the complex conductivity tensor. They observe a strong temperature dependence of the mid-infrared Hall conductivity in sharp contrast to the weak dependence of the longitudinal conductivity. By fitting the frequency dependent normal state Hall angle to a Lorentzian θ H (ω) = ω H /(γ H minus iω) they find the Hall frequency, ω H , is nearly independent of temperature. The Hall scattering rate, γ H , is consistent with γ H ∼ T 2 up to 200 K and is remarkably independent of IR frequency suggesting non-Fermi liquid behavior 18. Search for Higgs bosons using the L3 detector at LEP International Nuclear Information System (INIS) Kopp, A. 2000-02-01 This thesis is devoted to the search for Higgs bosons predicted by various theoretical models. By the introduction of these particles into the theory, the masses of bosons and fermions can be explained. The search is performed in experimentally related channels, which are characterised by charged leptons in the final state. The analysis uses data taken during the years 1996-1998 with the L3 detector at the large electron positron collider LEP. The observed candidates are consistent with the expectation from standard model background processes. Evidence for Higgs boson production could not be found. New mass limits were determined superseding previous mass limits established by L3 and other experiments. In the search for the Higgs boson of the standard model the channels hZ → b anti bl + l - (l = e,μ,τ) and hZ → τ + τ - q anti q were analysed at centre-of-mass energies between 183 and 189 GeV. A lower mass limit of m h > 87.5 GeV is derived at the 95% confidence level. (orig.) 19. Tau Polarization Measurement in the L3 Detector International Nuclear Information System (INIS) Garcia, P. 1996-01-01 The Polarization asymmetry (A p ) measurement can be obtained from the energy spectra of the tau lepton (tau) decay products. This measurement provides a precise determination of the weak mixing angel (sin''2 tilde char theta w ), one of the Standard Model fundamental parameters. Tau leptons are produced at LEP in e''+e''-yields tilde char f interactions at a center of mass energy of the order of the Z boson mass. In order to get A p we have calculated the analytical formulae of the tau decay products energy spectra, including radiative corrections, for all of the one prong tau decay channels. We have also extended this analytical formalism to the detector level, including the selection criteria effectsand the detector resolution (calibration) in the analytical expressions.Detailed studies have been performed concerning our measurement using this formalism. From the data collected with the L3 detector between 1991 and 1994, which corresponds to an integrated luminosity of 118.8 pb''1 at a center of mass energy of the order of the Z mass, we have identified and selected the following tau decay channel samples: tau yields e nu tilde char nu, tau yields mu nu tilde char nu, tau yields pi/K nu y tau yields p/K*nu. From the analysis of these samples we get the tau polarization asymmetry measurement: A p =3D0.143+-0.014+-0.010, which corresponds to a value of sin''2 tilde char theta w =3D0.2320+-0.0018+-0.0013. (Author) 24 refs 20. Simulating Ru L3-edge X-ray absorption spectroscopy with time-dependent density functional theory: model complexes and electron localization in mixed-valence metal dimers. Science.gov (United States) Van Kuiken, Benjamin E; Valiev, Marat; Daifuku, Stephanie L; Bannan, Caitlin; Strader, Matthew L; Cho, Hana; Huse, Nils; Schoenlein, Robert W; Govind, Niranjan; Khalil, Munira 2013-05-30 Ruthenium L3-edge X-ray absorption (XA) spectroscopy probes unoccupied 4d orbitals of the metal atom and is increasingly being used to investigate the local electronic structure in ground and excited electronic states of Ru complexes. The simultaneous development of computational tools for simulating Ru L3-edge spectra is crucial for interpreting the spectral features at a molecular level. This study demonstrates that time-dependent density functional theory (TDDFT) is a viable and predictive tool for simulating ruthenium L3-edge XA spectroscopy. We systematically investigate the effects of exchange correlation functional and implicit and explicit solvent interactions on a series of Ru(II) and Ru(III) complexes in their ground and electronic excited states. The TDDFT simulations reproduce all of the experimentally observed features in Ru L3-edge XA spectra within the experimental resolution (0.4 eV). Our simulations identify ligand-specific charge transfer features in complicated Ru L3-edge spectra of [Ru(CN)6](4-) and Ru(II) polypyridyl complexes illustrating the advantage of using TDDFT in complex systems. We conclude that the B3LYP functional most accurately predicts the transition energies of charge transfer features in these systems. We use our TDDFT approach to simulate experimental Ru L3-edge XA spectra of transition metal mixed-valence dimers of the form [(NC)5M(II)-CN-Ru(III)(NH3)5](-) (where M = Fe or Ru) dissolved in water. Our study determines the spectral signatures of electron delocalization in Ru L3-edge XA spectra. We find that the inclusion of explicit solvent molecules is necessary for reproducing the spectral features and the experimentally determined valencies in these mixed-valence complexes. This study validates the use of TDDFT for simulating Ru 2p excitations using popular quantum chemistry codes and providing a powerful interpretive tool for equilibrium and ultrafast Ru L3-edge XA spectroscopy. 1. LOFT/L3-6, Loss of Fluid Test, 6. NRC L3 Small Break LOCA Experiment International Nuclear Information System (INIS) 1992-01-01 1 - Description of test facility: The LOFT Integral Test Facility is a scale model of a LPWR. The intent of the facility is to model the nuclear, thermal-hydraulic phenomena which would take place in a LPWR during a LOCA. The general philosophy in scaling coolant volumes and flow areas in LOFT was to use the ratio of the LOFT core [50 MW(t)] to a typical LPWR core [3000 MW(t)]. For some components, this factor is not applied; however, it is used as extensively as practical. In general, components used in LOFT are similar in design to those of a LPWR. Because of scaling and component design, the LOFT LOCA is expected to closely model a LPWR LOCA. 2 - Description of test: This was the sixth in the NRC L3 Series of small-break LOCA experiments. A 10-cm (2.5-in.) cold-leg non-communicative-break LOCA was simulated. Pumps were running. The experiment was conducted on 10 December 1980 2. LOFT/L3-5, Loss of Fluid Test, 5. NRC L3 Small Break LOCA Experiment International Nuclear Information System (INIS) 1991-01-01 1 - Description of test facility: The LOFT Integral Test Facility is a scale model of a LPWR. The intent of the facility is to model the nuclear, thermal-hydraulic phenomena which would take place in a LPWR during a LOCA. The general philosophy in scaling coolant volumes and flow areas in LOFT was to use the ratio of the LOFT core [50 MW(t)] to a typical LPWR core [3000 MW(t)]. For some components, this factor is not applied; however, it is used as extensively as practical. In general, components used in LOFT are similar in design to those of a LPWR. Because of scaling and component design, the LOFT LOCA is expected to closely model a LPWR LOCA. 2 - Description of test: This was the fifth in the NRC L3 Series of small-break LOCA experiments. A 10-cm (2.5-in.) cold-leg non-communicative-break LOCA was simulated. Pumps were shut off. The experiment was conducted on 29 September 1980 3. Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2 Science.gov (United States) Firoz Islam, SK; Benjamin, Colin 2016-09-01 The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms. 4. Exploring 4D quantum Hall physics with a 2D topological charge pump Science.gov (United States) Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel 2018-01-01 The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted. 5. Exploring 4D quantum Hall physics with a 2D topological charge pump. Science.gov (United States) Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel 2018-01-03 The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted. 6. Sub-grid-scale effects on short-wave instability in magnetized hall-MHD plasma International Nuclear Information System (INIS) Miura, H.; Nakajima, N. 2010-11-01 Aiming to clarify effects of short-wave modes on nonlinear evolution/saturation of the ballooning instability in the Large Helical Device, fully three-dimensional simulations of the single-fluid MHD and the Hall MHD equations are carried out. A moderate parallel heat conductivity plays an important role both in the two kinds of simulations. In the single-fluid MHD simulations, the parallel heat conduction effectively suppresses short-wave ballooning modes but it turns out that the suppression is insufficient in comparison to an experimental result. In the Hall MHD simulations, the parallel heat conduction triggers a rapid growth of the parallel flow and enhance nonlinear couplings. A comparison between single-fluid and the Hall MHD simulations reveals that the Hall MHD model does not necessarily improve the saturated pressure profile, and that we may need a further extension of the model. We also find by a comparison between two Hall MHD simulations with different numerical resolutions that sub-grid-scales of the Hall term should be modeled to mimic an inverse energy transfer in the wave number space. (author) 7. Spin Hall effect by surface roughness KAUST Repository Zhou, Lingjun; Grigoryan, Vahram L.; Maekawa, Sadamichi; Wang, Xuhui; Xiao, Jiang 2015-01-01 induced by surface roughness subscribes only to the side-jump contribution but not the skew scattering. The paradigm proposed in this paper provides the second, not if only, alternative to generate a sizable spin Hall effect. 8. Mesoscopic effects in the quantum Hall regime Indian Academy of Sciences (India) . When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance ... 9. Plasmon Geometric Phase and Plasmon Hall Shift Science.gov (United States) Shi, Li-kun; Song, Justin C. W. 2018-04-01 The collective plasmonic modes of a metal comprise a simple pattern of oscillating charge density that yields enhanced light-matter interaction. Here we unveil that beneath this familiar facade plasmons possess a hidden internal structure that fundamentally alters its dynamics. In particular, we find that metals with nonzero Hall conductivity host plasmons with an intricate current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This nontrivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wave packets to acquire geometric phases as they scatter. At boundaries, these phases accumulate allowing plasmon waves that reflect off to experience a nonreciprocal parallel shift. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displaces the incident and reflected plasmon trajectories and can be readily probed by near-field photonics techniques. Anomalous plasmon geometric phases dramatically enrich the nanophotonics toolbox, and yield radical new means for directing plasmonic beams. 10. A system for pulse Hall effect measurements International Nuclear Information System (INIS) Orzechowski, T.; Kupczak, R. 1975-01-01 Measuring system for fast Hall-voltage changes in an n-type germanium sample irradiated at liquid nitrogen temperature with a high-energy electron-beam from the Van de Graaff accelerator is described. (author) 11. Novel optical probe for quantum Hall system Indian Academy of Sciences (India) to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped ... Keywords. Surface photovoltage spectroscopy; quantum Hall effect; Landau levels; edge states. ... An optical fibre carries light from tunable diode laser. 12. AA under construction in its hall CERN Multimedia CERN PhotoLab 1980-01-01 The Antiproton Accumulator was installed in a specially built hall. Here we see it at an "early" stage of installation, just a few magnets on the floor, no vacuum chamber at all, but: 3 months later there was circulating beam ! 13. Elementary theory of quantum Hall effect Directory of Open Access Journals (Sweden) Keshav N. Shrivastava 2008-04-01 Full Text Available The Hall effect is the generation of a current perpendicular to both the direction of the applied electric as well as magnetic field in a metal or in a semiconductor. It is used to determine the concentration of electrons. The quantum Hall effect with integer quantization was discovered by von Klitzing and fractionally charged states were found by Tsui, Stormer and Gossard. Robert Laughlin explained the quantization of Hall current by using “flux quantization” and introduced incompressibility to obtain the fractional charge. We have developed the theory of the quantum Hall effect by using the theory of angular momentum. Our predicted fractions are in accord with those measured. We emphasize our explanation of the observed phenomena. We use spin to explain the fractional charge and hence we discover spin-charge locking. 14. NAS Decadal Review Town Hall Science.gov (United States) The National Academies of Sciences, Engineering and Medicine is seeking community input for a study on the future of materials research (MR). Frontiers of Materials Research: A Decadal Survey will look at defining the frontiers of materials research ranging from traditional materials science and engineering to condensed matter physics. Please join members of the study committee for a town hall to discuss future directions for materials research in the United States in the context of worldwide efforts. In particular, input on the following topics will be of great value: progress, achievements, and principal changes in the R&D landscape over the past decade; identification of key MR areas that have major scientific gaps or offer promising investment opportunities from 2020-2030; and the challenges that MR may face over the next decade and how those challenges might be addressed. This study was requested by the Department of Energy and the National Science Foundation. The National Academies will issue a report in 2018 that will offer guidance to federal agencies that support materials research, science policymakers, and researchers in materials research and other adjoining fields. Learn more about the study at http://nas.edu/materials. 15. Are tent halls subject to property tax? Directory of Open Access Journals (Sweden) Mariusz Macudziński 2016-12-01 Full Text Available The presented publication is a response to currently asked questions and interpretative doubts of taxpayers and tax authorities, namely whether tent halls are subject to property tax. General issues connected with an entity and a subject of taxation of this tax are presented herein. The answer to the question asked is then provided through the qualification of constructions works and the allocation of tent halls in the proper category of the works, with the use of the current law. 16. Fractional statistics and fractional quantized Hall effect International Nuclear Information System (INIS) Tao, R.; Wu, Y.S. 1985-01-01 The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references 17. L1 and L2 Distance Effects in Learning L3 Dutch Science.gov (United States) Schepens, Job J.; der Slik, Frans; Hout, Roeland 2016-01-01 Many people speak more than two languages. How do languages acquired earlier affect the learnability of additional languages? We show that linguistic distances between speakers' first (L1) and second (L2) languages and their third (L3) language play a role. Larger distances from the L1 to the L3 and from the L2 to the L3 correlate with lower… 18. The Coulomb deflection effect on the L3-subshell alignment in low-velocity proton impact ionisation International Nuclear Information System (INIS) Palinkas, J.; Schlenk, B.; Valek, A. 1981-01-01 The alignment parameter of the L 3 subshell of gold has been determined by measuring the angular distribution of the Lsub(l)/Lsub(γ) intensity ratio following proton impact ionisation in the 0.25-0.60 MeV energy range. The experimental results make it clear that the minimum of the alignment parameter at low energies found earlier for He + impact also exists in the case of proton impact ionisation. (author) 19. Transcriptomes and pathways associated with infectivity, survival and immunogenicity in Brugia malayi L3 Directory of Open Access Journals (Sweden) Spiro David 2009-06-01 Full Text Available Abstract Background Filarial nematode parasites cause serious diseases such as elephantiasis and river blindness in humans, and heartworm infections in dogs. Third stage filarial larvae (L3 are a critical stage in the life cycle of filarial parasites, because this is the stage that is transmitted by arthropod vectors to initiate infections in mammals. Improved understanding of molecular mechanisms associated with this transition may provide important leads for development of new therapies and vaccines to prevent filarial infections. This study explores changes in gene expression associated with the transition of Brugia malayi third stage larvae (BmL3 from mosquitoes into mammalian hosts and how these changes are affected by radiation. Radiation effects are especially interesting because irradiated L3 induce partial immunity to filarial infections. The underlying molecular mechanisms responsible for the efficacy of such vaccines are unkown. Results Expression profiles were obtained using a new filarial microarray with 18, 104 64-mer elements. 771 genes were identified as differentially expressed in two-way comparative analyses of the three L3 types. 353 genes were up-regulated in mosquito L3 (L3i relative to cultured L3 (L3c. These genes are important for establishment of filarial infections in mammalian hosts. Other genes were up-regulated in L3c relative to L3i (234 or irradiated L3 (L3ir (22. These culture-induced transcripts include key molecules required for growth and development. 165 genes were up-regulated in L3ir relative to L3c; these genes encode highly immunogenic proteins and proteins involved in radiation repair. L3ir and L3i have similar transcription profiles for genes that encode highly immunogenic proteins, antioxidants and cuticle components. Conclusion Changes in gene expression that normally occur during culture under conditions that support L3 development and molting are prevented or delayed by radiation. This may explain 20. Tau Polarization Measurement in the L3 Detector; Medida de la polarizacion del Tau en el detector L3 Energy Technology Data Exchange (ETDEWEB) Garcia, P 1996-06-01 The Polarization asymmetry (A{sub p}) measurement can be obtained from the energy spectra of the tau lepton (tau) decay products. This measurement provides a precise determination of the weak mixing angel (sin2 tilde char theta{sub w}), one of the Standard Model fundamental parameters. Tau leptons are produced at LEP in e+e-yields tilde char f interactions at a center of mass energy of the order of the Z boson mass. In order to get A{sub p} we have calculated the analytical formulae of the tau decay products energy spectra, including radiative corrections, for all of the one prong tau decay channels. We have also extended this analytical formalism to the detector level, including the selection criteria effects and the detector resolution (calibration) in the analytical expressions. Detailed studies have been performed concerning our measurement using this formalism. From the data collected with the L3 detector between 1991 and 1994, which corresponds to an integrated luminosity of 118.8 pb1 at a center of mass energy of the order of the Z mass, we have identified and selected the following tau decay channel samples: tau yields e nu tilde char nu, tau yields mu nu tilde char nu, tau yields pi/K nu y tau yields p/K*nu. From the analysis of these samples we get the tau polarization asymmetry measurement: A{sub p}=0.143+-0.014+-0.010, which corresponds to a value of sin2 tilde char theta{sub w}=0.2320+-0.0018+-0.0013. (Author) 24 refs 1. Contribution to the elaboration and implementation of LEP-L3 second level microcoded Trigger International Nuclear Information System (INIS) Chollet, F. 1988-03-01 This thesis is devoted to the elaboration of the L3 second level trigger which is based on the dedicated programmable XOP processor. This system will reduce the trigger rate by a factor of ten and will ensure that the hardwired level-one processors function correctly. The present document describes all developments that L.A.P.P. is engaged in from the system design up to the complete experimental set up, especially: - The hardware development of the fast input memories as well as the FASTBUS interface unit which allows the microprocessor XOP to run as a performant FASTBUS Master, - the associated software developments, - the implementation of a VME test system dedicated to all control tasks [fr 2. Hall effect measurement for precise sheet resistance and thickness evaluation of Ruthenium thin films using non-equidistant four-point probes Directory of Open Access Journals (Sweden) Frederik Westergaard Østerberg 2018-05-01 Full Text Available We present a new micro Hall effect measurement method using non-equidistant electrodes. We show theoretically and verify experimentally that it is advantageous to use non-equidistant electrodes for samples with low Hall sheet resistance. We demonstrate the new method by experiments where Hall sheet carrier densities and Hall mobilities of Ruthenium thin films (3-30 nm are determined. The measurements show that it is possible to measure Hall mobilities as low as 1 cm2V−1s−1 with a relative standard deviation of 2-3%. We show a linear relation between measured Hall sheet carrier density and film thickness. Thus, the method can be used to monitor thickness variations of ultra-thin metal films. 3. Detection of fractional solitons in quantum spin Hall systems Science.gov (United States) Fleckenstein, C.; Traverso Ziani, N.; Trauzettel, B. 2018-03-01 We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating the fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier. 4. New approach for measuring the microwave Hall mobility of semiconductors International Nuclear Information System (INIS) Murthy, D. V. B.; Subramanian, V.; Murthy, V. R. K. 2006-01-01 Measurement of Hall mobility in semiconductor samples using bimodal cavity method gives distinct advantages due to noncontact nature as well as the provision to measure anisotropic mobility. But the measurement approaches followed till now have a disadvantage of having high error values primarily due to the problem in evaluating the calibration constant of the whole experimental arrangement. This article brings out a new approach that removes such disadvantage and presents the calibration constant with 1% accuracy. The overall error in the carrier mobility values is within 5% 5. Magnon Spin Hall Magnetoresistance of a Gapped Quantum Paramagnet Science.gov (United States) Ulloa, Camilo; Duine, R. A. 2018-04-01 Motivated by recent experimental work, we consider spin transport between a normal metal and a gapped quantum paramagnet. We model the latter as the magnonic Mott-insulating phase of an easy-plane ferromagnetic insulator. We evaluate the spin current mediated by the interface exchange coupling between the ferromagnet and the adjacent normal metal. For the strongly interacting magnons that we consider, this spin current gives rise to a spin Hall magnetoresistance that strongly depends on the magnitude of the magnetic field, rather than its direction. This Letter may motivate electrical detection of the phases of quantum magnets and the incorporation of such materials into spintronic devices. 6. 75 FR 22770 - Gary E. Hall and Rita Hall; Notice of Availability of Environmental Assessment Science.gov (United States) 2010-04-30 ... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission [Project No. 13652-000-Montana] Gary E. Hall and Rita Hall; Notice of Availability of Environmental Assessment April 22, 2010. In accordance with the National Environmental Policy Act of 1969, as amended, and the Federal Energy Regulatory... 7. Experiments on Quantum Hall Topological Phases in Ultra Low Temperatures International Nuclear Information System (INIS) Du, Rui-Rui 2015-01-01 This project is to cool electrons in semiconductors to extremely low temperatures and to study new states of matter formed by low-dimensional electrons (or holes). At such low temperatures (and with an intense magnetic field), electronic behavior differs completely from ordinary ones observed at room temperatures or regular low temperature. Studies of electrons at such low temperatures would open the door for fundamental discoveries in condensed matter physics. Present studies have been focused on topological phases in the fractional quantum Hall effect in GaAs/AlGaAs semiconductor heterostructures, and the newly discovered (by this group) quantum spin Hall effect in InAs/GaSb materials. This project consists of the following components: 1) Development of efficient sample cooling techniques and electron thermometry: Our goal is to reach 1 mK electron temperature and reasonable determination of electron temperature; 2) Experiments at ultra-low temperatures: Our goal is to understand the energy scale of competing quantum phases, by measuring the temperature-dependence of transport features. Focus will be placed on such issues as the energy gap of the 5/2 state, and those of 12/5 (and possible 13/5); resistive signature of instability near 1/2 at ultra-low temperatures; 3) Measurement of the 5/2 gaps in the limit of small or large Zeeman energies: Our goal is to gain physics insight of 5/2 state at limiting experimental parameters, especially those properties concerning the spin polarization; 4) Experiments on tuning the electron-electron interaction in a screened quantum Hall system: Our goal is to gain understanding of the formation of paired fractional quantum Hall state as the interaction pseudo-potential is being modified by a nearby screening electron layer; 5) Experiments on the quantized helical edge states under a strong magnetic field and ultralow temperatures: our goal is to investigate both the bulk and edge states in a quantum spin Hall insulator under 8. Alignment following Au L_{3}photoionization by synchrotron radiation CERN Document Server Yamaoka, H; Takahiro, K; Morikawa, T; Ito, S; Mizumaki, M; Semenov, S; Cherepkov, N; Kabachnik, N M; Mukoyama, T; 10.1088/0953-4075/36/19/001 2003-01-01 The alignment of Au/sup +/ ions following L/sub 3/ photoionization has been studied using a high-resolution X-ray spectrometer. We observed a small anisotropy for the angular dependence of Au L/sub l/ and L alpha emissions. The alignment parameter A/sub 20/ derived from the experimental results is compared with theoretical calculations by Hartree-Fock approximation and random phase approximation with exchange. The contribution to the alignment of quadruple interaction is discussed. (40 refs). 9. Wendelstein 7-X Torus Hall Layout and System Integration International Nuclear Information System (INIS) Hartmann, D.; Damiani, C.; Hartfuss, H.-J.; Krampitz, R.; Neuner, U. 2006-01-01 Wendelstein 7-X is an experimental fusion device presently under construction in Greifswald, Germany, to study the stellarator concept at reactor relevant parameters und steady-state conditions. The heart of the machine consists of the torus that houses the superconducting coils and the plasma vacuum vessel. It is located nearly in the center of a 30 m x 30 m x 20 m hall. A large number of components need to be placed in close proximity of the torus to provide the system with the required means, e.g. cryogenic gases, cooling water, electricity, and to integrate it with the peripheral diagnostic and heating components. The arrangement of these components has to be supported by suitable structures, and has to be optimized to allow for installation, maintenance, and repair. In addition, space has to be provided for escape routes and for sufficient distance between components that could negatively influence each other's performance, etc. The layout of the components has been done over many years using 3D CAD software. It was based on simple geometric models of the components and of the additionally required space. Presently the layout design is being detailed and updated by replacing the original coarse models with more refined estimates or - in some cases - with as-built models. All interface requirements are carefully taken into account. Detailed routing was specified for the cryo and cooling water supply lines whose design and installation is outsourced. Due to the limited space available and severely restricted access during experimental campaigns, the requirement to put auxiliary components like electronic racks into the torus hall is being queried. The paper summarizes the present state of the component layout in the torus hall, and how the peripheral supply, diagnostics, and heating systems are integrated into the machine. (author) 10. Charge carrier coherence and Hall effect in organic semiconductors Science.gov (United States) Yi, H. T.; Gartstein, Y. N.; Podzorov, V. 2016-01-01 Hall effect measurements are important for elucidating the fundamental charge transport mechanisms and intrinsic mobility in organic semiconductors. However, Hall effect studies frequently reveal an unconventional behavior that cannot be readily explained with the simple band-semiconductor Hall effect model. Here, we develop an analytical model of Hall effect in organic field-effect transistors in a regime of coexisting band and hopping carriers. The model, which is supported by the experiments, is based on a partial Hall voltage compensation effect, occurring because hopping carriers respond to the transverse Hall electric field and drift in the direction opposite to the Lorentz force acting on band carriers. We show that this can lead in particular to an underdeveloped Hall effect observed in organic semiconductors with substantial off-diagonal thermal disorder. Our model captures the main features of Hall effect in a variety of organic semiconductors and provides an analytical description of Hall mobility, carrier density and carrier coherence factor. PMID:27025354 11. Charge carrier coherence and Hall effect in organic semiconductors. Science.gov (United States) Yi, H T; Gartstein, Y N; Podzorov, V 2016-03-30 Hall effect measurements are important for elucidating the fundamental charge transport mechanisms and intrinsic mobility in organic semiconductors. However, Hall effect studies frequently reveal an unconventional behavior that cannot be readily explained with the simple band-semiconductor Hall effect model. Here, we develop an analytical model of Hall effect in organic field-effect transistors in a regime of coexisting band and hopping carriers. The model, which is supported by the experiments, is based on a partial Hall voltage compensation effect, occurring because hopping carriers respond to the transverse Hall electric field and drift in the direction opposite to the Lorentz force acting on band carriers. We show that this can lead in particular to an underdeveloped Hall effect observed in organic semiconductors with substantial off-diagonal thermal disorder. Our model captures the main features of Hall effect in a variety of organic semiconductors and provides an analytical description of Hall mobility, carrier density and carrier coherence factor. 12. The quantum Hall effect at 5/2 filling factor International Nuclear Information System (INIS) Willett, R L 2013-01-01 Experimental discovery of a quantized Hall state at 5/2 filling factor presented an enigmatic finding in an established field of study that has remained an open issue for more than twenty years. In this review we first examine the experimental requirements for observing this state and outline the initial theoretical implications and predictions. We will then follow the chronology of experimental studies over the years and present the theoretical developments as they pertain to experiments, directed at sets of issues. These topics will include theoretical and experimental examination of the spin properties at 5/2; is the state spin polarized? What properties of the higher Landau levels promote development of the 5/2 state, what other correlation effects are observed there, and what are their interactions with the 5/2 state? The 5/2 state is not a robust example of the fractional quantum Hall effect: what experimental and material developments have allowed enhancement of the effect? Theoretical developments from initial pictures have promoted the possibility that 5/2 excitations are exceptional; do they obey non-abelian statistics? The proposed experiments to determine this and their executions in various forms will be presented: this is the heart of this review. Experimental examination of the 5/2 excitations through interference measurements will be reviewed in some detail, focusing on recent results that demonstrate consistency with the picture of non-abelian charges. The implications of this in the more general physics picture is that the 5/2 excitations, shown to be non-abelian, should exhibit the properties of Majorana operators. This will be the topic of the last review section. (review article) 13. Dr. Hall and the work cure. Science.gov (United States) Reed, Kathlyn L 2005-01-01 Herbert James Hall, MD (1870-1923), was a pioneer in the systematic and organized study of occupation as therapy for persons with nervous and mental disorders that he called the "work cure." He began his work in 1904 during the early years of the Arts and Crafts Movement in the United States. His primary interest was the disorder neurasthenia, a condition with many symptoms including chronic fatigue, stress, and inability to work or perform everyday tasks. The prevailing treatment of the day was absolute bed rest known as the "rest cure." Hall believed that neurasthenia was not caused by overwork but by faulty living habits that could be corrected through an ordered life schedule and selected occupations. He identified several principles of therapy that are still used today including graded activity and energy conservation. Dr. Adolph Meyer credits Hall for organizing the ideas on the therapeutic use of occupation (Meyer, 1922). Hall also provided the name American Occupational Therapy Association for the professional organization and served as the fourth president. For his many contributions to the profession Hall deserves to be recognized as a major contributor to the development and organization of occupational therapy. 14. A new CMOS Hall angular position sensor Energy Technology Data Exchange (ETDEWEB) Popovic, R.S.; Drljaca, P. [Swiss Federal Inst. of Tech., Lausanne (Switzerland); Schott, C.; Racz, R. [SENTRON AG, Zug (Switzerland) 2001-06-01 The new angular position sensor consists of a combination of a permanent magnet attached to a shaft and of a two-axis magnetic sensor. The permanent magnet produces a magnetic field parallel with the magnetic sensor plane. As the shaft rotates, the magnetic field also rotates. The magnetic sensor is an integrated combination of a CMOS Hall integrated circuit and a thin ferromagnetic disk. The CMOS part of the system contains two or more conventional Hall devices positioned under the periphery of the disk. The ferromagnetic disk converts locally a magnetic field parallel with the chip surface into a field perpendicular to the chip surface. Therefore, a conventional Hall element can detect an external magnetic field parallel with the chip surface. As the direction of the external magnetic field rotates in the chip plane, the output voltage of the Hall element varies as the cosine of the rotation angle. By placing the Hall elements at the appropriate places under the disk periphery, we may obtain the cosine signals shifted by 90 , 120 , or by any other angle. (orig.) 15. Field theory approach to quantum hall effect International Nuclear Information System (INIS) Cabo, A.; Chaichian, M. 1990-07-01 The Fradkin's formulation of statistical field theory is applied to the Coulomb interacting electron gas in a magnetic field. The electrons are confined to a plane in normal 3D-space and also interact with the physical 3D-electromagnetic field. The magnetic translation group (MTG) Ward identities are derived. Using them it is shown that the exact electron propagator is diagonalized in the basis of the wave functions of the free electron in a magnetic field whenever the MTG is unbroken. The general tensor structure of the polarization operator is obtained and used to show that the Chern-Simons action always describes the Hall effect properties of the system. A general proof of the Streda formula for the Hall conductivity is presented. It follows that the coefficient of the Chern-Simons terms in the long-wavelength approximation is exactly given by this relation. Such a formula, expressing the Hall conductivity as a simple derivative, in combination with diagonal form of the full propagator allows to obtain a simple expressions for the filling factor and the Hall conductivity. Indeed, these results, after assuming that the chemical potential lies in a gap of the density of states, lead to the conclusion that the Hall conductivity is given without corrections by σ xy = νe 2 /h where ν is the filling factor. In addition it follows that the filling factor is independent of the magnetic field if the chemical potential remains in the gap. (author). 21 ref, 1 fig 16. Exchange magnetic field torques in YIG/Pt bilayers observed by the spin-Hall magnetoresistance NARCIS (Netherlands) Vlietstra, N.; Shan, J.; Castel, V.; Ben Youssef, J.; Bauer, G. E. W.; van Wees, B. J. 2013-01-01 The effective field torque of an yttrium-iron-garnet (YIG) film on the spin accumulation in an attached platinum (Pt) film is measured by the spin-Hall magnetoresistance (SMR). As a result, the magnetization direction of a ferromagnetic insulating layer can be measured electrically. Experimental 17. Exchange-biased planar Hall effect sensor optimized for biosensor applications DEFF Research Database (Denmark) Damsgaard, Christian Danvad; Freitas, S.C.; Freitas, P.P. 2008-01-01 This article presents experimental investigations of exchange-biased Permalloy planar Hall effect sensor crosses with a fixed active area of w x w = 40 x 40 mu m(2) and Permalloy thicknesses of t = 20, 30, and 50 nm. It is shown that a single domain model describes the system well... 18. Diagnostic Setup for Characterization of Near-Anode Processes in Hall Thrusters International Nuclear Information System (INIS) Dorf, L.; Raitses, Y.; Fisch, N.J. 2003-01-01 A diagnostic setup for characterization of near-anode processes in Hall-current plasma thrusters consisting of biased and emissive electrostatic probes, high-precision positioning system and low-noise electronic circuitry was developed and tested. Experimental results show that radial probe insertion does not cause perturbations to the discharge and therefore can be used for accurate near-anode measurements 19. Summary and evaluation: fuel dynamics loss-of-flow experiments (tests L2, L3, and L4) International Nuclear Information System (INIS) Barts, E.W.; Deitrich, L.W.; Eberhart, J.G.; Fischer, A.K.; Meek, C.C. 1975-09-01 Three similar experiments conducted to support the analyses of hypothetical LMFBR unprotected-loss-of-flow accidents are summarized and evaluated. The tests, designated L2, L3, and L4, provided experimental data against which accident-analysis codes could be compared, so as to guide further analysis and modeling of the initiating phases of the hypothetical accident. The tests were conducted using seven-pin bundles of mixed-oxide fuel pins in Mark-II flowing-sodium loops in the TREAT reactor. Test L2 used fresh fuel. Tests L3 and L4 used irradiated fuel pins having, respectively, ''intermediate-power'' (no central void) and ''high-power'' (fully developed central void) microstructure. 12 references 20. Localization in a quantum spin Hall system. Science.gov (United States) Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto 2007-02-16 The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system. 1. Hall probe magnetometer for SSC magnet cables International Nuclear Information System (INIS) Cross, R.W.; Goldfarb, R.B. 1991-01-01 The authors of this paper constructed a Hall probe magnetometer to measure the magnetization hysteresis loops of Superconducting Super Collider magnet cables. The instrument uses two Hall-effect field sensors to measure the applied field H and the magnetic induction B. Magnetization M is calculated from the difference of the two quantities. The Hall probes are centered coaxially in the bore of a superconducting solenoid with the B probe against the sample's broad surface. An alternative probe arrangement, in which M is measured directly, aligns the sample probe parallel to the field. The authors measured M as a function of H and field cycle rate both with and without a dc transport current. Flux creep as a function of current was measured from the dependence of ac loss on the cycling rate and from the decay of magnetization with time. Transport currents up to 20% of the critical current have minimal effect on magnetization and flux creep 2. Analytical theory and possible detection of the ac quantum spin Hall effect. Science.gov (United States) Deng, W Y; Ren, Y J; Lin, Z X; Shen, R; Sheng, L; Sheng, D N; Xing, D Y 2017-07-11 We develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means. 3. Local orbitals approach to the anomalous Hall and Nernst effects in itinerant ferromagnets Directory of Open Access Journals (Sweden) Středa Pavel 2014-07-01 Full Text Available Linear response of the orbital momentum to the gradient of the chemical potential is used to obtain anomalous Hall conductivity. Transition from the ideal Bloch system for which the conductivity is determined by the Berry phase curvatures to the case of strong disorder for which the conductivity becomes dependent on the relaxation time is analysed. Presented tight-binding model reproduces experimentally observed qualitative features of the anomalous Hall conductivity and the transverse Peltier coefficient in the so called bad-metal and scattering-independent regimes. 4. Developments in Scanning Hall Probe Microscopy Science.gov (United States) Chouinard, Taras; Chu, Ricky; David, Nigel; Broun, David 2009-05-01 Low temperature scanning Hall probe microscopy is a sensitive means of imaging magnetic structures with high spatial resolution and magnetic flux sensitivity approaching that of a Superconducting Quantum Interference Device. We have developed a scanning Hall probe microscope with novel features, including highly reliable coarse positioning, in situ optimization of sensor-sample alignment and capacitive transducers for linear, long range positioning measurement. This has been motivated by the need to reposition accurately above fabricated nanostructures such as small superconducting rings. Details of the design and performance will be presented as well as recent progress towards time-resolved measurements with sub nanosecond resolution. 5. Enhanced Performance of Cylindrical Hall Thrusters International Nuclear Information System (INIS) Raitses, Y.; Smirnov, A.; Fisch, N.J. 2007-01-01 The cylindrical thruster differs significantly in its underlying physical mechanisms from the conventional annular Hall thruster. It features high ionization efficiency, quiet operation, ion acceleration in a large volume-to-surface ratio channel, and performance comparable with the state-of-the-art conventional Hall thrusters. Very significant plume narrowing, accompanied by the increase of the energetic ion fraction and improvement of ion focusing, led to 50-60% increase of the thruster anode efficiency. These improvements were achieved by overrunning the discharge current in the magnetized thruster plasma 6. Prototype dining hall energy efficiency study Energy Technology Data Exchange (ETDEWEB) Mazzucchi, R.P.; Bailey, S.A.; Zimmerman, P.W. 1988-06-01 The energy consumption of food service facilities is among the highest of any commercial building type, owing to the special requirements for food preparation, sanitation, and ventilation. Consequently, the US Air Force Engineering and Services Center (AFESC) contracted with Pacific Northwest Laboratory (PNL) to collect and analyze end-use energy consumption data for a prototypical dining hall and make specific recommendations on cost-effective energy conservation options. This information will be used to establish or update criteria for dining hall designs and retrofits as appropriate. 6 refs., 21 figs., 23 tabs. 7. Acoustics in rock and pop music halls DEFF Research Database (Denmark) Larsen, Niels Werner; Thompson, Eric Robert; Gade, Anders Christian 2007-01-01 The existing body of literature regarding the acoustic design of concert halls has focused almost exclusively on classical music, although there are many more performances of rhythmic music, including rock and pop. Objective measurements were made of the acoustics of twenty rock music venues...... in Denmark and a questionnaire was used in a subjective assessment of those venues with professional rock musicians and sound engineers. Correlations between the objective and subjective results lead, among others, to a recommendation for reverberation time as a function of hall volume. Since the bass... 8. Proton knock-out in Hall A International Nuclear Information System (INIS) Jager, K. de 2003-01-01 Proton knock-out is studied in a broad program in Hall A at Jefferson Lab. The first experiment performed in Hall A studied the 16 O(e,e'p) reaction. Since then proton knock-out experiments have studied a variety of aspects of that reaction, from single-nucleon properties to its mechanism, such as final-state interactions and two-body currents, in nuclei from 2 H to 16 O. In this review the accomplishments of this program will be summarized and an outlook given of expected future results. (orig.) 9. Theory of fractional quantum Hall effect International Nuclear Information System (INIS) Kostadinov, I.Z. 1984-09-01 A theory of the fractional quantum Hall effect is constructed by introducing 3-particle interactions breaking the symmetry for ν=1/3 according to a degeneracy theorem proved here. An order parameter is introduced and a gap in the single particle spectrum is found. The critical temperature, critical filling number and critical behaviour are determined as well as the Ginzburg-Landau equation coefficients. A first principle calculation of the Hall current is given. 3, 5, 7 electron tunneling and Josephson interference effects are predicted. (author) 10. Hall effect driven by non-collinear magnetic polarons in diluted magnetic semiconductors Science.gov (United States) Denisov, K. S.; Averkiev, N. S. 2018-04-01 In this letter, we develop the theory of Hall effect driven by non-collinear magnetic textures (topological Hall effect—THE) in diluted magnetic semiconductors (DMSs). We show that a carrier spin-orbit interaction induces a chiral magnetic ordering inside a bound magnetic polaron (BMP). The inner structure of non-collinear BMP is controlled by the type of spin-orbit coupling, allowing us to create skyrmion- (Rashba) or antiskyrmion-like (Dresselhaus) configurations. The asymmetric scattering of itinerant carriers on polarons leads to the Hall response which exists in weak external magnetic fields and at low temperatures. We point out that DMS-based systems allow one to investigate experimentally the dependence of THE both on a carrier spin polarization and on a non-collinear magnetic texture shape. 11. Engineering the quantum anomalous Hall effect in graphene with uniaxial strains Energy Technology Data Exchange (ETDEWEB) Diniz, G. S., E-mail: [email protected]; Guassi, M. R. [Institute of Physics, University of Brasília, 70919-970 Brasília-DF (Brazil); Qu, F. [Institute of Physics, University of Brasília, 70919-970 Brasília-DF (Brazil); Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States) 2013-12-28 We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency. 12. Engineering the quantum anomalous Hall effect in graphene with uniaxial strains International Nuclear Information System (INIS) Diniz, G. S.; Guassi, M. R.; Qu, F. 2013-01-01 We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency 13. Voltage transients in thin-film InSb Hall sensor Directory of Open Access Journals (Sweden) Alexey Bardin Full Text Available The work is reached to study temperature transients in thin-film Hall sensors. We experimentally study InSb thin-film Hall sensor. We find transients of voltage with amplitude about 10 μV on the sensor ports after current switching. We demonstrate by direct measurements that the transients is caused by thermo-e.m.f., and both non-stationarity and heterogeneity of temperature in the film. We find significant asymmetry of temperature field for different direction of the current, which is probably related to Peltier effect. The result can be useful for wide range of scientist who works with switching of high density currents in any thin semiconductor films. 2000 MSC: 41A05, 41A10, 65D05, 65D17, Keywords: Thin-films, Semiconductors, Hall sensor, InSb, thermo-e.m.f. 14. Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries International Nuclear Information System (INIS) Cooper, N. R.; Lankvelt, F. J. M. van; Reijnders, J. W.; Schoutens, K. 2005-01-01 We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t c 1 . For tunneling well below t c 1 one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids 15. Parity effect of bipolar quantum Hall edge transport around graphene antidots. Science.gov (United States) Matsuo, Sadashige; Nakaharai, Shu; Komatsu, Katsuyoshi; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke 2015-06-30 Parity effect, which means that even-odd property of an integer physical parameter results in an essential difference, ubiquitously appears and enables us to grasp its physical essence as the microscopic mechanism is less significant in coarse graining. Here we report a new parity effect of quantum Hall edge transport in graphene antidot devices with pn junctions (PNJs). We found and experimentally verified that the bipolar quantum Hall edge transport is drastically affected by the parity of the number of PNJs. This parity effect is universal in bipolar quantum Hall edge transport of not only graphene but also massless Dirac electron systems. These results offer a promising way to design electron interferometers in graphene. 16. Hall MHD Modeling of Two-dimensional Reconnection: Application to MRX Experiment International Nuclear Information System (INIS) Lukin, V.S.; Jardin, S.C. 2003-01-01 Two-dimensional resistive Hall magnetohydrodynamics (MHD) code is used to investigate the dynamical evolution of driven reconnection in the Magnetic Reconnection Experiment (MRX). The initial conditions and dimensionless parameters of the simulation are set to be similar to the experimental values. We successfully reproduce many features of the time evolution of magnetic configurations for both co- and counter-helicity reconnection in MRX. The Hall effect is shown to be important during the early dynamic X-phase of MRX reconnection, while effectively negligible during the late ''steady-state'' Y-phase, when plasma heating takes place. Based on simple symmetry considerations, an experiment to directly measure the Hall effect in MRX configuration is proposed and numerical evidence for the expected outcome is given 17. Giant Planar Hall Effect in the Dirac Semimetal ZrTe5 KAUST Repository Li, Peng 2018-03-03 Exploration and understanding of exotic topics in quantum physics such as Dirac and Weyl semimetals have become highly popular in the area of condensed matter. It has recently been predicted that a theoretical giant planar Hall effect can be induced by a chiral anomaly in Dirac and Weyl semimetals. ZrTe5 is considered an intriguing Dirac semimetal at the boundary of weak and strong topological insulators, though this claim is still controversial. In this study, we report the observation in ZrTe5 of giant planar Hall resistivity. We have also noted three different dependences of this resistivity on the magnetic field, as predicted by theory, maximum planar Hall resistivity occurs at the Lifshitz transition temperature. In addition, we have discovered a nontrivial Berry phase, as well as a chiral-anomaly-induced negative longitudinal and a giant in-plane anisotropic magnetoresistance. All these experimental observations coherently demonstrate that ZrTe5 is a Dirac semimetal. 18. Nonlinear response of the quantum Hall system to a strong electromagnetic radiation International Nuclear Information System (INIS) Avetissian, H.K.; Mkrtchian, G.F. 2016-01-01 We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect. 19. Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems Science.gov (United States) Milletarı, Mirco; Offidani, Manuel; Ferreira, Aires; Raimondi, Roberto 2017-12-01 We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies. 20. A review of the quantum Hall effects in MgZnO/ZnO heterostructures Science.gov (United States) Falson, Joseph; Kawasaki, Masashi 2018-05-01 This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg x Zn1-x O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility (μ > 1000 000 cm2 Vs‑1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic. 1. AdS/QHE: towards a holographic description of quantum Hall experiments International Nuclear Information System (INIS) Bayntun, Allan; Burgess, C P; Lee, Sung-Sik; Dolan, Brian P 2011-01-01 Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analogue of the old 'composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value 2/5 for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42±0.01. 2. Hepatic CREB3L3 controls whole-body energy homeostasis and improves obesity and diabetes. Science.gov (United States) Nakagawa, Yoshimi; Satoh, Aoi; Yabe, Sachiko; Furusawa, Mika; Tokushige, Naoko; Tezuka, Hitomi; Mikami, Motoki; Iwata, Wakiko; Shingyouchi, Akiko; Matsuzaka, Takashi; Kiwata, Shiori; Fujimoto, Yuri; Shimizu, Hidehisa; Danno, Hirosuke; Yamamoto, Takashi; Ishii, Kiyoaki; Karasawa, Tadayoshi; Takeuchi, Yoshinori; Iwasaki, Hitoshi; Shimada, Masako; Kawakami, Yasushi; Urayama, Osamu; Sone, Hirohito; Takekoshi, Kazuhiro; Kobayashi, Kazuto; Yatoh, Shigeru; Takahashi, Akimitsu; Yahagi, Naoya; Suzuki, Hiroaki; Yamada, Nobuhiro; Shimano, Hitoshi 2014-12-01 Transcriptional regulation of metabolic genes in the liver is the key to maintaining systemic energy homeostasis during starvation. The membrane-bound transcription factor cAMP-responsive element-binding protein 3-like 3 (CREB3L3) has been reported to be activated during fasting and to regulate triglyceride metabolism. Here, we show that CREB3L3 confers a wide spectrum of metabolic responses to starvation in vivo. Adenoviral and transgenic overexpression of nuclear CREB3L3 induced systemic lipolysis, hepatic ketogenesis, and insulin sensitivity with increased energy expenditure, leading to marked reduction in body weight, plasma lipid levels, and glucose levels. CREB3L3 overexpression activated gene expression levels and plasma levels of antidiabetic hormones, including fibroblast growth factor 21 and IGF-binding protein 2. Amelioration of diabetes by hepatic activation of CREB3L3 was also observed in several types of diabetic obese mice. Nuclear CREB3L3 mutually activates the peroxisome proliferator-activated receptor (PPAR) α promoter in an autoloop fashion and is crucial for the ligand transactivation of PPARα by interacting with its transcriptional regulator, peroxisome proliferator-activated receptor gamma coactivator-1α. CREB3L3 directly and indirectly controls fibroblast growth factor 21 expression and its plasma level, which contributes at least partially to the catabolic effects of CREB3L3 on systemic energy homeostasis in the entire body. Therefore, CREB3L3 is a therapeutic target for obesity and diabetes. 3. Hall MHD Stability and Turbulence in Magnetically Accelerated Plasmas Energy Technology Data Exchange (ETDEWEB) H. R. Strauss 2012-11-27 The object of the research was to develop theory and carry out simulations of the Z pinch and plasma opening switch (POS), and compare with experimental results. In the case of the Z pinch, there was experimental evidence of ion kinetic energy greatly in excess of the ion thermal energy. It was thought that this was perhaps due to fine scale turbulence. The simulations showed that the ion energy was predominantly laminar, not turbulent. Preliminary studies of a new Z pinch experiment with an axial magnetic field were carried out. The axial magnetic is relevant to magneto - inertial fusion. These studies indicate the axial magnetic field makes the Z pinch more turbulent. Results were also obtained on Hall magnetohydrodynamic instability of the POS. 4. Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems Directory of Open Access Journals (Sweden) Maissam Barkeshli 2014-11-01 Full Text Available The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be used as robust “topological qubits” to store and process quantum information. In this paper, we propose a new experimental setup that can realize topological qubits in a simple bilayer fractional quantum Hall system with proper electric gate configurations. Our proposal is accessible with current experimental techniques, involves well-established topological states, and, moreover, can realize a large class of topological qubits, generalizing the Majorana zero modes studied in recent literature to more computationally powerful possibilities. We propose three tunneling and interferometry experiments to detect the existence and nonlocal topological properties of the topological qubits. 5. Bound values for Hall conductivity of heterogeneous medium under ... Indian Academy of Sciences (India) - ditions in inhomogeneous medium has been studied. It is shown that bound values for. Hall conductivity differ from bound values for metallic conductivity. This is due to the unusual character of current percolation under quantum Hall effect ... 6. A Small Modular Laboratory Hall Effect Thruster Science.gov (United States) Lee, Ty Davis Electric propulsion technologies promise to revolutionize access to space, opening the door for mission concepts unfeasible by traditional propulsion methods alone. The Hall effect thruster is a relatively high thrust, moderate specific impulse electric propulsion device that belongs to the class of electrostatic thrusters. Hall effect thrusters benefit from an extensive flight history, and offer significant performance and cost advantages when compared to other forms of electric propulsion. Ongoing research on these devices includes the investigation of mechanisms that tend to decrease overall thruster efficiency, as well as the development of new techniques to extend operational lifetimes. This thesis is primarily concerned with the design and construction of a Small Modular Laboratory Hall Effect Thruster (SMLHET), and its operation on argon propellant gas. Particular attention was addressed at low-cost, modular design principles, that would facilitate simple replacement and modification of key thruster parts such as the magnetic circuit and discharge channel. This capability is intended to facilitate future studies of device physics such as anomalous electron transport and magnetic shielding of the channel walls, that have an impact on thruster performance and life. Preliminary results demonstrate SMLHET running on argon in a manner characteristic of Hall effect thrusters, additionally a power balance method was utilized to estimate thruster performance. It is expected that future thruster studies utilizing heavier though more expensive gases like xenon or krypton, will observe increased efficiency and stability. 7. June 1992 Hall B collaboation meeting International Nuclear Information System (INIS) Dennis, L. 1992-01-01 The Hall B collaboration meeting at the CEBAF 1992 Summer Workshop consisted of technical and physics working group meetings, a special beam line devices working group meeting the first meeting of the membership committee, a technical representatives meeting and a full collaboration meeting. Highlights of these meetings are presented in this report 8. Chapin Hall Projects and Publications. Autumn 1999. Science.gov (United States) Chicago Univ., IL. Chapin Hall Center for Children. This guide chronicles the ongoing work and writings of the Chapin Hall Center for Children at the University of Chicago, a policy research center dedicated to bringing sound information, rigorous analyses, innovative ideas, and an independent, multidisciplinary perspective to bear on policies and programs affecting children. This guide, organized… 9. Quantum Hall Conductivity and Topological Invariants Science.gov (United States) Reyes, Andres 2001-04-01 A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula. 10. Room acoustic properties of concert halls DEFF Research Database (Denmark) Gade, Anders Christian 1996-01-01 A large database of values of various room acoustic parameters has provided the basis for statistical analyses of how and how much the acoustic properties of concert halls are influenced by their size, shape, and absorption area (as deduced from measured reverberation time). The data have been... 11. Pseudospin anisotropy classification of quantum Hall ferromagnets Czech Academy of Sciences Publication Activity Database Jungwirth, Tomáš; MacDonald, A. H. 2000-01-01 Roč. 63, č. 3 (2000), s. 035305-1 - 035305-9 ISSN 0163-1829 R&D Projects: GA ČR GA202/98/0085 Institutional research plan: CEZ:AV0Z1010914 Keywords : quantum Hall ferromagnets * anisotropy Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.065, year: 2000 12. Anomalous Hall effect in disordered multiband metals Czech Academy of Sciences Publication Activity Database Kovalev, A.A.; Sinova, Jairo; Tserkovnyak, Y. 2010-01-01 Roč. 105, č. 3 (2010), 036601/1-036601/4 ISSN 0031-9007 Institutional research plan: CEZ:AV0Z10100521 Keywords : anomalous Hall effect * spintronics Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.621, year: 2010 13. Anomalous Hall conductivity: Local orbitals approach Czech Academy of Sciences Publication Activity Database Středa, Pavel 2010-01-01 Roč. 82, č. 4 (2010), 045115/1-045115/9 ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100521 Keywords : anomalous Hall effect * Berry phase correction * orbital polarization momentum Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.772, year: 2010 14. Quantization and hall effect: necessities and difficulties International Nuclear Information System (INIS) Ahmed Bouketir; Hishamuddin Zainuddin 1999-01-01 The quantization procedure is a necessary tool for a proper understanding of many interesting quantum phenomena in modern physics. In this note, we focus on geometrical framework for such procedures, particularly the group-theoretic approach and their difficulties. Finally we look through the example of Hall effect as a quantized macroscopic phenomenon with group-theoretic quantization approach. (author) 15. Prospect of quantum anomalous Hall and quantum spin Hall effect in doped kagome lattice Mott insulators. Science.gov (United States) Guterding, Daniel; Jeschke, Harald O; Valentí, Roser 2016-05-17 Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions. 16. TRIPOLI calculation of the neutron field in the hall of the SILENE reactor International Nuclear Information System (INIS) Bourdet, L. 1986-05-01 This study concerns the utilization of the experimental reactor SILENE as radiation source. Its aim is to get a theoretical estimation of the neutron field characteristics in different points of the irradiation hall (spectra, fluences, equivalents of biological doses and reaction yields). These estimations are compared to results obtained by several experimental techniques; they allow to know better this neutron field with or without lead shield [fr 17. Digital technology impacts on the Arnhem transfer hall structural design NARCIS (Netherlands) Van de Straat, R.; Hofman, S.; Coenders, J.L.; Paul, J.C. 2015-01-01 The new Transfer Hall in Arnhem is one of the key projects to prepare the Dutch railways for the increased future demands for capacity. UNStudio developed a master plan in 1996 for the station area of which the completion of the Transfer Hall in 2015 will be a final milestone. The Transfer Hall is a 18. Magnetoresistance in quantum Hall metals due to Pancharatnam ... Indian Academy of Sciences (India) Abstract. We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate (and crossed) Landau levels, and in the presence of changing magnetic field strength, one can invoke two physical processes responsible for the electron ... 19. Destruction of the fractional quantum Hall effect by disorder International Nuclear Information System (INIS) Laughlin, R.B. 1985-07-01 It is suggested that Hall steps in the fractional quantum Hall effect are physically similar to those in the ordinary quantum Hall effect. This proposition leads to a simple scaling diagram containing a new type of fixed point, which is identified with the destruction of the fractional states by disorder. 15 refs., 3 figs 20. A Hall probe technique for characterizing high-temperature superconductors International Nuclear Information System (INIS) Zhang, J.; Sheldon, P.; Ahrenkiel, R.K. 1992-01-01 Thin-film GaAs Hall probes were fabricated by molecular beam epitaxy technology. A contactless technique was developed to characterize thin-film, high-temperature superconducting (HTSC) materials. The Hall probes detected the ac magnetic flux penetration through the high-temperature superconducting materials. The Hall detector has advantages over the mutual inductance magnetic flux detector 1. Spin-singlet hierarchy in the fractional quantum Hall effect OpenAIRE Ino, Kazusumi 1999-01-01 We show that the so-called permanent quantum Hall states are formed by the integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel conformal field theory description along with this picture is deduced. The odd denominator plateaux observed around\ 2. Bacillus licheniformis BlaR1 L3 Loop Is a Zinc Metalloprotease Activated by Self-Proteolysis Science.gov (United States) Sépulchre, Jérémy; Amoroso, Ana; Joris, Bernard 2012-01-01 In Bacillus licheniformis 749/I, BlaP β-lactamase is induced by the presence of a β-lactam antibiotic outside the cell. The first step in the induction mechanism is the detection of the antibiotic by the membrane-bound penicillin receptor BlaR1 that is composed of two functional domains: a carboxy-terminal domain exposed outside the cell, which acts as a penicillin sensor, and an amino-terminal domain anchored to the cytoplasmic membrane, which works as a transducer-transmitter. The acylation of BlaR1 sensor domain by the antibiotic generates an intramolecular signal that leads to the activation of the L3 cytoplasmic loop of the transmitter by a single-point cleavage. The exact mechanism of L3 activation and the nature of the secondary cytoplasmic signal launched by the activated transmitter remain unknown. However, these two events seem to be linked to the presence of a HEXXH zinc binding motif of neutral zinc metallopeptidases. By different experimental approaches, we demonstrated that the L3 loop binds zinc ion, belongs to Gluzincin metallopeptidase superfamily and is activated by self-proteolysis. PMID:22623956 3. Subsidence of the pit slab at SLC experimental hall International Nuclear Information System (INIS) Inaba, J.; Himeno, Yoichi; Katsura, Yutaka 1992-01-01 Detectors installed at particle accelerator facilities are quite heavy, weighing thousands of tons. On the other hand, ground subsidence caused by the installation of a detector adversely affects the beam line alignment of the collider. It becomes, therefore, very important to figure out the expected amount of ground settlement by means of adequate evaluation methods in advance. At Stanford Linear Accelerator Center (SLAC), a 1700 mT (metric tons) Mark II detector was replaced with a 4000 mT SLD detector in Stanford Linear Collider (SLC). The exchange started in December 1990 and lasted until March 1991, and the amount of ground settlement was measured by SLAC during that period. We performed simulation studies to evaluate the subsidence of the pit slab using several analysis methods. Parameters used for the analyses were decided based on the information of the SLC structure and the ground conditions at the SLAC area. The objective of this study is to verify the applicability of several simulation methods by comparing the analytical results with the actual subsidence data obtained by SLAC 4. Simulations of Hall reconnection in partially ionized plasmas Science.gov (United States) Innocenti, Maria Elena; Jiang, Wei; Lapenta, Giovanni 2017-04-01 Magnetic reconnection occurs in the Hall, partially ionized regime in environments as diverse as molecular clouds, protostellar disks and regions of the solar chromosphere. While much is known about Hall reconnection in fully ionized plasmas, Hall reconnection in partially ionized plasmas is, in comparison, still relatively unexplored. This notwithstanding the fact that partial ionization is expected to affect fundamental processes in reconnection such as the transition from the slow, fluid to the fast, kinetic regime, the value of the reconnection rate and the dimensions of the diffusion regions [Malyshkin and Zweibel 2011 , Zweibel et al. 2011]. We present here the first, to our knowledge, fully kinetic simulations of Hall reconnection in partially ionized plasmas. The interaction of electrons and ions with the neutral background is realistically modelled via a Monte Carlo plug-in coded into the semi-implicit, fully kinetic code iPic3D [Markidis 2010]. We simulate a plasma with parameters compatible with the MRX experiments illustrated in Zweibel et al. 2011 and Lawrence et al. 2013, to be able to compare our simulation results with actual experiments. The gas and ion temperature is T=3 eV, the ion to electron temperature ratio is Tr=0.44, ion and electron thermal velocities are calculated accordingly resorting to a reduced mass ratio and a reduced value of the speed of light to reduce the computational costs of the simulations. The initial density of the plasma is set at n= 1.1 1014 cm-3 and is then left free to change during the simulation as a result of gas-plasma interaction. A set of simulations with initial ionisation percentage IP= 0.01, 0.1, 0.2, 0.6 is presented and compared with a reference simulation where no background gas is present (full ionization). In this first set of simulations, we assume to be able to externally control the initial relative densities of gas and plasma. Within this parameter range, the ion but not the electron population is 5. The Bilingual Advantage in L3 Learning: A Developmental Study of Rhotic Sounds Science.gov (United States) Kopecková, Romana 2016-01-01 Facilitative effects of bilingualism on general aspects of third language (L3) proficiency have been demonstrated in numerous studies conducted in bilingual communities and classrooms around the world. When it comes to L3 phonology, however, empirical evidence has been scarce and inconclusive in respect to the question of whether and/or how… 6. Quantum Hall bilayers and the chiral sine-Gordon equation International Nuclear Information System (INIS) Naud, J.D.; Pryadko, Leonid P.; Sondhi, S.L. 2000-01-01 The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon form. We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon theory, contrary to a previous assertion by Renn, and that the theory is manifestly sensible only at a discrete set of values of the inverse period of the cosine interaction (β-circumflex). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β-circumflex at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (β-circumflex 2 =4) is of greatest interest: the spectrum of the interacting theory is that of two Majorana fermions with different, dynamically generated, velocities. For the experimentally observed bilayer 331 state at filling factor 1/2, this implies the trifurcation of electrons added to the edge. We also present a method for fermionizing the theory at the discrete points (β-circumflex 2 is an element of Z + ) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers 7. Xenon spectator and diagram L3-M4,5M4,5 Auger intensities near the L3 threshold International Nuclear Information System (INIS) Armen, G.B.; Levin, J.C.; Southworth, S.H.; LeBrun, T.; Arp, U.; MacDonald, M.A. 1997-01-01 Calculations based on the theory of radiationless resonant Raman scattering are employed in the interpretation of new XeL 3 -M 4,5 M 4,5 Auger spectra recorded using synchrotron radiation tuned to energies across the L 3 edge. Fits of theoretical line shapes to the spectra are employed in separating intensities due to nd spectator (resonant) and diagram Auger processes. Near-threshold Auger intensity, previously attributed to diagram decay, is found to be due to the large-n spectator lines that result from postcollision-interaction endash induced open-quotes recaptureclose quotes of threshold photoelectrons to nd orbitals. copyright 1997 The American Physical Society 8. Valence determination of rare earth elements in lanthanide silicates by L 3-XANES spectroscopy International Nuclear Information System (INIS) Kravtsova, Antonina N; Guda, Alexander A; Soldatov, Alexander V; Goettlicher, Joerg; Taroev, Vladimir K; Suvorova, Lyudmila F; Tauson, Vladimir L; Kashaev, Anvar A 2016-01-01 Lanthanide silicates have been hydrothermally synthesized using Cu and Ni containers. Chemical formulae of the synthesized compounds correspond to K 3 Eu[Si 6 O 15 ] 2H 2 O, HK 6 Eu[Si 10 O 25 ], K 7 Sm 3 [Si 12 O 32 ], K 2 Sm[AlSi 4 O 12 ] 0.375H 2 O, K 4 Yb 2 [Si 8 O 21 ], K 4 Ce 2 [Al 2 Si 8 O 24 ]. The oxidation state of lanthanides (Eu, Ce, Tb, Sm, Yb) in these silicates has been determined using XANES spectroscopy at the Eu, Ce, Tb, Sm, Yb, L 3 - edges. The experimental XANES spectra were recorded using the synchrotron radiation source ANKA (Karlsruhe Institute of Technology) and the X-ray laboratory spectrometer Rigaku R- XAS. By comparing the absorption edge energies and white line intensities of the silicates with the ones of reference spectra the oxidation state of lanthanides Eu, Ce, Tb, Sm, Yb has been found to be equal to +3 in all investigated silicates except of the Ce-containing silicate from the run in Cu container where the cerium oxidation state ranges from +3 (Ce in silicate apatite and in a KCe silicate with Si 12 O 32 layers) to +4 (starting CeO 2 or oxidized Ce 2 O 3 ). (paper) 9. Search for neutralinos in e+e- reactions at the L3 experiment International Nuclear Information System (INIS) Starosta, R. 1992-10-01 The present thesis deals with the search for neutralinos, which are predicted in the framework of the minimal supersymmetric standard model (MSSM). The lightest of the neutralinos is favorized as the lightest supersymmetric particle. With it, how far this assumption is confirmed, all decay chains of other SUSY particles would end. The data, on which the experimental studies are based, were collected in the year 1990 with the L3 detector at the e + e - -storage ring LEP at a c.m. energy around 91 GeV. In them no hint on the existence of SUSY particles is found, whereby a) deviations of the decay width of the Z 0 boson from the standard-model prediction and b) in hadronic final states directly detectable neutralinos are looked for. The results are presented in form of regions in the parameter space of the MSSM - tan β, M 2 , μ- as well as masses for the lightest neutralinos in dependence on tan β, which are excluded with 95% c.l. Quite generally it can be stated, that a neutralino with a mass of less than 19 geV for tan β>3 is no more allowed in the framework of the MSSM. (orig.) [de 10. Diagnostics Systems for Permanent Hall Thrusters Development Science.gov (United States) Ferreira, Jose Leonardo; Soares Ferreira, Ivan; Santos, Jean; Miranda, Rodrigo; Possa, M. Gabriela This work describes the development of Permanent Magnet Hall Effect Plasma Thruster (PHALL) and its diagnostic systems at The Plasma Physics Laboratory of University of Brasilia. The project consists on the construction and characterization of plasma propulsion engines based on the Hall Effect. Electric thrusters have been employed in over 220 successful space missions. Two types stand out: the Hall-Effect Thruster (HET) and the Gridded Ion Engine (GIE). The first, which we deal with in this project, has the advantage of greater simplicity of operation, a smaller weight for the propulsion subsystem and a longer shelf life. It can operate in two configurations: magnetic layer and anode layer, the difference between the two lying in the positioning of the anode inside the plasma channel. A Hall-Effect Thruster-HET is a type of plasma thruster in which the propellant gas is ionized and accelerated by a magneto hydrodynamic effect combined with electrostatic ion acceleration. So the essential operating principle of the HET is that it uses a J x B force and an electrostatic potential to accelerate ions up to high speeds. In a HET, the attractive negative charge is provided by electrons at the open end of the Thruster instead of a grid, as in the case of the electrostatic ion thrusters. A strong radial magnetic field is used to hold the electrons in place, with the combination of the magnetic field and the electrostatic potential force generating a fast circulating electron current, the Hall current, around the axis of the Thruster, mainly composed by drifting electrons in an ion plasma background. Only a slow axial drift towards the anode occurs. The main attractive features of the Hall-Effect Thruster are its simple design and operating principles. Most of the Hall-Effect Thrusters use electromagnet coils to produce the main magnetic field responsible for plasma generation and acceleration. In this paper we present a different new concept, a Permanent Magnet Hall 11. Valley-chiral quantum Hall state in graphene superlattice structure Science.gov (United States) Tian, H. Y.; Tao, W. W.; Wang, J.; Cui, Y. H.; Xu, N.; Huang, B. B.; Luo, G. X.; Hao, Y. H. 2016-05-01 We theoretically investigate the quantum Hall effect in a graphene superlattice (GS) system, in which the two valleys of graphene are coupled together. In the presence of a perpendicular magnetic field, an ordinary quantum Hall effect is found with the sequence σxy=ν e^2/h(ν=0,+/-1,+/-2,\\cdots) . At the zeroth Hall platform, a valley-chiral Hall state stemming from the single K or K' valley is found and it is localized only on one sample boundary contributing to the longitudinal conductance but not to the Hall conductivity. Our findings may shed light on the graphene-based valleytronics applications. 12. Accurate micro Hall effect measurements on scribe line pads DEFF Research Database (Denmark) Østerberg, Frederik Westergaard; Petersen, Dirch Hjorth; Wang, Fei 2009-01-01 Hall mobility and sheet carrier density are important parameters to monitor in advanced semiconductor production. If micro Hall effect measurements are done on small pads in scribe lines, these parameters may be measured without using valuable test wafers. We report how Hall mobility can...... be extracted from micro four-point measurements performed on a rectangular pad. The dimension of the investigated pad is 400 × 430 ¿m2, and the probe pitches range from 20 ¿m to 50 ¿m. The Monte Carlo method is used to find the optimal way to perform the Hall measurement and extract Hall mobility most... 13. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Science.gov (United States) Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C 2018-01-03 When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics. 14. Photonic topological boundary pumping as a probe of 4D quantum Hall physics Science.gov (United States) Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P.; Kraus, Yaacov E.; Rechtsman, Mikael C. 2018-01-01 When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics. 15. L(3)mbt and the LINT complex safeguard cellular identity in the Drosophila ovary. Science.gov (United States) Coux, Rémi-Xavier; Teixeira, Felipe Karam; Lehmann, Ruth 2018-04-04 Maintenance of cellular identity is essential for tissue development and homeostasis. At the molecular level, cell identity is determined by the coordinated activation and repression of defined sets of genes. The tumor suppressor L(3)mbt has been shown to secure cellular identity in Drosophila larval brains by repressing germline-specific genes. Here, we interrogate the temporal and spatial requirements for L(3)mbt in the Drosophila ovary, and show that it safeguards the integrity of both somatic and germline tissues. l(3)mbt mutant ovaries exhibit multiple developmental defects, which we find to be largely caused by the inappropriate expression of a single gene, nanos , a key regulator of germline fate, in the somatic ovarian cells. In the female germline, we find that L(3)mbt represses testis-specific and neuronal genes. At the molecular level, we show that L(3)mbt function in the ovary is mediated through its co-factor Lint-1 but independently of the dREAM complex. Together, our work uncovers a more complex role for L(3)mbt than previously understood and demonstrates that L(3)mbt secures tissue identity by preventing the simultaneous expression of original identity markers and tissue-specific misexpression signatures. © 2018. Published by The Company of Biologists Ltd. 16. Mutations in the Bacterial Ribosomal Protein L3 and Their Association with Antibiotic Resistance Science.gov (United States) Klitgaard, Rasmus N.; Ntokou, Eleni; Nørgaard, Katrine; Biltoft, Daniel; Hansen, Lykke H.; Trædholm, Nicolai M.; Kongsted, Jacob 2015-01-01 Different groups of antibiotics bind to the peptidyl transferase center (PTC) in the large subunit of the bacterial ribosome. Resistance to these groups of antibiotics has often been linked with mutations or methylations of the 23S rRNA. In recent years, there has been a rise in the number of studies where mutations have been found in the ribosomal protein L3 in bacterial strains resistant to PTC-targeting antibiotics but there is often no evidence that these mutations actually confer antibiotic resistance. In this study, a plasmid exchange system was used to replace plasmid-carried wild-type genes with mutated L3 genes in a chromosomal L3 deletion strain. In this way, the essential L3 gene is available for the bacteria while allowing replacement of the wild type with mutated L3 genes. This enables investigation of the effect of single mutations in Escherichia coli without a wild-type L3 background. Ten plasmid-carried mutated L3 genes were constructed, and their effect on growth and antibiotic susceptibility was investigated. Additionally, computational modeling of the impact of L3 mutations in E. coli was used to assess changes in 50S structure and antibiotic binding. All mutations are placed in the loops of L3 near the PTC. Growth data show that 9 of the 10 mutations were well accepted in E. coli, although some of them came with a fitness cost. Only one of the mutants exhibited reduced susceptibility to linezolid, while five exhibited reduced susceptibility to tiamulin. PMID:25845869 17. Giant photonic Hall effect in magnetophotonic crystals. Science.gov (United States) Merzlikin, A M; Vinogradov, A P; Inoue, M; Granovsky, A B 2005-10-01 We have considered a simple, square, two-dimensional (2D) PC built of a magneto-optic matrix with square holes. It is shown that using such a magnetophotonic crystal it is possible to deflect a light beam at very large angles by applying a nonzero external magnetic field. The effect is called the giant photonic Hall effect (GPHE) or the magnetic superprism effect. The GPHE is based on magneto-optical properties, as is the photonic Hall effect [B. A. van Tiggelen and G. L. J. A. Rikken, in, edited by V. M. Shalaev (Springer-Verlag, Berlin, 2002), p. 275]; however GPHE is not caused by asymmetrical light scattering but rather by the influence of an external magnetic field on the photonic band structure. 18. Assessment of elevator rope using Hall Sensor Energy Technology Data Exchange (ETDEWEB) Lee, Jong O; Yoon, Woon Ha; Son, Young Ho; Kim, Jung Woo [Korea Institute of Machinery and Materials, Daejeon (Korea, Republic of); Lee, Jong Ku [Pukyung National University, Pusan (Korea, Republic of) 2003-07-01 Defect detection of wire rope for an elevator was investigated through the measurement of magnetic flux leakage. The types of defect usually found in wire rope categorized such as inner and outer wire breakage and wear. The specimens that has artificial defects were magnetized via permanent magnet, and measurement of magnetic flux leakage on the defects was performed with Hall sensor. In wire broken model, a defect smaller than 0.4 mm and 1 mm in depth on outer and inner wire rope, respectively, could be detected well. In wear model, smaller defect could not be detected clearly, however, appearance of changing of total magnetic flux during magnetic pole of the sensor passing through a defect 0.2 mm in depth at 4 mm or above width could make possible to detect it. From the results, the measurement via Hall sensor might be useful tool for defect detection of wire rope. 19. Assesment of elevator rope using hall sensor Energy Technology Data Exchange (ETDEWEB) Lee, Jong O; Yoon, Woon Ha; Son, Young Ho [Korea Institute of Machinery and Materials, Daejeon (Korea, Republic of); Kim, Jung Woo; Lee, Jong Ku [Pukyong National University, Pusan (Korea, Republic of) 2003-05-15 Defect detection of wire rope for an elevator was investigated through the measurement of magnetic flux leakage. The types of defect usually found in wire rope categorized such as inner and outer wire breakage and wear. The specimens that has artificial defects were magnetized via permanent magnet, and measurement of magnetic flux leakage on the defects was performed with Hall sensor. In wire broken model, a defect smaller than 0.4mm and 1mm in depth on outer and inner wire rope, respectively, could be detected well. In wear model, smaller defect could not be detected clearly, however, appearance of changing of total magnetic flux during magnetic pole of the sensor passing through a defect 0.2mm in depth at 4mm or above width could make possible to detect it. From the results, the measurement via Hall sensor might be useful tool for defect detection of wire rope. 20. Infinite symmetry in the quantum Hall effect Directory of Open Access Journals (Sweden) Lütken C.A. 2014-04-01 Full Text Available The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect. 1. Stuart Hall and Cultural Studies, circa 1983 Directory of Open Access Journals (Sweden) Ann Curthoys 2017-11-01 Full Text Available Stuart Hall sought to internationalise theoretical debates and to create Cultural Studies as interdisciplinary. We chart his theoretical journey through a detailed examination of a series of lectures delivered in 1983 and now published for the first time. In these lectures, he discusses theorists such as E.P. Thompson, Raymond Williams, Louis Althusser, Levi Strauss and Antonio Gramsci, and explores the relationship between ideas and social structure, the specificities of class and race, and the legacies of slavery. We note his turn towards metaphors of divergence and dispersal and highlight how autobiographical and deeply personal Hall is in these lectures, especially in his ego histoire moment of traumatic memory recovery. 2. Hall magnetohydrodynamics: Conservation laws and Lyapunov stability International Nuclear Information System (INIS) Holm, D.D. 1987-01-01 Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions 3. Music hall Markneukirchen; Musikhalle in Markneukirchen Energy Technology Data Exchange (ETDEWEB) Anon. 1996-01-01 The article presents the new building of the music hall Markneukirchen. From the planned use of the building result very high demands on the ventilation system in order to keep to a sound power level of less than 30 dB(A) in the hall. The building services are dealt with using numerous flowsheets and diagrams: Heat supply, ventilation system, sanitary system, building management, instrumentation and control, electric and lighting systems. (BWI) [Deutsch] Der vorliegende Beitrag stellt den Neubau der Musikhalle Markneukirchen vor. Durch das Nutzungskonzept ergeben sich fuer die Einhaltung eines Schalleistungspegels von weniger als 30 dB(A) im Saalbereich an die Lueftungsanlage sehr hohe Ansprueche. Es werden die raumlufttechnischen Anlagen anhand zahlreicher Flussbilder und Abbildungen vorgestellt: Waermeversorgung, Lueftungstechnik, Sanitaertechnik, Gebaeudeleit- und MSR-Technik, Elektro- und Lichttechnik. (BWI) 4. Theory of fractional quantum hall effect International Nuclear Information System (INIS) 1985-08-01 A theory of the Fractional Quantum Hall Effect is constructed based on magnetic flux fractionization, which lead to instability of the system against selfcompression. A theorem is proved stating that arbitrary potentials fail to lift a specific degeneracy of the Landau level. For the case of 1/3 fractional filling a model 3-particles interaction is constructed breaking the symmetry. The rigid 3-particles wave function plays the role of order parameter. In a BCS type of theory the gap in the single particles spectrum is produced by the 3-particles interaction. The mean field critical behaviour and critical parameters are determined as well as the Ginsburg-Landau equation coefficients. The Hall conductivity is calculated from the first principles and its temperature dependence is found. The simultaneous tunnelling of 3,5,7 etc. electrons and quantum interference effects are predicted. (author) 5. Assessment of elevator rope using Hall Sensor International Nuclear Information System (INIS) Lee, Jong O; Yoon, Woon Ha; Son, Young Ho; Kim, Jung Woo; Lee, Jong Ku 2003-01-01 Defect detection of wire rope for an elevator was investigated through the measurement of magnetic flux leakage. The types of defect usually found in wire rope categorized such as inner and outer wire breakage and wear. The specimens that has artificial defects were magnetized via permanent magnet, and measurement of magnetic flux leakage on the defects was performed with Hall sensor. In wire broken model, a defect smaller than 0.4 mm and 1 mm in depth on outer and inner wire rope, respectively, could be detected well. In wear model, smaller defect could not be detected clearly, however, appearance of changing of total magnetic flux during magnetic pole of the sensor passing through a defect 0.2 mm in depth at 4 mm or above width could make possible to detect it. From the results, the measurement via Hall sensor might be useful tool for defect detection of wire rope. 6. Assesment of elevator rope using hall sensor International Nuclear Information System (INIS) Lee, Jong O; Yoon, Woon Ha; Son, Young Ho; Kim, Jung Woo; Lee, Jong Ku 2003-01-01 Defect detection of wire rope for an elevator was investigated through the measurement of magnetic flux leakage. The types of defect usually found in wire rope categorized such as inner and outer wire breakage and wear. The specimens that has artificial defects were magnetized via permanent magnet, and measurement of magnetic flux leakage on the defects was performed with Hall sensor. In wire broken model, a defect smaller than 0.4mm and 1mm in depth on outer and inner wire rope, respectively, could be detected well. In wear model, smaller defect could not be detected clearly, however, appearance of changing of total magnetic flux during magnetic pole of the sensor passing through a defect 0.2mm in depth at 4mm or above width could make possible to detect it. From the results, the measurement via Hall sensor might be useful tool for defect detection of wire rope. 7. Judy Estes Hall (1940-2015). Science.gov (United States) Sammons, Morgan T; Boucher, Andrew 2016-01-01 Presents an obituary for Judy Estes Hall, who passed away on November 24, 2015. Hall served as the Executive Officer of the National Register of Health Service Psychologists until her retirement in 2013. She is a recognized expert in the development of education and training standards for the profession of psychology, she also made significant contributions in the field of international psychology, where she was a renowned expert in cross-national credentialing and an advocate for commonality in licensing standards. She was the coauthor of one edited volume and author of more than 60 journal articles, book chapters, and professional publications. A passionate advocate for the advancement of women in psychology, a devoted mother and grandmother, a connoisseur of wine and international traveler extraordinaire, she touched the personal and professional lives of many. (PsycINFO Database Record (c) 2016 APA, all rights reserved). 8. The behaviour of the L3 muon chambers in a magnetic field International Nuclear Information System (INIS) Onvlee, J. 1989-01-01 L3 is one of the four detectors at LEP. It consists of many parts, each of which measures a specific property of the particles produced in the electron positron collisions. One of the specialities of the L3 detector is the high precision measurement of the momenta of the muons produced in the collisions. In order to curve the muon trajectories the detector is placed in a magnetic field of about 0.5 Tesla. The behaviour of the L3 muon drift chambers in this magnetic field is the main subject of this thesis. (author). 45 refs.; 47 figs.; 12 tabs 9. L3 physics at the Z resonance and a search for the Higgs particle International Nuclear Information System (INIS) Coan, T.A.; Kinnison, W.W.; Kapustinsky, J.; Shukla, J. 1997-01-01 This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory. Electroweak interactions were studied using the L3 Detector on the Large Electron-Positron Collider (LEP) at the European Center for Nuclear Study (CERN). The specific physics studied utilized the Silicon Microvertex Detector (SMD) of L3, which Los Alamos had previously played a major role in proposing, designing, constructing, and commissioning. This detector enabled L3 to investigate short-lived mesons containing b-quarks 10. Results of L3 BGO calorimeter calibration using an RFQ accelerator CERN Document Server Chaturvedi, U K; Gataullin, M; Gratta, Giorgio; Kirkby, D; Lu, W; Newman, H; Shvorob, A V; Tully, C; Zhu, R 2000-01-01 A novel calibration system based on a radiofrequency-quadrupole (RFQ) accelerator has been installed in the L3 experiment. Radiative capture of 1.85 MeV protons from the RFQ accelerator in a lithium target produces a flux of 17.6 MeV photons which are used to calibrate 11000 crystals of the L3 BGO calorimeter. In this paper we present results of the RFQ run taken in November 1997. A calibration precision of 0.6% was reached in the barrel of the L3 BGO calorimeter, and 0.7% in the BGO endcaps. (8 refs). 11. Homotopy arguments for quantized Hall conductivity CERN Document Server Richter, T 2002-01-01 Using the strong localization bounds obtained by the Aizenman-Molcanov method for a particle in a magnetic field and a disordered potential, we show that the zero-temperature Hall conductivity of a gas of such particles is quantized and constant as long as both Fermi energy and disorder coupling parameter vary in a region of strong localization of the corresponding two-dimensional phase diagram. 12. SPS beam to the West Hall CERN Multimedia CERN PhotoLab 1976-01-01 One of the two target stations feeding the West Hall (see Annual Report 1976). After the proton beam was split into three branches, the outer two were directed on to targets in the cast iron shielding box, the centre one passing through the box to another target station downstream. Five different targets could be put in each beam, controlled by the mechanism seen on top. 13. Anomalous hall effect in ferromagnetic semiconductors Czech Academy of Sciences Publication Activity Database Jungwirth, Tomáš; Niu, Q.; MacDonald, A. H. 2002-01-01 Roč. 88, č. 20 (2002), s. 207208-1-207208-4 ISSN 0031-9007 R&D Projects: GA ČR GA202/02/0912; GA MŠk OC P5.10 Institutional research plan: CEZ:AV0Z1010914 Keywords : ferromagnetic semiconductors * anomalous Hall effect Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.323, year: 2002 14. Determination of the Hall Thruster Operating Regimes; TOPICAL International Nuclear Information System (INIS) L. Dorf; V. Semenov; Y. Raitses; N.J. Fisch 2002-01-01 A quasi one-dimensional (1-D) steady-state model of the Hall thruster is presented. For the same discharge voltage two operating regimes are possible - with and without the anode sheath. For given mass flow rate, magnetic field profile and discharge voltage a unique solution can be constructed, assuming that the thruster operates in one of the regimes. However, we show that for a given temperature profile the applied discharge voltage uniquely determines the operating regime: for discharge voltages greater than a certain value, the sheath disappears. That result is obtained over a wide range of incoming neutral velocities, channel lengths and widths, and cathode plane locations. It is also shown that a good correlation between the quasi 1-D model and experimental results can be achieved by selecting an appropriate electron mobility and temperature profile 15. The bremsstrahlung tagged photon beam in Hall B at JLab CERN Document Server Sober, D I; Longhi, A; Matthews, S K; O'Brien, J T; Berman, B L; Briscoe, W J; Cole, P L; Connelly, J P; Dodge, W R; Murphy, L Y; Philips, S A; Dugger, M K; Lawrence, D; Ritchie, B G; Smith, E S; Lambert, J M; Anciant, E; Audit, G; Auger, T; Marchand, C; Klusman, M; Napolitano, J; Khandaker, M A; Salgado, C W; Sarty, A J 2000-01-01 We describe the design and commissioning of the photon tagging beamline installed in experimental Hall B at the Thomas Jefferson National Accelerator Facility (JLab). This system can tag photon energies over a range from 20% to 95% of the incident electron energy, and is capable of operation with beam energies up to 6.1 GeV. A single dipole magnet is combined with a hodoscope containing two planar arrays of plastic scintillators to detect energy-degraded electrons from a thin bremsstrahlung radiator. The first layer of 384 partially overlapping small scintillators provides photon energy resolution, while the second layer of 61 larger scintillators provides the timing resolution necessary to form a coincidence with the corresponding nuclear interaction triggered by the tagged photon. The definitions of overlap channels in the first counter plane and of geometric correlation between the two planes are determined using digitized time information from the individual counters. Auxiliary beamline devices are briefl... 16. Planar Hall effect sensor with magnetostatic compensation layer DEFF Research Database (Denmark) Dalslet, Bjarke Thomas; Donolato, Marco; Hansen, Mikkel Fougt 2012-01-01 Demagnetization effects in cross-shaped planar Hall effect sensors cause inhomogeneous film magnetization and a hysteretic sensor response. Furthermore, when using sensors for detection of magnetic beads, the magnetostatic field from the sensor edges attracts and holds magnetic beads near...... the sensor edges causing inhomogeneous and non-specific binding of the beads. We show theoretically that adding a compensation magnetic stack beneath the sensor stack and exchange-biasing it antiparallel to the sensor stack, the magnetostatic field is minimized. We show experimentally that the compensation...... stack removes nonlinear effects from the sensor response, it strongly reduces hysteresis, and it increases the homogeneity of the bead distribution. Finally, it reduces the non-specific binding due to magnetostatic fields allowing us to completely remove beads from the compensated sensor using a water... 17. Hall Thruster Modeling with a Given Temperature Profile International Nuclear Information System (INIS) Dorf, L.; Semenov, V.; Raitses, Y.; Fisch, N.J. 2002-01-01 A quasi one-dimensional steady-state model of the Hall thruster is presented. For given mass flow rate, magnetic field profile, and discharge voltage the unique solution can be constructed, assuming that the thruster operates in one of the two regimes: with or without the anode sheath. It is shown that for a given temperature profile, the applied discharge voltage uniquely determines the operating regime; for discharge voltages greater than a certain value, the sheath disappears. That result is obtained over a wide range of incoming neutral velocities, channel lengths and widths, and cathode plane locations. A good correlation between the quasi one-dimensional model and experimental results can be achieved by selecting an appropriate temperature profile. We also show how the presented model can be used to obtain a two-dimensional potential distribution 18. Generic superweak chaos induced by Hall effect Science.gov (United States) Ben-Harush, Moti; Dana, Itzhack 2016-05-01 We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems. 19. Josephson tunneling in bilayer quantum Hall system International Nuclear Information System (INIS) Ezawa, Z.F.; Tsitsishvili, G.; Sawada, A. 2012-01-01 A Bose–Einstein condensation is formed by composite bosons in the quantum Hall state. A composite boson carries the fundamental charge (−e). We investigate Josephson tunneling of such charges in the bilayer quantum Hall system at the total filling ν=1. We show the existence of the critical current for the tunneling current to be coherent and dissipationless. Our results explain recent experiments due to [L. Tiemann, Y. Yoon, W. Dietsche, K. von Klitzing, W. Wegscheider, Phys. Rev. B 80 (2009) 165120] and due to [Y. Yoon, L. Tiemann, S. Schmult, W. Dietsche, K. von Klitzing, Phys. Rev. Lett. 104 (2010) 116802]. We predict also how the critical current changes as the sample is tilted in the magnetic field. -- Highlights: ► Composite bosons undergo Bose–Einstein condensation to form the bilayer quantum Hall state. ► A composite boson is a single electron bound to a flux quantum and carries one unit charge. ► Quantum coherence develops due to the condensation. ► Quantum coherence drives the supercurrent in each layer and the tunneling current. ► There exists the critical input current so that the tunneling current is coherent and dissipationless. Science.gov (United States) Talsania, Mitali; Sharma, Rohan; Sughrue, Michael E; Scofield, R Hal; Lim, Jonea 2017-10-01 1. EX1004L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX1004L3: Exploration Indonesia - Bitung... 2. EX0909L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX0909L3: Mapping Field Trials - Hawaiian... 3. EX1502L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX1502L3: Caribbean Exploration (ROV)... 4. EX1605L3 Dive02 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 5. EX1504L3 Dive07 Ancillary Data Collection including reports, kmls, spreadsheets, images and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1504L3: CAPSTONE Leg III:... 6. EX1605L3 Dive07 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 7. EX1605L3 Dive05 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 8. EX1504L3 Dive06 Ancillary Data Collection including reports, kmls, spreadsheets, images and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1504L3: CAPSTONE Leg III:... 9. EX1605L3 Dive19 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 10. EX1504L3 Dive02 Ancillary Data Collection including reports, kmls, spreadsheets, images and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1504L3: CAPSTONE Leg III:... 11. TES/Aura L3 H2O Monthly Gridded V004 Data.gov (United States) National Aeronautics and Space Administration — The TES Aura L3 H2O data consist of daily atmospheric temperature and VMR for the atmospheric species. Data are provided at 2 degree latitude X 4 degree longitude... 12. EX1402L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX1402L3: Gulf of Mexico Mapping and ROV... 13. EX1504L3 Dive04 Ancillary Data Collection including reports, kmls, spreadsheets, images and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1504L3: CAPSTONE Leg III:... 14. EX1605L3 Dive12 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 15. A lead-scintillating fiber calorimeter to increase L3 hermeticity CERN Document Server Basti, G 1997-01-01 A lead-scintillating fiber calorimeter has been built to fill the gap between endcap and barrel of the L3 BGO electromagnetic calorimeter. We report details of the construction, as well as results from test-beam and simulation. 16. EX1202L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX1202L3: Gulf of Mexico Exploration... 17. EX1605L3 Dive01 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 18. EX1605L3 Dive13 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 19. EX1605L3 Dive20 Ancillary Data Collection including reports, kmls, spreadsheets, and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1605L3: CAPSTONE CNMI &... 20. EX1504L3 Water Column Summary Report and Profile Data Collection Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — A complete set of water column profile data and CTD Summary Report (if generated) generated by the Okeanos Explorer during EX1504L3: CAPSTONE Leg III: Main Hawaiian... 1. EX1504L3 Dive03 Ancillary Data Collection including reports, kmls, spreadsheets, images and data Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — Standard suite of ancillary data files generated through a scripting process following an ROV dive on NOAA Ship Okeanos Explorer during EX1504L3: CAPSTONE Leg III:... 2. Magnetotransport properties of Ni-Mn-In Heusler Alloys: Giant Hall angle Energy Technology Data Exchange (ETDEWEB) Dubenko, I; Pathak, A K; Ali, N [Department of Physics, Southern Illinois University, Carbondale, IL 62901 (United States); Kovarskii, Y A; Prudnikov, V N; Perov, N S; Granovsky, A B, E-mail: [email protected] [Faculty of Physics, Moscow State University, Moscow, 111991 (Russian Federation) 2010-01-01 We report experimental results on phase transitions, magnetic properties, resistivity, and Hall effect in Ni{sub 50}Mn{sub 50-x}In{sub x} (15Hall resistivity {rho}{sub H}(at H = 15 kOe) is positive in martensitic and negative in austenitic phase, sharply increases in the vicinity of T{sub M} up to {rho}{sub H}(15 kOe)= 50 {mu}{Omega}{center_dot}cm. This value is almost two orders of magnitude larger than that observed at high temperature (T{approx}200 K) for any common magnetic materials, and comparable to the giant Hall effect resistivity in magnetic nanogranular alloys. The Hall angle {Theta}{sub H}=tan{sup -} {sup 1}({rho}{sub H}/{rho}) close to T{sub M} reaches tan{sup -1}(0.5) which is the highest value for known magnetic materials. 3. A simulation Model of the Reactor Hall Ventilation and air Conditioning Systems of ETRR-2 International Nuclear Information System (INIS) Abd El-Rahman, M.F. 2004-01-01 Although the conceptual design for any system differs from one designer to another. each of them aims to achieve the function of the system required. the ventilation and air conditioning system of reactors hall is one of those systems that really differs but always dose its function for which it is designed. thus, ventilation and air conditioning in some reactor hall constitute only one system whereas in some other ones, they are separate systems. the Egypt Research Reactor-2 (ETRR-2)represents the second type. most studies conducted on ventilation and air conditioning simulation models either in traditional building or for research rectors show that those models were not designed similarly to the model of the hall of ETRR-2 in which ventilation and air conditioning constitute two separate systems.besides, those studies experimented on ventilation and air conditioning simulation models of reactor building predict the temperature and humidity inside these buildings at certain outside condition and it is difficult to predict when the outside conditions are changed . also those studies do not discuss the influences of reactor power changes. therefore, the present work deals with a computational study backed by infield experimental measurements of the performance of the ventilation and air conditioning systems of reactor hall during normal operation at different outside conditions as well as at different levels of reactor power 4. A constricted quantum Hall system as a beam-splitter: understanding ballistic transport on the edge International Nuclear Information System (INIS) Lal, Siddhartha 2007-09-01 We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer- Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction(ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1. (author) 5. Commemorative Symposium on the Hall Effect and its Applications CERN Document Server Westgate, C 1980-01-01 In 1879, while a graduate student under Henry Rowland at the Physics Department of The Johns Hopkins University, Edwin Herbert Hall discovered what is now universally known as the Hall effect. A symposium was held at The Johns Hopkins University on November 13, 1979 to commemorate the lOOth anniversary of the discovery. Over 170 participants attended the symposium which included eleven in­ vited lectures and three speeches during the luncheon. During the past one hundred years, we have witnessed ever ex­ panding activities in the field of the Hall effect. The Hall effect is now an indispensable tool in the studies of many branches of condensed matter physics, especially in metals, semiconductors, and magnetic solids. Various components (over 200 million!) that utilize the Hall effect have been successfully incorporated into such devices as keyboards, automobile ignitions, gaussmeters, and satellites. This volume attempts to capture the important aspects of the Hall effect and its applications. It includes t... 6. Space Charge Saturated Sheath Regime and Electron Temperature Saturation in Hall Thrusters International Nuclear Information System (INIS) Raitses, Y.; Staack, D.; Smirnov, A.; Fisch, N.J. 2005-01-01 Secondary electron emission in Hall thrusters is predicted to lead to space charge saturated wall sheaths resulting in enhanced power losses in the thruster channel. Analysis of experimentally obtained electron-wall collision frequency suggests that the electron temperature saturation, which occurs at high discharge voltages, appears to be caused by a decrease of the Joule heating rather than by the enhancement of the electron energy loss at the walls due to a strong secondary electron emission 7. Scattering Effect on Anomalous Hall Effect in Ferromagnetic Transition Metals KAUST Repository Zhang, Qiang 2017-11-30 The anomalous Hall effect (AHE) has been discovered for over a century, but its origin is still highly controversial theoretically and experimentally. In this study, we investigated the scattering effect on the AHE for both exploring the underlying physics and technical applications. We prepared Cox(MgO)100-x granular thin films with different Co volume fraction (34≤≤100) and studied the interfacial scattering effect on the AHE. The STEM HAADF images confirmed the inhomogeneous granular structure of the samples. As decreases from 100 to 34, the values of longitudinal resistivity () and anomalous Hall resistivity (AHE) respectively increase by about four and three orders in magnitude. The linear scaling relation between the anomalous Hall coefficient () and the measured at 5 K holds in both the as-prepared and annealed samples, which suggests a skew scattering dominated mechanism in Cox(MgO)100-x granular thin films. We prepared (Fe36//Au12/), (Ni36//Au12/) and (Ta12//Fe36/) multilayers to study the interfacial scattering effect on the AHE. The multilayer structures were characterized by the XRR spectra and TEM images of cross-sections. For the three serials of multilayers, both the and AHE increase with , which clearly shows interfacial scattering effect. The intrinsic contribution decreases with increases in the three serials of samples, which may be due to the crystallinity decaying or the finite size effect. In the (Fe36//Au12/) samples, the side-jump contribution increases with , which suggests an interfacial scattering-enhanced side jump. In the (Ni36//Au12/) samples, the side-jump contribution decreases with increases, which could be explained by the opposite sign of the interfacial scattering and grain boundary scattering contributed side jump. In the (Ta12//Fe36/) multilayers, the side-jump contribution changed from negative to positive, which is also because of the opposite sign of the interfacial scattering and grain boundary scattering 8. Hall Sensor Output Signal Fault-Detection & Safety Implementation Logic Directory of Open Access Journals (Sweden) Lee SangHun 2016-01-01 Full Text Available Recently BLDC motors have been popular in various industrial applications and electric mobility. Recently BLDC motors have been popular in various industrial applications and electric mobility. In most brushless direct current (BLDC motor drives, there are three hall sensors as a position reference. Low resolution hall effect sensor is popularly used to estimate the rotor position because of its good comprehensive performance such as low cost, high reliability and sufficient precision. Various possible faults may happen in a hall effect sensor. This paper presents a fault-tolerant operation method that allows the control of a BLDC motor with one faulty hall sensor and presents the hall sensor output fault-tolerant control strategy. The situations considered are when the output from a hall sensor stays continuously at low or high levels, or a short-time pulse appears on a hall sensor signal. For fault detection, identification of a faulty signal and generating a substitute signal, this method only needs the information from the hall sensors. There are a few research work on hall effect sensor failure of BLDC motor. The conventional fault diagnosis methods are signal analysis, model based analysis and knowledge based analysis. The proposed method is signal based analysis using a compensation signal for reconfiguration and therefore fault diagnosis can be fast. The proposed method is validated to execute the simulation using PSIM. 9. The Hall module of an exact category with duality OpenAIRE Young, Matthew B. 2012-01-01 We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced sigma-analogue of the quantum Kac-Moody algebra attached to the quiver. For finite type quivers, we explicitly determin... 10. Multi-analysis and modeling of asymmetry offset for Hall effect structures Energy Technology Data Exchange (ETDEWEB) Paun, Maria-Alexandra, E-mail: [email protected] 2017-03-15 The topological (asymmetry) offset voltage of CMOS cross-like Hall cells is analyzed in this paper. In order to attain the stated objective, different approaches have been considered. Both circuit and three-dimensional models have been developed. Variation of the misalignment offset with the biasing current has been studied through physical and circuit models. The latter is a non-homogenous finite elements model, which relies on using parameterized resistances and current-controlled current sources, of CMOS Hall cells. The displacement offset for various asymmetries and the offset variation with the temperature were investigated through the circuit model developed. Various experimental results for the single and magnetic equivalent offset have also been provided. - Highlights: • In this paper both physical and circuit models have been proposed for the evaluation of Hall cells offset. • Variation of the misalignment offset with the biasing current has been studied. • The displacement offset for various asymmetries and the offset variation with the temperature were investigated. • Various experimental results for single and magnetic equivalent offset were provided. • The obtained simulation results are in accordance with the experimental data. 11. Anomalous field dependence of the Hall coefficient in disordered metals International Nuclear Information System (INIS) 1988-01-01 We report on a comprehensive study of the Hall coefficient, R/sub H/, in disordered three-dimensional In 2 O/sub 3-//sub x/ films as a function of the magnetic field strength, temperature, and degree of spatial disorder. Our main result is that, at sufficiently small fields, R/sub H/ is virtually temperature, field, and disorder independent, even at the metal-insulator transition itself. On the other hand, at the limit of strong magnetic fields, R/sub H/ has an explicit temperature dependence, in apparent agreement with the prediction of Al'tshuler, Aronov, and Lee. For intermediate values of fields, R/sub H/ is field and temperature dependent. It is also shown that the behavior of the conductivity as a function of temperature, σ(T), at small fields, is qualitatively different than that measured at the limit of strong magnetic fields. The low- and high-field regimes seem to correlate with the respective regimes in terms of the Hall-coefficient behavior. It is suggested that the magnetotransport in the high-field limit is considerably influenced by Coulomb-correlation effects. However, in the low-field regime, where both correlations and weak-localization effects are, presumably, equally important (and where both theories are the more likely to be valid), is problematic; neither R/sub H/ nor σ(T) gives any unambiguous evidence to the existence of interaction effects. This problem is discussed in light of the experimental results pertaining to the behavior of R/sub H/(T) in two-dimensional In 2 O/sub 3-//sub x/ films as well as in other disordered systems 12. DESIGN OF SUBSOIL IMPROVEMENT BELOW HALL FLOORS Directory of Open Access Journals (Sweden) Peter Turček 2017-10-01 Full Text Available The construction of an industrial park is now being prepared near the town of Nitra. The investor fixed very strict conditions for the bearing capacity and, above all, the settlement of halls and their floors. The geological conditions at the construction site are difficult: there are soft clay soils with high compressibility and low bearing capacity. A detailed analysis of soil improvement was made. Stone columns were prepared to be fitted into an approximately 5 m thick layer of soft clay. The paper shows the main steps used in the design of the stone columns. 13. Optically induced Hall effect in semiconductors Energy Technology Data Exchange (ETDEWEB) Idrish Miah, M; Gray, E Mac A, E-mail: [email protected] [Nanoscale Science and Technology Centre, Griffith University, Nathan, Brisbane, QLD 4111 (Australia) 2009-03-01 We describe an experiment which investigates the effect of a longitudinal electric field on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a Hall voltage resulting from nonequilibrium magnetization induced by the spin-carrier electrons accumulating at the transverse boundaries of the sample as a result of asymmetries in scattering for spin-up and spin-down electrons in the presence of spin-orbit interaction. It is found that the effect depends on the longitudinal electric field and doping density as well as on temperature. The results are presented by discussing the dominant spin relaxation mechanisms in semiconductors. 14. Fractional quantization and the quantum hall effect International Nuclear Information System (INIS) Guerrero, J.; Calixto, M.; Aldaya, V. 1998-01-01 Quantization with constrains is considered in a group-theoretical framework, providing a precise characterization of the set of good operators, i.e., those preserving the constrained Hilbert space, in terms of the representation of the subgroup of constraints. This machinery is applied to the quantization of the torus as symplectic manifold, obtaining that fractional quantum numbers are permitted, provided that we allow for vector valued representations. The good operators turn out to be the Wilson loops and, for certain representations of the subgroup of constraints, the modular transformations. These results are applied to the Fractional Quantum Hall Effect, where interesting implications are derived 15. Excitons in the Fractional Quantum Hall Effect Science.gov (United States) Laughlin, R. B. 1984-09-01 Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean. 16. The fractional quantum Hall effect goes organic International Nuclear Information System (INIS) Smet, Jurgen 2000-01-01 Physicists have been fascinated by the behaviour of two-dimensional electron gases for the past two decades. All of these experiments were performed on inorganic semiconductor devices, most of them based on gallium arsenide. Indeed, until recently it was thought that the subtle effects that arise due to electron-electron interactions in these devices required levels of purity that could not be achieved in other material systems. However, Hendrik Schoen, Christian Kloc and Bertram Batlogg of Bell Laboratories in the US have now observed the fractional quantum Hall effect - the most dramatic signature of electron-electron interactions - in two organic semiconductors. (U.K.) 17. A Compton polarimeter for CEBAF Hall A Energy Technology Data Exchange (ETDEWEB) Bardin, G; Cavata, C; Frois, B; Juillard, M; Kerhoas, S; Languillat, J C; Legoff, J M; Mangeot, P; Martino, J; Platchkov, S; Rebourgeard, P; Vernin, P; Veyssiere, C; CEBAF Hall A Collaboration 1994-09-01 The physic program at CEBAF Hall A includes several experiments using 4 GeV polarized electron beam: parity violation in electron elastic scattering from proton and {sup 4}He, electric form factor of the proton by recoil polarization, neutron spin structure function at low Q{sup 2}. Some of these experiments will need beam polarization measurement and monitoring with an accuracy close to 4%, for beam currents ranging from 100 nA to 100 microA. A project of a Compton Polarimeter that will meet these requirements is presented. It will comprise four dipoles and a symmetric cavity consisting of two identical mirrors. 1 fig., 10 refs. 18. Hall conductivity for two dimensional magnetic systems International Nuclear Information System (INIS) Desbois, J.; Ouvry, S.; Texier, C. 1996-01-01 A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). (author) 19. Antigenicity of Anisakis simplex s.s. L3 in parasitized fish after heating conditions used in the canning processing. Science.gov (United States) Tejada, Margarita; Olivares, Fabiola; de las Heras, Cristina; Careche, Mercedes; Solas, María Teresa; García, María Luisa; Fernandez, Agustín; Mendizábal, Angel; Navas, Alfonso; Rodríguez-Mahillo, Ana Isabel; González-Muñoz, Miguel 2015-03-30 Some technological and food processing treatments applied to parasitized fish kill the Anisakis larvae and prevent infection and sensitization of consumers. However, residual allergenic activity of parasite allergens has been shown. The aim here was to study the effect of different heat treatments used in the fish canning processing industry on the antigen recognition of Anisakis L3. Bigeye tuna (Thunnus obesus) and yellowfin tuna (Thunnus albacares) were experimentally infected with live L3 Anisakis. After 48 h at 5 ± 1 °C, brine was added to the muscle, which was then canned raw (live larvae) or heated (90 °C, 30 min) (dead larvae) and treated at 113 °C for 60 min or at 115 °C for 90 min. Anisakis antigens and Ani s 4 were detected with anti-crude extract and anti-Ani s 4 antisera respectively. Ani s 4 decreased in all lots, but the muscle retained part of the allergenicity irrespective of the canning method, as observed by immunohistochemistry. Dot blot analysis showed a high loss of Ani s 4 recognition after canning, but residual antigenicity was present. The results indicate that heat treatment for sterilization under the conditions studied produces a decrease in Ani s 4 and suggest a potential exposure risk for Anisakis-sensitized patients. © 2014 Society of Chemical Industry. 20. The Impact of a Health Campaign on Hand Hygiene and Upper Respiratory Illness among College Students Living in Residence Halls. Science.gov (United States) White, Cindy; Kolble, Robin; Carlson, Rebecca; Lipson, Natasha 2005-01-01 Hand hygiene is a key element in preventing the transmission of cold and flu viruses. The authors conducted an experimental-control design study in 4 campus residence halls to determine whether a message campaign about hand hygiene and the availability of gel hand sanitizer could decrease cold and flu illness and school and work absenteeism. Their… 1. Extended fenske-hall calculation of inner-shell binding energies using ( Z + 1)-bazis sets: Sulfur-containing molecules Science.gov (United States) Zwanziger, Ch.; Zwanziger, H.; Szargan, R.; Reinhold, J. 1981-08-01 It is shown that the S1s and S2p binding energies and their chemical shifts in the molecules H 2S, SO 2, SF 6 and COS obtained with hole-state calculations using an extended Fenske-Hall method are in good agreement with experimental values if mixed ( Z + 1)-basis sets are applied. 2. Equivalence of donor and acceptor fits of temperature dependent Hall carrier density and Hall mobility data: Case of ZnO International Nuclear Information System (INIS) Brochen, Stéphane; Feuillet, Guy; Pernot, Julien 2014-01-01 In this work, statistical formulations of the temperature dependence of ionized and neutral impurity concentrations in a semiconductor, needed in the charge balance equation and for carrier scattering calculations, have been developed. These formulations have been used in order to elucidate a confusing situation, appearing when compensating acceptor (donor) levels are located sufficiently close to the conduction (valence) band to be thermally ionized and thereby to emit (capture) an electron to (from) the conduction (valence) band. In this work, the temperature dependent Hall carrier density and Hall mobility data adjustments are performed in an attempt to distinguish the presence of a deep acceptor or a deep donor level, coexisting with a shallower donor level and located near the conduction band. Unfortunately, the present statistical developments, applied to an n-type hydrothermal ZnO sample, lead in both cases to consistent descriptions of experimental Hall carrier density and mobility data and thus do not allow to determine the nature, donor or acceptor, of the deep level. This demonstration shows that the emission of an electron in the conduction band, generally assigned to a (0/+1) donor transition from a donor level cannot be applied systematically and could also be attributed to a (−1/0) donor transition from an acceptor level. More generally, this result can be extended for any semiconductor and also for deep donor levels located close to the valence band (acceptor transition) 3. Development and characterization of high-efficiency, high-specific impulse xenon Hall thrusters Science.gov (United States) Hofer, Richard Robert This dissertation presents research aimed at extending the efficient operation of 1600 s specific impulse Hall thruster technology to the 2000--3000 s range. While recent studies of commercially developed Hall thrusters demonstrated greater than 4000 s specific impulse, maximum efficiency occurred at less than 3000 s. It was hypothesized that the efficiency maximum resulted as a consequence of modern magnetic field designs, optimized for 1600 s, which were unsuitable at high-specific impulse. Motivated by the industry efforts and mission studies, the aim of this research was to develop and characterize xenon Hall thrusters capable of both high-specific impulse and high-efficiency operation. The research divided into development and characterization phases. During the development phase, the laboratory-model NASA-173M Hall thrusters were designed with plasma lens magnetic field topographies and their performance and plasma characteristics were evaluated. Experiments with the NASA-173M version 1 (v1) validated the plasma lens design by showing how changing the magnetic field topography at high-specific impulse improved efficiency. Experiments with the NASA-173M version 2 (v2) showed there was a minimum current density and optimum magnetic field topography at which efficiency monotonically increased with voltage. Between 300--1000 V, total specific impulse and total efficiency of the NASA-173Mv2 operating at 10 mg/s ranged from 1600--3400 s and 51--61%, respectively. Comparison of the thrusters showed that efficiency can be optimized for specific impulse by varying the plasma lens design. During the characterization phase, additional plasma properties of the NASA-173Mv2 were measured and a performance model was derived accounting for a multiply-charged, partially-ionized plasma. Results from the model based on experimental data showed how efficient operation at high-specific impulse was enabled through regulation of the electron current with the magnetic field. The 4. Some applications of the field theory to condensed matter physics: the different sides of the quantum Hall effect International Nuclear Information System (INIS) Chandelier, F. 2003-12-01 The quantum Hall effect appears in low temperature electron systems submitted to intense magnetic fields. Electrons are trapped in a thin layer (∼ 100.10 -8 cm thick) at the interface between 2 semiconductors or between a semiconductor and an insulating material. This thesis presents 3 personal contributions to the physics of plane systems and particularly to quantum Hall effect systems. The first contribution is a topological approach, it involves the study of Landau's problem in a geometry nearing that of Hall effect experiments. A mathematical formalism has been defined and by using the Kubo's formula, the quantification of the Hall conductivity can be linked to the Chern class of threaded holes. The second contribution represents a phenomenological approach based on dual symmetries and particularly on modular symmetries. This contribution uses visibility diagrams that have already produced right predictions concerning resistivity curves or band structures. The introduction of a physical equivalence has allowed us to build a phase diagram for the quantum Hall effect at zero temperature. This phase diagram agrees with the experimental facts concerning : -) the existence of 2 insulating phases, -) direct transitions between an insulating phase and any Hall phase through integer or fractionary values of the filling factor (ν), -) selection rules, and -) classification of the Hall states and their distribution around a metal state. The third contribution concerns another phenomenological approach based on duality symmetries. We have considered a class of (2+1)-dimensional effective models with a Maxwell-Chern-Simons part that includes a non-locality. This non-locality implies the existence of a hidden duality symmetry with a Z 2 component: z → 1/z. This symmetry has allowed us to meet the results of the Fisher's law concerning the components of the resistivity tensor. (A.C.) 5. Measurement of the masses of the electroweak gauge bosons at L3; Bestimmung der Massen der elektroschwachen Eichbosonen bei L3 Energy Technology Data Exchange (ETDEWEB) Rosenbleck, C. 2006-10-09 This thesis presents the measurement of the masses of the carriers of the weak force in the Standard Model of Particle Physics, the gauge bosons W and Z. The masses are determined using the kinematics of the bosons' decay products. The data were collected by the L3 experiment at the Large Electron Positron Collider (LEP) at centre-of-mass energies, {radical}(s), between 183 GeV and 209 GeV in the years 1997 to 2000. The Z-boson mass is determined to be m{sub Z}=91.272{+-}0.046 GeV. The second part of this analysis describes the measurement of the mass of the W-boson. The W-boson mass is determined to be m{sub W}=80.242{+-}0.057 GeV in this analysis. If combined with the L3 results at lower centre-of-mass energies, the final W boson mass value is m{sub W}=80.270{+-}0.055 GeV. The {rho} parameter is defined as {rho}=m{sup 2}{sub W}/(m{sup 2}{sub Z} . cos{sup 2} {theta}{sub W}). Using the value of m{sub Z} obtained in the Z resonance scan, the final value for m{sub W} and the value of {theta}{sub W}, {rho} is obtained to be {rho}=0.9937{+-}0.0024, yielding a 2.6{sigma} deviation from 1. Combining the L3 value for m{sub W} with the results of the LEP experiments ALEPH, DELPHI, and OPAL and the TEVATRON experiments CDF and DOe yields a W boson mass of m{sub W}=80.392{+-}0.029 GeV. Together with other measurements this determines the best value of the Higgs-boson mass to be m{sub H}=85{sub -28}{sup +39} GeV. (orig.) 6. Asymmetric light transmission based on coupling between photonic crystal waveguides and L1/L3 cavity Science.gov (United States) Zhang, Jinqiannan; Chai, Hongyu; Yu, Zhongyuan; Cheng, Xiang; Ye, Han; Liu, Yumin 2017-09-01 A compact design of all-optical diode with mode conversion function based on a two-dimensional photonic crystal waveguide and an L1 or L3 cavity is theoretically investigated. The proposed photonic crystal structures comprise a triangular arrangement of air holes embedded in a silicon substrate. Asymmetric light propagation is achieved via the spatial mode match/mismatch in the coupling region. The simulations show that at each cavity's resonance frequency, the transmission efficiency of the structure with the L1 and L3 cavities reach 79% and 73%, while the corresponding unidirectionalities are 46 and 37 dB, respectively. The functional frequency can be controlled by simply adjusting the radii of specific air holes in the L1 and L3 cavities. The proposed structure can be used as a frequency filter, a beam splitter and has potential applications in all-optical integrated circuits. 7. Cylindrical Hall Thrusters with Permanent Magnets International Nuclear Information System (INIS) Raitses, Yevgeny; Merino, Enrique; Fisch, Nathaniel J. 2010-01-01 The use of permanent magnets instead of electromagnet coils for low power Hall thrusters can offer a significant reduction of both the total electric power consumption and the thruster mass. Two permanent magnet versions of the miniaturized cylindrical Hall thruster (CHT) of different overall dimensions were operated in the power range of 50W-300 W. The discharge and plasma plume measurements revealed that the CHT thrusters with permanent magnets and electromagnet coils operate rather differently. In particular, the angular ion current density distribution from the permanent magnet thrusters has an unusual halo shape, with a majority of high energy ions flowing at large angles with respect to the thruster centerline. Differences in the magnetic field topology outside the thruster channel and in the vicinity of the channel exit are likely responsible for the differences in the plume characteristics measured for the CHTs with electromagnets and permanent magnets. It is shown that the presence of the reversing-direction or cusp-type magnetic field configuration inside the thruster channel without a strong axial magnetic field outside the thruster channel does not lead to the halo plasma plume from the CHT. 8. Bimetric Theory of Fractional Quantum Hall States Directory of Open Access Journals (Sweden) Andrey Gromov 2017-11-01 Full Text Available We present a bimetric low-energy effective theory of fractional quantum Hall (FQH states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k^{6} order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism. 9. Bimetric Theory of Fractional Quantum Hall States Science.gov (United States) Gromov, Andrey; Son, Dam Thanh 2017-10-01 We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP) mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k6 order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH) transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism. 10. Repurposing the Caltech Robinson Hall Coelostat Science.gov (United States) Treffers, Richard R.; Loisos, G.; Ubbelohde, M.; Douglas, S.; Martinez, M. 2013-01-01 We describe the repurposing of the historic coelostat atop Caltech’s Robinson Hall for building lighting, public education and scientific research. The coelostat was originally part of George Ellery Hale’s vision of the Astrophysical Laboratory on the Caltech campus in 1932. The coelostat, designed by Russell Porter, has a 36 inch diameter primary mirror a 30 inch diameter secondary mirror and provides a 24 inch un-vignetted beam of sunlight into the building. Although constructed in the 1930s, due to wartime pressures and other projects, it was used only briefly in the 1970s and never fully realized. Recently Robinson Hall has been fully renovated to house the Ronald and Maxine Linde Center for Global Environmental Science. The coelostat operation was modernized replacing the old motors and automating all the motions. Each morning, if the weather cooperates, the dome slit opens, the mirrors configured and sunlight pours into the building. The beam of sunlight is divided into three parts. One part goes into a refracting telescope which projects a ten inch diameter of the sun onto a ground glass screen visible to the public. A second fraction is distributed to fiber optic fixtures that illuminate some of the basement rooms. The final fraction goes into two laboratories where it is used in experiments monitoring trace constituents of our atmosphere and for solar catalysis experiments. The instrument as originally conceived required at least two human operators. Now it is fully automatic and doing real science 11. Undulator Hall Air Temperature Fault Scenarios International Nuclear Information System (INIS) Sevilla, J. 2010-01-01 Recent experience indicates that the LCLS undulator segments must not, at any time following tuning, be allowed to change temperature by more than about ±2.5 C or the magnetic center will irreversibly shift outside of acceptable tolerances. This vulnerability raises a concern that under fault conditions the ambient temperature in the Undulator Hall might go outside of the safe range and potentially could require removal and retuning of all the segments. In this note we estimate changes that can be expected in the Undulator Hall air temperature for three fault scenarios: (1) System-wide power failure; (2) Heating Ventilation and Air Conditioning (HVAC) system shutdown; and (3) HVAC system temperature regulation fault. We find that for either a system-wide power failure or an HVAC system shutdown (with the technical equipment left on), the short-term temperature changes of the air would be modest due to the ability of the walls and floor to act as a heat ballast. No action would be needed to protect the undulator system in the event of a system-wide power failure. Some action to adjust the heat balance, in the case of the HVAC power failure with the equipment left on, might be desirable but is not required. On the other hand, a temperature regulation failure of the HVAC system can quickly cause large excursions in air temperature and prompt action would be required to avoid damage to the undulator system. 12. Benchmark experiments on neutron streaming through JET Torus Hall penetrations Science.gov (United States) Batistoni, P.; Conroy, S.; Lilley, S.; Naish, J.; Obryk, B.; Popovichev, S.; Stamatelatos, I.; Syme, B.; Vasilopoulou, T.; contributors, JET 2015-05-01 Neutronics experiments are performed at JET for validating in a real fusion environment the neutronics codes and nuclear data applied in ITER nuclear analyses. In particular, the neutron fluence through the penetrations of the JET torus hall is measured and compared with calculations to assess the capability of state-of-art numerical tools to correctly predict the radiation streaming in the ITER biological shield penetrations up to large distances from the neutron source, in large and complex geometries. Neutron streaming experiments started in 2012 when several hundreds of very sensitive thermo-luminescence detectors (TLDs), enriched to different levels in 6LiF/7LiF, were used to measure the neutron and gamma dose separately. Lessons learnt from this first experiment led to significant improvements in the experimental arrangements to reduce the effects due to directional neutron source and self-shielding of TLDs. Here we report the results of measurements performed during the 2013-2014 JET campaign. Data from new positions, at further locations in the South West labyrinth and down to the Torus Hall basement through the air duct chimney, were obtained up to about a 40 m distance from the plasma neutron source. In order to avoid interference between TLDs due to self-shielding effects, only TLDs containing natural Lithium and 99.97% 7Li were used. All TLDs were located in the centre of large polyethylene (PE) moderators, with natLi and 7Li crystals evenly arranged within two PE containers, one in horizontal and the other in vertical orientation, to investigate the shadowing effect in the directional neutron field. All TLDs were calibrated in the quantities of air kerma and neutron fluence. This improved experimental arrangement led to reduced statistical spread in the experimental data. The Monte Carlo N-Particle (MCNP) code was used to calculate the air kerma due to neutrons and the neutron fluence at detector positions, using a JET model validated up to the 13. STAR-CCM+ (CFD) Calculations and Validation L3:VVI.H2L.P15.02 Energy Technology Data Exchange (ETDEWEB) Gilkey, Lindsay [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) 2017-09-05 This milestone presents a demonstration of the High-to-Low (Hi2Lo) process in the VVI focus area. Validation and additional calculations with the commercial computational fluid dynamics code, STAR-CCM+, were performed using a 5x5 fuel assembly with non-mixing geometry and spacer grids. This geometry was based on the benchmark experiment provided by Westinghouse. Results from the simulations were compared to existing experimental data and to the subchannel thermal-hydraulics code COBRA-TF (CTF). An uncertainty quantification (UQ) process was developed for the STAR-CCM+ model and results of the STAR UQ were communicated to CTF. Results from STAR-CCM+ simulations were used as experimental design points in CTF to calibrate the mixing parameter β and compared to results obtained using experimental data points. This demonstrated that CTF’s β parameter can be calibrated to match existing experimental data more closely. The Hi2Lo process for the STAR-CCM+/CTF code coupling was documented in this milestone and closely linked L3:VVI.H2LP15.01 milestone report. 14. The second level trigger of the L3 experiment. Pt. 1 International Nuclear Information System (INIS) Bertsch, Y.; Blaising, J.J.; Bonnefon, H.; Chollet-Le Flour, F.; Degre, A.; Dromby, G.; Lecoq, J.; Morand, R.; Moynot, M.; Perrot, G.; Riccadonna, X. 1993-07-01 The second level trigger of the L3 experiment performs online background rejection and reduces the first level trigger rate to a value fitting with the third level trigger processing capability. Designed around a set of 3 bit-slice XOP microprocessors, it can process up to 500 first level triggers per second without significant dead time in the data acquisition. The system described here ensures the L3 data taking since the beginning of LEP in July 1989 and the online rejection since 1990. (authors). 24 refs., 8 figs., 3 tabs 15. Safety analysis report for packaging (onsite) L3-181 N basin cask International Nuclear Information System (INIS) 1996-01-01 Purpose of this Safety Analysis Report (SARP) is to authorize the onsite transfer of a Type B, Fissile Excepted, non-highway route controlled quantity in the L3-181 packaging from the N Basin to a storage/disposal facility within 200 West Area. This SARP provides the evaluation necessary to demonstrate that the L3-181 meets the requirements of the 'Hazardous Material Packaging and Shipping', WHC- CM-2-14, by meeting the applicable performance requirements for normal conditions of transport 16. Experimental Test of the Spin Mixing Interface Conductivity Concept NARCIS (Netherlands) Weiler, M.; Althammer, M.; Schreier, M.; Lotze, J.; Pernpeintner, M.; Meyer, S.; Huebl, H.; Gross, R.; Kamra, A.; Xiao, J.; Chen, Y.T.; Jiao, H.J.; Bauer, G.E.W.; Goennenwein, S.T.B. 2013-01-01 We perform a quantitative, comparative study of the spin pumping, spin Seebeck, and spin Hall magnetoresistance effects, all detected via the inverse spin Hall effect in a series of over 20??yttrium???iron?garnet/Pt samples. Our experimental results fully support present, exclusively spin 17. A simple approach to detect and correct signal faults of Hall position sensors for brushless DC motors at steady speed Science.gov (United States) Shi, Yongli; Wu, Zhong; Zhi, Kangyi; Xiong, Jun 2018-03-01 In order to realize reliable commutation of brushless DC motors (BLDCMs), a simple approach is proposed to detect and correct signal faults of Hall position sensors in this paper. First, the time instant of the next jumping edge for Hall signals is predicted by using prior information of pulse intervals in the last electrical period. Considering the possible errors between the predicted instant and the real one, a confidence interval is set by using the predicted value and a suitable tolerance for the next pulse edge. According to the relationship between the real pulse edge and the confidence interval, Hall signals can be judged and the signal faults can be corrected. Experimental results of a BLDCM at steady speed demonstrate the effectiveness of the approach. 18. Excess hall effect in epitaxial YBCO film under moderate magnetic fields, approached by renormalized superconducting fluctuations model International Nuclear Information System (INIS) Puica, I.; Lang, W.; Goeb, W.; Sobolewski, R. 2002-01-01 Full text: Measurements of the Hall effect and the resistivity on precisely-patterned YBCO thin film in moderate magnetic fields B from 0.5 to 6 T oriented parallel to the crystallographic c axis reveal a sign reversal of the Hall coefficient for B < 3 T. The data are confronted with the full quantitative expressions given by the renormalized fluctuation model for the excess Hall conductivity. The model offers a satisfactory quantitative approach to the experimental results, for moderate fields and temperatures near the critical region, provided the inhomogeneity of the critical temperature distribution is also taken into account. For lower fields and temperatures, the adequacy of the model is altered by vortex pinning. (author) 19. Effect of non-uniform Hall parameter on the electrode voltage drop in Faraday-type combustion MHD generators International Nuclear Information System (INIS) Gupta, G.P.; Rohatgi, V.K. 1982-01-01 Following a simplified approach, an expression is derived for the gas-dynamic voltage drop in a finitely segmented Faraday-type combustion MHD generator, taking into account the non-uniform Hall parameter across the channel. Combining the electrical sheath voltage drop, discussed briefly, with the gas-dynamic voltage drop, the effect of a non-uniform Hall parameter on the electrode voltage drop is studied using the theoretical and experimental input parameters of the Indian MHD channel test. The condition for the validity of the usual assumption of uniform Hall parameter across the channel is pointed out. Analysis of the measured electrode voltage drop predicts the real gas conductivity in the core to be in the range of 60 to 75 per cent of the theoretically calculated core conductivity. (author) 20. Mary E. Hall: Dawn of the Professional School Librarian Science.gov (United States) Alto, Teresa 2012-01-01 A century ago, a woman named Mary E. Hall convinced school leaders of the need for the professional school librarian--a librarian who cultivated a love of reading, academic achievement, and independent learning skills. After graduating from New York City's Pratt Institute Library School in 1895, Hall developed her vision for the high school… 1. What is the Hallé? | Smith | Philosophical Papers African Journals Online (AJOL) The bulk of the paper examines the difficulty of reconciling the view that the Hallé is several individuals with two prima facie plausible theses about the manner of its persistence through time. The paper is structured around some remarks made by Peter Simons about groups, and the Hallé in particular, in his Parts. 2. Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic Energy Technology Data Exchange (ETDEWEB) Martin, L. N.; Dmitruk, P. [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Gomez, D. O. [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio, CONICET, Buenos Aires (Argentina) 2012-05-15 We analyze the effect of the Hall term in the magnetohydrodynamic turbulence under a strong externally supported magnetic field, seeing how this changes the energy cascade, the characteristic scales of the flow, and the dynamics of global magnitudes, with particular interest in the dissipation. Numerical simulations of freely evolving three-dimensional reduced magnetohydrodynamics are performed, for different values of the Hall parameter (the ratio of the ion skin depth to the macroscopic scale of the turbulence) controlling the impact of the Hall term. The Hall effect modifies the transfer of energy across scales, slowing down the transfer of energy from the large scales up to the Hall scale (ion skin depth) and carrying faster the energy from the Hall scale to smaller scales. The final outcome is an effective shift of the dissipation scale to larger scales but also a development of smaller scales. Current sheets (fundamental structures for energy dissipation) are affected in two ways by increasing the Hall effect, with a widening but at the same time generating an internal structure within them. In the case where the Hall term is sufficiently intense, the current sheet is fully delocalized. The effect appears to reduce impulsive effects in the flow, making it less intermittent. 3. Quantifying Spin Hall Angles from Spin Pumping : Experiments and Theory NARCIS (Netherlands) Mosendz, O.; Pearson, J.E.; Fradin, F.Y.; Bauer, G.E.W.; Bader, S.D.; Hoffmann, A. 2010-01-01 Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating Ni80Fe20|normal metal (N) bilayers into a coplanar 4. Stuart Hall on Racism and the Importance of Diasporic Thinking Science.gov (United States) Rizvi, Fazal 2015-01-01 In this article, I want to show how my initial encounter with the work of Stuart Hall was grounded in my reading of the later philosophy of Ludwig Wittgenstein, and was shaped by my interest in understanding the nature of racism across the three countries in which I had lived. Over the years, Hall's various writings have helped me to make sense of… 5. Theory of the quantum hall effects in lattice systems International Nuclear Information System (INIS) Kliros, G.S. 1990-06-01 The Fractional Quantum Hall Effect is identified as an Integral Quantum Hall Effect of electrons on a lattice with an even number of statistical flux quanta. A variational wavefunction in terms of the Hofstadter lattice eigenstates is proposed. (author). 21 refs 6. A Residential Paradox?: Residence Hall Attributes and College Student Outcomes Science.gov (United States) Bronkema, Ryan; Bowman, Nicholas A. 2017-01-01 The researchers of this brief observed that few environments have the potential to shape the outcomes of college students as much as residence halls. As a result, residence halls have the capacity to foster a strong sense of community as well as other important outcomes such as college satisfaction and academic achievement. However, given the high… 7. Bulk Versus Edge in the Quantum Hall Effect OpenAIRE Kao, Y. -C.; Lee, D. -H. 1996-01-01 The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\\it is} the underlying principle of the edge approach'' of quantum Hall effect. In that approach, $\\sxy$ should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem. 8. Critical current in the Integral Quantum Hall Effect International Nuclear Information System (INIS) 1985-11-01 A multiparticle theory of the Integral Quantum Hall Effect (IQHE) was constructed operating with pairs wave function as an order parameter. The IQHE is described with bosonic macroscopic states while the fractional QHE with fermionic ones. The calculation of the critical current and Hall conductivity temperature dependence is presented. (author) 9. Useful Pedagogical Applications of the Classical Hall Effect Science.gov (United States) Houari, Ahmed 2007-01-01 One of the most known phenomena in physics is the Hall effect. This is mainly due to its simplicity and to the wide range of its theoretical and practical applications. To complete the pedagogical utility of the Hall effect in physics teaching, I will apply it here to determine the Faraday constant as a fundamental physical number and the number… 10. A Novel Hall Effect Sensor Using Elaborate Offset Cancellation Method Directory of Open Access Journals (Sweden) Vlassis N. Petoussis 2009-01-01 Full Text Available The Hall effect is caused by a traverse force that is formed in the electrons or holes of metal element or semiconductor when are polarized by current source and simultaneously all the system it is found vertical in external magnetic field. Result is finally the production of difference of potential (Hall voltage in address vertical in that of current and magnetic field directions. In the present work is presented a new Hall sensor exploiting the former operation. In combination with his pioneering form and using dynamic spinning current technique with an elaborate sequence, it leads to satisfactory results of produced Hall voltage with small noise in a presence of external magnetic field. Anyone can see both the spinning current and anti-Hall technique in the same sensor simultaneously. 11. Migrants and Their Experiences of Time: Edward T. Hall Revisited Directory of Open Access Journals (Sweden) Elisabeth Schilling 2009-01-01 Full Text Available In this paper we reassess the scientific heritage of Edward T. HALL and his contribution to the area of intercultural communication. The key objectives of our study are to demonstrate the applicability of HALL's theory of culture to empirical research and to establish its compatibility with other methods. Specifically, we propose that Alfred SCHÜTZ's phenomenology of sociality be taken as an extension to HALL. The connection between HALL and SCHÜTZ is made possible by the mutual emphases on the temporal dimension of culture and the temporal aspects of migration. With these foci we analyze six narratives by two groups of migrants: German and Russian. By combining HALL's theory of the cultural time with SCHÜTZ's phenomenological perspective on time and the Other and then applying them to empirical data, we show the terms in which different cultures experience time. URN: urn:nbn:de:0114-fqs0901357 12. Magnetic Measurements of the Background Field in the Undulator Hall International Nuclear Information System (INIS) Fisher, Andrew 2010-01-01 The steel present in the construction of the undulator hall facility has the potential for changing the ambient fields present in the undulator hall. This note describes a measurement done to make a comparison between the fields in the hall and in the Magnetic Measurement Facility. In order for the undulators to have the proper tuning, the background magnetic field in the Undulator Hall should agree with the background field in the Magnetic Measurements Facility within .5 gauss. In order to verify that this was the case measurements were taken along the length of the undulator hall, and the point measurements were compared to the mean field which was measured on the MMF test bench. 13. Angular Magnetoresistance and Hall Measurements in New Dirac Material, ZrSiS Science.gov (United States) Ali, Mazhar; Schoop, Leslie; Lotsch, Bettina; Parkin, Stuart Dirac and Weyl materials have shot to the forefront of condensed matter research in the last few years. Recently, the square-net material, ZrSiS, was theorized and experimentally shown (via ARPES) to host several highly dispersive Dirac cones, including the first Dirac cone demanded by non-symmorphic symmetry in a Si square net. Here we report the magnetoresistance and Hall Effect measurements in this compound. ZrSiS samples with RRR = 40 were found to have MR values up to 6000% at 2 K, be predominantly p-type with a carrier concentration of ~8 x 1019 cm-3 and mobility ~8500 cm2/Vs. Angular magnetoresistance measurements reveal a peculiar behavior with multiple local maxima, depending on field strength, indicating of a sensitive and sensitive Fermi surface. SdH oscillations analysis confirms Hall and angular magnetoresistance measurements. These results, in the context of the theoretical and ARPES results, will be discussed. 14. Quasiparticle-mediated spin Hall effect in a superconductor. Science.gov (United States) Wakamura, T; Akaike, H; Omori, Y; Niimi, Y; Takahashi, S; Fujimaki, A; Maekawa, S; Otani, Y 2015-07-01 In some materials the competition between superconductivity and magnetism brings about a variety of unique phenomena such as the coexistence of superconductivity and magnetism in heavy-fermion superconductors or spin-triplet supercurrent in ferromagnetic Josephson junctions. Recent observations of spin-charge separation in a lateral spin valve with a superconductor evidence that these remarkable properties are applicable to spintronics, although there are still few works exploring this possibility. Here, we report the experimental observation of the quasiparticle-mediated spin Hall effect in a superconductor, NbN. This compound exhibits the inverse spin Hall (ISH) effect even below the superconducting transition temperature. Surprisingly, the ISH signal increases by more than 2,000 times compared with that in the normal state with a decrease of the injected spin current. The effect disappears when the distance between the voltage probes becomes larger than the charge imbalance length, corroborating that the huge ISH signals measured are mediated by quasiparticles. 15. Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state. Science.gov (United States) Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa 2015-02-06 We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems. 16. Voltage transients in thin-film InSb Hall sensor Science.gov (United States) Bardin, Alexey; Ignatjev, Vyacheslav; Orlov, Andrey; Perchenko, Sergey The work is reached to study temperature transients in thin-film Hall sensors. We experimentally study InSb thin-film Hall sensor. We find transients of voltage with amplitude about 10 μ V on the sensor ports after current switching. We demonstrate by direct measurements that the transients is caused by thermo-e.m.f., and both non-stationarity and heterogeneity of temperature in the film. We find significant asymmetry of temperature field for different direction of the current, which is probably related to Peltier effect. The result can be useful for wide range of scientist who works with switching of high density currents in any thin semiconductor films. 17. The aerogel threshold Cherenkov detector for the high momentum spectrometer in Hall C at Jefferson lab International Nuclear Information System (INIS) Razmik Asaturyan; Rolf Ent; Howard Fenker; David Gaskell; Garth Huber; Mark Jones; David Mack; Hamlet Mkrtchyan; Bert Metzger; Nadia Novikoff; Vardan Tadevosyan; William Vulcan; Stephen Wood 2004-01-01 We describe a new aerogel threshold Cherenkov detector installed in the HMS spectrometer in Hall C at Jefferson Lab. The Hall C experimental program in 2003 required an improved particle identification system for better identification of π/K/p, which was achieved by installing an additional threshold Cherenkov counter. Two types of aerogel with n = 1.03 and n = 1.015 allow one to reach ∼10 -3 proton and 10 -2 kaon rejection in the 1-5 GeV/c momentum range with pion detection efficiency better than 99% (97%). The detector response shows no significant position dependence due to a diffuse light collection technique. The diffusion box was equipped with 16 Photonis XP4572 PMT's. The mean number of photoelectrons in saturation was ∼16 and ∼8, respectively. Moderate particle identification is feasible near threshold 18. Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect International Nuclear Information System (INIS) Bliokh, Konstantin Yu. 2006-01-01 We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed 19. Determination of the Pt spin diffusion length by spin-pumping and spin Hall effect Energy Technology Data Exchange (ETDEWEB) Zhang, Wei; Pearson, John E.; Hoffmann, Axel [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Vlaminck, Vincent [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Colegio de Ciencias e Ingenería, Universidad San Fransciso de Quito, Quito (Ecuador); Divan, Ralu [Center for Nanoscale Materials, Argonne National Laboratory, Illinois 60439 (United States); Bader, Samuel D. [Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Center for Nanoscale Materials, Argonne National Laboratory, Illinois 60439 (United States) 2013-12-09 The spin diffusion length of Pt at room temperature and at 8 K is experimentally determined via spin pumping and spin Hall effect in permalloy/Pt bilayers. Voltages generated during excitation of ferromagnetic resonance from the inverse spin Hall effect and anisotropic magnetoresistance effect were investigated with a broadband approach. Varying the Pt layer thickness gives rise to an evolution of the voltage line shape due to the superposition of the above two effects. By studying the ratio of the two voltage components with the Pt layer thickness, the spin diffusion length of Pt can be directly extracted. We obtain a spin diffusion length of ∼1.2 nm at room temperature and ∼1.6 nm at 8 K. 20. Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect. Science.gov (United States) Bliokh, Konstantin Yu 2006-07-28 We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed. 1. Valley polarized quantum Hall effect and topological insulator phase transitions in silicene KAUST Repository Tahir, M. 2013-01-25 The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction. 2. Mover Position Detection for PMTLM Based on Linear Hall Sensors through EKF Processing. Science.gov (United States) Yan, Leyang; Zhang, Hui; Ye, Peiqing 2017-04-06 Accurate mover position is vital for a permanent magnet tubular linear motor (PMTLM) control system. In this paper, two linear Hall sensors are utilized to detect the mover position. However, Hall sensor signals contain third-order harmonics, creating errors in mover position detection. To filter out the third-order harmonics, a signal processing method based on the extended Kalman filter (EKF) is presented. The limitation of conventional processing method is first analyzed, and then EKF is adopted to detect the mover position. In the EKF model, the amplitude of the fundamental component and the percentage of the harmonic component are taken as state variables, and they can be estimated based solely on the measured sensor signals. Then, the harmonic component can be calculated and eliminated. The proposed method has the advantages of faster convergence, better stability and higher accuracy. Finally, experimental results validate the effectiveness and superiority of the proposed method. 3. The automatic test system for the L3 muon drift chamber amplifiers International Nuclear Information System (INIS) Bove, A.; Caiazzo, L.; Lanzano, S.; Manna, F.; Manto, G.; Parascandolo, L.; Parascandolo, P.; Parmentola, A.; Paternoster, G. 1987-01-01 We describe the system we developed to test the linearity of wire chambers amplifiers of the muon spectrometer presently in construction for the L3 experiment at LEP. The system, controlled by an Apple II computer, is capable of localizing both defective components and faults in the printed board. It will be used to perform the large scale quality control of the amplifier cards 4. Inter- and Intralingual Lexical Influences in Advanced Learners' French L3 Oral Production Science.gov (United States) Lindqvist, Christina 2010-01-01 The present study investigates lexical inter- and intralingual influences in the oral production of 14 very advanced learners of French L3. Lexical deviances are divided into two main categories: formal influence and meaning-based influence. The results show that, as predicted with respect to advanced learners, meaning-based influence is the most… 5. Joint International Workshop on Professional Learning, Competence Development and Knowledge Management - LOKMOL and L3NCD NARCIS (Netherlands) Memmel, Martin; Ras, Eric; Weibelzahl, Stephan; Burgos, Daniel; Olmedilla, Daniel; Wolpers, Martin 2006-01-01 Memmel, M., Ras, E., Weibelzahl, S., Burgos, D., Olmedilla, D., & Wolpers, M. (2006). Joint International Workshop on Professional Learning, Competence Development and Knowledge Management - LOKMOL and L3NCD. Proceedings of ECTEL 2006. October 2nd-4th, Crete, Greece. Retrieved October 2nd, 2006, 6. The Expansion of mtDNA Haplogroup L3 within and out of Africa Czech Academy of Sciences Publication Activity Database Soares, P.; Alshamali, F.; Pereira, J. B.; Fernandes, V.; Silva, N. M.; Afonso, C.; Costa, M. D.; Musilová, E.; Macaulay, V.; Richards, M. B.; Černý, Viktor; Pereira, L. 2012-01-01 Roč. 29, č. 3 (2012), s. 915-927 ISSN 0737-4038 R&D Projects: GA MŠk ME 917 Institutional research plan: CEZ:AV0Z80020508 Keywords : mtDNA * complete genomes * haplogroup L3 * out of Africa * modern human expansions Sub ject RIV: AC - Archeology, Anthropology, Ethnology Impact factor: 10.353, year: 2012 7. Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect KAUST Repository Bisig, André 2017-01-04 We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter β are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (β/α>1) in magnetic vortex cores or Skyrmions. 8. Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect KAUST Repository Bisig, André ; Akosa, Collins Ashu; Moon, Jung-Hwan; Rhensius, Jan; Moutafis, Christoforos; von Bieren, Arndt; Heidler, Jakoba; Kiliani, Gillian; Kammerer, Matthias; Curcic, Michael; Weigand, Markus; Tyliszczak, Tolek; Van Waeyenberge, Bartel; Stoll, Hermann; Schü tz, Gisela; Lee, Kyung-Jin; Manchon, Aurelien; Klä ui, Mathias 2017-01-01 We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter β are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (β/α>1) in magnetic vortex cores or Skyrmions. 9. Differential effect of L3T4+ cells on recovery from total-body irradiation International Nuclear Information System (INIS) Pantel, K.; Nakeff, A. 1990-01-01 We have examined the importance of L3T4+ (murine equivalent to CD4+) cells for hematopoietic regulation in vivo in unperturbed mice and mice recovering from total-body irradiation (TBI) using a cytotoxic monoclonal antibody (MoAb) raised with the GK 1.5 hybridoma. Ablating L3T4+ cells in normal (unperturbed) B6D2F1 mice substantially decreased the S-phase fraction (determined by in vivo hydroxyurea suicide) of erythroid progenitor cells (erythroid colony-forming units, CFU-E) as compared to the pretreatment level (10% +/- 14.1% [day 3 following depletion] vs 79.8% +/- 15.9%, respectively) with a corresponding decrease in the marrow content of CFU-E at this time to approximately 1% of the pretreatment value. Although the S-phase fraction of CFU-GM was decreased to 2.2% +/- 3.1% 3 days after L3T4+ cell ablation from the 21.3% +/- 8.3% pretreatment value, CFU-GM cellularity showed little change over the 3 days following anti-L3T4 treatment. Anti-L3T4 MoAb treatment had little or no effect on either the S-phase fraction or the marrow content of hematopoietic stem cells (spleen colony-forming units, CFU-S) committed to myeloerythroid differentiation. Ablating L3T4+ cells prior to a single dose of 2 Gy TBI resulted in significantly reduced marrow contents of CFU-S on day 3 and granulocyte-macrophage colony-forming units (CFU-GM) on day 6 following TBI, with little or no effect on the corresponding recovery of CFU-E. The present findings provide the first in vivo evidence that L3T4+ cells are involved in: (1) maintaining the proliferative activity of CFU-E and CFU-GM in unperturbed mice and (2) supporting the restoration of CFU-S and CFU-GM following TBI-induced myelosuppression 10. Novel CREB3L3 Nonsense Mutation in a Family With Dominant Hypertriglyceridemia. Science.gov (United States) Cefalù, Angelo B; Spina, Rossella; Noto, Davide; Valenti, Vincenza; Ingrassia, Valeria; Giammanco, Antonina; Panno, Maria D; Ganci, Antonina; Barbagallo, Carlo M; Averna, Maurizio R 2015-12-01 Cyclic AMP responsive element-binding protein 3-like 3 (CREB3L3) is a novel candidate gene for dominant hypertriglyceridemia. To date, only 4 kindred with dominant hypertriglyceridemia have been found to be carriers of 2 nonsense mutations in CREB3L3 gene (245fs and W46X). We investigated a family in which hypertriglyceridemia displayed an autosomal dominant pattern of inheritance. The proband was a 49-year-old woman with high plasma triglycerides (≤1300 mg/dL; 14.68 mmol/L). Her father had a history of moderate hypertriglyceridemia, and her 51-year-old brother had triglycerides levels as high as 1600 mg/dL (18.06 mmol/L). To identify the causal mutation in this family, we analyzed the candidate genes of recessive and dominant forms of primary hypertriglyceridemia by direct sequencing. The sequencing of CREB3L3 gene led to the discovery of a novel minute frame shift mutation in exon 3 of CREB3L3 gene, predicted to result in the formation of a truncated protein devoid of function (c.359delG-p.K120fsX20). Heterozygosity for the c.359delG mutation resulted in a severe phenotype occurring later in life in the proband and her brother and a good response to diet and a hypotriglyceridemic treatment. The same mutation was detected in a 13-year-old daughter who to date is normotriglyceridemic. We have identified a novel pathogenic mutation in CREB3L3 gene in a family with dominant hypertriglyceridemia with a variable pattern of penetrance. © 2015 American Heart Association, Inc. 11. Planar Hall Effect Sensors for Biodetection DEFF Research Database (Denmark) Rizzi, Giovanni . In the second geometry (dPHEB) half of the sensor is used as a local negative reference to subtract the background signal from magnetic beads in suspension. In all applications below, the magnetic beads are magnetised using the magnetic field due to the bias current passed through the sensor, i.e., no external...... as labels and planar Hall effect bridge (PHEB) magnetic field sensor as readout for the beads. The choice of magnetic beads as label is motivated by the lack of virtually any magnetic background from biological samples. Moreover, magnetic beads can be manipulated via an external magnetic field...... hybridisation in real-time, in a background of suspended magnetic beads. This characteristic is employed in single nucleotide polymorphism (SNP) genotyping, where the denaturation of DNA is monitored in real-time upon washing with a stringency buffer. The sensor setup includes temperature control and a fluidic... 12. Quantum Hall effect on Riemann surfaces Science.gov (United States) Tejero Prieto, Carlos 2009-06-01 We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion. 13. Quantum Hall effect on Riemann surfaces International Nuclear Information System (INIS) Tejero Prieto, Carlos 2009-01-01 We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion. 14. Frequency spectrum of Calder Hall reactor noise International Nuclear Information System (INIS) Cummins, J.D. 1960-01-01 The frequency spectrum of the noise power of Calder Hall reactor No. 1 has been obtained by analysing a tape recording of the backed off power. The root mean square noise power due to all frequencies above 0.001 cycles per second was found to be 0.13%. The noise power for this reactor, is due mainly to modulations of the power level by reactivity variations caused in turn by gas temperature changes. These gas temperature changes are caused by a Cyclic variation in the feedwater regulator to the heat exchanger. The apparatus and method used to determine the noise power are described in this memorandum. It is shown that for frequencies in the range 0.001 to 0.030 cycles per second the noise spectrum falls at 60 decibels per decade of frequency. (author) 15. OPTICS. Quantum spin Hall effect of light. Science.gov (United States) Bliokh, Konstantin Y; Smirnova, Daria; Nori, Franco 2015-06-26 Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces. Copyright © 2015, American Association for the Advancement of Science. 16. Chaotic waves in Hall thruster plasma International Nuclear Information System (INIS) Peradzynski, Zbigniew; Barral, S.; Kurzyna, J.; Makowski, K.; Dudeck, M. 2006-01-01 The set of hyperbolic equations of the fluid model describing the acceleration of plasma in a Hall thruster is analyzed. The characteristic feature of the flow is the existence of a trapped characteristic; i.e. there exists a characteristic line, which never intersects the boundary of the flow region in the thruster. To study the propagation of short wave perturbations, the approach of geometrical optics (like WKB) can be applied. This can be done in a linear as well as in a nonlinear version. The nonlinear version describes the waves of small but finite amplitude. As a result of such an approach one obtains so called transport equation, which are governing the wave amplitude. Due to the existence of trapped characteristics this transport equation appears to have chaotic (turbulent) solutions in both, linear and nonlinear versions 17. Concept of Operating Indoor Skiing Halls with DEFF Research Database (Denmark) Paul, Joachim 2003-01-01 Indoor skiing halls are conventionally operated at low temperatures and with either crushed ice as snow substitute or snow made from freezing water in cold air. Both systems have a high energy demand for air cooling, floor freezing and consequently snow harvest. At the same time the snow at the top...... floor cooling/freezing and insulation become obsolete, significant savings in piping and building costs can be achieved. Due to the much higher evaporating temperature for the refrigeration system, the energy demand is kept low. Since the same equipment is used for both snowmaking and air cooling......, the running time of the equipment is high, resulting in a better economy. Using Binary Snow, with its unique qualities such as fluffy, crisp, white and ¿ since made daily ¿ "fresh and hygienic", offers great advantages in operating costs, investment costs and quality.... 18. Geometrical Description of fractional quantum Hall quasiparticles Science.gov (United States) Park, Yeje; Yang, Bo; Haldane, F. D. M. 2012-02-01 We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized guiding-center spin'' times the Gaussian curvature of a guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as `punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation. 19. Cathode Effects in Cylindrical Hall Thrusters Energy Technology Data Exchange (ETDEWEB) Granstedt, E.M.; Raitses, Y.; Fisch, N. J. 2008-09-12 Stable operation of a cylindrical Hall thruster (CHT) has been achieved using a hot wire cathode, which functions as a controllable electron emission source. It is shown that as the electron emission from the cathode increases with wire heating, the discharge current increases, the plasma plume angle reduces, and the ion energy distribution function shifts toward higher energies. The observed effect of cathode electron emission on thruster parameters extends and clarifies performance improvements previously obtained for the overrun discharge current regime of the same type of thruster, but using a hollow cathode-neutralizer. Once thruster discharge current saturates with wire heating, further filament heating does not affect other discharge parameters. The saturated values of thruster discharge parameters can be further enhanced by optimal placement of the cathode wire with respect to the magnetic field. 20. On-Chip Microwave Quantum Hall Circulator Directory of Open Access Journals (Sweden) A. C. Mahoney 2017-01-01 Full Text Available Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size 1/1000th the wavelength by exploiting the chiral, “slow-light” response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with 330  μm diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip. 1. 50 KW Class Krypton Hall Thruster Performance Science.gov (United States) Jacobson, David T.; Manzella, David H. 2003-01-01 The performance of a 50-kilowatt-class Hall thruster designed for operation on xenon propellant was measured using kryton propellant. The thruster was operated at discharge power levels ranging from 6.4 to 72.5 kilowatts. The device produced thrust ranging from 0.3 to 2.5 newtons. The thruster was operated at discharge voltages between 250 and 1000 volts. At the highest anode mass flow rate and discharge voltage and assuming a 100 percent singly charged condition, the discharge specific impulse approached the theoretical value. Discharge specific impulse of 4500 seconds was demonstrated at a discharge voltage of 1000 volts. The peak discharge efficiency was 64 percent at 650 volts. 2. Magnon Hall effect on the Lieb lattice. Science.gov (United States) Cao, Xiaodong; Chen, Kai; He, Dahai 2015-04-29 Ferromagnetic insulators without inversion symmetry may show magnon Hall effect (MHE) in the presence of a temperature gradient due to the existence of Dzyaloshinskii-Moriya interaction (DMI). In this theoretical study, we investigate MHE on a lattice with inversion symmetry, namely the Lieb lattice, where the DMI is introduced by adding an external electric field. We show the nontrivial topology of this model by examining the existence of edge states and computing the topological phase diagram characterized by the Chern numbers of different bands. Together with the topological phase diagram, we can further determine the sign and magnitude of the transverse thermal conductivity. The impact of the flat band possessed by this model on the thermal conductivity is discussed by computing the Berry curvature analytically. 3. Photonic spin Hall effect at metasurfaces. Science.gov (United States) Yin, Xiaobo; Ye, Ziliang; Rho, Junsuk; Wang, Yuan; Zhang, Xiang 2013-03-22 The spin Hall effect (SHE) of light is very weak because of the extremely small photon momentum and spin-orbit interaction. Here, we report a strong photonic SHE resulting in a measured large splitting of polarized light at metasurfaces. The rapidly varying phase discontinuities along a metasurface, breaking the axial symmetry of the system, enable the direct observation of large transverse motion of circularly polarized light, even at normal incidence. The strong spin-orbit interaction deviates the polarized light from the trajectory prescribed by the ordinary Fermat principle. Such a strong and broadband photonic SHE may provide a route for exploiting the spin and orbit angular momentum of light for information processing and communication. 4. Shielding in experimental areas International Nuclear Information System (INIS) Stevens, A.; Tarnopolsky, G.; Thorndike, A.; White, S. 1979-01-01 The amount of shielding necessary to protect experimental detectors from various sources of background radiation is discussed. As illustrated an experiment has line of sight to sources extending approx. 90 m upstream from the intersection point. Packing a significant fraction of this space with shielding blocks would in general be unacceptable because primary access to the ring tunnel is from the experimental halls. (1) From basic machine design considerations and the inherent necessity to protect superconducting magnets it is expected that experimental areas in general will be cleaner than at any existing accelerator. (2) Even so, it will likely be necessary to have some shielding blocks available to protect experimental apparatus, and it may well be necessary to have a large amount of shielding available in the WAH. (3) Scraping will likely have some influence on all halls, and retractable apparatus may sometimes be necessary. (4) If access to any tunnel is needed to replace a magnet, one has 96 h (4 days) available to move shielding away to permit access without additional downtime. This (the amount of shielding one can shuffle about in 96 h) is a reasonable upper limit to shielding necessary in a hall 5. Residencia hall del Obispado, en Gescher, Alemania Directory of Open Access Journals (Sweden) Deilmann, Harald 1969-02-01 6. Nonadiabatic effects in the Quantum Hall regime International Nuclear Information System (INIS) Page, D.A.; Brown, E. 1993-01-01 The authors consider the effect of a finite electric field on the states of a Bloch electron in two dimensions, with a uniform magnetic field present. They make use of the concept of electric time translation symmetry and treat the electric and magnetic fields symmetrically in a time dependent formalism. In addition to a wave vector k, the states are characterized by a frequency specifying the behavior under electric time translations. An effective Hamiltonian is employed to obtain the splitting of an isolated Bloch band into open-quotes frequencyclose quotes subbands. The time-averaged velocity and energy of the states are expressed in terms of the frequency dispersion. The relationship to the Stark ladder eigenstates in a scalar potential representation of the electric field is examined. This is seen to justify the use of the averaged energy in determining occupation of the states. In the weak electric field (adiabatic) limit, an expression is recovered for the quantized Hall conductivity of a magnetic subband as a topological invariant. A numerical procedure is outlined and results obtained over a range of electric field strengths. A transition between strong and weak field regimes is seen, with level repulsions between the frequencies playing an important role. The numerical results show how the magnetic subband structure and quantized Hall conductivity emerge as the electric field becomes weaker. In this regime, the behavior can be understood by comparison to the predictions of the adiabatic approximation. The latter predicts crossings in the frequencies at certain locations in wave vector space. Nonadiabatic effects are seen to produce gaps in the frequency spectrum at these locations. 35 refs., 14 figs 7. Temperature dependence of collapse of quantized hall resistance International Nuclear Information System (INIS) Tanaka, Hiroyasu; Kawashima, Hironori; Iizuka, Hisamitsu; Fukuda, Hideaki; Kawaji, Shinji 2006-01-01 Similarity is observed in the deviation of Hall resistance from the quantized value with the increase in the source-drain current I SD in our butterfly-type Hall bars and in the Hall bars used by Jeanneret et al., while changes in the diagonal resistivity ρ xx with I SD are significantly different between these Hall bars. The temperature dependence of the critical Hall electric field F cr (T) for the collapse of R H (4) measured in these Hall bars is approximated using F cr (T) = F cr (0)(1 - (T/T cr ) 2 ). Here, the critical Hall electric field at zero temperature depends on the magnetic field B as F cr (0) ∝ B 3/2 . Theoretical considerations are given on F cr (T) on the basis of a temperature-dependent mobility edge model and a schema of temperature-dependent inter-Landau level tunneling probability arising from the Fermi distribution function. The former does not fit in with the I SD dependence of activation energy in ρ xx . (author) 8. Hall current effects in dynamic magnetic reconnection solutions International Nuclear Information System (INIS) Craig, I.J.D.; Heerikhuisen, J.; Watson, P.G. 2003-01-01 The impact of Hall current contributions on flow driven planar magnetic merging solutions is discussed. The Hall current is important if the dimensionless Hall parameter (or normalized ion skin depth) satisfies c H >η, where η is the inverse Lundquist number for the plasma. A dynamic analysis of the problem shows, however, that the Hall current initially manifests itself, not by modifying the planar reconnection field, but by inducing a non-reconnecting perpendicular 'separator' component in the magnetic field. Only if the stronger condition c H 2 >η is satisfied can Hall currents be expected to affect the planar merging. These analytic predictions are then tested by performing a series of numerical experiments in periodic geometry, using the full system of planar magnetohydrodynamic (MHD) equations. The numerical results confirm that the nature of the merging changes dramatically when the Hall coupling satisfies c H 2 >η. In line with the analytic treatment of sheared reconnection, the coupling provided by the Hall term leads to the emergence of multiple current layers that can enhance the global Ohmic dissipation at the expense of the reconnection rate. However, the details of the dissipation depend critically on the symmetries of the simulation, and when the merging is 'head-on' (i.e., comprises fourfold symmetry) the reconnection rate can be enhanced 9. Graphene and the universality of the quantum Hall effect DEFF Research Database (Denmark) Tzalenchuk, A.; Janssen, T. J.B.M.; Kazakova, O. 2013-01-01 The quantum Hall effect allows the standard for resistance to be defined in terms of the elementary charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK=h/e2=25812.8074434(84) Ω (Mohr P. J....... the unconventional quantum Hall effect and then present in detail the route, which led to the most precise quantum Hall resistance universality test ever performed.......The quantum Hall effect allows the standard for resistance to be defined in terms of the elementary charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK=h/e2=25812.8074434(84) Ω (Mohr P. J....... et al., Rev. Mod. Phys., 84 (2012) 1527), the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology, a few parts per billion, has been achieved only in silicon and III-V heterostructure devices. In this lecture we show... 10. Experimentation at HERA International Nuclear Information System (INIS) 1983-10-01 These proceedings contain three articles concerning the physics which can be studied by HERA, which were presented at the named workshop, together with convenor reports on working groups which concern technologies, the intersecting regions, photoproduction at HERA, currents and structure functions, exotic phenomena at HERA, and the use of existing detectors. Finally the experimental halls at HERA are described. Separated abstracts were prepared for the articles in these proceedings. (HSI) 11. Signal conditioning and processing for metallic Hall sensors. Czech Academy of Sciences Publication Activity Database Entler, Slavomír; Ďuran, Ivan; Sládek, P.; Vayakis, G.; Kočan, M. 2017-01-01 Roč. 123, November (2017), s. 783-786 ISSN 0920-3796. [SOFT 2016: Symposium on Fusion Technology /29./. Prague, 05.09.2016-09.09.2016] R&D Projects: GA MŠk LG14002 Institutional support: RVO:61389021 Keywords : Hall sensor * Lock-in * Synchronous detection * Current spinning * Hall effect * Planar hall effect suppression Subject RIV: JF - Nuclear Energetics OBOR OECD: Nuclear related engineering Impact factor: 1.319, year: 2016 http://www.sciencedirect.com/science/article/pii/S0920379617305070 12. Anomalous Hall effect in Fe/Gd bilayers KAUST Repository Xu, W. J.; Zhang, Bei; Liu, Z. X.; Wang, Z.; Li, W.; Wu, Z. B.; Yu, R. H.; Zhang, Xixiang 2010-01-01 Non-monotonic dependence of anomalous Hall resistivity on temperature and magnetization, including a sign change, was observed in Fe/Gd bilayers. To understand the intriguing observations, we fabricated the Fe/Gd bilayers and single layers of Fe and Gd simultaneously. The temperature and field dependences of longitudinal resistivity, Hall resistivity and magnetization in these films have also been carefully measured. The analysis of these data reveals that these intriguing features are due to the opposite signs of Hall resistivity/or spin polarization and different Curie temperatures of Fe and Gd single-layer films. Copyright (C) EPLA, 2010 13. Hall conductance and topological invariant for open systems. Science.gov (United States) Shen, H Z; Wang, W; Yi, X X 2014-09-24 The Hall conductivity given by the Kubo formula is a linear response of quantum transverse transport to a weak electric field. It has been intensively studied for quantum systems without decoherence, but it is barely explored for systems subject to decoherence. In this paper, we develop a formulism to deal with this issue for topological insulators. The Hall conductance of a topological insulator coupled to an environment is derived, the derivation is based on a linear response theory developed for open systems in this paper. As an application, the Hall conductance of a two-band topological insulator and a two-dimensional lattice is presented and discussed. 14. Acoustic investigations of concert halls for rock music DEFF Research Database (Denmark) 2007-01-01 Objective measurement data and subjective evaluations have been collected from 20 small-/medium-sized halls in Denmark used for amplified rhythmic music concerts (pop, rock, jazz). The purpose of the study was to obtain knowledge about optimum acoustic conditions for this type of hall. The study...... is motivated by the fact that most concert tickets sold in Denmark relate to concerts within these genres in this kind of venue. The subjective evaluations were carried out by professional musicians and sound engineers who responded on the basis of their experiences working in these (and other) halls. From... 15. Anomalous Hall effect in Fe/Gd bilayers KAUST Repository Xu, W. J. 2010-04-01 Non-monotonic dependence of anomalous Hall resistivity on temperature and magnetization, including a sign change, was observed in Fe/Gd bilayers. To understand the intriguing observations, we fabricated the Fe/Gd bilayers and single layers of Fe and Gd simultaneously. The temperature and field dependences of longitudinal resistivity, Hall resistivity and magnetization in these films have also been carefully measured. The analysis of these data reveals that these intriguing features are due to the opposite signs of Hall resistivity/or spin polarization and different Curie temperatures of Fe and Gd single-layer films. Copyright (C) EPLA, 2010 16. All Optical Measurement Proposed for the Photovoltaic Hall Effect International Nuclear Information System (INIS) Oka, Takashi; Aoki, Hideo 2011-01-01 We propose an all optical way to measure the recently proposed p hotovoltaic Hall effect , i.e., a Hall effect induced by a circularly polarized light in the absence of static magnetic fields. This is done in a pump-probe experiment with the Faraday rotation angle being the probe. The Floquet extended Kubo formula for photo-induced optical response is formulated and the ac-Hall conductivity is calculated. We also point out the possibility of observing the effect in two layered graphene, three-dimensional graphite, and more generally in multi-band systems such as materials described by the dp-model. 17. Determination of intrinsic spin Hall angle in Pt Energy Technology Data Exchange (ETDEWEB) Wang, Yi; Deorani, Praveen; Qiu, Xuepeng; Kwon, Jae Hyun; Yang, Hyunsoo, E-mail: [email protected] [Department of Electrical and Computer Engineering, National University of Singapore, 117576 (Singapore) 2014-10-13 The spin Hall angle in Pt is evaluated in Pt/NiFe bilayers by spin torque ferromagnetic resonance measurements and is found to increase with increasing the NiFe thickness. To extract the intrinsic spin Hall angle in Pt by estimating the total spin current injected into NiFe from Pt, the NiFe thickness dependent measurements are performed and the spin diffusion in the NiFe layer is taken into account. The intrinsic spin Hall angle of Pt is determined to be 0.068 at room temperature and is found to be almost constant in the temperature range of 13–300 K. 18. Determination of intrinsic spin Hall angle in Pt International Nuclear Information System (INIS) Wang, Yi; Deorani, Praveen; Qiu, Xuepeng; Kwon, Jae Hyun; Yang, Hyunsoo 2014-01-01 The spin Hall angle in Pt is evaluated in Pt/NiFe bilayers by spin torque ferromagnetic resonance measurements and is found to increase with increasing the NiFe thickness. To extract the intrinsic spin Hall angle in Pt by estimating the total spin current injected into NiFe from Pt, the NiFe thickness dependent measurements are performed and the spin diffusion in the NiFe layer is taken into account. The intrinsic spin Hall angle of Pt is determined to be 0.068 at room temperature and is found to be almost constant in the temperature range of 13–300 K. 19. Hall effect thruster with an AlN chamber International Nuclear Information System (INIS) Barral, S.; Jayet, Y.; Mazouffre, S.; Veron, E.; Echegut, P.; Dudeck, M. 2005-01-01 The plasma discharge of a Hall-effect thruster (SPT) is strongly depending of the plasma-insulated wall interactions. These interactions are mainly related to the energy deposition, potential sheath effect and electron secondary emission rate (e.s.e.). In usual SPT, the annular channel is made of BN-SiO 2 . The SPT100-ML (laboratory model will be tested with an AlN chamber in the French test facility Pivoine in the laboratoire d'Aerothermique (Orleans-France). The different parameters such as discharge current, thrust, plasma oscillations and wall temperature will studied for several operating conditions. The results will be compared with a fluid model developed in IPPT (Warsaw-Poland) taking into account electron emission from the internal and external walls and using previous experimental measurements of e.s.e. for AlN from ONERA (Toulouse-France). The surface state of AlN will be analysed before and after experiments by an Environmental Scanning Electron Microscope and by a Strength Electron Microscope. (author) 20. AC conductivity of a quantum Hall line junction International Nuclear Information System (INIS) Agarwal, Amit; Sen, Diptiman 2009-01-01 We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter- or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit (ω→0), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures. 1. Superconducting Analogue of the Parafermion Fractional Quantum Hall States Directory of Open Access Journals (Sweden) Abolhassan Vaezi 2014-07-01 Full Text Available Read-Rezayi Z_{k} parafermion wave functions describe ν=2+(k/kM+2 fractional quantum Hall (FQH states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Z_{k} parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Z_{k} parafermions when k<4. By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Z_{k} parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z_{3} parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations. 2. Best estimate prediction for LOFT nuclear experiment L3-2 International Nuclear Information System (INIS) Kee, E.J.; Shinko, M.S.; Grush, W.H.; Condie, K.G. 1980-02-01 Comprehensive analyses using both the RELAP4 and the RELAP5 computer codes were performed to predict the LOFT transient thermal-hydraulic response for nuclear Loss-of-Coolant Experiment L3-2 to be performed in the Loss-of-Fluid Test (LOFT) facility. The LOFT experiment will simulate a small break in one of the cold legs of a large four-loop pressurized water reactor and will be conducted with the LOFT reactor operating at 50 MW. The break in LOCE L3-2 is sized to cause the break flow to be approximately equal to the high-pressure injection system flow at an intermediate pressure of approximately 7.6 MPa 3. XPS and Ag L3-edge XANES characterization of silver and silver-gold sulfoselenides Science.gov (United States) Mikhlin, Yuri L.; Pal'yanova, Galina A.; Tomashevich, Yevgeny V.; Vishnyakova, Elena A.; Vorobyev, Sergey A.; Kokh, Konstantin A. 2018-05-01 Gold and silver sulfoselenides are of interest as materials with high ionic conductivity and promising magnetoresistive, thermoelectric, optical, and other physico-chemical properties, which are strongly dependent on composition and structure. Here, we applied X-ray photoelectron spectroscopy and Ag L3 X-ray absorption near-edge structure (XANES) to study the electronic structures of low-temperature compounds and solid solutions Ag2SxSe1-x (0 compounds; in particular, the Ag L3-edge peak is about 35% lower for AgAuS relative to Ag2S. At the same time, the Au 4f binding energy and, therefore, charge at Au(I) sites increase with increasing S content due to the transfer of electron density from Au to Ag atoms. It was concluded that the effects mainly originate from shortening of the metal-chalcogen and especially the Ausbnd Ag interatomic distances in substances having similar coordination geometry. 4. Results on the calibration of the L3 BGO calorimeter with cosmic rays International Nuclear Information System (INIS) Bakken, J.A.; Barone, L.; Bay, A.; Blaising, J.J.; Borgia, B.; Bourilkov, D.; Boutigny, D.; Brock, I.C.; Buisson, C.; Capell, M.; Chaturvedi, U.K.; Chemarin, M.; Clare, R.; Coignet, G.; Denes, P.; DeNotaristefani, F.; Diemoz, M.; Duchesneau, D.; El Mamouni, H.; Extermann, P.; Fay, J.; Ferroni, F.; Gailloud, M.; Goujon, D.; Gratta, G.; Gupta, V.K.; Hilgers, K.; Ille, B.; Janssen, H.; Karyotakis, Y.; Kasser, A.; Kienzle-Focacci, M.N.; Krenz, W.; Lebrun, P.; Lecoq, P.; Leonardi, E.; Linde, F.L.; Lindemann, B.; Longo, E.; Lu, Y.S.; Luci, C.; Luckey, D.; Martin, J.P.; Merk, M.; Micke, M.; Morganti, S.; Newman, H.; Organtini, G.; Piroue, P.A.; Read, K.; Rosier-Lees, S.; Rosselet, P.; Sauvage, G.; Schmitz, D.; Schneegans, M.; Schwenke, J.; Stickland, D.P.; Tully, C.; Valente, E.; Vivargent, M.; Vuilleumier, L.; Wang, Y.F.; Weber, A.; Weill, R.; Wenninger, J. 1994-01-01 During 1991 two cosmic rays runs took place for the calibration of the L3 electromagnetic calorimeter. In this paper we present the results of the first high statistics cosmic ray calibration of the calorimeter in situ, including the end caps. Results show that the accuracy on the measurement of the calibration constants that can be achieved in one month of data taking is of 1.3%. (orig.) 5. The effect of symmetry on the U L3 NEXAFS of octahedral coordinated uranium(vi) Energy Technology Data Exchange (ETDEWEB) Bagus, Paul S. [Department of Chemistry, University of North Texas, Denton, Texas 76203-5017, USA; Nelin, Connie J. [Consultant, Austin, Texas 78730, USA; Ilton, Eugene S. [Pacific Northwest National Laboratory, Richland, Washington 99352, USA 2017-03-21 We describe a detailed theoretical analysis of how distortions from ideal cubic or Oh symmetry affect the shape, in particular the width, of the U L3-edge NEXAFS for U(VI) in octahedral coordination. The full-width-half-maximum (FWHM) of the L3-edge white line decreases with increasing distortion from Oh symmetry due to the mixing of symmetry broken t2g and eg components of the excited state U(6d) orbitals. The mixing is allowed because of spin-orbit splitting of the ligand field split 6d orbitals. Especially for higher distortions, it is possible to identify a mixing between one of the t2g and one of the eg components, allowed in the double group representation when the spin-orbit interaction is taken into account. This mixing strongly reduces the ligand field splitting, which, in turn, leads to a narrowing of the U L3 white line. However, the effect of this mixing is partially offset by an increase in the covalent anti-bonding character of the highest energy spin-orbit split eg orbital. At higher distortions, mixing overwhelms the increasing anti-bonding character of this orbital which leads to an accelerated decrease in the FWHM with increasing distortion. Additional evidence for the effect of mixing of t2g and eg components is that the FWHM of the white line narrows whether the two axial U-O bond distances shorten or lengthen. Our ab initio theory uses relativistic wavefunctions for cluster models of the structures; empirical or semi-empirical parameters were not used to adjust prediction to experiment. A major advantage is that it provides a transparent approach for determining how the character and extent of the covalent mixing of the relevant U and O orbitals affect the U L3-edge white line. 6. Monitoring and control of the muon detector in the L3 experiment at LEP International Nuclear Information System (INIS) Gonzalez, E. 1990-01-01 In this report the monitoring system of the muon spectrometer of the L3 detector in LEP at CERN is presented. The system is based on a network of VME's using the OS9 operating system. The design guiding lines and the present system configuration are described both from the hardware and the software point of view. In addition, the report contains the description of the monitored parameters showing typical data collected durintg the first months of LEP operation. (Author) 7. A study on evacuation time from lecture halls in Faculty of Engineering, Universiti Putra Malaysia Science.gov (United States) Othman, W. N. A. W.; Tohir, M. Z. M. 2018-04-01 An evacuation situation in any building involves many risks. The geometry of building and high potential of occupant load may affect the efficiency of evacuation process. Although fire safety rules and regulations exist, they remain insufficient to guarantee the safety of all building occupants and do not prevent the dramatic events to be repeated. The main objective of this project is to investigate the relationship between the movement time, travel speed and occupant density during a series of evacuation drills specifically for lecture halls. Generally, this study emphasizes on the movement of crowd within a limited space and includes the aspects of human behaviour. A series of trial evacuations were conducted in selected lecture halls at Faculty of Engineering, Universiti Putra Malaysia with the aim of collecting actual data for numerical analysis. The numerical data obtained during trial evacuations were used to determine the evacuation time, crowd movement and behaviour during evacuation process particularly for lecture halls. The evacuation time and number of occupants exiting from each exit were recorded. Video camera was used to record and observe the movement behaviour of occupants during evacuations. EvacuatioNZ was used to simulate the trials evacuations of DK 5 and the results predicted were compared with experimental data. EvacuatioNZ was also used to predict the evacuation time and the flow of occupants exiting from each door for DK 4 and DK 8. 8. A Redundancy Mechanism Design for Hall-Based Electronic Current Transformers Directory of Open Access Journals (Sweden) Kun-Long Chen 2017-03-01 Full Text Available Traditional current transformers (CTs suffer from DC and AC saturation and remanent magnetization in many industrial applications. Moreover, the drawbacks of traditional CTs, such as closed iron cores, bulky volume, and heavy weight, further limit the development of an intelligent power protection system. In order to compensate for these drawbacks, we proposed a novel current measurement method by using Hall sensors, which is called the Hall-effect current transformer (HCT. The existing commercial Hall sensors are electronic components, so the reliability of the HCT is normally worse than that of the traditional CT. Therefore, our study proposes a redundancy mechanism for the HCT to strengthen its reliability. With multiple sensor modules, the method has the ability to improve the accuracy of the HCT as well. Additionally, the proposed redundancy mechanism monitoring system provides a condition-based maintenance for the HCT. We verify our method with both simulations and an experimental test. The results demonstrate that the proposed HCT with a redundancy mechanism can almost achieve Class 0.2 for measuring CTs according to IEC Standard 60044-8. 9. Assessment of bilayer silicene to probe as quantum spin and valley Hall effect Science.gov (United States) Rehman, Majeed Ur; Qiao, Zhenhua 2018-02-01 Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene. 10. Role of helical edge modes in the chiral quantum anomalous Hall state. Science.gov (United States) Mani, Arjun; Benjamin, Colin 2018-01-22 Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. In this work we deal with a substantial 'What If?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically-protected then the QAH edge modes wont be topologically-protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological-protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The 'how' of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes. 11. Stability and activation gaps of the parafermionic Hall states in the second Landau level International Nuclear Information System (INIS) Georgiev, L.S. 2002-01-01 Analyzing the effective conformal field theory for the parafermionic Hall states, corresponding to filling fractions ν k =2+k/(kM+2), k=2,3,..., M odd, we show that the even k plateaux are expected to be more stable than their odd k neighbors. The reason is that the parafermion chiral algebra can be locally extended for k even. This reconciles the theoretical implication, that the bigger the k the less stable the fluid, with the experimental fact that, for M=1, the k=2 and k=4 plateaux are already observed at electron temperature T e ≅8 mK, while the Hall resistance for k=3 is not precisely quantized at that temperature in the sample of Pan et al. Using a heuristic gap ansatz we estimate the activation energy gap for ν 3 =13/5 to be approximately 0.015 K, which implies that the quantization of the Hall conductance could be observed for temperature below 1 mK in the same sample. We also find an appealing exact relation between the fractional electric charge and fractional statistics of the quasiholes. Finally, we argue that besides the Moore-Read phase for the ν 2 =5/2 state there is another relevant phase, in which the fundamental quasiholes obey abelian statistics and carry half-integer electric charge 12. Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States Directory of Open Access Journals (Sweden) Netanel H. Lindner 2012-10-01 Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation. 13. Nontrivial transition of transmission in a highly open quantum point contact in the quantum Hall regime Science.gov (United States) Hong, Changki; Park, Jinhong; Chung, Yunchul; Choi, Hyungkook; Umansky, Vladimir 2017-11-01 Transmission through a quantum point contact (QPC) in the quantum Hall regime usually exhibits multiple resonances as a function of gate voltage and high nonlinearity in bias. Such behavior is unpredictable and changes sample by sample. Here, we report the observation of a sharp transition of the transmission through an open QPC at finite bias, which was observed consistently for all the tested QPCs. It is found that the bias dependence of the transition can be fitted to the Fermi-Dirac distribution function through universal scaling. The fitted temperature matches quite nicely to the electron temperature measured via shot-noise thermometry. While the origin of the transition is unclear, we propose a phenomenological model based on our experimental results that may help to understand such a sharp transition. Similar transitions are observed in the fractional quantum Hall regime, and it is found that the temperature of the system can be measured by rescaling the quasiparticle energy with the effective charge (e*=e /3 ). We believe that the observed phenomena can be exploited as a tool for measuring the electron temperature of the system and for studying the quasiparticle charges of the fractional quantum Hall states. 14. Search for supersymmetry in 2 different topologies with the L3 detector at Lep International Nuclear Information System (INIS) Balandras, A. 2000-01-01 The present thesis presents two different aspects of my work in the L3 experiment, which are on one side the search for supersymmetric particles, the scalar leptons, in two different topologies 'electron + X + E' and '2 leptons + 2 photons + E', each of them being related to two theoretical SUSY models, m-SUGRA and GMSB. On the other side my work has been completed by the study of the BGO crystal electromagnetic calorimeter of L3, and the calibration of the electromagnetic calorimeter EGAP. After the essential motivations being reviewed, the production and disintegration modes are detailed concerning the scalar lepton sector at LEP. Then one presents the analysis techniques which I used to perform my selection, and also the results obtained from the data collected by L3 for center of mass energies between √ S =183 GeV and 202 GeV. The selection criteria that allow to isolate the events I looked for, including efficiencies but also the background rate coming from Standard Model that one can expect are presented. The final interpretations of those results in both frameworks of m-SUGRA and GMSB are detailed at the end of this thesis. I took benefit of those results to derive some limits on the masses of the scalar leptons that do not depend on the free parameters of the SUSY models, especially on the selectron mass in the framework of m-SUGRA: M e -tilde R > 71.2 GeV. (authors) 15. Search for scalar leptons at LEP with the L3 detector CERN Document Server Xia, Lei 2002-01-01 In this thesis, I present a search for scalar leptons in e+e- annihilation using the L3 detector at LEP. Data collected in 1999 and 2000, at center-of-mass energies between 192 GeV and 208 GeV, was used in this analysis. This work covered the scalar lepton searches in both SUGRA and GMSB models. To achieve this analysis, a parametrized selection was developed to handle the different event signatures in SUGRA models. Improvement of the L3 simulation and reconstruction program packages was carried out so that one can simulated the scalar leptons in GMSB models correctly. The simulation of the L3 Time Expansion Chamber (TEC) dE/dx measurement was rewritten to facilitate the analysis for a stable slepton signal, which is relevant in some parts of the parameter space in GMSB models. In this analysis, we didn't abserve any significant indication of scalar lepton production of any type. We achieved the following mass exclusion limits for scalar leptons in SUGRA models, for large dM: M(scalar e) > 97 GeV (expected 97... 16. Determination of the masses of electrical weak gauge bosons with L3 CERN Document Server Rosenbleck, Christian 2006-01-01 This thesis presents the measurement of the masses of the carriers of the weak force in the Standard Model of Particle Physics, the gauge bosons W and Z. The masses are determined using the kinematics of the bosons' decay products. The data were collected by the L3 experiment at the Large Electron Positron Collider (LEP) at centre-of-mass energies, sqrt(s), between 183 GeV and 209 GeV in the years 1997 to 2000. The mass of the Z-boson, mZ, is already known very precisely: The L3 collaboration determined it to be mZ = 91.1898 +- 0.0031 GeV from a scan of the Z resonance. Therefore the main aim of this analysis is not the determination of the numerical value of mZ; instead the analysis is used to cross-check the measurement of the W boson mass since the methods are similar. Alternatively, the analysis can be used to measure the mean centre-of-mass energy at the L3 interaction point. The Z-boson mass is determined to be mZ = 91.272 +- 0.046 GeV. If interpreted as measurement of the centre-of-mass energy, this va... 17. Psychometric Properties of the Italian Version of the Young Schema Questionnaire L-3: Preliminary Results Directory of Open Access Journals (Sweden) Aristide Saggino 2018-03-01 Full Text Available Schema Therapy (ST is a well-known approach for the treatment of personality disorders. This therapy integrates different theories and techniques into an original and systematic treatment model. The Young Schema Questionnaire L-3 (YSQ-L3 is a self-report instrument, based on the ST model, designed to assess 18 Early Maladaptive Schemas (EMSs. During the last decade, it has been translated and validated in different countries and languages. This study aims to establish the psychometric properties of the Italian Version of the YSQ-L3. We enrolled two groups: a clinical (n = 148 and a non-clinical one (n = 918. We investigated the factor structure, reliability and convergent validity with anxiety and depression between clinical and non-clinical groups. The results highlighted a few relevant findings. Cronbach's alpha showed significant values for all the schemas. All of the factor models do not seem highly adequate, even if the hierarchical model has proven to be the most significant one. Furthermore, the questionnaire confirms the ability to discriminate between clinical and non-clinical groups and could represent a useful tool in the clinical practice. Limitations and future directions are discussed. 18. Resonant Hall effect under generation of a self-sustaining mode of spin current in nonmagnetic bipolar conductors with identical characters between holes and electrons Science.gov (United States) Sakai, Masamichi; Takao, Hiraku; Matsunaga, Tomoyoshi; Nishimagi, Makoto; Iizasa, Keitaro; Sakuraba, Takahito; Higuchi, Koji; Kitajima, Akira; Hasegawa, Shigehiko; Nakamura, Osamu; Kurokawa, Yuichiro; Awano, Hiroyuki 2018-03-01 We have proposed an enhancement mechanism of the Hall effect, the signal of which is amplified due to the generation of a sustaining mode of spin current. Our analytic derivations of the Hall resistivity revealed the conditions indispensable for the observation of the effect: (i) the presence of the transverse component of an effective electric field due to spin splitting in chemical potential in addition to the longitudinal component; (ii) the simultaneous presence of holes and electrons each having approximately the same characteristics; (iii) spin-polarized current injection from magnetized electrodes; (iv) the boundary condition for the transverse current (J c, y = 0). The model proposed in this study was experimentally verified by using van der Pauw-type Hall devices consisting of the nonmagnetic bipolar conductor YH x (x ≃ 2) and TbFeCo electrodes. Replacing Au electrodes with TbFeCo electrodes alters the Hall resistivity from the ordinary Hall effect to the anomalous Hall-like effect with an enhancement factor of approximately 50 at 4 T. We interpreted the enhancement phenomenon in terms of the present model. 19. Quantum Theory of Conducting Matter Superconductivity and Quantum Hall Effect CERN Document Server

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http://mathhelpforum.com/pre-calculus/131710-calculating-inflation-rates.html

1. ## Calculating Inflation rates In a country where inflation is a concern, prices have risen by 40% over a 5-year period. a) By what percent do the prices rise each year? b) How long does it take for prices to rise by 5%? So how would I start out this problem? When it says inflation that means the prices are going up. Should I use this formula: P0e^k*t = P0 e^k*5 = 1.4 to solve and find the answer to a? If so then should the answer to a) be 0.067294447 or 6.7294447%? Also for b) should the set up be like this? 1(1.067294447)^t = 1.05? Solve for t If so should the answer to b) be 0.749155419? 2. Originally Posted by krzyrice In a country where inflation is a concern, prices have risen by 40% over a 5-year period. a) By what percent do the prices rise each year? b) How long does it take for prices to rise by 5%? So how would I start out this problem? When it says inflation that means the prices are going up. Should I use this formula: P0e^k*t = P0 e^k*5 = 1.4 to solve and find the answer to a? Inflation acts like "compounding continuously" so that would be correct. If so then should the answer to a) be 0.067294447 or 6.7294447%? If you are asking "which", the problem say "By what percent" so the second is correct. Also for b) should the set up be like this? 1(1.067294447)^t = 1.05? Solve for t If so should the answer to b) be 0.749155419? No, you should use the formula you used to get .06729447: [tex]e^{.06729447 t}= 1.05. , , ### how to calculate inflation rate in mathematics Click on a term to search for related topics.

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https://math.stackexchange.com/questions/2546454/is-it-true-that-sum-k-0m-binomn-kk-outputs-the-n1th-fibonacci-numbe

# Is it true that $\sum_{k=0}^m\binom{n-k}k$ outputs the $(n+1)$th Fibonacci number, where $m=\frac{n-1}2$ for odd $n$ and $m=\frac n2$ for even $n$? Does $$\sum_{k=0}^m\binom{n-k}k=F_{n+1}$$ where $m=\left\{\begin{matrix} \frac{n-1}{2}, \text{for odd} \,n\\ \frac n2, \text{for even} \,n \end{matrix}\right.$ hold for all positive integers $n$? Attempt: I have not yet found a counterexample, so I will attempt to prove it. $$\text{LHS} =\binom n0 + \binom{n-1}1+\binom{n-2}2+...+\left\{\begin{matrix} \binom{1+(n-1)/2}{(n-1)/2}, \text{for odd} \,n\\ \binom{n/2}{n/2}, \text{for even} \,n \end{matrix}\right.$$ Now using the identity that $\binom nk + \binom n{k+1}=\binom {n+1}{k+1}$, where $k$ is a positive integer, I find that $$\binom{n-1}1=\binom n1 - 1, \\ \binom {n-2}2=\binom n2-2\binom n1+3,\\ \binom {n-3}{3} =\binom n3 - 3\binom n2 + 6 \binom n1 - 10, \\ ...$$ This pattern suggests that the coefficients of $\binom{n-4}4$ will be square numbers, those of $\binom{n-5}5$ will be pentagonal numbers, etc. However, I cannot see a way to link these results to any Fibonacci identity. Edit: @Jack D'Aurizio♢ has provided a very succinct proof to this, but is there a more algebraic method to show the equality? • – Guy Fsone Dec 1 '17 at 18:58 • @GuyFsone: the point here is not to prove the hockey stick (or stars and bars) identity, but to understand how it is related to Fibonacci numbers. – Jack D'Aurizio Dec 1 '17 at 19:15 • @JackD'Aurizio I got it thanks – Guy Fsone Dec 1 '17 at 19:19 • – Felix Marin Dec 1 '17 at 23:50 There is a simple combinatorial interpretation. Let $S_n$ be the set of strings over the alphabet $\Sigma=\{0,1\}$ with length $n$ and no occurrence of the substring $11$. Let $L_n=|S_n|$. We clearly have $L_1=2$ and $L_2=3$, and $L_n=F_{n+2}$ is straightforward to prove by induction, since every element of $S_n$, for $n\geq 3$, is either $0\text{(element of }S_{n-1})$ or $10\text{(element of }S_{n-2})$, so $L_{n+2}=L_{n+1}+L_n$. On the other hand, we may consider the elements of $S_n$ with exactly $k$ characters $1$. There are as many elements with such structure as ways of writing $n+2-k$ as the sum of $k+1$ positive natural numbers. Here it is an example for $n=8$ and $k=3$: $$00101001\mapsto \color{grey}{0}00101001\color{grey}{0}\mapsto \color{red}{000}1\color{red}{0}1\color{red}{00}1\color{red}{0}\mapsto3+1+2+1.$$ By stars and bars it follows that: $$L_n = F_{n+2} = \sum_{k=0}^{n}[x^{n+2-k}]\left(\frac{x}{1-x}\right)^{k+1}=\sum_{k=0}^{n}\binom{n+1-k}{k}$$ and by reindexing we get $F_{n+1}=\sum_{k=0}^{n}\binom{n-k}{k}$ as wanted. • I don't really get the interpretation of $S_n$. Say we have the string $0101$. What does that mean? – TheSimpliFire Dec 1 '17 at 19:34 • @TheSimpliFire: $0101$ it is an element of $S_4$, associated with $k=2$ and $2+1+1$. – Jack D'Aurizio Dec 1 '17 at 19:40 • $S_4$ has $8$ elements, namely $$0000,0001,0010,0100,0101,1000,1001,1010$$ associated with $$6, 4+1,3+2,2+3,2+1+1,1+4,1+2+1,1+1+2.$$ – Jack D'Aurizio Dec 1 '17 at 19:45 • Thank you. But why is $0010$ associated with $3+2$? – TheSimpliFire Dec 1 '17 at 19:52 • @TheSimpliFire: add an initial and a final zero to get $000100\mapsto 3+2$. – Jack D'Aurizio Dec 1 '17 at 19:58 Here is more of an algebraic solution through generating functions. We have \begin{align} \sum_{n=0}^{\infty}\sum_{k=0}^{\lfloor n/2\rfloor}\binom{n-k}{k}x^n &=\sum_{k=0}^{\infty}\sum_{n=k}^{\infty}\binom{n}{k}x^{n+k+1}\\ &=\sum_{k=0}^{\infty}x^{2k+1}\sum_{n=k}^{\infty}\binom{n}{k}x^{n-k}\\ &=\sum_{k=0}^{\infty}x^{2k+1}\sum_{n=0}^{\infty}\binom{n+k}{k}x^{n}\\ &=\sum_{k=0}^{\infty}x^{2k+1}\frac{1}{(1-x)^{k+1}}\\ &=\frac{x}{1-x}\sum_{k=0}^{\infty}\left(\frac{x^2}{1-x}\right)^k\\ &=\frac{x}{1-x}\frac{1}{1-\frac{x^2}{1-x}}\\ &=\frac{x}{1-x-x^2} \end{align} where on the last line we arrived at the well known generating function for fibonacci numbers. So by equality of coefficients it follows $$F_{n+1} = \sum_{k=0}^{\lfloor (n)/2\rfloor}\binom{n-k}{k}.$$ • clever use of summations and series! – TheSimpliFire Dec 2 '17 at 14:05

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https://math.stackexchange.com/questions/3738214/is-there-a-geometric-analog-of-absolute-value

# Is there a geometric analog of absolute value? I'm wondering whether there exists a geometric analog concept of absolute value. In other words, if absolute value can be defined as $$\text{abs}(x) =\max(x,-x)$$ intuitively the additive distance from $$0$$ to $$x$$, is there a geometric version $$\text{Geoabs}(x) = \max(x, 1/x)$$ which is intuitively the multiplicative "distance" from $$1$$ to $$x$$? Update: Agreed it only makes sense for $$Geoabs()$$ to be restricted to positive reals. To give some context on application, I am working on the solution of an optimization problem something like: $$\begin{array}{ll} \text{minimize} & \prod_i Geoabs(x_i) \\ \text{subject to} & \prod_{i \in S_j} x_i = C_j && \forall j \\ &x_i > 0 && \forall i . \end{array}$$ Basically want to satisfy all these product equations $$j$$ by moving $$x_i$$'s as little as possible from $$1$$. Note by the construction there are always infinite feasible solutions. • Is the triangular inequality satisfied ? Jun 28, 2020 at 22:15 • Interesting idea but I'd consider revising the definition to $\operatorname{geoabs}(x)=\operatorname{sign}\left(x\right)\max\left(\left|x\right|,\left|\frac{1}{x}\right|\right)$, which would take $x$ over $(-\infty,-1]$ and $1/x$ on $(-1,0)$ instead of the other way round as you have. Your version has small or large negative values multiplicatively close $1$ while $-1$ is the most distal from $1$, which should be reversed. – Jam Jun 28, 2020 at 22:22 • @hamam_Abdallah I believe it is if you consider positive $x$ only. – Jam Jun 28, 2020 at 22:26 • The length of a vector is an absolute value. Jun 29, 2020 at 10:05 • Interesting question, but my initial reaction is "Have you thought about re-stating the problem in terms of the variables $y_i$, where $y_i = \log x_i$"? Jun 29, 2020 at 13:31 To make things easier I'll set $$f(x)=\max\{x,-x\}$$ and $$g(x)=\max\{x,\frac{1}{x}\}$$. So we understand that $$f:\mathbb{R}\to \mathbb{R}^+$$ and $$g: \mathbb{R}^+\to \mathbb{R}^+$$. Then $$\exp(f(x))=g(\exp(x))$$. So we can use this to translate some properties like the triangle inequality. $$g(xy)=g(\exp(\log(xy)))=\exp(f(\log(xy)))=\exp(f(\log(x)+\log(y)))$$ $$\leq \exp(f(\log x)+f(\log y))=\exp(f(\log x))\exp(f(\log y))=g(\exp(\log(x))g(\exp(\log(x))$$ $$=g(x)g(y)$$ So $$g(xy)\leq g(x)g(y)$$ and we have the multiplicative triangle inequality. Of course this is easier to show directly but the method emphasizes the "transfer". Another good sign is $$g(x)=1$$ if and only if $$x=1$$. All in all it looks like you're moving between $$(\mathbb{R},+)$$ and $$(\mathbb{R}^+,\cdot)$$ with $$\log$$ and $$\exp$$. So a nice question. I'm sure there's more to say. Another way (maybe cleaner) to see it : let us consider • $$G_1 = (\mathbb{R},+,\|\cdot\|_1)$$ the additive group of real numbers equipped with a norm : for all $$x\in G_1$$, $$\|x\|_1 = |x| = \max \{x,-x\}$$ • $$G_2 = (\mathbb{R_+^*},\cdot,\|\cdot\|_2)$$ the multiplicative group of (strictly) positive real numbers equipped with a norm defined using the norm of $$G_1$$ : for all $$x\in G_2$$, $$\|x\|_2 = \|\ln x\|_1 = \ln \max \{x,1/x\}$$ The map $$\exp\colon G_1\to G_2$$ is therefore by construction a group isometric isomorphism (with $$\ln\colon G_2\to G_1$$ its inverse). Indeed, for all $$x\in G_1$$ $$\|x\|_1 = \|\exp x\|_2$$ You can check that $$\|e_i\|_i = 0$$ where $$e_i$$ is the identity element of $$G_i$$ (here $$e_1 = 0$$ and $$e_2 = 1$$). If you forget the $$\ln$$ map in the definition of $$\|\cdot\|_2$$, it is not anymore a norm.

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https://realdevtalk.com/tag/pytorch/

## Tensors & Machine Learning When it comes to building neural network models, there’s a lot of factors to consider such as hyperparameter tuning, model architecture, whether to use a pre-trained model or not, and so on and so forth. While it’s true that these are all important aspects to consider, I would argue that proper understanding of data representations […]

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https://openreview.net/forum?id=MljXVdp4A3N

## Know Your Action Set: Learning Action Relations for Reinforcement Learning 29 Sept 2021, 00:30 (modified: 16 Mar 2022, 08:08)ICLR 2022 PosterReaders: Everyone Keywords: reinforcement learning, varying action space, relational reasoning Abstract: Intelligent agents can solve tasks in various ways depending on their available set of actions. However, conventional reinforcement learning (RL) assumes a fixed action set. This work asserts that tasks with varying action sets require reasoning of the relations between the available actions. For instance, taking a nail-action in a repair task is meaningful only if a hammer-action is also available. To learn and utilize such action relations, we propose a novel policy architecture consisting of a graph attention network over the available actions. We show that our model makes informed action decisions by correctly attending to other related actions in both value-based and policy-based RL. Consequently, it outperforms non-relational architectures on applications where the action space often varies, such as recommender systems and physical reasoning with tools and skills. Results and code at https://sites.google.com/view/varyingaction . One-sentence Summary: Learning action interdependence for reinforcement learning under a varying action space. Supplementary Material: zip 10 Replies

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http://mathhelpforum.com/calculus/20472-acceleration-velocity-models-problem.html

# Math Help - Acceleration-Velocity Models problem 1. ## Acceleration-Velocity Models problem A woman bails out of an airplane at an altitude of 10,000fts, falls freely for 20s, then open her parachute. How long will it take her to reach the ground? Assume linear air resistance pv ft/s^2, taking p = 0.15 without the parachute and p = 1.5 with the parachute. My solution so far: I recognize that Acceleration = gravity - resistance x velocity, since Velocity' = Acceleration, we have v' = g - pv or dv/dt = 32.2ft - 0.15v by separation of variables, I obtain V(t), integrating that, I get X(t), the position function. But in the end, I cannot solve for t in the X(t), since one t is by itself, while I have two ts in the e^. Any help? A woman bails out of an airplane at an altitude of 10,000fts, falls freely for 20s, then open her parachute. How long will it take her to reach the ground? Assume linear air resistance pv ft/s^2, taking p = 0.15 without the parachute and p = 1.5 with the parachute. My solution so far: I recognize that Acceleration = gravity - resistance x velocity, since Velocity' = Acceleration, we have v' = g - pv or dv/dt = 32.2ft - 0.15v by separation of variables, I obtain V(t), integrating that, I get X(t), the position function. But in the end, I cannot solve for t in the X(t), since one t is by itself, while I have two ts in the e^. Any help? That's correct. You have a displacement function of the form $x(t) = at + be^{-ct}$ (a, b, and c, are just constants. a is not meant to represent acceleration.) Probably the best way to solve this is by a "successive guess" technique: see if you can find a t such that x = 10000 ft. -Dan

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http://math.stackexchange.com/questions/591983/showing-that-a-functor-is-not-representable

# Showing that a functor is not representable. Let $Y,Z$ be sets. We define a functor $F:Set\rightarrow Set$ in the following manner: $F(X)=Hom(X,Y)\amalg Hom(X,Z)$, $F(f)=Hom(X,f)\amalg Hom(X,f)$. How to prove that $F$ is not representable unless one of $Y,Z$ is empty? Thank you in anticipation. - Probably no-one is responding because it is easy for you all, but a solution will be greatly appreciated, thank you for your time. –  keka Dec 4 '13 at 7:43 Does $\amalg$ mean disjoint union? And what is $X$ in $F(f) = Hom(X, f) \amalg Hom(X, f)$. Should this be $Hom(Y, f) \amalg Hom(Z, f)$? –  Aleš Bizjak Dec 4 '13 at 8:00 Or perhaps even $\mathrm{Hom}(f, Y) \amalg \mathrm{Hom}(f, Z)$? –  Zhen Lin Dec 4 '13 at 8:16 ## 1 Answer If $F = \hom(-,Y) \sqcup \hom(-,Z) \cong \hom(-,S)$ for some set $S$, then by plugging in $1$ (the set with one element) we get $Y \sqcup Z = S$. It follows that the natural map $\hom(-,Y) \sqcup \hom(-,Z) \to \hom(-,Y \sqcup Z)$ is an isomorphism. In other words, if $X \to Y \sqcup Z$ is an arbitrary map, then its image lies in $Y$ or in $Z$. Of course this fails when $Y,Z \neq \emptyset$ (consider $X=2$). - Thank you Martin. –  keka Dec 4 '13 at 15:17

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https://math.stackexchange.com/questions/3173125/what-are-the-integer-coeffcients-of-a-cubic-polynomial-having-two-particular-pro/3183314

# What are the integer coeffcients of a cubic polynomial having two particular properties? Let $$f(x) = x^3 + a x^2 + b x + c$$ and $$g(x) = x^3 + b x^2 + c x + a\,$$ where $$a, b, c$$ are integers and $$c\neq 0\,$$. Suppose that the following conditions hold: 1. $$f(1)=0$$ 2. The roots of $$g(x)$$ are squares of the roots of $$f(x)$$. I'd like to find $$a, b$$ and $$c$$. I tried solving equations made using condition 1. and relation between the roots, but couldn't solve. The equation which I got in $$c$$ is $$c^4 + c^2 +3 c-1=0$$ (edit: eqn is wrong). Also I was able to express $$a$$ and $$b$$ in terms of $$c$$. But the equation isn't solvable by hand. • Welcome to MSE. Click on the "edit" button below your question to add details, like exactly what equation you derived from conditions 1 and 2, and how you attempted to solve them; then you'll be more likely to get help that's well-targeted. Simple "do my homework for me questions" don't get nearly as much traction here as ones that show you've done some work yourself (and therefore don't waste our time giving detailed answers when it's a simple matter of a missing minus-sign, for instance). – John Hughes Apr 3 at 11:32 • Which equations could you write down? – Math-fun Apr 3 at 11:35 • Also: I've edited to clean up the MathJax: in general, go ahead and put anything math-like between dollar signs. Rather than things like $a$ = $b$x + $c$ which produces $a$ = $b$x + $c$ let MathJax do its magic at formatting equations: $a = bx + c$ will produce $a = bx + c$. – John Hughes Apr 3 at 11:35 • Edited with Eq. – Meet Shah Apr 3 at 11:36 • I don't understand how you got that equation in $c$. And if you were "able to express $a$ and $b$ in terms of $c$," why not tell us what the expression was? Go ahead and type a little more, so that we understand what you know/don't know and what you can and cannot do. – John Hughes Apr 3 at 11:44 Let $$u$$, $$v$$ and $$w$$ be the roots of $$f$$, so that $$u^2$$, $$v^2$$ and $$w^2$$ are the roots of $$g$$. Then comparing the coefficients of $$(x-u)(x-v)(x-w)=f(x)=x^3+ax^2+bx+c,$$ $$(x-u^2)(x-v^2)(x-w^2)=g(x)=x^3+bx^2+cx+a,$$ yields the equations $$\begin{eqnarray*} a&=&-u-v-w&=&-u^2v^2w^2,\\ b&=&uv+uw+vw&=&-u^2-v^2-w^2,\\ c&=&-uvw&=&u^2v^2+u^2w^2+v^2w^2. \end{eqnarray*}$$ This immediately shows that $$a=-c^2$$, and the identities $$\begin{eqnarray*} u^2+v^2+w^2&=&(u+v+w)^2-2(uv+uw+vw),\\ u^2v^2+u^2w^2+v^2w^2&=&uvw(u+v+w)-(uv+uw+vw)^2, \end{eqnarray*}$$ show that $$-b=a^2-2b$$ and $$c=ac-b^2$$, respectively, hence $$b=a^2=c^4$$ and so $$f(x)=x^3-c^2x^2+c^4x+c,$$ for some $$c$$. Then $$f(1)=1$$ implies that $$c^4-c^2+c+1=0,$$ which has the clear root $$c=-1$$. Then $$a=-1$$ and $$b=1$$. Hint: Condition 2 can be expressed as $$f(x)$$ divides $$g(x^2)$$. The conditions 1 and 2 imply that • $$\;c\,$$ must be $$\,0\,$$ or $$\,-1$$, • $$\;a= -c^2$$, and $$\:b= c^2-c-1\,$$. Condition 1 gives $$0=f(1)=1+a+b+c=g(1)\,.\,$$ Hence both $$f$$ and $$g$$ have a zero at $$1$$ and factor as $$f(x) \,=\, (x-1)\big(x^2 + (a+1)x -c\big)\\[1.5ex] g(x) \,=\, (x-1)\big(x^2 -(a+c)x -a\big)\,.$$ Denote the roots of the quadratic factor of $$f$$ by $$x_1$$ and $$x_2$$. Condition 2 says that the roots of $$g$$ are contained in $$\{1,x_1^2,x_2^2\}$$. By Vieta's formula one gets $$\,-a \,=\, x_1^2x_2^2=(-c)^2 \,=\, c^2\,,\;\text{thus}\;\; b \,=\, -a-c-1 \,=\, c^2-c-1\,.\tag{1}$$ Note that condition 2 remains true when restricted to the quadratic factors of $$f$$ and $$\,g$$. These are $$q_f \,=\,x^2 + \left(1-c^2\right)x -c\tag{2}\\ q_g \,=\,x^2 -c\,(1-c)x +c^2$$ when written in terms of $$\,c$$. It is shown next that condition 2 cannot hold if $$c\neq 0\,$$ or $$\,-1$$. 1. Assume $$c\geqslant 1$$. Then $$q_f(0)=-c<0$$, and the roots $$x_1,x_2$$ of $$q_f$$ are real and distinct. By Vieta's formula regarding $$q_g$$ one reaches the contradiction $$0. 2. Assume $$c\leq -2\,$$. Then the discriminant $$\left(1-c^2\right)^2+4c$$ in $$(2)$$ is positive, and we run into the same contradiction as before. So we are left with the two solutions (with condition 2 obviously satisfied) • $$a=0,b=-1,c=0\:$$ which was ruled out a priori then $$f(x)=x(x+1)(x-1)\:$$ and $$\:g(x)=x^2(x-1)$$ • $$a=-1,b=1,c=-1\:$$ where $$f(x)=\left(x^2+1\right)(x-1)\:$$ and $$\:g(x)=(x+1)^2(x-1)$$

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https://en.m.wikipedia.org/wiki/Dot_product

Dot product In mathematics, the dot product or scalar product[note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not the only inner product that can be defined on Euclidean space; see also inner product space. Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In modern geometry, Euclidean spaces are often defined by using vector spaces. In this case, the dot product is used for defining lengths (the length of a vector is the square root of the dot product of the vector by itself) and angles (the cosine of the angle of two vectors is the quotient of their dot product by the product of their lengths). The name "dot product" is derived from the centered dot· " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the vector product in three-dimensional space. Definition The dot product may be defined algebraically or geometrically. The geometric definition is based on the notions of angle and distance (magnitude of vectors). The equivalence of these two definitions relies on having a Cartesian coordinate system for Euclidean space. In modern presentations of Euclidean geometry, the points of space are defined in terms of their Cartesian coordinates, and Euclidean space itself is commonly identified with the real coordinate space Rn. In such a presentation, the notions of length and angles are defined by means of the dot product. The length of a vector is defined as the square root of the dot product of the vector by itself, and the cosine of the (non oriented) angle of two vectors of length one is defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations of Euclidean geometry. Algebraic definition The dot product of two vectors a = [a1, a2, …, an] and b = [b1, b2, …, bn] is defined as:[1] ${\displaystyle \mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} =\sum _{i=1}^{n}{\color {red}a}_{i}{\color {blue}b}_{i}={\color {red}a}_{1}{\color {blue}b}_{1}+{\color {red}a}_{2}{\color {blue}b}_{2}+\cdots +{\color {red}a}_{n}{\color {blue}b}_{n}}$ where Σ denotes summation and n is the dimension of the vector space. For instance, in three-dimensional space, the dot product of vectors [1, 3, −5] and [4, −2, −1] is: {\displaystyle {\begin{aligned}\ [{\color {red}1,3,-5}]\cdot [{\color {blue}4,-2,-1}]&=({\color {red}1}\times {\color {blue}4})+({\color {red}3}\times {\color {blue}-2})+({\color {red}-5}\times {\color {blue}-1})\\&=4-6+5\\&=3\end{aligned}}} If vectors are identified with row matrices, the dot product can also be written as a matrix product ${\displaystyle \mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} =\mathbf {\color {red}a} \mathbf {\color {blue}b} ^{\top },}$ where ${\displaystyle \mathbf {\color {blue}b} ^{\top }}$  denotes the transpose of ${\displaystyle \mathbf {\color {blue}b} }$ . Expressing the above example in this way, a 1 × 3 matrix (row vector) is multiplied by a 3 × 1 matrix (column vector) to get a 1 × 1 matrix that is identified with its unique entry: ${\displaystyle {\begin{bmatrix}\color {red}1&\color {red}3&\color {red}-5\end{bmatrix}}{\begin{bmatrix}\color {blue}4\\\color {blue}-2\\\color {blue}-1\end{bmatrix}}=\color {purple}3}$ . Geometric definition Illustration showing how to find the angle between vectors using the dot product In Euclidean space, a Euclidean vector is a geometric object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction that the arrow points to. The magnitude of a vector a is denoted by ${\displaystyle \left\|\mathbf {a} \right\|}$ . The dot product of two Euclidean vectors a and b is defined by[2][3] ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\|\mathbf {a} \|\ \|\mathbf {b} \|\cos(\theta ),}$ where θ is the angle between a and b. In particular, if a and b are orthogonal (the angle between vectors is 90°) then due to ${\displaystyle \cos(90^{\circ })=0}$ ${\displaystyle \mathbf {a} \cdot \mathbf {b} =0.}$ At the other extreme, if they are codirectional, then the angle between them is 0° and ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\left\|\mathbf {a} \right\|\,\left\|\mathbf {b} \right\|}$ This implies that the dot product of a vector a with itself is ${\displaystyle \mathbf {a} \cdot \mathbf {a} =\left\|\mathbf {a} \right\|^{2},}$ which gives ${\displaystyle \left\|\mathbf {a} \right\|={\sqrt {\mathbf {a} \cdot \mathbf {a} }},}$ the formula for the Euclidean length of the vector. Scalar projection and first properties Scalar projection The scalar projection (or scalar component) of a Euclidean vector a in the direction of a Euclidean vector b is given by ${\displaystyle a_{b}=\left\|\mathbf {a} \right\|\cos \theta ,}$ where θ is the angle between a and b. In terms of the geometric definition of the dot product, this can be rewritten ${\displaystyle a_{b}=\mathbf {a} \cdot {\widehat {\mathbf {b} }},}$ where ${\displaystyle {\widehat {\mathbf {b} }}=\mathbf {b} /\left\|\mathbf {b} \right\|}$  is the unit vector in the direction of b. Distributive law for the dot product The dot product is thus characterized geometrically by[4] ${\displaystyle \mathbf {a} \cdot \mathbf {b} =a_{b}\left\|\mathbf {b} \right\|=b_{a}\left\|\mathbf {a} \right\|.}$ The dot product, defined in this manner, is homogeneous under scaling in each variable, meaning that for any scalar α, ${\displaystyle (\alpha \mathbf {a} )\cdot \mathbf {b} =\alpha (\mathbf {a} \cdot \mathbf {b} )=\mathbf {a} \cdot (\alpha \mathbf {b} ).}$ It also satisfies a distributive law, meaning that ${\displaystyle \mathbf {a} \cdot (\mathbf {b} +\mathbf {c} )=\mathbf {a} \cdot \mathbf {b} +\mathbf {a} \cdot \mathbf {c} .}$ These properties may be summarized by saying that the dot product is a bilinear form. Moreover, this bilinear form is positive definite, which means that ${\displaystyle \mathbf {a} \cdot \mathbf {a} }$  is never negative and is zero if and only if ${\displaystyle \mathbf {a} =\mathbf {0} }$ , the zero vector. Equivalence of the definitions If e1, ..., en are the standard basis vectors in Rn, then we may write {\displaystyle {\begin{aligned}\mathbf {a} &=[a_{1},\dots ,a_{n}]=\sum _{i}a_{i}\mathbf {e} _{i}\\\mathbf {b} &=[b_{1},\dots ,b_{n}]=\sum _{i}b_{i}\mathbf {e} _{i}.\end{aligned}}} The vectors ei are an orthonormal basis, which means that they have unit length and are at right angles to each other. Hence since these vectors have unit length ${\displaystyle \mathbf {e} _{i}\cdot \mathbf {e} _{i}=1}$ and since they form right angles with each other, if ij, ${\displaystyle \mathbf {e} _{i}\cdot \mathbf {e} _{j}=0.}$ Thus in general we can say that: ${\displaystyle \mathbf {e} _{i}\cdot \mathbf {e} _{j}=\delta _{ij}.}$ Where δ ij is the Kronecker delta. Also, by the geometric definition, for any vector ei and a vector a, we note ${\displaystyle \mathbf {a} \cdot \mathbf {e} _{i}=\left\|\mathbf {a} \right\|\,\left\|\mathbf {e} _{i}\right\|\cos \theta =\left\|\mathbf {a} \right\|\cos \theta =a_{i},}$ where ai is the component of vector a in the direction of ei. Now applying the distributivity of the geometric version of the dot product gives ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\mathbf {a} \cdot \sum _{i}b_{i}\mathbf {e} _{i}=\sum _{i}b_{i}(\mathbf {a} \cdot \mathbf {e} _{i})=\sum _{i}b_{i}a_{i}=\sum _{i}a_{i}b_{i},}$ which is precisely the algebraic definition of the dot product. So the geometric dot product equals the algebraic dot product. Properties The dot product fulfills the following properties if a, b, and c are real vectors and r is a scalar.[1][2] 1. Commutative: ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\mathbf {b} \cdot \mathbf {a} ,}$ which follows from the definition (θ is the angle between a and b): ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\left\|\mathbf {a} \right\|\left\|\mathbf {b} \right\|\cos \theta =\left\|\mathbf {b} \right\|\left\|\mathbf {a} \right\|\cos \theta =\mathbf {b} \cdot \mathbf {a} .}$ 2. Distributive over vector addition: ${\displaystyle \mathbf {a} \cdot (\mathbf {b} +\mathbf {c} )=\mathbf {a} \cdot \mathbf {b} +\mathbf {a} \cdot \mathbf {c} .}$ 3. Bilinear: ${\displaystyle \mathbf {a} \cdot (r\mathbf {b} +\mathbf {c} )=r(\mathbf {a} \cdot \mathbf {b} )+(\mathbf {a} \cdot \mathbf {c} ).}$ 4. Scalar multiplication: ${\displaystyle (c_{1}\mathbf {a} )\cdot (c_{2}\mathbf {b} )=c_{1}c_{2}(\mathbf {a} \cdot \mathbf {b} ).}$ 5. Not associative because the dot product between a scalar (a ⋅ b) and a vector (c) is not defined, which means that the expressions involved in the associative property, (a ⋅ b) ⋅ c or a ⋅ (b ⋅ c) are both ill-defined.[5] Note however that the previously mentioned scalar multiplication property is sometimes called the "associative law for scalar and dot product"[6] or one can say that "the dot product is associative with respect to scalar multiplication" because c (ab) = (c a) ⋅ b = a ⋅ (c b).[7] 6. Orthogonal: Two non-zero vectors a and b are orthogonal if and only if ab = 0. 7. No cancellation: Unlike multiplication of ordinary numbers, where if ab = ac, then b always equals c unless a is zero, the dot product does not obey the cancellation law: If ab = ac and a0, then we can write: a ⋅ (bc) = 0 by the distributive law; the result above says this just means that a is perpendicular to (bc), which still allows (bc) ≠ 0, and therefore bc. 8. Product Rule: If a and b are functions, then the derivative (denoted by a prime ′) of ab is a′ ⋅ b + ab. Application to the law of cosines Triangle with vector edges a and b, separated by angle θ. Given two vectors a and b separated by angle θ (see image right), they form a triangle with a third side c = ab. The dot product of this with itself is: {\displaystyle {\begin{aligned}\mathbf {\color {gold}c} \cdot \mathbf {\color {gold}c} &=(\mathbf {\color {red}a} -\mathbf {\color {blue}b} )\cdot (\mathbf {\color {red}a} -\mathbf {\color {blue}b} )\\&=\mathbf {\color {red}a} \cdot \mathbf {\color {red}a} -\mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} -\mathbf {\color {blue}b} \cdot \mathbf {\color {red}a} +\mathbf {\color {blue}b} \cdot \mathbf {\color {blue}b} \\&={\color {red}a}^{2}-\mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} -\mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} +{\color {blue}b}^{2}\\&={\color {red}a}^{2}-2\mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} +{\color {blue}b}^{2}\\{\color {gold}c}^{2}&={\color {red}a}^{2}+{\color {blue}b}^{2}-2{\color {red}a}{\color {blue}b}\cos {\color {purple}\theta }\\\end{aligned}}} which is the law of cosines. Triple product There are two ternary operations involving dot product and cross product. The scalar triple product of three vectors is defined as ${\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )=\mathbf {b} \cdot (\mathbf {c} \times \mathbf {a} )=\mathbf {c} \cdot (\mathbf {a} \times \mathbf {b} ).}$ Its value is the determinant of the matrix whose columns are the Cartesian coordinates of the three vectors. It is the signed volume of the Parallelepiped defined by the three vectors. The vector triple product is defined by[1][2] ${\displaystyle \mathbf {a} \times (\mathbf {b} \times \mathbf {c} )=\mathbf {b} (\mathbf {a} \cdot \mathbf {c} )-\mathbf {c} (\mathbf {a} \cdot \mathbf {b} ).}$ This identity, also known as Lagrange's formula may be remembered as "BAC minus CAB", keeping in mind which vectors are dotted together. This formula finds application in simplifying vector calculations in physics. Physics In physics, vector magnitude is a scalar in the physical sense, i.e. a physical quantity independent of the coordinate system, expressed as the product of a numerical value and a physical unit, not just a number. The dot product is also a scalar in this sense, given by the formula, independent of the coordinate system. Examples include:[8][9] Generalizations Complex vectors For vectors with complex entries, using the given definition of the dot product would lead to quite different properties. For instance the dot product of a vector with itself would be an arbitrary complex number, and could be zero without the vector being the zero vector (such vectors are called isotropic); this in turn would have consequences for notions like length and angle. Properties such as the positive-definite norm can be salvaged at the cost of giving up the symmetric and bilinear properties of the scalar product, through the alternative definition[10][1] ${\displaystyle \mathbf {a} \cdot \mathbf {b} =\sum {a_{i}{\overline {b_{i}}}},}$ where bi is the complex conjugate of bi. Then the scalar product of any vector with itself is a non-negative real number, and it is nonzero except for the zero vector. However this scalar product is thus sesquilinear rather than bilinear: it is conjugate linear and not linear in a, and the scalar product is not symmetric, since ${\displaystyle \mathbf {a} \cdot \mathbf {b} ={\overline {\mathbf {b} \cdot \mathbf {a} }}.}$ The angle between two complex vectors is then given by ${\displaystyle \cos \theta ={\frac {\operatorname {Re} (\mathbf {a} \cdot \mathbf {b} )}{\left\|\mathbf {a} \right\|\,\left\|\mathbf {b} \right\|}}.}$ This type of scalar product is nevertheless useful, and leads to the notions of Hermitian form and of general inner product spaces. Inner product The inner product generalizes the dot product to abstract vector spaces over a field of scalars, being either the field of real numbers ${\displaystyle \mathbb {R} }$  or the field of complex numbers ${\displaystyle \mathbb {C} }$ . It is usually denoted using angular brackets by ${\displaystyle \left\langle \mathbf {a} \,,\mathbf {b} \right\rangle }$ . The inner product of two vectors over the field of complex numbers is, in general, a complex number, and is sesquilinear instead of bilinear. An inner product space is a normed vector space, and the inner product of a vector with itself is real and positive-definite. Functions The dot product is defined for vectors that have a finite number of entries. Thus these vectors can be regarded as discrete functions: a length-n vector u is, then, a function with domain {k ∈ ℕ ∣ 1 ≤ kn}, and ui is a notation for the image of i by the function/vector u. This notion can be generalized to continuous functions: just as the inner product on vectors uses a sum over corresponding components, the inner product on functions is defined as an integral over some interval axb (also denoted [a, b]):[1] ${\displaystyle \left\langle u,v\right\rangle =\int _{a}^{b}u(x)v(x)dx}$ Generalized further to complex functions ψ(x) and χ(x), by analogy with the complex inner product above, gives[1] ${\displaystyle \left\langle \psi ,\chi \right\rangle =\int _{a}^{b}\psi (x){\overline {\chi (x)}}dx.}$ Weight function Inner products can have a weight function, i.e. a function which weights each term of the inner product with a value. Explicitly, the inner product of functions ${\displaystyle u(x)}$  and ${\displaystyle v(x)}$  with respect to the weight function ${\displaystyle r(x)>0}$  is ${\displaystyle \left\langle u,v\right\rangle =\int _{a}^{b}r(x)u(x)v(x)dx.}$ Matrices have the Frobenius inner product, which is analogous to the vector inner product. It is defined as the sum of the products of the corresponding components of two matrices A and B having the same size: ${\displaystyle \mathbf {A} :\mathbf {B} =\sum _{i}\sum _{j}A_{ij}{\overline {B_{ij}}}=\mathrm {tr} (\mathbf {B} ^{\mathrm {H} }\mathbf {A} )=\mathrm {tr} (\mathbf {A} \mathbf {B} ^{\mathrm {H} }).}$ ${\displaystyle \mathbf {A} :\mathbf {B} =\sum _{i}\sum _{j}A_{ij}B_{ij}=\mathrm {tr} (\mathbf {B} ^{\mathrm {T} }\mathbf {A} )=\mathrm {tr} (\mathbf {A} \mathbf {B} ^{\mathrm {T} })=\mathrm {tr} (\mathbf {A} ^{\mathrm {T} }\mathbf {B} )=\mathrm {tr} (\mathbf {B} \mathbf {A} ^{\mathrm {T} }).}$  (For real matrices) Dyadics have a dot product and "double" dot product defined on them, see Dyadics (Product of dyadic and dyadic) for their definitions. Tensors The inner product between a tensor of order n and a tensor of order m is a tensor of order n + m − 2, see tensor contraction for details. Computation Algorithms The straightforward algorithm for calculating a floating-point dot product of vectors can suffer from catastrophic cancellation. To avoid this, approaches such as the Kahan summation algorithm are used. Libraries A dot product function is included in BLAS level 1. Notes 1. ^ The term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.[citation needed] References 1. S. Lipschutz; M. Lipson (2009). Linear Algebra (Schaum’s Outlines) (4th ed.). McGraw Hill. ISBN 978-0-07-154352-1. 2. ^ a b c M.R. Spiegel; S. Lipschutz; D. Spellman (2009). Vector Analysis (Schaum’s Outlines) (2nd ed.). McGraw Hill. ISBN 978-0-07-161545-7. 3. ^ A I Borisenko; I E Taparov (1968). Vector and tensor analysis with applications. Translated by Richard Silverman. Dover. p. 14. 4. ^ Arfken, G. B.; Weber, H. J. (2000). Mathematical Methods for Physicists (5th ed.). Boston, MA: Academic Press. pp. 14–15. ISBN 978-0-12-059825-0.. 5. ^ Weisstein, Eric W. "Dot Product." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DotProduct.html 6. ^ T. Banchoff; J. Wermer (1983). Linear Algebra Through Geometry. Springer Science & Business Media. p. 12. ISBN 978-1-4684-0161-5. 7. ^ A. Bedford; Wallace L. Fowler (2008). Engineering Mechanics: Statics (5th ed.). Prentice Hall. p. 60. ISBN 978-0-13-612915-8. 8. ^ K.F. Riley; M.P. Hobson; S.J. Bence (2010). Mathematical methods for physics and engineering (3rd ed.). Cambridge University Press. ISBN 978-0-521-86153-3. 9. ^ M. Mansfield; C. O’Sullivan (2011). Understanding Physics (4th ed.). John Wiley & Sons. ISBN 978-0-47-0746370. 10. ^ Berberian, Sterling K. (2014) [1992], Linear Algebra, Dover, p. 287, ISBN 978-0-486-78055-9

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http://tex.stackexchange.com/questions/48260/xparse-bug-in-optional-arguments-simply-not-working

# xparse bug in optional arguments (simply not working)? [closed] The follow code returns -NoValue- instead of 3 It seems I'm wrong in that I thought xparse took a single argument and parsed it instead of all the arguments of a macro. \documentclass[11pt]{book} % use larger type; default would be 10pt \usepackage{pgffor} \usepackage{xparse} \begin{document} \DeclareDocumentCommand{\Dotparse}{o m} { #1 } % Passes each value in the array to an xparse command. \def\Dots#1 { \foreach \n in {#1}{ \Dotparse{\n} }} \Dots{[3]f4s3,f12s5,s2f14,[5]e,f,g,1,2,3,4,5,6,7} \end{document} - Actually, \Dotparse[3]{f4s3} prints 3. \Dotparse{[3]f4s3} has no optional argument. :) –  Paulo Cereda Mar 16 '12 at 13:24 Ok, That makes sense... I simplified this example and didn't think about it. I'll post the full code. Actually, I had a misconception about xparse. I thought it took an argument and parsed it given the specification. –  Uiy Mar 16 '12 at 13:29 add comment ## closed as too localized by egreg, Paulo Cereda, Yiannis Lazarides, Thorsten, lockstepMar 17 '12 at 15:48 This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. ## 1 Answer First of all this is no bug. You defined a command \Dotparse with one mandatory and one optional argument. The mandatory argument is braced by curly brackets {....} and the optional one by square brackets [...]. If you type \Dotparse{[3]f4s3} LaTeX reads only one mandatory argument because the outer brackets are {...}. So the correct form is \Dotparse[3]{f4s3} to set the optional and the mandatory argument. The output -NoValue is a special key provided by xparse. xparse provides several optional argument types whereby o has the following meaning: • If no optional argument without square brackets is given the argument is set to \NoValue. • If square brackets are given the argument is set to this value. Note: An empty optional arguments doesn't set \NoValue. Based on this information you can use the conditional \IfNoValueTF to test whether an optional argument is given or not. EDIT I can't understand your question. But your example looks really weird for me. You should tell us what's your intention. You can do the following: 1. Every definition of macros and functions should be done in the header. 2. The variable \n must be expanded before the function \Dotparse works 3. You need not to use extra brackets around the variable n. 4. Use the argument type u which has the following syntax u<token> this argument type reads everything until the given token is found whereby the given token isn't part of the argument. I used the token \nil. The whole example: \documentclass[11pt]{book} % use larger type; default would be 10pt \usepackage{pgffor} \usepackage{xparse} \DeclareDocumentCommand{\Dotparse}{o u \nil } {#1\textbullet } \def\Dots#1 { \foreach \n in {#1}{ \n\qquad \expandafter\Dotparse\n\nil \par }} \begin{document} \Dots{[3]f4s3,f12s5,s2f14,[5]e,f,g,1,2,3,4,5,6,7} \end{document} EDIT 2: @BrunoLeFloch suggested an alternative using \clist_map_inline:Nn. In this way you don't need the package pgffor and you don't regard any expansion. \documentclass{article} \usepackage{xparse} \ExplSyntaxOn \NewDocumentCommand{\Dotparse}{o u \nil } { \IfNoValueTF { #1 } {no~optional~Argument~given} {The~optional~argument~is~#1} \par } \clist_new:N \l_dot_store_clist \NewDocumentCommand{\Dots}{ m } { \clist_set:Nn \l_dot_store_clist { #1 } \clist_map_inline:Nn \l_dot_store_clist { \Dotparse ##1 \nil } } \ExplSyntaxOff \begin{document} \Dots{[3]f4s3,f12s5,s2f14,[5]e,f,g,1,2,3,4,5,6,7} \end{document} - What does \nil do? –  Tobi Mar 16 '12 at 14:43 @Tobi: \nil is a single token and the argument type u reads everything until the given token is found. You can also use \hippopotamus ;-) –  Marco Daniel Mar 16 '12 at 16:19 Instead of \foreach I'd use \SplitList and \tl_map_inline, or directly \clist_map_inline. That avoids loading pgffor. –  Bruno Le Floch Mar 16 '12 at 16:47 @BrunoLeFloch: You mean as an alternativ of the algorithm of the OP. The benefit I can avoid the expandafter ;-) –  Marco Daniel Mar 16 '12 at 16:48 Your answer is very complete. One small improvement is that you don't need to store the clist in a temporary variable: just use \clist_map_inline:nn {#1}{\Dotparse ##1\nil}. As for the choice of syntax of the OP, well, let's simply dub it "non-standard". –  Bruno Le Floch Mar 16 '12 at 19:17 show 4 more comments

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https://math.stackexchange.com/questions/2624032/given-is-a-uniformly-distributed-random-variable-u-in-0-1-and-density-how

# Given is a uniformly distributed random variable $u \in (0,1)$ and density. How can you create a random variable with that density? Assume you have an uniformly distributed random variable $u \in (0,1).$ How can you create a random variable with density $f(x)=\left\{\begin{matrix} \frac{1}{\pi}\frac{1}{1+x^2}\text{ if }x\geq 0\\ \frac{1}{2}e^x \;\;\;\;\text{ else} \end{matrix}\right. \;\;\;\;$ ? We first need to know the (cumulative) distribution function of the density function, so we can continue by inverting that distribution function. The distribution function is $$F(x)=\begin{cases} \frac12e^x & \mbox{if }x < 0 \\ \frac12+\frac1\pi \arctan (x) & \mbox{if } x \ge0 \end{cases}$$ (which is correct because my previous question was about it: Determine the distribution function of this density function). We are looking for its inverse now (I'm not sure if it's correct like that): $$i = \frac{1}{2}e^x \Leftrightarrow 2i = e^x \Leftrightarrow x = \ln(2i)$$ $$i=\frac{1}{2}+\frac{1}{\pi} \arctan(x) \Leftrightarrow i-\frac{1}{2}= \frac{1}{\pi}\arctan(x) \Leftrightarrow \pi\left(i-\frac{1}{2}\right)=\arctan(x) \Leftrightarrow \\ \Leftrightarrow x = \tan\left(\pi\left(i-\frac{1}{2}\right)\right)$$ Thus the inverse of the distribution function is $$F^{-1}(i)=\begin{cases} \ln(2i) & \mbox{if }i > 0 \\ \tan\left(\pi\left(i-\frac{1}{2}\right)\right) & \mbox{if } i \le0 \end{cases}$$ Assuming this is correct, how would you get the random variable by this? Is it the maximum possible $i$? • what does it mean create? what does the uniform have to to with X? – Hard Core Jan 27 '18 at 21:31 • @HardCore Actually I wasn't sure how to phrase it :p Maybe I should have rather written "simulate a random variable by the given density" or something like that ;) – cnmesr Jan 27 '18 at 21:48 Observe that if $F(x) = y$ then $y \in [0,1]$. Also, in your case, $F(0) = 1/2$. Therefore, $$F^{-1}(y) = \left\{\begin{matrix}\ln(2y) & \text{if 0 \le y \le \frac{1}{2};}\\ \tan\left(\pi\left(y-\frac{1}{2}\right)\right) & \text{if \frac{1}{2} \le y \le 1.}\end{matrix}\right.$$ Now, set $X = F^{-1}(U)$, where $U$ is a uniform random variable that takes on values between $0$ and $1$. It is easy to observe that $$F_X(x) = \Pr(X \le x) = \Pr(F^{-1}(U) \le x) = \Pr(U \le F(x)) = F(x).$$ Here, I have used the fact that $F_U(u) = \Pr(U \le u)= u$ for $u \in [0,1]$. The domain of the inverse is $(0,1)$. The switch between the two pieces of the original CDF is at the $y$ value of $1/2$, so that will be where the switch in the inverse happens. Other than that, your inverse is correct. The point of this is then that if $U$ is $\mathrm{Unif}(0,1)$ distributed then $F^{-1}(U)$ has the distribution of the variable you want. This trick is called the probability integral transformation; it is one of the main ways that random variables are sampled in numerical computation. If you want a practical answer it is very simple. The theoretical framework you want to look at is called inverse transform method, you can google it. Once you have obtained the inverse CDF as you did you would use a software to generate random numbers from a uniform between 0 and 1. The outcome of the simulation is your $i$. You would therefore feed the outcome of the simulation to the $F^{-1}(i)$ and you are done. $F^{-1}(i)$ is your random number simulated from the CDF $F$ (basically is your $x$).

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https://www.physicsforums.com/threads/neutron-stability.168776/

# Neutron Stability 1. May 3, 2007 I have a question about current experimental findings on the status of the neutron N while contained within nuclear radius of a stable atom, say Helium-4. It is well known that the N will undergo beta(-) decay when it is free from a nucleus (takes ~ 14 minutes). But... My question is--do the two N in stable Helium-4 maintain a stable identity with no beta (-) decay or, do they exist as a continuous back-forth transformation of N <----> P mediated by mesons ? Thanks for any help. If you can point me to a peered reviewed citation where this question has been addressed that would be appreciated. 2. May 4, 2007 ### mormonator_rm I would say that virtual pion exchange may account for that. Virtual pi- emission from a neutron would allow the neutron to become a proton, and the absorbing proton could become a neutron, with both of the nucleons remaining in the same spin state, and thus not changing their status with respect to the Pauli exclusion principle. This mechanism would result in the same long-range attractive force experienced by nucleons when pi0 exchange occurs. Anyone else have a comment or correction? 3. May 4, 2007 ### Meir Achuz A neutron in Helium cannot beta decay because any (pppn) state has higher mass than He4. The two n and two p in He are in an isospin eigenstate (I=0). As an easier example in the deuteron, \psi=(pn+np )/sqrt{2}. Thus particle 1 is a mixture of p and n. This need not (although it happens to be) be mediated by pions. It is not "a continuous back-forth transformation of N <----> P". 4. May 5, 2007 Thank you, but I am not sure I made myself clear. So, for your deuteron example, I am not asking if the N and P within deuteron have a continuous back-forth N <-----> P transformation. What I am asking is if the [N] in the deuteron is itself undergoing a transformation independent of the nearby [P]. Thus the picture of interactions would be: { [N] <----> [P] } <-----> [P] If so, then we can say the [N] is "unstable" within a "stable" deuteron. The other option is that the [N] is "stable" within a "stable" deuteron, and the picture of interactions would then be this: [N] <------> [P] Hope this makes sense. 5. May 5, 2007 ### mormonator_rm I had to think about that, but that does make more sense than what I said at first. I'm with you on that one. 6. May 5, 2007 ### mormonator_rm Actually, Meir is right. The reason it is stable is because the binding energy of the nucleus makes it the lightest available nuclear state, and hence a beta decay would cause it to increase in mass rather than decrease. Because these consequenses are incompatible, the helium-4 nucleus is literally forced to remain in its stable state. I believe this is what Meir was getting at. 7. May 5, 2007 Thank you, but in beta (-) decay (decay of N to P) after the transformation we have a decrease in atomic mass (not increase as you say) because the P (1007825.03207 mass units) is lighter mass than the N (1008664.9157 mass units). So, if we "start" the motion with beta (-) decay [ N -----> P], then quickly (say at same speed (17 trillion times/sec) recently documented for transformation of matter & antimatter quarks in Bs-meson--see this link http://www.photonics.com/content/news/2006/April/5/82000.aspx [Broken]) the reverse motion of beta (+) decay [ P ------> N], you see, the net mass must remain constant if we observe at any moment of time. Recall my OP question, I am asking if the 2 neutrons in He-4 can undergo this type of transformation independent of the 2 protons. But as Meir suggests, let us consider the more simple case of deuteron [NP]. Where is the experimental evidence that we do not have the [N] as unstable with quick (say many trillion times/sec) back-forth beta (-) <-----> beta (+) decay while the [P] remains unchanged ? Of course, we really must look to the dynamics at the microscopic level of the quarks. Now the [N] has quark structure (ddu) and the [P] has (uud). So my OP question, now for deuteron [NP] at level of quarks, becomes this question, is it possible that we have this type of transformation within deuteron ?: { (ddu) <-- many trillion times/sec --> (uud)} bonded to {(uud)} ps/ Does anyone know the "speed" of the weak force d ----> u transformation or the reverse u -----> d, is it at speed of light ? I hope I am making myself clear. in edit: Recall that while [P] is very, very stable outside nucleus, inside nucleus the [P] will undergo beta (+) decay--this is the source of the positron in PET scans used in medical research: .....When a nucleus decays by positron emission, a proton in the nucleus converts into a neutron, and a positron and a neutrino are ejected. The neutrino leaves the scene without a trace, while the positron rapidly annihilates with a nearby electron.... see here: http://physicsweb.org/articles/world/15/6/7 Last edited by a moderator: May 2, 2017 Similar Discussions: Neutron Stability

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https://www.physicsforums.com/threads/which-formula-for-energy-and-heat-transfer.680185/

# Which formula for energy and heat transfer? 1. Mar 22, 2013 ### Marshiewoo A perfect gas is compressed in a cylinder reversibly according to the law pV1.3 = C. The initial condition of the gas is 1.05 bar, 0.34 m3 and 17 oC. If the final pressure is 6.32 bar; and given that cv = 0.7175 kJkg-1 and R = 0.287 kJkg-1. Calculate the following. (a) The work transfer to the gas compressed (b) The heat transfer during the compression I would like to ask, what formula can I use to calculate the answers. I have found in my book that the following formula might work, but I am not sure what d is. It is such a frustrating subject so please don't slate me saying I havent tried because I really have I promise. Thanks 2. Mar 22, 2013

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https://projecteuclid.org/euclid.jsl/1183745801

## Journal of Symbolic Logic ### Transfering Saturation, The Finite Cover Property, and Stability #### Abstract $\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ if and only if there is an expansion T$_1$ of T with $\mid T_1 \mid$ = $\mid T \mid$ such that if M is a $\mu$-saturated model of T$_1$ and $\mid M \mid \geq \kappa$ then the reduct M $\mid L(T)$ is $\kappa$-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is ($\aleph_0, \lambda$)- transferable or ($\kappa (T), \lambda$)-transferable for all $\lambda$. Further if for some $\mu \geq \mid T \mid, 2^\mu > \mu^+$, stability is equivalent to for all $\mu \geq \mid T \mid$, saturation is ($\mu, 2^\mu$)- transferable. #### Article information Source J. Symbolic Logic, Volume 64, Issue 2 (1999), 678-684. Dates First available in Project Euclid: 6 July 2007 https://projecteuclid.org/euclid.jsl/1183745801 Mathematical Reviews number (MathSciNet) MR1777778 Zentralblatt MATH identifier 0929.03041 JSTOR

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http://mathhelpforum.com/math-topics/27516-pka-pkb-calculation.html

# Thread: pKa and pKb calculation 1. ## pKa and pKb calculation Hey, anyone know how I would work this out? Calculate the pH of 0.1M dichloroacetic acid, Ka = 3.3 x 10-2. Thanks 2. Originally Posted by Dan167 Hey, anyone know how I would work this out? Calculate the pH of 0.1M dichloroacetic acid, Ka = 3.3 x 10-2. Thanks we are given little to work with here, we have to go the long way around. (unless you are dealing with a buffer and you neglected to mention the molarity of the basic part of the acid). what is the formula for dichloroacetic acid? we have to write an equation for the ionization reaction using it 3. Originally Posted by Jhevon we are given little to work with here, we have to go the long way around. (unless you are dealing with a buffer and you neglected to mention the molarity of the basic part of the acid). what is the formula for dichloroacetic acid? we have to write an equation for the ionization reaction using it Hi, have a look here: Dichloroacetic acid - Wikipedia, the free encyclopedia 4. well we have enough information to solve his (providing we make a few assumptions) $Ka = \frac{[H+] \cdot [salt]}{[Acid]}$ if we assume that the solution is not buffered then $[H+] = [Salt] = x$ so then $Ka = \frac{x^2}{[Acid] - x }$ and there you have enough information to solve the equation. 5. Originally Posted by bobak well we have enough information to solve his (providing we make a few assumptions) $Ka = \frac{[H+] \cdot [salt]}{[Acid]}$ if we assume that the solution is not buffered then $[H+] = [Salt] = x$ so then $Ka = \frac{x^2}{[Acid] - x }$ and there you have enough information to solve the equation. indeed. i wanted to write out the ionization reaction just to be sure. it been a while since i did this. we have that $pH = - \log x$ if that is the equation for the Ka. the [Acid] - x seems weird to me, but as i said, it's been a while 6. Originally Posted by Jhevon the equation for the Ka. the [Acid] - x seems weird to me, but as i said, it's been a while well in chemistry class we are usually allowed to assume that the change in concentration of the acid may be neglected as it is so small so most people just leave the denominator as [Acid]. however this assumption is only really valid for very small values in Ka, but chemistry teachers don't really want to waste time teaching students how to solve quadratic equations so they usually make the assumption to allow easier computation of the ph 7. Wow i'm confused ... Thats all that is given I guess we have to make assumptions.... Does anyone mind going through it step by step 8. Originally Posted by Dan167 Wow i'm confused ... Thats all that is given I guess we have to make assumptions.... Does anyone mind going through it step by step we are told [Acid] = 0.1 M. use this to solve for x in the equation (which you should be familiar with) that bobak posted. once you have x, pH = -log(x). that's it 9. Originally Posted by Jhevon we are told [Acid] = 0.1 M. use this to solve for x in the equation (which you should be familiar with) that bobak posted. once you have x, pH = -log(x). that's it Lol i'm not familiar with it ... how do you solve it for x? 10. Originally Posted by Dan167 Lol i'm not familiar with it ... how do you solve it for x? you have $K_a = \frac {x^2}{0.1 - x}$ $\Rightarrow K_a(0.1 - x) = x^2$ $\Rightarrow x^2 - K_a(0.1 - x) = 0$ $\Rightarrow x^2 + K_ax - 0.1K_a = 0$ plug in the value for $K_a$, you will get a quadratic equation. then just use the quadratic formula to solve for $x$ 12. Originally Posted by Dan167 given a quadratic equation (in the variable x) of the form $ax^2 + bx + c = 0$ we can find the solutions to this equation by using the formula $x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$ 13. Originally Posted by Jhevon given a quadratic equation (in the variable x) of the form $ax^2 + bx + c = 0$ we can find the solutions to this equation by using the formula $x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$ Right .... I think i've got it, thanks. 14. Ok nope i'm lost .... 15. Originally Posted by Dan167 Ok nope i'm lost .... ok, how about you post your attempt, so we can see where you're getting stuck and direct you Page 1 of 2 12 Last

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http://export.arxiv.org/abs/2211.12147?context=nlin

nlin (what is this?) # Title: Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems Abstract: Fast scrambling, quantified by the exponential initial growth of Out-of-Time-Ordered-Correlators (OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of interacting systems, and constitutes a characteristic signature of local unstable dynamics. As such, it may equally manifest both in systems displaying chaos or in integrable systems around criticality. Here, we go beyond these extreme regimes with an exhaustive study of the interplay between local criticality and chaos right at the intricate phase space region where the integrability-chaos transition first appears. We address systems with a well defined classical (mean-field) limit, as coupled large spins and Bose-Hubbard chains, thus allowing for semiclassical analysis. Our aim is to investigate the dependence of the exponential growth of the OTOCs, defining the quantum Lyapunov exponent $\lambda_{\textrm{q}}$ on quantities derived from the classical system with mixed phase space, specifically the local stability exponent of a fixed point $\lambda_{\textrm{loc}}$ as well as the maximal Lyapunov exponent $\lambda_{\textrm{L}}$ of the chaotic region around it. By extensive numerical simulations covering a wide range of parameters we give support to a conjectured linear dependence $2\lambda_{\textrm{q}}=a\lambda_{\textrm{L}}+b\lambda_{\textrm{loc}}$, providing a simple route to characterize scrambling at the border between chaos and integrability. Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2211.12147 [quant-ph] (or arXiv:2211.12147v2 [quant-ph] for this version) ## Submission history From: Felix Meier [view email] [v1] Tue, 22 Nov 2022 10:26:17 GMT (16130kb,D) [v2] Thu, 2 Mar 2023 16:24:36 GMT (5909kb,D) Link back to: arXiv, form interface, contact.

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https://www.physicsforums.com/threads/physics-help-fast-thanks.53244/

# Physics help fast thanks 1. Nov 18, 2004 ### Michelle025 physics help fast thanks!! A force acting on a particle is conservative if: 1 the work done by it equals the change in the kinetic energy of the particle 2 it obeys Newton's 3rd 3 it obeys Newton's 2nd 4 its work depends on the end points of the motion, not the path between 5 it is not a friction force thanks 2. Nov 18, 2004 ### Michelle025 i think it's 4 3. Nov 18, 2004 ### James R 1,2 and 3 are true for all forces, conservative or not. Friction is a non-conservative force, but not the only one.

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https://www.quantumcalculus.org/tag/energy/

Tensor Products Everywhere The tensor product is defined both for geometric objects as well as for morphisms between geometric objects. It appears naturally in connection calculus. Energy, Entropy and Gibbs free Energy Energy U and Entropy S are fundamental functionals on a simplicial complex equipped with a probability measure. Gibbs free energy U-S combines them and should lead to interesting minima.

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http://math.stackexchange.com/questions/157377/complement-of-the-diagonal-in-product-of-schemes/157398

# Complement of the diagonal in product of schemes Let $S$ be a noetherian scheme and $X \rightarrow S$ be an affine morphism of schemes. Consider the diagonal morphism $\Delta: X \rightarrow X \times_S X$. If $\Delta (X)$ is the closed subset of $X \times_S X$, then one can look at the open embedding $j: U \rightarrow X \times_S X$ of the open complement of $\Delta(X)$. Has $j$ a chance to be itself an affine morphism of schemes? Or what additional hypotheses would one need to get this property? - First notice that $j: U\to S$ is affine if and only if $U\to X\times_S X$ is affine (to check this, one can suppose $S$ is affine, then use the facts that $X\times_S X$ is affine and $U$ is open in $X\times_S X$). So we are reduced to see whether $U$ is an affine scheme when $S$, and hence $X$ are affine. It is well known that then the complementary $\Delta(X)$ of $U$ in $X\times_S X$ is purely 1-codimensional. This is true essentially only when $X\to S$ has relative dimension $1$ (for reasonable schemes). In particular, if $X$ is any algebraic variety of dimension $d>1$, then $U$ can't be affine. Claim: Let $C$ be a smooth projective geometrically connected curve of genus $g$ over a field $k$, let $X\subset C$ be the complementary of $r$ points with $r+1-g >0$. Then $U$ is affine. Proof. We can suppose $k$ is algebraically closed (the affiness can be checked over any field extension). Let $D$ be the divisor $D=C\setminus X$ and $$H=D\times C+C\times D + \Delta(C).$$ Then $U=C\times C\setminus H$. It is enough to show that $H$ is an ample divisor on the smooth projective surface $C\times C$. To do this, we will use Nakai-Moishezon criterion (see Hartshorne, Theorem V.1.10). It is easy to see that $(D\times C)^2=0$ (because $D \sim D'$ with the support of $D'$ disjoint from that of $D$), $(D\times C).(C\times D)=r^2$, $(D\times C).\Delta(C)=r$, and $$\Delta(C)^2=\deg O_{C\times C}(\Delta(C))|_{\Delta(C)}=\deg \Omega_{C/k}^{-1}=2-2g.$$ Thus $H^2=2(r^2+r+1-g)>0$. Let $\Gamma$ be an irreducible curve on $C\times C$. If $\Gamma\ne \Delta(C)$, it is easy to see that $H.\Gamma>0$. On the other hand, $H.\Delta(C)=2r+2-2g=2(r+1-g)>0$ and we are done. I didn't check the details because it is time to sleep, but I believe the proof is essentially correct. EDIT (1). In the above claim, we can remove the condition $r+1-g>0$: Let $C$ be a smooth projective connected curve over a field $k$, let $X$ be an affine open subset of $C$. Then $U$ is affine. The proof is the same as above, but consider $H=n (D\times C+ C\times D)+\Delta(C)$ for $n > g-1$. The same proof shows that $H$ is ample. (2). Let $S$ be noetherian, and let $C\to S$ be a smooth projective morphism with one dimensional connected fibers, let $D$ be a closed subset of $C$ finite surjective over $S$. Let $X=C\setminus D$. Then $U$ is affine. Proof. One can see that $D$ is a relative Cartier divisor on $C$ (because $D_s$ is a Cartier divisor for all $s\in S$). So the $H$ defined as above is a relative Cartier divisor on $C\times_S C$. We showed that $H_s$ is ample for all $s$. This implies that $H$ is relatively ample for $C\times_S C\to S$ (EGV III.4.7.1). So $U$ is affine. - Der QiL, it is perfectly correct, thanks a lot. What I don't see is if one can extract from this the claim for the relative situation, say $X$ the complement of the zero section of an elliptic curve $C$ over $S$. –  Cyril Jun 13 '12 at 7:28 @Cyril, I will add some details. –  user18119 Jun 13 '12 at 22:17 Thanks for the edit. Is it clear that the complement of a relatively ample divisor is affine relative $S$ or is there a reference for this? One knows of course that this is true fiberwise, but I think affineness is not a fiberwise property. –  Cyril Jun 14 '12 at 6:03 @Cyril, yes you are right. However affineness is local on the target, so we can always work with ''small'' $S$. Here $H$ is the trace of some hyperplane $L$ of some projective space $P/S$. As $H_s$ is ample for every $s\in S$, $L_s$ is a hyperplane in $P_s$. So in a small open neighborhood of $s$, $L$ is defined by a homogeneous polynomial of degree 1 whose coefficients generate the unit ideal in the base ring. Therefore $P\setminus L$ (and thus $C\times_S \setminus H$ is affine). Hope this helps. –  user18119 Jun 14 '12 at 21:15 Thanks for clarifying this point. –  Cyril Jun 15 '12 at 5:41 (EDIT: deleted wrong answer, but left up for those reading comments- I had said affine two-space times itself over a line, but see below). - or easier, affine four space minus $(x, y, x, y)$ isn't affine (i.e. the base is a point and the scheme is a plane). –  user29743 Jun 12 '12 at 14:40 Dear countinghaus, I can't follow your argumentation. The set of points $(x,y,x,w)$ with $w\neq y$ looks to me like the complement of the (hyper)plane $w=y$ in affine three space $\mathbb A^3$ with coordinates $x,y,w$. Such a complement is affine (and actually isomorphic to $\mathbb A^2 \times \mathbb G_m$). –  Georges Elencwajg Jun 12 '12 at 17:45

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http://mathhelpforum.com/calculus/163120-curvilinear-integral-doubt-print.html

# Curvilinear integral doubt • November 13th 2010, 02:58 PM Ulysses Curvilinear integral doubt Hi. I have a doubt with this exercise. I'm not sure about what it asks me to do, when it asks me for the curvilinear integral. The exercise says: Calculate the next curvilinear integral: $\displaystyle\int_{C}^{}(x^2-2xy)dx+(y^2-2xy)dy$, C the arc of parabola $y=x^2$ which connect the point $(-2,4)$ y $(1,1)$ I've made a parametrization for C, thats easy: $\begin{Bmatrix} x=t \\y=t^2\end{matrix}$ $\begin{Bmatrix} x'(t)=1 \\y'(t)=2t\end{matrix}$ And then I've made this integral: $\displaystyle\int_{-2}^{1}t^2-2t^3+(t^4-2t^3)2t dt$ $\displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt$ But now I don't know if I should use the module, I did this: $\displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt$ and I dont know when I should use this: $\displaystyle\int_{a}^{b}F(\sigma(t)) \cdot ||\sigma'(t)||dt$ I mean, both are curvilinear integrals, right? I think that I understand what both cases means, but I don't know which one I should use when it asks me for the "curvilinear integral". The first case represents the area between the curve and the trajectory, and the second case represents the projection of a vector field over the trajectoriy, i.e. the work in a physical sense, but I know it have other interpretations and uses. Well, thats all. Bye there, thanks for posting. • November 13th 2010, 03:24 PM Prove It Quote: Originally Posted by Ulysses Hi. I have a doubt with this exercise. I'm not sure about what it asks me to do, when it asks me for the curvilinear integral. The exercise says: Calculate the next curvilinear integral: $\displaystyle\int_{C}^{}(x^2-2xy)dx+(y^2-2xy)dy$, C the arc of parabola $y=x^2$ which connect the point $(-2,4)$ y $(1,1)$ I've made a parametrization for C, thats easy: $\begin{Bmatrix} x=t \\y=t^2\end{matrix}$ $\begin{Bmatrix} x'(t)=1 \\y'(t)=2t\end{matrix}$ And then I've made this integral: $\displaystyle\int_{-2}^{1}t^2-2t^3+(t^4-2t^3)2t dt$ $\displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt$ But now I don't know if I should use the module, I did this: $\displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt$ and I dont know when I should use this: $\displaystyle\int_{a}^{b}F(\sigma(t)) \cdot ||\sigma'(t)||dt$ I mean, both are curvilinear integrals, right? I think that I understand what both cases means, but I don't know which one I should use when it asks me for the "curvilinear integral". The first case represents the area between the curve and the trajectory, and the second case represents the projection of a vector field over the trajectoriy, i.e. the work in a physical sense, but I know it have other interpretations and uses. Well, thats all. Bye there, thanks for posting. You're correct up to $\displaystyle \int_{-2}^1{t^2 - 2t^3+(t^4 - 2t^3)2t\,dt}$ $\displaystyle = \int_{-2}^1{t^2 - 2t^3 + 2t^5 - 4t^4\,dt}$. Go from here.

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https://scicomp.stackexchange.com/questions/10866/updating-an-approximate-solution-to-a-linear-system-in-response-to-a-small-chang

Updating an approximate solution to a linear system in response to a small change This question was original posted on SO but it was suggested that I post it here. I'm working on a program in which I have a banded matrix M and a vector b, and I want to maintain an approximate solution vector x such that Mxb. Is there a speedy algorithm or way of modeling this so that I can change individual elements of M and correspondingly update x, without having to do a full matrix inversion? One thing I'm considering is maintaining an approximate inverse of M, using the Sherman Morrison Algorithm in combination with a fast approximate matrix multiplication algorithm like this. Apologies for what will probably be a comment-answer hybrid (and a comment probably too long to fit in the comment box). One thing you say in your question is that you want an approximate solution vector. Have you considered iterative methods? There, the approximate inverse of $M$ could be used as a preconditioner in concert with some iterative method (GMRES, BiCGStab, etc.) to maintain approximate solution vectors, and the approximate solution for one linear system could then be used as an initial guess for the solution of a perturbed linear system. To update the preconditioner in response to single-element (or low-rank) perturbations, you could use Sherman-Morrison(-Woodbury). Depending on the perturbation, the approximate inverse may still be an effective preconditioner even without updating. I don't know how fast approximate matrix multiplication might degrade the solution of an iterative linear system; I would guess that it would be more forgiving in forming the preconditioner, since that can be approximate. After forming the preconditioner, I would stick to standard matrix-vector products for the solver iterations (for GMRES iterations, or whatever iterative method you consider using). Of course, this entire discussion might be moot, depending on the size of $M$. If it's sufficiently small, it might be worth just solving every time; I assume it's relatively large, or we wouldn't be having this discussion. • Yes, M is very big. Could you by chance link to some descriptions of these iterative methods? I'm a scientific computation newbie. – Chris Conlon Feb 23 '14 at 21:51 • Saad's textbook, Iterative Methods for Sparse Linear Systems is available online. A quicker introduction to some of these methods is The Idea Behind Krylov Methods. – Geoff Oxberry Feb 23 '14 at 21:58 • These methods works only for sparse matrices? – mrgloom Sep 29 '14 at 9:24 • @mrgloom: Iterative methods can also work for dense matrices, but direct methods are typically used, except in cases where you have a good preconditioner for iterative methods, or there is some exploitable special structure. – Geoff Oxberry Sep 29 '14 at 17:37

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https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Support_Course_for_Elementary_Statistics%3A__ISP/03%3A_Operations_on_Numbers/3.03%3A_Powers_and_Roots

3.3: Powers and Roots Learning Outcomes 1. Raise a number to a power using technology. 2. Take the square root of a number using technology. 3. Apply the order of operations when there is root or a power. It can be a challenge when we first try to use technology to raise a number to a power or take a square root of a number. In this section, we will go over some pointers on how to successfully take powers and roots of a number. We will also continue our practice with the order of operations, remembering that as long as there are no parentheses, exponents always come before all other operations. We will see that taking a power of a number comes up in probability and taking a root comes up in finding standard deviations. Powers Just about every calculator, computer, and smartphone can take powers of a number. We just need to remember that the symbol "^" is used to mean "to the power of". We also need to remember to use parentheses if we need to force other arithmetic to come before the exponentiation. Example $$\PageIndex{1}$$ Evaluate: $$1.04^5$$ and round to two decimal places. Solution This definitely calls for the use of technology. Most calculators, whether hand calculators or computer calculators, use the symbol "^" (shift 6 on the keyboard) for exponentiation. We type in: $1.04^5 = 1.2166529\nonumber$ We are asked to round to two decimal places. Since the third decimal place is a 6 which is 5 or greater, we round up to get: $1.04^5\approx1.22\nonumber$ Example $$\PageIndex{2}$$ Evaluate: $$2.8^{5.3\times0.17}$$ and round to two decimal places. Solution First note that on a computer we use "*" (shift 8) to represent multiplication. If we were to put in 2.8 ^ 5.3 * 0.17 into the calculator, we would get the wrong answer, since it will perform the exponentiation before the multiplication. Since the original question has the multiplication inside the exponent, we have to force the calculator to perform the multiplication first. We can ensure that multiplication occurs first by including parentheses: $2.8 ^{5.3 \times 0.17} = 2.52865\nonumber$ Now round to decimal places to get: $2.8^{5.3\times0.17}\approx2.53\nonumber$ Example $$\PageIndex{3}$$ If we want to find the probability that if we toss a six sided die five times that the first two rolls will each be a 1 or a 2 and the last three die rolls will be even, then the probability is: $\left(\frac{1}{3}\right)^2\:\times\left(\frac{1}{2}\right)^3\nonumber$ What is this probability rounded to three decimal places? Solution We find: $(1 / 3) ^ 2 (1 / 2) ^ 3 \approx 0.013888889\nonumber$ Now round to three decimal places to get $\left(\frac{1}{3}\right)^2\:\times\left(\frac{1}{2}\right)^3 \approx0.014\nonumber$ Square Roots Square roots come up often in statistics, especially when we are looking at standard deviations. We need to be able to use a calculator or computer to compute a square root of a number. There are two approaches that usually work. The first approach is to use the $$\sqrt{\:\:}$$ symbol on the calculator if there is one. For a computer, using sqrt() usually works. For example if you put 10*sqrt(2) in the Google search bar, it will show you 14.1421356. A second way that works for pretty much any calculator, whether it is a hand held calculator or a computer calculator, is to realize that the square root of a number is the same thing as the number to the 1/2 power. In order to not have to wrap 1/2 in parentheses, it is easier to type in the number to the 0.5 power. Example $$\PageIndex{3}$$ Evaluate $$\sqrt{42}$$ and round your answer to two decimal places. Solution Depending on the technology you are using you will either enter the square root symbol and then the number 42 and then close the parentheses if they are presented and then hit enter. If you are using a computer, you can use sqrt(42). The third way that will work for both is to enter: $42^{0.5} \approx 6.4807407\nonumber$ You must then round to two decimal places. Since 0 is less than 5, we round down to get: $\sqrt{42}\approx6.48\nonumber$ Example $$\PageIndex{4}$$ The "z-score" is for the value of 28 for a sampling distribution with sample size 60 coming from a population with mean 28.3 and standard deviation 5 is defined by: $z=\frac{28-28.3}{\frac{5}{\sqrt{60}}}\nonumber$ Find the z-score rounded to two decimal places. Solution We have to be careful about the order of operations when putting it into the calculator. We enter: $(28 - 28.3)/(5 / 60 ^\wedge 0.5) = -0.464758\nonumber$ Finally, we round to 2 decimal places. Since 4 is smaller than 5, we round down to get: $z=\frac{28-28.3}{\frac{5}{\sqrt{60}}}=-0.46\nonumber$ Exercise The standard error, which is an average of how far sample means are from the population mean is defined by: $\sigma_\bar x=\frac{\sigma}{\sqrt{n}}\nonumber$ where $$\sigma_\bar x$$ is the standard error, $$\sigma$$ is the standard deviation, and $$n$$ is the sample size. Find the standard error if the population standard deviation, $$\sigma$$, is 14 and the sample size, $$n$$, is 11.

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http://math.stackexchange.com/users/72/isaac?tab=summary

Isaac Reputation 26,331 84/100 score 8 69 122 Impact ~1.6m people reached 107 Is $0.999999999\ldots = 1$? 87 Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$? 74 Is there a general formula for solving 4th degree equations? 67 How to prove Euler's formula: $e^{it}=\cos t +i\sin t$? 56 Proof that the irrational numbers are uncountable ### Reputation (26,331) +5 Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots$ +10 Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$? +10 How to prove Euler's formula: $e^{it}=\cos t +i\sin t$? +10 Is there a general formula for solving 4th degree equations? ### Questions (20) 43 Proving that 1- and 2-d simple symmetric random walks return to the origin with probability 1 38 Bad Fraction Reduction That Actually Works 24 Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots$ 23 Probability that a stick randomly broken in two places can form a triangle 21 Useful examples of pathological functions ### Tags (150) 597 algebra-precalculus × 128 177 complex-numbers × 11 518 geometry × 142 146 polynomials × 16 383 calculus × 72 145 fake-proofs × 4 293 trigonometry × 78 129 analytic-geometry × 45 185 euclidean-geometry × 44 116 arithmetic × 13 ### Accounts (40) Mathematics 26,331 rep 869122 Stack Overflow 6,040 rep 42946 Area 51 1,811 rep 3215 Mathematica 1,399 rep 1429 Meta Stack Exchange 547 rep 1316

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http://mathhelpforum.com/algebra/88678-solved-multiplication-algerbraic-fractions.html

# Thread: [SOLVED] Multiplication of Algerbraic Fractions 1. ## [SOLVED] Multiplication of Algerbraic Fractions Q. Simplify: $\frac {4}{21 - 9x} \div \frac {8}{14 - 6x}$ this is the furthest i've gotten $\frac {4}{9(3 - x)} \times \frac {2(7 - 3x)}{8}$ the answer is: $\frac 1 3$ im not even sure if my working out so far is right . thanks 2. Originally Posted by waven Q. Simplify: $\frac {4}{21 - 9x} \div \frac {8}{14 - 6x}$ this is the furthest i've gotten $\frac {4}{9(3 - x)} \times \frac {2(7 - 3x)}{8}$ e^(i*pi) : 9 is not a factor of 21 the answer is: $\frac 1 3$ im not even sure if my working out so far is right . thanks $\frac {4}{21 - 9x} \div \frac {8}{14 - 6x} = \frac{4}{3(7-3x)} \times \frac{2(7-3x)}{8}$ The 2 and the 4 on the top will cancel with the 8 on the bottom and (7-3x) will cancel to give 1/3

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https://www.varsitytutors.com/gre_math-help/how-to-find-absolute-value

GRE Math : How to find absolute value Example Questions Example Question #1 : How To Find Absolute Value Quantitative Comparison: Column A |–3 + 4| Column B |–3| + |4| Column A and B are equal Column B is greater Cannot be determined Column A is greater Column B is greater Explanation: The operations in the absolute value are always done first. So in Column A, |–3 + 4| = |1| = 1.  In Column B, |–3| + |4| = 3 + 4 = 7. Example Question #141 : Integers Quantitative Comparison |x – 3| = 3 Quantity A: x Quantity B: 2 Quantity B is greater. The relationship cannot be determined from the information given. Quantity A is greater. The two quantities are equal. The relationship cannot be determined from the information given. Explanation: It's important to remember that absolute value functions yield two equations, not just one. Here we have x – 3 = 3 AND x – 3 = –3. Therefore x = 6 or x = 0, so the answer cannot be determined. If we had just used the quation x – 3 = 3 and forgotten about the second equation, we would have had x = 6 as the only solution, giving us the wrong answer. Example Question #791 : Gre Quantitative Reasoning Quantitative Comparison Quantity A: |10| – |16| Quantity B: |1 – 5| – |3 – 6| Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given. Quantity A is greater. Quantity B is greater. Explanation: Quantity A: |10| = 10, |16| = 16, so |10| – |16| = 10 – 16 = –6. Quantity B: |1 – 5| = 4, |3 – 6| = 3, so |1 – 5| - |3 – 6| = 4 – 3 = 1. 1 is bigger than –6, so Quantity B is greater. Example Question #1 : How To Find Absolute Value Quantitative Comparison Quantity A: (|–4 + 1| + |–10|)2 Quantity B: |(–4 + 1 – 10)2| The two quantities are equal. The relationship cannot be determined from the information given. Quantity B is greater. Quantity A is greater. The two quantities are equal. Explanation: Quantity A: |–4 + 1| = |–3| = 3 and |–10| = 10, so (|–4 + 1| + |–10|)2 = (3 + 10)2 = 13= 169 Quantity B: |(–4 + 1 – 10)2| = |(–13)2| = 169 The two quantities are equal. Example Question #1 : How To Find Absolute Value Quantity A: Quantity B: Quantity A is greater Quantity B is greater The relationship cannot be determined from the information given The two quantities are equal Quantity B is greater Explanation: If , then either  or  must be negative, but not both. Making them both positive, as in quantity B, and then adding them, would produce a larger number than adding them first and making the result positive. Example Question #1 : How To Find Absolute Value What is the absolute value of the following equation when

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https://www.physicsforums.com/threads/harmonic-potential-of-non-interacting-particles.587196/

# Homework Help: Harmonic Potential of Non-Interacting Particles 1. Mar 15, 2012 ### Lyons_63 Two Non Interacting Particles Interact with a external harmonic Potential. What are the energy levels of the system, and the partition functions when assuming the particles are (b) Bosons and (c) Fermions 2. Relevant equations Energy of the system E=(ρ1)^2/2m + (ρ2)^2/2m+ mω^2/2 (x1+x2) ρ= momentum ω=angular frequency of the system 3. The attempt at a solution The energy levels for a single oscillator are given by E=hbar ω (n + 1/2) I am not sure to go from here and how to incorporate the fact that there are two particles in the system Any help would be great! 2. Mar 18, 2012 ### Redbelly98 Staff Emeritus Since there are two particles, each will be found in one of the states n. So the state of the system would be characterized by two numbers rather than one -- you could call them n1 and n2. So first you'd need to write down the total energy of the system, when one particle is in state n1 and the other is in state n2.

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https://astarmathsandphysics.com/university-maths-notes/complex-analysis/1820-differentiating-under-the-integral-sign.html?tmpl=component&print=1&page=

## Differentiating Under the Integral Sign Let R be a region and let K be a complex valued function of two variables z in R and t in [a,b] such that 1. is analytic inas a function offor each 2. andare continuous onas functions of t for each 3. For somefor Then the functionwithis analytic onandfor(1) Proof: Letand choose a circleinwith centreand radiussuch that the inside oflies entirely inIflies insidethen we have by assumption 1 and Cauchy's Integral Formula, and and by Cauchy's First Derivative Formula,for each t in [a,b]. Hence, if f is given by (1) then say. We need to show thatas henceas

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http://www.physicsforums.com/showthread.php?p=4232434

# How can ellipticity angle be negative. by yungman Tags: angle, ellipticity, negative P: 3,830 In plane wave elliptical polarization, the book said if the Ellipticity angle is possitive, it is a Left Hand Circular polarization(LHC). If Ellipticity angle is negative, it is Right Hand Circular polarization(RHC). My question is how can Ellipticity angle be negative? http://en.wikipedia.org/wiki/Polarization_%28waves%29 Can anyone show a picture of negative Ellipticity angle? In case this sounds ridiculous, attached is the scan of the paragraph from the "Engineering Electromagnetics" by Ulaby. I have to scan in two part to fit the size limit. First is Ulaby1 and then Ulaby2. Thanks Attached Thumbnails Sci Advisor P: 3,265 I don't see what is the problem with a negative ellipticity angle. The sign of the arcus tangens is not fixed by it's argument, it can be either positive or negative. To decide which one to choose, you have to look at the polarisation of the wave. P: 3,830 Quote by DrDu I don't see what is the problem with a negative ellipticity angle. The sign of the arcus tangens is not fixed by it's argument, it can be either positive or negative. To decide which one to choose, you have to look at the polarisation of the wave. The question is how to draw a negative ellipticity angle physically? $$\chi\;=\;\tan^{-1} \frac {a_{\eta}}{a_{\epsilon}}$$ Both are just length and is never negative. Related Discussions Automotive Engineering 4 Introductory Physics Homework 3 General Astronomy 3 Precalculus Mathematics Homework 2 Introductory Physics Homework 9

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https://benjaminwhiteside.com/2014/02/17/topological-invariants/

Before we can talk about topological invariants we need to know two things: 1) what is a topology, and 2) what is an invariant. Simply put, a topology is a collection of sets, each of which, vaguely speaking, has fuzzy edges. An invariant, on the other hand, is basically something which doesn’t change. In the remainder of this article I will slowly introduce the concept of a topological invariant and then having done so will illustrate what you can do with them. To properly define a topology let’s start with a non-empty set. We can, of course, give it a name: $X$ and it will consist of one or more objects, or subsets. Suppose further that we collect up a bunch of these subsets in a very particular way (explained in a second) and call it the Greek letter tau, or $\tau$. If the way in which we pick our subsets adheres to the following rules (or axioms): 1. The empty set $\emptyset$ and the entire set $X$ are in $\tau$ 2. Any union (possibly infinite) of any open set is in $\tau$. 3. The intersection of any finite number of the open sets is, again, open. then the collection of subsets gets a special name, of course, it is called a topology on the set $X$. The objects within this special kind of collection get their own name too, we call them open sets. Open sets are nice sets; we can pick elements out of them without having to worry about accidentally going too far and picking an element that isn’t in it. Formally speaking, an open set does not contain any of its boundary points and this gives us freedom to draw little circles around each and every element inside an open set and know for a fact that the little circle (also called a neighbourhood) is entirely within the set. Taking the set that we began with $X$ and the collection of subsets $\tau$ we form the tuple $(X,\tau)$, and this is called a topological space. A topological space thus consists of some set along with a collection of subsets that are nice and fuzzy. All in all, this is a pretty big space, almost all of mathematics takes place in some topological space or another. Topological spaces allow you to, obviously define sets and open subsets, which in turn allow you to define neighbourhoods which carry a diameter of sorts, which in turn allows you to define a primitive notion of distance (think of everything being measured in terms of the diameter of the little circles, or $\epsilon$ as it’s denoted). A notion of distance gives rise to the 3 C’s: Continuity, Connectedness and Convergence. And this, my friends, is where calculus lives. The second concept we need is that of an invariant. An invariant is a class of mathematical objects that don’t change when you move the object out of one environment and in to another (or back to the original one). Technically speaking, moving an object doesn’t really happen, what actually happens is that you move the object’s elements and the way in which that is done is by use of a mapping, usually denoted by $f$. The mapping takes an element, say $x$ of some set $X$, and maps it to another element $y$ in some other set $Y$. Once you do this to each and every element of $X$, if the destination set $Y$ shares a property with $X$ then we say that the original set $X$ is invariant under $f$. Let’s begin by talking about an invariant of a homeomorphism. In case you don’t recall, a homeomorphism is a mapping (a way of getting from point A to point B), call it $h$, from a topological space $X_1$ to another topological space $X_2$ that preserves the topological properties of the first space.

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http://www.onlineprediction.net/?n=Main.ConformalPredictiveSystem

# Conformal Predictive System Conformal predictive systems are introduced in the recent technical report Vovk et al. (2017). Essentially, these are conformal transducers that, for each training sequence and each test object, output p-values that are increasing as a function of the label , assumed to be a real number. The function is then called a predictive distribution. A wide class of conformity measures that often lead to conformal predictive systems is where is the prediction for the label of based on the training sequence and . An even wider class is where is an estimate of the variability or difficulty of computed from the training sequence and . (The methods for computing and are supposed invariant with respect to permutations of .) The width of such conformal predictive distributions is typically equal to , where is the length of the training sequence, except for at most values of . The formal definition of conformal predictive systems takes account of the fact that, in the case of smoothed conformal predictors, also depends on the random number , and a fuller notation is . It is also required that as and as . Notice that in the context of conformal predictive systems the p-values acquire properties of probabilities. Besides, they have some weak properties of object conditionality: e.g., the central prediction regions are not empty, except in very pathological cases. There are universally consistent predictive distributions (Vovk, 2017). ## Conformal decision making Conformal predictive systems can be applied for the purpose of decision making. Universally consistent predictive distributions can be used for making asymptotically efficient decisions. Bibliography

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http://mathoverflow.net/questions/134419/hard-lefschetz-in-de-rham-cohomology

# Hard Lefschetz in De Rham cohomology I'm looking for a reference for Hard Lefschetz theorem in algebraic De Rham cohomology. By this I mean the statement that If $i: Y \hookrightarrow X$ is a smooth hyperplane section of a smooth projective algebraic variety $X$ of dimension $n$ over a field $k$ of characteristic zero and $\omega \in H^2_{DR}(X)$ is its image under the cycle class map, then the operator $L^j: H^{n-j}_{DR}(X) \to H^{n+j} _{DR}(X)$ sending $x$ to $x \cdot \omega^j$ is an isomorphism for $j=1, \ldots, n$. Is a proof of this written somewhere? Weak Lefschetz is proved in Hartshorne's paper "On the de Rham cohomology..." chapter III, section 7 but I was completely unable to find a reference for the former. Thanks Francesco. Is that a proof for algebraic de Rham cohomology or the analytic one? I guess if you know how to do that for analytic you can deduce it for algebraic but you need some small argument when the base field is not $\CC$, don't you? – vicban Jun 21 '13 at 18:50 To expand Francesco's comment: after a field reduction followed an extension, you can assume that the ground field is $\mathbb{C}$. Apply Grothendieck's algebraic de Rham theorem to see that algebraic de Rham cohomology is isomorphic to singular cohomology. After this, the standard proof applies. However, if you are asking for a completely self contained elementary proof, then there isn't one. – Donu Arapura Jun 21 '13 at 18:57

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http://studyphysicswithme.com/blog/2017/01/26/thermodynamics-ideal-gas/

# Why are gases important? The gaseous state of matter behaves differently from solids and liquids. It is neither limited in volume nor in compressibility. A gas fills entire volume of the container it is kept in, and distributes itself uniformly. This property makes them very useful and interesting because we can change its physical properties (volume, temperature, pressure etc.) to a large extent. These properties are not independent of each other and any of them can be manipulated by changing other variables. We can derive “work” from gases and thus gases were studied extensively in the early days of thermodynamics(e.g. for designing steam engines). On the other hand, physical states of solids and liquids don’t change that much and there is little to be studied unless you transform them into another state (e.g. melting a solid or freezing a liquid). # The Ideal Gas Traditionally, the study of Thermodynamics begins with the properties of an Ideal gas. By ideal, we mean that the gas molecules behave totally independently of each other and are point particles. The behaviour overall is governed by simple laws and is easy to understand. Under certain conditions, Real gases behave very much like an ideal gas. We will discuss what these conditions are below. ## The main properties of an ideal gas are twofold: 1. Each molecule behaves like a point particle and has no volume of its own. 2. There are no intermolecular interactions except collisions among themselves or with the walls of the container. At high temperature, real gas molecules have enough kinetic energy to “jiggle around” with high speeds. Under low pressure, the gas is diluted enough so that no two molecules get very close to each other(thus avoiding attractive intermolecular forces). With the two conditions combined, the molecules are all running around with high speeds, interacting only through collisions. Hence, we can see that: At high temperatures and low pressures, behaviour of real gases can be approximated to the ideal gas behaviour. # Properties of an Ideal Gas The most important properties of an ideal gas are its Pressure(P), Volume(V), Temperature(T) and number of molecules(or moles, n). These are not independent, however. The relationships between these properties were first discovered empirically by various scientists and later shown to be derivable from Newton’s laws of Motion (studied in the domain of Kinetic Theory of Gases). These laws are as follows: Boyle’s Law Charles’ Law Gay-Lussac’s Law The above relations can be combined in a single equation, known as the ideal gas law: or, where R = gas constant = 8.31441 J K-1 mol-1 where n = No. of moles, N = No. of molecules and NA = Avogadro’s number = 6.022 x 1023 The ideal gas law can also be expressed as where kB = Boltzmann constant = 1.38064852 × 10-23 mkg s-2 K-1 Thermodynamics: Ideal Gas Tagged on: This site uses Akismet to reduce spam. Learn how your comment data is processed.

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https://tex.stackexchange.com/questions/248064/non-math-fonts-with-unicode-math-kill-widetilde-and-widehat

# Non-math fonts with unicode-math kill \widetilde and \widehat I suspect this might be a bug in unicode-math, but you never know. It appears that loading any non-math font for any purpose at all breaks \widehat and \widetilde. Consider, for instance, the MWE below where I load XITS Math as my math font, but try some other fonts for \mathbfup. That should have absolutely no effect for what happens to my math except when using bold upright math. However, even though the font does not change for the math I type, the \widetildeand \widehat become either normal \tilde and \hat... or disappear completely, depending on the font I load. Is this a bug, or am I doing something wrong somewhere? (As the MWE suggests, I am compiling using LuaLaTeX.) % !TeX program=luatex \documentclass{article} \usepackage{unicode-math} \setmathfont{XITS Math} \begin{document} $\widetilde X\widehat X$ \setmathfont[range=\mathbfup]{Minion Pro Bold} $\widetilde X\widehat X$ \setmathfont[range=\mathbfup]{Linux Libertine O Bold} $\widetilde X\widehat X$ \end{document} EDIT: Compiling using XeLaTeX, I get the following instead. This makes me even more confident that there is a bug somewhere. The workaround suggested by Ulrike Fischer in her answer to \sqrt[x]{y} Breaks With unicode-math works also in this case: \documentclass{article} \usepackage{unicode-math} \setmathfont{XITS Math} \setmathfont[range=\mathbfup]{Linux Libertine O Bold} \setmathfont[range=\int]{XITS Math} \begin{document} $\widetilde X\widehat X\mathbf{X}$ \end{document} Note that you shouldn't be changing math font inside the document. The problem is that unicode-math gets some values for math typesetting from the last loaded math font. Since Linux Libertine isn't a math font, it doesn't have some necessary parameters. Note that the last glyph is from Linux Libertine. • I guess this is the cleaner solution, since it directly addresses the cause of the issue. Accepted. Isn't it kind of a bug that the last loaded font determines how fractions and accents look? Shouldn't that come from the main math font? – Gaussler Jun 2 '15 at 6:27 • do you think it would cause problems to just put the line \setmathfont{XITS Math} last, after all other \setmathfonts? – Gaussler Jun 2 '15 at 16:14 • @Gaussler I prefer not doing it, just for consistency, but you can experiment. – egreg Jun 2 '15 at 16:15 The accent is not there as warned in the log Missing character: There is no ̃ (U+0303) in font "MinionProBold:mode=base;scri pt=latn;language=DFLT;"! Why \widetilde is being redefined to use the new \symnum_fam1 allocated to the bold minion font, I'm not sure, but you can define it back again: % !TeX program=luatex \documentclass{article} \show\widetilde \usepackage{unicode-math} \setmathfont{XITS Math} \begin{document} \show\widetilde \show\symoperators $\widetilde X\widehat X$ \let\oldwidetilde\widetilde \let\oldwidehat\widehat \setmathfont[range=\mathbfup]{Minion Pro Bold} \let\widetilde\oldwidetilde \let\widehat\oldwidehat $\widetilde X\widehat X$ \setmathfont[range=\mathbfup]{Linux Libertine O Bold} $\widetilde X\widehat X$ \end{document} I don't think unicode-math really claims to support non math fonts in this way, so it's not clearly a bug, but may be worth raising on the unicode-math issue tracker anyway. • In order for the interface to work logically, I think that changing what happens in \mathbfup should have no effect on what happens to the rest of the math. Particularly so when replacing range=\mathbfup by range=\mathbfup/{latin,Latin,greek,Greek}; however, it also happens in that case. – Gaussler Jun 1 '15 at 19:09

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http://www.lightandmatter.com/html_books/lm/ch03/ch03.html

You are viewing the html version of Light and Matter, by Benjamin Crowell. This version is only designed for casual browsing, and may have some formatting problems. For serious reading, you want the Adobe Acrobat version. Table of Contents Galileo's contradiction of Aristotle had serious consequences. He was interrogated by the Church authorities and convicted of teaching that the earth went around the sun as a matter of fact and not, as he had promised previously, as a mere mathematical hypothesis. He was placed under permanent house arrest, and forbidden to write about or teach his theories. Immediately after being forced to recant his claim that the earth revolved around the sun, the old man is said to have muttered defiantly “and yet it does move.” The story is dramatic, but there are some omissions in the commonly taught heroic version. There was a rumor that the Simplicio character represented the Pope. Also, some of the ideas Galileo advocated had controversial religious overtones. He believed in the existence of atoms, and atomism was thought by some people to contradict the Church's doctrine of transubstantiation, which said that in the Catholic mass, the blessing of the bread and wine literally transformed them into the flesh and blood of Christ. His support for a cosmology in which the earth circled the sun was also disreputable because one of its supporters, Giordano Bruno, had also proposed a bizarre synthesis of Christianity with the ancient Egyptian religion. # Chapter 3. Acceleration and free fall ## 3.1 The motion of falling objects a / According to Galileo's student Viviani, Galileo dropped a cannonball and a musketball simultaneously from the leaning tower of Pisa, and observed that they hit the ground at nearly the same time. This contradicted Aristotle's long-accepted idea that heavier objects fell faster. c / The $$v-t$$ graph of a falling object is a line. d / Galileo's experiments show that all falling objects have the same motion if air resistance is negligible. e / 1. Aristotle said that heavier objects fell faster than lighter ones. 2. If two rocks are tied together, that makes an extra- heavy rock, which should fall faster. 3. But Aristotle's theory would also predict that the light rock would hold back the heavy rock, resulting in a slower fall. The motion of falling objects is the simplest and most common example of motion with changing velocity. The early pioneers of physics had a correct intuition that the way things drop was a message directly from Nature herself about how the universe worked. Other examples seem less likely to have deep significance. A walking person who speeds up is making a conscious choice. If one stretch of a river flows more rapidly than another, it may be only because the channel is narrower there, which is just an accident of the local geography. But there is something impressively consistent, universal, and inexorable about the way things fall. Stand up now and simultaneously drop a coin and a bit of paper side by side. The paper takes much longer to hit the ground. That's why Aristotle wrote that heavy objects fell more rapidly. Europeans believed him for two thousand years. Now repeat the experiment, but make it into a race between the coin and your shoe. My own shoe is about 50 times heavier than the nickel I had handy, but it looks to me like they hit the ground at exactly the same moment. So much for Aristotle! Galileo, who had a flair for the theatrical, did the experiment by dropping a bullet and a heavy cannonball from a tall tower. Aristotle's observations had been incomplete, his interpretation a vast oversimplification. It is inconceivable that Galileo was the first person to observe a discrepancy with Aristotle's predictions. Galileo was the one who changed the course of history because he was able to assemble the observations into a coherent pattern, and also because he carried out systematic quantitative (numerical) measurements rather than just describing things qualitatively. Why is it that some objects, like the coin and the shoe, have similar motion, but others, like a feather or a bit of paper, are different? Galileo speculated that in addition to the force that always pulls objects down, there was an upward force exerted by the air. Anyone can speculate, but Galileo went beyond speculation and came up with two clever experiments to probe the issue. First, he experimented with objects falling in water, which probed the same issues but made the motion slow enough that he could take time measurements with a primitive pendulum clock. With this technique, he established the following facts: • All heavy, streamlined objects (for example a steel rod dropped point-down) reach the bottom of the tank in about the same amount of time, only slightly longer than the time they would take to fall the same distance in air. • Objects that are lighter or less streamlined take a longer time to reach the bottom. This supported his hypothesis about two contrary forces. He imagined an idealized situation in which the falling object did not have to push its way through any substance at all. Falling in air would be more like this ideal case than falling in water, but even a thin, sparse medium like air would be sufficient to cause obvious effects on feathers and other light objects that were not streamlined. Today, we have vacuum pumps that allow us to suck nearly all the air out of a chamber, and if we drop a feather and a rock side by side in a vacuum, the feather does not lag behind the rock at all. ### How the speed of a falling object increases with time Galileo's second stroke of genius was to find a way to make quantitative measurements of how the speed of a falling object increased as it went along. Again it was problematic to make sufficiently accurate time measurements with primitive clocks, and again he found a tricky way to slow things down while preserving the essential physical phenomena: he let a ball roll down a slope instead of dropping it vertically. The steeper the incline, the more rapidly the ball would gain speed. Without a modern video camera, Galileo had invented a way to make a slow-motion version of falling. b / Velocity increases more gradually on the gentle slope, but the motion is otherwise the same as the motion of a falling object. Although Galileo's clocks were only good enough to do accurate experiments at the smaller angles, he was confident after making a systematic study at a variety of small angles that his basic conclusions were generally valid. Stated in modern language, what he found was that the velocity-versus-time graph was a line. In the language of algebra, we know that a line has an equation of the form $$y=ax+b$$, but our variables are $$v$$ and $$t$$, so it would be $$v=at+b$$. (The constant $$b$$ can be interpreted simply as the initial velocity of the object, i.e., its velocity at the time when we started our clock, which we conventionally write as $$v_\text{o}$$.) self-check: An object is rolling down an incline. After it has been rolling for a short time, it is found to travel 13 cm during a certain one-second interval. During the second after that, it goes 16 cm. How many cm will it travel in the second after that? (answer in the back of the PDF version of the book) ### A contradiction in Aristotle's reasoning Galileo's inclined-plane experiment disproved the long-accepted claim by Aristotle that a falling object had a definite “natural falling speed” proportional to its weight. Galileo had found that the speed just kept on increasing, and weight was irrelevant as long as air friction was negligible. Not only did Galileo prove experimentally that Aristotle had been wrong, but he also pointed out a logical contradiction in Aristotle's own reasoning. Simplicio, the stupid character, mouths the accepted Aristotelian wisdom: Simplicio: There can be no doubt but that a particular body ... has a fixed velocity which is determined by nature... Salviati: If then we take two bodies whose natural speeds are different, it is clear that, [according to Aristotle], on uniting the two, the more rapid one will be partly held back by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion? Simplicio: You are unquestionably right. Salviati: But if this is true, and if a large stone moves with a speed of, say, eight [unspecified units] while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly. ### What is gravity? The physicist Richard Feynman liked to tell a story about how when he was a little kid, he asked his father, “Why do things fall?” As an adult, he praised his father for answering, “Nobody knows why things fall. It's a deep mystery, and the smartest people in the world don't know the basic reason for it.” Contrast that with the average person's off-the-cuff answer, “Oh, it's because of gravity.” Feynman liked his father's answer, because his father realized that simply giving a name to something didn't mean that you understood it. The radical thing about Galileo's and Newton's approach to science was that they concentrated first on describing mathematically what really did happen, rather than spending a lot of time on untestable speculation such as Aristotle's statement that “Things fall because they are trying to reach their natural place in contact with the earth.” That doesn't mean that science can never answer the “why” questions. Over the next month or two as you delve deeper into physics, you will learn that there are more fundamental reasons why all falling objects have $$v-t$$ graphs with the same slope, regardless of their mass. Nevertheless, the methods of science always impose limits on how deep our explanation can go. ## 3.2 Acceleration f / Example 1. g / Example 2. ### Definition of acceleration for linear $$v-t$$ graphs Galileo's experiment with dropping heavy and light objects from a tower showed that all falling objects have the same motion, and his inclined-plane experiments showed that the motion was described by $$v=at+v_\text{o}$$. The initial velocity $$v_\text{o}$$ depends on whether you drop the object from rest or throw it down, but even if you throw it down, you cannot change the slope, $$a$$, of the $$v-t$$ graph. Since these experiments show that all falling objects have linear $$v-t$$ graphs with the same slope, the slope of such a graph is apparently an important and useful quantity. We use the word acceleration, and the symbol $$a$$, for the slope of such a graph. In symbols, $$a=\Delta v/\Delta$$t. The acceleration can be interpreted as the amount of speed gained in every second, and it has units of velocity divided by time, i.e., “meters per second per second,” or m/s/s. Continuing to treat units as if they were algebra symbols, we simplify “m/s/s” to read $$“\text{m}/\text{s}^2$$.” Acceleration can be a useful quantity for describing other types of motion besides falling, and the word and the symbol “$$a$$” can be used in a more general context. We reserve the more specialized symbol “$$g$$” for the acceleration of falling objects, which on the surface of our planet equals $$9.8\ \text{m}/\text{s}^2$$. Often when doing approximate calculations or merely illustrative numerical examples it is good enough to use $$g=10\ \text{m}/\text{s}^2$$, which is off by only 2%. ##### Example 1: Finding final speed, given time $$\triangleright$$ A despondent physics student jumps off a bridge, and falls for three seconds before hitting the water. How fast is he going when he hits the water? $$\triangleright$$ Approximating $$g$$ as $$10\ \text{m}/\text{s}^2$$, he will gain 10 m/s of speed each second. After one second, his velocity is 10 m/s, after two seconds it is 20 m/s, and on impact, after falling for three seconds, he is moving at 30 m/s. ##### Example 2: Extracting acceleration from a graph $$\triangleright$$ The $$x-t$$ and $$v-t$$ graphs show the motion of a car starting from a stop sign. What is the car's acceleration? $$\triangleright$$ Acceleration is defined as the slope of the v-t graph. The graph rises by 3 m/s during a time interval of 3 s, so the acceleration is $$(3\ \text{m}/\text{s})/(3\ \text{s})=1\ \text{m}/\text{s}^2$$. Incorrect solution #1: The final velocity is 3 m/s, and acceleration is velocity divided by time, so the acceleration is $$(3\ \text{m}/\text{s})/(10\ \text{s})=0.3\ \text{m}/\text{s}^2$$. The solution is incorrect because you can't find the slope of a graph from one point. This person was just using the point at the right end of the v-t graph to try to find the slope of the curve. Incorrect solution #2: Velocity is distance divided by time so $$v=(4.5$$ m)/(3 $$s)=1.5$$ m/s. Acceleration is velocity divided by time, so $$a=(1.5$$ m/s)/(3 $$s)=0.5\ \text{m}/\text{s}^2$$. The solution is incorrect because velocity is the slope of the tangent line. In a case like this where the velocity is changing, you can't just pick two points on the x-t graph and use them to find the velocity. ##### Example 3: Converting $$g$$ to different units $$\triangleright$$ What is $$g$$ in units of $$\text{cm}/\text{s}^2$$? $$\triangleright$$ The answer is going to be how many cm/s of speed a falling object gains in one second. If it gains 9.8 m/s in one second, then it gains 980 cm/s in one second, so $$g=980\ \text{cm}/\text{s}^2$$. Alternatively, we can use the method of fractions that equal one: $\begin{equation*} \frac{9.8\ {\text{m}}}{\text{s}^2}\times\frac{100\ \text{cm}}{1\ {\text{m}}} =\frac{980\ \text{cm}}{\text{s}^2} \end{equation*}$ $$\triangleright$$ What is $$g$$ in units of $$\text{miles}/\text{hour}^2$$? $$\triangleright$$ $\begin{equation*} \frac{9.8\ \text{m}}{\text{s}^2} \times \frac{1\ \text{mile}}{1600\ \text{m}} \times \left(\frac{3600\ \text{s}}{1\ \text{hour}}\right)^2 = 7.9\times 10^4\ \text{mile}/\text{hour}^2 \end{equation*}$ This large number can be interpreted as the speed, in miles per hour, that you would gain by falling for one hour. Note that we had to square the conversion factor of 3600 s/hour in order to cancel out the units of seconds squared in the denominator. $$\triangleright$$ What is $$g$$ in units of miles/hour/s? $$\triangleright$$ $\begin{equation*} \frac{9.8\ \text{m}}{\text{s}^2} \times \frac{1\ \text{mile}}{1600\ \text{m}} \times \frac{3600\ \text{s}}{1\ \text{hour}} = 22\ \text{mile}/\text{hour}/\text{s} \end{equation*}$ This is a figure that Americans will have an intuitive feel for. If your car has a forward acceleration equal to the acceleration of a falling object, then you will gain 22 miles per hour of speed every second. However, using mixed time units of hours and seconds like this is usually inconvenient for problem-solving. It would be like using units of foot-inches for area instead of $$\text{ft}^2$$ or $$\text{in}^2$$. ### The acceleration of gravity is different in different locations. Everyone knows that gravity is weaker on the moon, but actually it is not even the same everywhere on Earth, as shown by the sampling of numerical data in the following table. location latitude elevation (m) g textupmtextups2) north pole 90∘N 0 9.8322 Reykjavik, Iceland 64∘N 0 9.8225 Guayaquil, Ecuador 2∘S 0 9.7806 Mt. Cotopaxi, Ecuador 1∘S 5896 9.7624 Mt. Everest 28∘N 8848 9.7643 The main variables that relate to the value of $$g$$ on Earth are latitude and elevation. Although you have not yet learned how $$g$$ would be calculated based on any deeper theory of gravity, it is not too hard to guess why $$g$$ depends on elevation. Gravity is an attraction between things that have mass, and the attraction gets weaker with increasing distance. As you ascend from the seaport of Guayaquil to the nearby top of Mt. Cotopaxi, you are distancing yourself from the mass of the planet. The dependence on latitude occurs because we are measuring the acceleration of gravity relative to the earth's surface, but the earth's rotation causes the earth's surface to fall out from under you. (We will discuss both gravity and rotation in more detail later in the course.) h / This false-color map shows variations in the strength of the earth's gravity. Purple areas have the strongest gravity, yellow the weakest. The overall trend toward weaker gravity at the equator and stronger gravity at the poles has been artificially removed to allow the weaker local variations to show up. The map covers only the oceans because of the technique used to make it: satellites look for bulges and depressions in the surface of the ocean. A very slight bulge will occur over an undersea mountain, for instance, because the mountain's gravitational attraction pulls water toward it. The US government originally began collecting data like these for military use, to correct for the deviations in the paths of missiles. The data have recently been released for scientific and commercial use (e.g., searching for sites for off-shore oil wells). Much more spectacular differences in the strength of gravity can be observed away from the Earth's surface: location g textupmtextups2) asteroid Vesta (surface) 0.3 Earth’s moon (surface) 1.6 Mars (surface) 3.7 Earth (surface) 9.8 Jupiter (cloud-tops) 26 Sun (visible surface) 270 typical neutron star (surface) 1012 black hole (center) infinite according to some theories, on the order of1052 according to others A typical neutron star is not so different in size from a large asteroid, but is orders of magnitude more massive, so the mass of a body definitely correlates with the $$g$$ it creates. On the other hand, a neutron star has about the same mass as our Sun, so why is its $$g$$ billions of times greater? If you had the misfortune of being on the surface of a neutron star, you'd be within a few thousand miles of all its mass, whereas on the surface of the Sun, you'd still be millions of miles from most of its mass. ##### Discussion Questions What is wrong with the following definitions of $$g?$$ (1) “$$g$$ is gravity.” (2) “$$g$$ is the speed of a falling object.” (3) “$$g$$ is how hard gravity pulls on things.” When advertisers specify how much acceleration a car is capable of, they do not give an acceleration as defined in physics. Instead, they usually specify how many seconds are required for the car to go from rest to 60 miles/hour. Suppose we use the notation “$$a$$” for the acceleration as defined in physics, and “$$a_\text{car ad}$$” for the quantity used in advertisements for cars. In the US's non-metric system of units, what would be the units of $$a$$ and $$a_\text{car ad}$$? How would the use and interpretation of large and small, positive and negative values be different for $$a$$ as opposed to $$a_\text{car ad}$$? Two people stand on the edge of a cliff. As they lean over the edge, one person throws a rock down, while the other throws one straight up with an exactly opposite initial velocity. Compare the speeds of the rocks on impact at the bottom of the cliff. ## 3.3 Positive and negative acceleration i / The ball's acceleration stays the same --- on the way up, at the top, and on the way back down. It's always negative. Discussion question C. Gravity always pulls down, but that does not mean it always speeds things up. If you throw a ball straight up, gravity will first slow it down to $$v=0$$ and then begin increasing its speed. When I took physics in high school, I got the impression that positive signs of acceleration indicated speeding up, while negative accelerations represented slowing down, i.e., deceleration. Such a definition would be inconvenient, however, because we would then have to say that the same downward tug of gravity could produce either a positive or a negative acceleration. As we will see in the following example, such a definition also would not be the same as the slope of the $$v-t$$ graph. Let's study the example of the rising and falling ball. In the example of the person falling from a bridge, I assumed positive velocity values without calling attention to it, which meant I was assuming a coordinate system whose $$x$$ axis pointed down. In this example, where the ball is reversing direction, it is not possible to avoid negative velocities by a tricky choice of axis, so let's make the more natural choice of an axis pointing up. The ball's velocity will initially be a positive number, because it is heading up, in the same direction as the $$x$$ axis, but on the way back down, it will be a negative number. As shown in the figure, the $$v-t$$ graph does not do anything special at the top of the ball's flight, where $$v$$ equals 0. Its slope is always negative. In the left half of the graph, there is a negative slope because the positive velocity is getting closer to zero. On the right side, the negative slope is due to a negative velocity that is getting farther from zero, so we say that the ball is speeding up, but its velocity is decreasing! To summarize, what makes the most sense is to stick with the original definition of acceleration as the slope of the $$v-t$$ graph, $$\Delta v/\Delta t$$. By this definition, it just isn't necessarily true that things speeding up have positive acceleration while things slowing down have negative acceleration. The word “deceleration” is not used much by physicists, and the word “acceleration” is used unblushingly to refer to slowing down as well as speeding up: “There was a red light, and we accelerated to a stop.” ##### Example 4: Numerical calculation of a negative acceleration $$\triangleright$$ In figure i, what happens if you calculate the acceleration between $$t=1.0$$ and 1.5 s? $$\triangleright$$ Reading from the graph, it looks like the velocity is about $$-1$$ m/s at $$t=1.0$$ s, and around $$-6$$ m/s at $$t=1.5$$ s. The acceleration, figured between these two points, is $\begin{equation*} a = \frac{\Delta v}{\Delta t} = \frac{(-6\ \text{m}/\text{s})-(-1\ \text{m}/\text{s})}{(1.5\ \text{s})-(1.0\ \text{s})} = -10\ \text{m}/\text{s}^2 . \end{equation*}$ Even though the ball is speeding up, it has a negative acceleration. Another way of convincing you that this way of handling the plus and minus signs makes sense is to think of a device that measures acceleration. After all, physics is supposed to use operational definitions, ones that relate to the results you get with actual measuring devices. Consider an air freshener hanging from the rear-view mirror of your car. When you speed up, the air freshener swings backward. Suppose we define this as a positive reading. When you slow down, the air freshener swings forward, so we'll call this a negative reading on our accelerometer. But what if you put the car in reverse and start speeding up backwards? Even though you're speeding up, the accelerometer responds in the same way as it did when you were going forward and slowing down. There are four possible cases: motion of car accelerometer swings slope of v-t graph direction of force acting on car forward, speeding up backward + forward forward, slowing down forward − backward backward, speeding up forward − backward backward, slowing down backward + forward Note the consistency of the three right-hand columns --- nature is trying to tell us that this is the right system of classification, not the left-hand column. Because the positive and negative signs of acceleration depend on the choice of a coordinate system, the acceleration of an object under the influence of gravity can be either positive or negative. Rather than having to write things like “$$g=9.8\ \text{m}/\text{s}^2$$ or $$-9.8\ \text{m}/\text{s}^2$$” every time we want to discuss $$g$$'s numerical value, we simply define $$g$$ as the absolute value of the acceleration of objects moving under the influence of gravity. We consistently let $$g=9.8 \ \text{m}/\text{s}^2$$, but we may have either $$a=g$$ or $$a=-g$$, depending on our choice of a coordinate system. ##### Example 5: Acceleration with a change in direction of motion $$\triangleright$$ A person kicks a ball, which rolls up a sloping street, comes to a halt, and rolls back down again. The ball has constant acceleration. The ball is initially moving at a velocity of 4.0 m/s, and after 10.0 s it has returned to where it started. At the end, it has sped back up to the same speed it had initially, but in the opposite direction. What was its acceleration? $$\triangleright$$ By giving a positive number for the initial velocity, the statement of the question implies a coordinate axis that points up the slope of the hill. The “same” speed in the opposite direction should therefore be represented by a negative number, -4.0 m/s. The acceleration is \begin{align*} a &= \Delta v/\Delta t \\ &= (v_f-v_\text{o})/10.0\ \text{s} \\ &= [(-4.0 \ \text{m}/\text{s})-(4.0 \ \text{m}/\text{s})]/10.0 s \\ &= -0.80\ \text{m}/\text{s}^2 . \end{align*} The acceleration was no different during the upward part of the roll than on the downward part of the roll. Incorrect solution: Acceleration is $$\Delta v/\Delta$$t, and at the end it's not moving any faster or slower than when it started, so $$\Delta$$v=0 and $$a=0$$. The velocity does change, from a positive number to a negative number. Discussion question B. ##### Discussion Questions A child repeatedly jumps up and down on a trampoline. Discuss the sign and magnitude of his acceleration, including both the time when he is in the air and the time when his feet are in contact with the trampoline. The figure shows a refugee from a Picasso painting blowing on a rolling water bottle. In some cases the person's blowing is speeding the bottle up, but in others it is slowing it down. The arrow inside the bottle shows which direction it is going, and a coordinate system is shown at the bottom of each figure. In each case, figure out the plus or minus signs of the velocity and acceleration. It may be helpful to draw a $$v-t$$ graph in each case. Sally is on an amusement park ride which begins with her chair being hoisted straight up a tower at a constant speed of 60 miles/hour. Despite stern warnings from her father that he'll take her home the next time she misbehaves, she decides that as a scientific experiment she really needs to release her corndog over the side as she's on the way up. She does not throw it. She simply sticks it out of the car, lets it go, and watches it against the background of the sky, with no trees or buildings as reference points. What does the corndog's motion look like as observed by Sally? Does its speed ever appear to her to be zero? What acceleration does she observe it to have: is it ever positive? negative? zero? What would her enraged father answer if asked for a similar description of its motion as it appears to him, standing on the ground? Can an object maintain a constant acceleration, but meanwhile reverse the direction of its velocity? Can an object have a velocity that is positive and increasing at the same time that its acceleration is decreasing? ## 3.4 Varying acceleration j / Example 6. n / How position, velocity, and acceleration are related. So far we have only been discussing examples of motion for which the $$v-t$$ graph is linear. If we wish to generalize our definition to v-t graphs that are more complex curves, the best way to proceed is similar to how we defined velocity for curved $$x-t$$ graphs: ##### definition of acceleration The acceleration of an object at any instant is the slope of the tangent line passing through its $$v$$-versus-$$t$$ graph at the relevant point. ##### Example 6: A skydiver $$\triangleright$$ The graphs in figure k show the results of a fairly realistic computer simulation of the motion of a skydiver, including the effects of air friction. The $$x$$ axis has been chosen pointing down, so $$x$$ is increasing as she falls. Find (a) the skydiver's acceleration at $$t=3.0\ \text{s}$$, and also (b) at $$t=7.0\ \text{s}$$. $$\triangleright$$ The solution is shown in figure l. I've added tangent lines at the two points in question. (a) To find the slope of the tangent line, I pick two points on the line (not necessarily on the actual curve): $$(3.0\ \text{s},28 \text{m}/\text{s})$$ and $$(5.0\ \text{s},42\ \text{m}/\text{s})$$. The slope of the tangent line is $$(42\ \text{m}/\text{s}-28\ \text{m}/\text{s})/(5.0\ \text{s} - 3.0\ \text{s})=7.0\ \text{m}/\text{s}^2$$. (b) Two points on this tangent line are $$(7.0\ \text{s},47\ \text{m}/\text{s})$$ and $$(9.0\ \text{s}, 52\ \text{m}/\text{s})$$. The slope of the tangent line is $$(52\ \text{m}/\text{s}-47\ \text{m}/\text{s})/(9.0\ \text{s} - 7.0\ \text{s})=2.5\ \text{m}/\text{s}^2$$. Physically, what's happening is that at $$t=3.0\ \text{s}$$, the skydiver is not yet going very fast, so air friction is not yet very strong. She therefore has an acceleration almost as great as $$g$$. At $$t=7.0\ \text{s}$$, she is moving almost twice as fast (about 100 miles per hour), and air friction is extremely strong, resulting in a significant departure from the idealized case of no air friction. k / The solution to example 6. In example 6, the $$x-t$$ graph was not even used in the solution of the problem, since the definition of acceleration refers to the slope of the $$v-t$$ graph. It is possible, however, to interpret an $$x-t$$ graph to find out something about the acceleration. An object with zero acceleration, i.e., constant velocity, has an $$x-t$$ graph that is a straight line. A straight line has no curvature. A change in velocity requires a change in the slope of the $$x-t$$ graph, which means that it is a curve rather than a line. Thus acceleration relates to the curvature of the $$x-t$$ graph. Figure m shows some examples. In example 6, the $$x-t$$ graph was more strongly curved at the beginning, and became nearly straight at the end. If the $$x-t$$ graph is nearly straight, then its slope, the velocity, is nearly constant, and the acceleration is therefore small. We can thus interpret the acceleration as representing the curvature of the $$x-t$$ graph, as shown in figure m. If the “cup” of the curve points up, the acceleration is positive, and if it points down, the acceleration is negative. l / Acceleration relates to the curvature of the $$x-t$$ graph. Since the relationship between $$a$$ and $$v$$ is analogous to the relationship between $$v$$ and $$x$$, we can also make graphs of acceleration as a function of time, as shown in figure n. m / Examples of graphs of $$x$$, $$v$$, and $$a$$ versus $$t$$. 1. An object in free fall, with no friction. 2. A continuation of example 6, the skydiver. ◊ Solved problem: Drawing a $$v-t$$ graph. — problem 14 ◊ Solved problem: Drawing $$v-t$$ and $$a-t$$ graphs. — problem 20 Figure o summarizes the relationships among the three types of graphs. ##### Discussion Questions Describe in words how the changes in the $$a-t$$ graph in figure n/2 relate to the behavior of the $$v-t$$ graph. Explain how each set of graphs contains inconsistencies, and fix them. In each case, pick a coordinate system and draw $$x-t,v-t$$, and $$a-t$$ graphs. Picking a coordinate system means picking where you want $$x=0$$ to be, and also picking a direction for the positive $$x$$ axis. (1) An ocean liner is cruising in a straight line at constant speed. (2) You drop a ball. Draw two different sets of graphs (a total of 6), with one set's positive $$x$$ axis pointing in the opposite direction compared to the other's. (3) You're driving down the street looking for a house you've never been to before. You realize you've passed the address, so you slow down, put the car in reverse, back up, and stop in front of the house. ## 3.5 The area under the velocity-time graph o / The area under the $$v-t$$ graph gives $$\Delta x$$. q / Area underneath the axis is considered negative. A natural question to ask about falling objects is how fast they fall, but Galileo showed that the question has no answer. The physical law that he discovered connects a cause (the attraction of the planet Earth's mass) to an effect, but the effect is predicted in terms of an acceleration rather than a velocity. In fact, no physical law predicts a definite velocity as a result of a specific phenomenon, because velocity cannot be measured in absolute terms, and only changes in velocity relate directly to physical phenomena. The unfortunate thing about this situation is that the definitions of velocity and acceleration are stated in terms of the tangent-line technique, which lets you go from $$x$$ to $$v$$ to $$a$$, but not the other way around. Without a technique to go backwards from $$a$$ to $$v$$ to $$x$$, we cannot say anything quantitative, for instance, about the $$x-t$$ graph of a falling object. Such a technique does exist, and I used it to make the $$x-t$$ graphs in all the examples above. First let's concentrate on how to get $$x$$ information out of a $$v-t$$ graph. In example p/1, an object moves at a speed of $$20\ \text{m}/\text{s}$$ for a period of 4.0 s. The distance covered is $$\Delta x=v\Delta t=(20\ \text{m}/\text{s})\times(4.0\ \text{s})=80\ \text{m}$$. Notice that the quantities being multiplied are the width and the height of the shaded rectangle --- or, strictly speaking, the time represented by its width and the velocity represented by its height. The distance of $$\Delta x=80\ \text{m}$$ thus corresponds to the area of the shaded part of the graph. The next step in sophistication is an example like p/2, where the object moves at a constant speed of $$10\ \text{m}/\text{s}$$ for two seconds, then for two seconds at a different constant speed of $$20\ \text{m}/\text{s}$$. The shaded region can be split into a small rectangle on the left, with an area representing $$\Delta x=20\ \text{m}$$, and a taller one on the right, corresponding to another 40 m of motion. The total distance is thus 60 m, which corresponds to the total area under the graph. An example like p/3 is now just a trivial generalization; there is simply a large number of skinny rectangular areas to add up. But notice that graph p/3 is quite a good approximation to the smooth curve p/4. Even though we have no formula for the area of a funny shape like p/4, we can approximate its area by dividing it up into smaller areas like rectangles, whose area is easier to calculate. If someone hands you a graph like p/4 and asks you to find the area under it, the simplest approach is just to count up the little rectangles on the underlying graph paper, making rough estimates of fractional rectangles as you go along. p / An example using estimation of fractions of a rectangle. That's what I've done in figure q. Each rectangle on the graph paper is 1.0 s wide and $$2\ \text{m}/\text{s}$$ tall, so it represents 2 m. Adding up all the numbers gives $$\Delta x=41\ \text{m}$$. If you needed better accuracy, you could use graph paper with smaller rectangles. It's important to realize that this technique gives you $$\Delta x$$, not $$x$$. The $$v-t$$ graph has no information about where the object was when it started. The following are important points to keep in mind when applying this technique: • If the range of $$v$$ values on your graph does not extend down to zero, then you will get the wrong answer unless you compensate by adding in the area that is not shown. • As in the example, one rectangle on the graph paper does not necessarily correspond to one meter of distance. • Negative velocity values represent motion in the opposite direction, so as suggested by figure r, area under the $$t$$ axis should be subtracted, i.e., counted as “negative area.” • Since the result is a $$\Delta x$$ value, it only tells you $$x_{after}-x_{before}$$, which may be less than the actual distance traveled. For instance, the object could come back to its original position at the end, which would correspond to $$\Delta x$$=0, even though it had actually moved a nonzero distance. Finally, note that one can find $$\Delta v$$ from an $$a-t$$ graph using an entirely analogous method. Each rectangle on the $$a-t$$ graph represents a certain amount of velocity change. ##### Discussion Question Roughly what would a pendulum's $$v-t$$ graph look like? What would happen when you applied the area-under-the-curve technique to find the pendulum's $$\Delta x$$ for a time period covering many swings? ## 3.6 Algebraic results for constant acceleration r / The shaded area tells us how far an object moves while accelerating at a constant rate. Although the area-under-the-curve technique can be applied to any graph, no matter how complicated, it may be laborious to carry out, and if fractions of rectangles must be estimated the result will only be approximate. In the special case of motion with constant acceleration, it is possible to find a convenient shortcut which produces exact results. When the acceleration is constant, the $$v-t$$ graph is a straight line, as shown in the figure. The area under the curve can be divided into a triangle plus a rectangle, both of whose areas can be calculated exactly: $$A=bh$$ for a rectangle and $$A=bh/2$$ for a triangle. The height of the rectangle is the initial velocity, $$v_\text{o}$$, and the height of the triangle is the change in velocity from beginning to end, $$\Delta v$$. The object's $$\Delta x$$ is therefore given by the equation $$\Delta x = v_\text{o} \Delta t + \Delta v\Delta t/2$$. This can be simplified a little by using the definition of acceleration, $$a=\Delta v/\Delta t$$, to eliminate $$\Delta v$$, giving $\begin{multline*} \Delta x = v_\text{o} \Delta t + \frac{1}{2}a\Delta t^2 . \shoveright{\text{[motion with}}\\ \text{constant acceleration]} \end{multline*}$ Since this is a second-order polynomial in $$\Delta t$$, the graph of $$\Delta x$$ versus $$\Delta t$$ is a parabola, and the same is true of a graph of $$x$$ versus $$t$$ --- the two graphs differ only by shifting along the two axes. Although I have derived the equation using a figure that shows a positive $$v_\text{o}$$, positive $$a$$, and so on, it still turns out to be true regardless of what plus and minus signs are involved. Another useful equation can be derived if one wants to relate the change in velocity to the distance traveled. This is useful, for instance, for finding the distance needed by a car to come to a stop. For simplicity, we start by deriving the equation for the special case of $$v_\text{o}=0$$, in which the final velocity $$v_f$$ is a synonym for $$\Delta v$$. Since velocity and distance are the variables of interest, not time, we take the equation $$\Delta x=\frac{1}{2}a\Delta t^2$$ and use $$\Delta t=\Delta v/a$$ to eliminate $$\Delta t$$. This gives $$\Delta x=(\Delta v)^2/2a$$, which can be rewritten as $\begin{equation*} v_f^2 = 2a\Delta x . \shoveright{\text{[motion with constant acceleration, v_\text{o}=0]}} \end{equation*}$ For the more general case where $$v_\text{o}\ne 0$$, we skip the tedious algebra leading to the more general equation, $\begin{equation*} v_f^2 = v_\text{o}^2 + 2a\Delta x . \shoveright{\text{[motion with constant acceleration]}} \end{equation*}$ To help get this all organized in your head, first let's categorize the variables as follows: Variables that change during motion with constant acceleration: $$x$$ ,$$v$$, $$t$$ Variable that doesn't change: $$a$$ If you know one of the changing variables and want to find another, there is always an equation that relates those two: The symmetry among the three variables is imperfect only because the equation relating $$x$$ and $$t$$ includes the initial velocity. There are two main difficulties encountered by students in applying these equations: • The equations apply only to motion with constant acceleration. You can't apply them if the acceleration is changing. • Students are often unsure of which equation to use, or may cause themselves unnecessary work by taking the longer path around the triangle in the chart above. Organize your thoughts by listing the variables you are given, the ones you want to find, and the ones you aren't given and don't care about. ##### Example 7: Saving an old lady $$\triangleright$$ You are trying to pull an old lady out of the way of an oncoming truck. You are able to give her an acceleration of $$20\ \text{m}/\text{s}^2$$. Starting from rest, how much time is required in order to move her 2 m? $$\triangleright$$ First we organize our thoughts: Variables given: $$\Delta x$$, $$a$$, $$v_\text{o}$$ Variables desired: $$\Delta t$$ Irrelevant variables: $$v_f$$ Consulting the triangular chart above, the equation we need is clearly $$\Delta x=v_\text{o}\Delta t+\frac{1}{2}a\Delta t^2$$, since it has the four variables of interest and omits the irrelevant one. Eliminating the $$v_\text{o}$$ term and solving for $$\Delta t$$ gives $$\Delta t=\sqrt{2\Delta x/a}=0.4\ \text{s}$$. ◊ Solved problem: A stupid celebration — problem 15 ◊ Solved problem: Dropping a rock on Mars — problem 16 ◊ Solved problem: The Dodge Viper — problem 18 ◊ Solved problem: Half-way sped up — problem 22 ##### Discussion Questions In chapter 1, I gave examples of correct and incorrect reasoning about proportionality, using questions about the scaling of area and volume. Try to translate the incorrect modes of reasoning shown there into mistakes about the following question: If the acceleration of gravity on Mars is 1/3 that on Earth, how many times longer does it take for a rock to drop the same distance on Mars? Check that the units make sense in the three equations derived in this section. ## 3.7 A test of the principle of inertia (optional) Historically, the first quantitative and well documented experimental test of the principle of inertia (p. 80) was performed by Galileo around 1590 and published decades later when he managed to find a publisher in the Netherlands that was beyond the reach of the Roman Inquisition.1 It was ingenious but somewhat indirect, and required a layer of interpretation and extrapolation on top of the actual observations. As described on p. 95, he established that objects rolling on inclined planes moved according to mathematical laws that we would today describe as in section 3.6. He knew that his rolling balls were subject to friction, as well as random errors due to the limited precision of the water clock that he used, but he took the approximate agreement of his equations with experiment to indicate that they gave the results that would be exact in the absence of friction. He also showed, purely empirically, that when a ball went up or down a ramp inclined at an angle $$\theta$$, its acceleration was proportional to $$\sin\theta$$. Again, this required extrapolation to idealized conditions of zero friction. He then reasoned that if a ball was rolled on a horizontal ramp, with $$\theta=0$$, its acceleration would be zero. This is exactly what is required by the principle of inertia: in the absence of friction, motion continues indefinitely. ## 3.8 Applications of calculus (optional calculus-based section) In section 2.7, I discussed how the slope-of-the-tangent-line idea related to the calculus concept of a derivative, and the branch of calculus known as differential calculus. The other main branch of calculus, integral calculus, has to do with the area-under-the-curve concept discussed in section 3.5. Again there is a concept, a notation, and a bag of tricks for doing things symbolically rather than graphically. In calculus, the area under the $$v-t$$ graph between $$t=t_1$$ and $$t=t_2$$ is notated like this: $\begin{equation*} \text{area under curve} = \Delta x = \int_{t_1}^{t_2}v dt . \end{equation*}$ The expression on the right is called an integral, and the s-shaped symbol, the integral sign, is read as “integral of ...” Integral calculus and differential calculus are closely related. For instance, if you take the derivative of the function $$x(t)$$, you get the function $$v(t)$$, and if you integrate the function $$v(t)$$, you get $$x(t)$$ back again. In other words, integration and differentiation are inverse operations. This is known as the fundamental theorem of calculus. On an unrelated topic, there is a special notation for taking the derivative of a function twice. The acceleration, for instance, is the second (i.e., double) derivative of the position, because differentiating $$x$$ once gives $$v$$, and then differentiating $$v$$ gives $$a$$. This is written as $\begin{equation*} a = \frac{d^2 x}{dt^2} . \end{equation*}$ The seemingly inconsistent placement of the twos on the top and bottom confuses all beginning calculus students. The motivation for this funny notation is that acceleration has units of $$\text{m}/\text{s}^2$$, and the notation correctly suggests that: the top looks like it has units of meters, the bottom $$\text{seconds}^2$$. The notation is not meant, however, to suggest that $$t$$ is really squared. ## Vocabulary gravity — A general term for the phenomenon of attraction between things having mass. The attraction between our planet and a human-sized object causes the object to fall. acceleration — The rate of change of velocity; the slope of the tangent line on a $$v-t$$ graph. ## Notation $$v_o$$ — initial velocity $$v_f$$ — final velocity $$a$$ — acceleration $$g$$ — the acceleration of objects in free fall; the strength of the local gravitational field ## Summary {} Galileo showed that when air resistance is negligible all falling bodies have the same motion regardless of mass. Moreover, their $$v-t$$ graphs are straight lines. We therefore define a quantity called acceleration as the slope, $$\Delta v/\Delta$$t, of an object's $$v-t$$ graph. In cases other than free fall, the $$v-t$$ graph may be curved, in which case the definition is generalized as the slope of a tangent line on the $$v-t$$ graph. The acceleration of objects in free fall varies slightly across the surface of the earth, and greatly on other planets. Positive and negative signs of acceleration are defined according to whether the $$v-t$$ graph slopes up or down. This definition has the advantage that a force with a given sign, representing its direction, always produces an acceleration with the same sign. The area under the $$v-t$$ graph gives $$\Delta x$$, and analogously the area under the $$a-t$$ graph gives $$\Delta v$$. For motion with constant acceleration, the following three equations hold: \begin{align*} \Delta x &= v_\text{o}\Delta t + \frac{1}{2}a\Delta t^2 \\ v_f^2 &= v_\text{o}^2 + 2 a \Delta x \\ a &= \frac{\Delta v}{\Delta t} \end{align*} They are not valid if the acceleration is changing. The following form can be used for the homework problems that require sketching a set of graphs. ## Homework Problems s / Problem 3. t / Problem 5. u / Problem 14. v / Problem 19. w / Problem 20. x / Problem 23. y / Problem 27. z / Problem 31. aa / Problem 32. 1. The graph represents the velocity of a bee along a straight line. At $$t=0$$, the bee is at the hive. (a) When is the bee farthest from the hive? (b) How far is the bee at its farthest point from the hive? (c) At $$t=13$$ s, how far is the bee from the hive? [Hint: Try problem 19 first.] (answer check available at lightandmatter.com) 2. A rock is dropped into a pond. Draw plots of its position versus time, velocity versus time, and acceleration versus time. Include its whole motion, starting from the moment it is dropped, and continuing while it falls through the air, passes through the water, and ends up at rest on the bottom of the pond. Do your work on a photocopy or a printout of page 123. 3. In an 18th-century naval battle, a cannon ball is shot horizontally, passes through the side of an enemy ship's hull, flies across the galley, and lodges in a bulkhead. Draw plots of its horizontal position, velocity, and acceleration as functions of time, starting while it is inside the cannon and has not yet been fired, and ending when it comes to rest. There is not any significant amount of friction from the air. Although the ball may rise and fall, you are only concerned with its horizontal motion, as seen from above. Do your work on a photocopy or a printout of page 123. 4. Draw graphs of position, velocity, and acceleration as functions of time for a person bunjee jumping. (In bunjee jumping, a person has a stretchy elastic cord tied to his/her ankles, and jumps off of a high platform. At the bottom of the fall, the cord brings the person up short. Presumably the person bounces up a little.) Do your work on a photocopy or a printout of page 123. 5. A ball rolls down the ramp shown in the figure, consisting of a curved knee, a straight slope, and a curved bottom. For each part of the ramp, tell whether the ball's velocity is increasing, decreasing, or constant, and also whether the ball's acceleration is increasing, decreasing, or constant. Explain your answers. Assume there is no air friction or rolling resistance. Hint: Try problem 20 first. [Based on a problem by Hewitt.] 6. A toy car is released on one side of a piece of track that is bent into an upright $$U$$ shape. The car goes back and forth. When the car reaches the limit of its motion on one side, its velocity is zero. Is its acceleration also zero? Explain using a $$v-t$$ graph. [Based on a problem by Serway and Faughn.] 7. What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 seconds? Explain your answer. [Based on a problem by Hewitt.] 8. A physics homework question asks, “If you start from rest and accelerate at 1.54 $$\ \text{m}/\text{s}^2$$ for 3.29 s, how far do you travel by the end of that time?” A student answers as follows: $\begin{equation*} 1.54 \times 3.29 = 5.07\ \text{m} \end{equation*}$ His Aunt Wanda is good with numbers, but has never taken physics. She doesn't know the formula for the distance traveled under constant acceleration over a given amount of time, but she tells her nephew his answer cannot be right. How does she know? 9. You are looking into a deep well. It is dark, and you cannot see the bottom. You want to find out how deep it is, so you drop a rock in, and you hear a splash 3.0 seconds later. How deep is the well? (answer check available at lightandmatter.com) 10. You take a trip in your spaceship to another star. Setting off, you increase your speed at a constant acceleration. Once you get half-way there, you start decelerating, at the same rate, so that by the time you get there, you have slowed down to zero speed. You see the tourist attractions, and then head home by the same method. (a) Find a formula for the time, $$T$$, required for the round trip, in terms of $$d$$, the distance from our sun to the star, and $$a$$, the magnitude of the acceleration. Note that the acceleration is not constant over the whole trip, but the trip can be broken up into constant-acceleration parts. (b) The nearest star to the Earth (other than our own sun) is Proxima Centauri, at a distance of $$d=4\times10^{16}\ \text{m}$$. Suppose you use an acceleration of $$a=10\ \text{m}/\text{s}^2$$, just enough to compensate for the lack of true gravity and make you feel comfortable. How long does the round trip take, in years? (c) Using the same numbers for $$d$$ and $$a$$, find your maximum speed. Compare this to the speed of light, which is $$3.0\times10^8$$ \ \textup{m}/\textup{s}. (Later in this course, you will learn that there are some new things going on in physics when one gets close to the speed of light, and that it is impossible to exceed the speed of light. For now, though, just use the simpler ideas you've learned so far.) (answer check available at lightandmatter.com) 11. You climb half-way up a tree, and drop a rock. Then you climb to the top, and drop another rock. How many times greater is the velocity of the second rock on impact? Explain. (The answer is not two times greater.) 12. Alice drops a rock off a cliff. Bubba shoots a gun straight down from the edge of the same cliff. Compare the accelerations of the rock and the bullet while they are in the air on the way down. [Based on a problem by Serway and Faughn.] 13. A person is parachute jumping. During the time between when she leaps out of the plane and when she opens her chute, her altitude is given by an equation of the form $\begin{equation*} y = b - c\left(t+ke^{-t/k}\right) , \end{equation*}$ where $$e$$ is the base of natural logarithms, and $$b$$, $$c$$, and $$k$$ are constants. Because of air resistance, her velocity does not increase at a steady rate as it would for an object falling in vacuum. (a) What units would $$b$$, $$c$$, and $$k$$ have to have for the equation to make sense? (b) Find the person's velocity, $$v$$, as a function of time. [You will need to use the chain rule, and the fact that $$d(e^x)/dx=e^x$$.] (answer check available at lightandmatter.com) (c) Use your answer from part (b) to get an interpretation of the constant $$c$$. [Hint: $$e^{-x}$$ approaches zero for large values of $$x$$.] (d) Find the person's acceleration, $$a$$, as a function of time.(answer check available at lightandmatter.com) (e) Use your answer from part (d) to show that if she waits long enough to open her chute, her acceleration will become very small. ∫ 14. (solution in the pdf version of the book) The top part of the figure shows the position-versus-time graph for an object moving in one dimension. On the bottom part of the figure, sketch the corresponding v-versus-t graph. 15. (solution in the pdf version of the book) On New Year's Eve, a stupid person fires a pistol straight up. The bullet leaves the gun at a speed of 100 \ \textup{m}/\textup{s}. How long does it take before the bullet hits the ground? 16. (solution in the pdf version of the book) If the acceleration of gravity on Mars is 1/3 that on Earth, how many times longer does it take for a rock to drop the same distance on Mars? Ignore air resistance. 17. (solution in the pdf version of the book) A honeybee's position as a function of time is given by $$x=10t-t^3$$, where $$t$$ is in seconds and $$x$$ in meters. What is its acceleration at $$t=3.0$$ s? ∫ 18. (solution in the pdf version of the book) In July 1999, Popular Mechanics carried out tests to find which car sold by a major auto maker could cover a quarter mile (402 meters) in the shortest time, starting from rest. Because the distance is so short, this type of test is designed mainly to favor the car with the greatest acceleration, not the greatest maximum speed (which is irrelevant to the average person). The winner was the Dodge Viper, with a time of 12.08 s. The car's top (and presumably final) speed was 118.51 miles per hour (52.98 \ \textup{m}/\textup{s}). (a) If a car, starting from rest and moving with constant acceleration, covers a quarter mile in this time interval, what is its acceleration? (b) What would be the final speed of a car that covered a quarter mile with the constant acceleration you found in part a? (c) Based on the discrepancy between your answer in part b and the actual final speed of the Viper, what do you conclude about how its acceleration changed over time? 19. (solution in the pdf version of the book) The graph represents the motion of a ball that rolls up a hill and then back down. When does the ball return to the location it had at $$t=0?$$ 20. (solution in the pdf version of the book) (a) The ball is released at the top of the ramp shown in the figure. Friction is negligible. Use physical reasoning to draw $$v-t$$ and $$a-t$$ graphs. Assume that the ball doesn't bounce at the point where the ramp changes slope. (b) Do the same for the case where the ball is rolled up the slope from the right side, but doesn't quite have enough speed to make it over the top. 21. (solution in the pdf version of the book) You throw a rubber ball up, and it falls and bounces several times. Draw graphs of position, velocity, and acceleration as functions of time. 22. (solution in the pdf version of the book) Starting from rest, a ball rolls down a ramp, traveling a distance $$L$$ and picking up a final speed $$v$$. How much of the distance did the ball have to cover before achieving a speed of $$v/2?$$ [Based on a problem by Arnold Arons.] 23. The graph shows the acceleration of a chipmunk in a TV cartoon. It consists of two circular arcs and two line segments. At $$t=0$$.00 $$s$$, the chipmunk's velocity is $$-3.10\ \text{m}/\text{s}$$. What is its velocity at $$t=10.00$$ s? (answer check available at lightandmatter.com) 24. Find the error in the following calculation. A student wants to find the distance traveled by a car that accelerates from rest for 5.0 s with an acceleration of $$2.0\ \text{m}/\text{s}^2$$. First he solves $$a=\Delta v/\Delta t$$ for $$\Delta v=10 \ \text{m}/\text{s}$$. Then he multiplies to find $$(10\ \text{m}/\text{s})(5.0\ \text{s})=50\ \text{m}$$. Do not just recalculate the result by a different method; if that was all you did, you'd have no way of knowing which calculation was correct, yours or his. 25. Acceleration could be defined either as $$\Delta v/\Delta t$$ or as the slope of the tangent line on the $$v-t$$ graph. Is either one superior as a definition, or are they equivalent? If you say one is better, give an example of a situation where it makes a difference which one you use. 26. If an object starts accelerating from rest, we have $$v^2=2a\Delta x$$ for its speed after it has traveled a distance $$\Delta x$$. Explain in words why it makes sense that the equation has velocity squared, but distance only to the first power. Don't recapitulate the derivation in the book, or give a justification based on units. The point is to explain what this feature of the equation tells us about the way speed increases as more distance is covered. 27. The figure shows a practical, simple experiment for determining $$g$$ to high precision. Two steel balls are suspended from electromagnets, and are released simultaneously when the electric current is shut off. They fall through unequal heights $$\Delta x_1$$ and $$\Delta x_2$$. A computer records the sounds through a microphone as first one ball and then the other strikes the floor. From this recording, we can accurately determine the quantity $$T$$ defined as $$T=\Delta t_2-\Delta t_1$$, i.e., the time lag between the first and second impacts. Note that since the balls do not make any sound when they are released, we have no way of measuring the individual times $$\Delta t_2$$ and $$\Delta t_1$$. (a) Find an equation for $$g$$ in terms of the measured quantities $$T$$, $$\Delta x_1$$ and $$\Delta x_2$$.(answer check available at lightandmatter.com) (b) Check the units of your equation. (c) Check that your equation gives the correct result in the case where $$\Delta x_1$$ is very close to zero. However, is this case realistic? (d) What happens when $$\Delta x_1=\Delta x_2$$? Discuss this both mathematically and physically. 28. The speed required for a low-earth orbit is $$7.9\times10^3\ \text{m}/\text{s}$$ (see ch. 10). When a rocket is launched into orbit, it goes up a little at first to get above almost all of the atmosphere, but then tips over horizontally to build up to orbital speed. Suppose the horizontal acceleration is limited to $$3g$$ to keep from damaging the cargo (or hurting the crew, for a crewed flight). (a) What is the minimum distance the rocket must travel downrange before it reaches orbital speed? How much does it matter whether you take into account the initial eastward velocity due to the rotation of the earth? (b) Rather than a rocket ship, it might be advantageous to use a railgun design, in which the craft would be accelerated to orbital speeds along a railroad track. This has the advantage that it isn't necessary to lift a large mass of fuel, since the energy source is external. Based on your answer to part a, comment on the feasibility of this design for crewed launches from the earth's surface. {Problem 29. This spectacular series of photos from a 2011 paper by Burrows and Sutton (“Biomechanics of jumping in the flea,” J. Exp. Biology 214:836) shows the flea jumping at about a 45-degree angle, but for the sake of this estimate just consider the case of a flea jumping vertically.}} 29. Some fleas can jump as high as 30 cm. The flea only has a short time to build up speed --- the time during which its center of mass is accelerating upward but its feet are still in contact with the ground. Make an order-of-magnitude estimate of the acceleration the flea needs to have while straightening its legs, and state your answer in units of $$g$$, i.e., how many “$$g$$'s it pulls.” (For comparison, fighter pilots black out or die if they exceed about 5 or 10 $$g$$'s.) 30. Consider the following passage from Alice in Wonderland, in which Alice has been falling for a long time down a rabbit hole: Down, down, down. Would the fall never come to an end? “I wonder how many miles I've fallen by this time?” she said aloud. “I must be getting somewhere near the center of the earth. Let me see: that would be four thousand miles down, I think” (for, you see, Alice had learned several things of this sort in her lessons in the schoolroom, and though this was not a very good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over)... Alice doesn't know much physics, but let's try to calculate the amount of time it would take to fall four thousand miles, starting from rest with an acceleration of 10 $$\ \text{m}/\text{s}^2$$. This is really only a lower limit; if there really was a hole that deep, the fall would actually take a longer time than the one you calculate, both because there is air friction and because gravity gets weaker as you get deeper (at the center of the earth, $$g$$ is zero, because the earth is pulling you equally in every direction at once). (answer check available at lightandmatter.com) 31. The photo shows Apollo 16 astronaut John Young jumping on the moon and saluting at the top of his jump. The video footage of the jump shows him staying aloft for 1.45 seconds. Gravity on the moon is 1/6 as strong as on the earth. Compute the height of the jump.(answer check available at lightandmatter.com) 32. Most people don't know that Spinosaurus aegyptiacus, not Tyrannosaurus rex, was the biggest theropod dinosaur. We can't put a dinosaur on a track and time it in the 100 meter dash, so we can only infer from physical models how fast it could have run. When an animal walks at a normal pace, typically its legs swing more or less like pendulums of the same length $$\ell$$. As a further simplification of this model, let's imagine that the leg simply moves at a fixed acceleration as it falls to the ground. That is, we model the time for a quarter of a stride cycle as being the same as the time required for free fall from a height $$\ell$$. S. aegyptiacus had legs about four times longer than those of a human. (a) Compare the time required for a human's stride cycle to that for S. aegyptiacus.(answer check available at lightandmatter.com) (b) Compare their running speeds.(answer check available at lightandmatter.com) 33. Engineering professor Qingming Li used sensors and video cameras to study punches delivered in the lab by British former welterweight boxing champion Ricky “the Hitman” Hatton. For comparison, Li also let a TV sports reporter put on the gloves and throw punches. The time it took for Hatton's best punch to arrive, i.e., the time his opponent would have had to react, was about $$0.47$$ of that for the reporter. Let's assume that the fist starts from rest and moves with constant acceleration all the way up until impact, at some fixed distance (arm's length). Compare Hatton's acceleration to the reporter's.(answer check available at lightandmatter.com) 34. Aircraft carriers originated in World War I, and the first landing on a carrier was performed by E.H. Dunning in a Sopwith Pup biplane, landing on HMS Furious. (Dunning was killed the second time he attempted the feat.) In such a landing, the pilot slows down to just above the plane's stall speed, which is the minimum speed at which the plane can fly without stalling. The plane then lands and is caught by cables and decelerated as it travels the length of the flight deck. Comparing a modern US F-14 fighter jet landing on an Enterprise-class carrier to Dunning's original exploit, the stall speed is greater by a factor of 4.8, and to accomodate this, the length of the flight deck is greater by a factor of 1.9. Which deceleration is greater, and by what factor?(answer check available at lightandmatter.com) 35. In college-level women's softball in the U.S., typically a pitcher is expected to be at least 1.75 m tall, but Virginia Tech pitcher Jasmin Harrell is 1.62 m. Although a pitcher actually throws by stepping forward and swinging her arm in a circle, let's make a simplified physical model to estimate how much of a disadvantage Harrell has had to overcome due to her height. We'll pretend that the pitcher gives the ball a constant acceleration in a straight line, and that the length of this line is proportional to the pitcher's height. Compare the acceleration Harrell would have to supply with the acceleration that would suffice for a pitcher of the nominal minimum height, if both were to throw a pitch at the same speed.(answer check available at lightandmatter.com) 36. When the police engage in a high-speed chase on city streets, it can be extremely dangerous both to the police and to other motorists and pedestrians. Suppose that the police car must travel at a speed that is limited by the need to be able to stop before hitting a baby carriage, and that the distance at which the driver first sees the baby carriage is fixed. Tests show that in a panic stop from high speed, a police car based on a Chevy Impala has a deceleration 9% greater than that of a Dodge Intrepid. Compare the maximum safe speeds for the two cars.(answer check available at lightandmatter.com) (c) 1998-2013 Benjamin Crowell, licensed under the Creative Commons Attribution-ShareAlike license. Photo credits are given at the end of the Adobe Acrobat version. ##### Footnotes [1] Galileo, Discourses and Mathematical Demonstrations Relating to Two New Sciences, 1638. The experiments are described in the Third Day, and their support for the principle of inertia is discussed in the Scholium following Theorems I-XIV. Another experiment involving a ship is described in Galileo's 1624 reply to a letter from Fr. Ingoli, but although Galileo vigorously asserts that he really did carry it out, no detailed description or quantitative results are given.

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http://www.purplemath.com/learning/viewtopic.php?p=796

## solve inverse-cos(x) + inverse-cos(sq. rt. of 15x) = (pi/2) Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc. car.man Posts: 5 Joined: Tue Mar 24, 2009 6:18 pm ### solve inverse-cos(x) + inverse-cos(sq. rt. of 15x) = (pi/2) solve inverse-cos(x) + inverse-cos(square root of 15x) = (pi/2). No one was able to solve this problem. Please help! stapel_eliz Posts: 1738 Joined: Mon Dec 08, 2008 4:22 pm Contact: car.man wrote:solve inverse-cos(x) + inverse-cos(square root of 15x) = (pi/2). By definition of inverse cosine, the above means the following: . . . . .$\alpha\, +\, \beta\, =\, \frac{\pi}{2}$ ...for: . . . . .$\cos^{-1}(x)\, =\, \alpha\, \mbox{ and }\, \cos^{-1}(\sqrt{15}x)\, =\, \beta$ This is a sum of two angles, and involves cosines. What if we now take the cosine of both sides of the above? . . . . .$\cos(\alpha\, +\, \beta)\, =\, 0$ Using an angle-sum identity, we get: . . . . .$\cos(\alpha)\cos(\beta)\, -\, \sin(\alpha)\sin(\beta)\, =\, 0$ We can simplify the factors in the first product by using the definition of "inverse cosine": . . . . .$\cos\left(\cos^{-1}(x)\right)\cos\left(\cos^{-1}(\sqrt{15}x)\right)\, =\, (x)\left(\sqrt{15}x\right)\, =\, \sqrt{15}x^2$ To find the values of the sines, draw right triangles for each of the angles $\alpha$ and $\beta$. Using the Pythagorean Theorem, find the length of the "opposite" side for each triangle. Then read off the values of the sines. You should end up with an equation, after squaring, that looks like: . . . . .$15x^4\, =\, 1\, -\, 16x^2\, +\, 15x^4$ Then: . . . . .$0\, =\, 1\, -\, 16x^2\, =\, (1\, -\, 4x)(1\, +\, 4x)$ ...and so forth. car.man Posts: 5 Joined: Tue Mar 24, 2009 6:18 pm ### Re: solve inverse-cos(x) + inverse-cos(sq. rt. of 15x) = (pi/2) We got x=+-1/4 and x=+1/4 worked. Thank you!

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## Trigonometry (11th Edition) Clone Published by Pearson # Chapter 3 - Radian Measure and the Unit Circle - Section 3.1 Radian Measure - 3.1 Exercises - Page 105: 48 4.623 radian #### Work Step by Step $264.9\times \frac{\pi}{180} = 4.623$ radian After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

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http://mathoverflow.net/feeds/question/37021

Is Fourier analysis a special case of representation theory or an analogue? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T22:31:00Z http://mathoverflow.net/feeds/question/37021 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue Is Fourier analysis a special case of representation theory or an analogue? David Corwin 2010-08-29T03:47:43Z 2012-12-06T00:36:58Z <p>I'm asking this question because I've been told by some people that Fourier analysis is "just representation theory of $S^1$."</p> <p>I've been introduced to the idea that Fourier analysis is related to representation theory. Specifically, when considering the representations of a finite abelian group $A$, these representations are all $1$-dimensional, hence correspond to characters $A \to \mathbb{R}/\mathbb{Z} \cong S^1 \subseteq \mathbb{C}$. On the other side, finite Fourier analysis is, in a simplistic sense, the study of characters of finite abelian groups. Classical Fourier analysis is, then, the study of continuous characters of locally compact abelian groups like $\mathbb{R}$ (classical Fourier transform) or $S^1$ (Fourier series). However, in the case of Fourier analysis, we have something beyond characters/representations: We have the Fourier series / transform. In the finite case, this is a sum which looks like $\frac{1}{n} \sum_{0 \le r &lt; n} \omega^r \rho(r)$ for some character $\rho$, and in the infinite case, we have the standard Fourier series and integrals (or, more generally, the abstract Fourier transform). So it seems like there is something more you're studying in Fourier analysis, beyond the representation theory of abelian groups. To phrase this as a question (or two):</p> <p>(1) What is the general Fourier transform which applies to abelian and non-abelian groups?</p> <p>(2) What is the category of group representations we consider (and attempt to classify) in Fourier analysis? That is, it seems like Fourier analysis is more than just the special case of representation theory for abelian groups. It seems like Fourier analysis is trying to do more than classify the category of representations of a locally compact abelian group $G$ on vector spaces over some fixed field. Am I right? Or can everything we do in Fourier analysis (including the Fourier transform) be seen as one piece in the general goal of classifying representations?</p> <p>Let me illustrate this in another way. The basic result of Fourier series is that every function in $L^2(S^1)$ has a Fourier series, or in other words that $L^2$ decomposes as a (Hilbert space) direct sum of one dimensional subspaces corresponding to $e^{2 \pi i n x}$ for $n \in \mathbb{Z}$. If we encode this in a purely representation-theoretic fact, this says that $L^2(S^1)$ decomposes into a direct sum of the representations corresponding to the unitary characters of $S^1$ (which correspond to $\mathbb{Z}$). But this fact is not why Fourier analysis is interesting (at least in the sense of $L^2$-convergence; I'm not even worrying about pointwise convergence). Fourier analysis states furthermore an <em>explicit</em> formula for the function in $L^2$ giving this representation. Though I guess by knowing the character corresponding to the representation would tell you what the function is.</p> <p>So is Fourier analysis merely similar to representation theory, or is it none other than the abelian case of representation theory?</p> <p>(Aside: This leads into a more general question of mine about the use of representation theory as a generalization of modular forms. My question is the following: I understand that a classical Hecke eigenform (of some level $N$) can be viewed as an element of $L^2(GL_2(\mathbb{Q})\ GL_2(\mathbb{A}_{\mathbb{Q}})$ which corresponds to a subrepresentation. But what I don't get is why the representation tells you everything you would have wanted to know about the classical modular form. A representation is nothing more than a vector space with an action of a group! So how does this encode the information about the modular form?)</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/37031#37031 Answer by Yemon Choi for Is Fourier analysis a special case of representation theory or an analogue? Yemon Choi 2010-08-29T07:19:02Z 2010-08-30T00:02:55Z <p>Since David's asked or suggested that some remarks be written up as an answer, let me repeat what I said in the comments:</p> <ul> <li><p>in my opinion, the answer to the question in the title is "neither";</p></li> <li><p>my answer to Q1 would be "look up Fourier transform and noncommutative harmonic analysis" - if one is only interested in compact groups then there is a very satisfactory theory, outlined in Hewitt &amp; Ross volume 2 for example;</p></li> <li><p>and my answer to Q2 would be "not applicable - the question is founded on a debatable premise".</p></li> </ul> <p>Actually, in the middle of the salvo that he's labelled as "Question 2", David asks</p> <blockquote> <p>That is, it seems like Fourier analysis is more than just the special case of representation theory for abelian groups. It seems like Fourier analysis is trying to do more than classify the category of representations of a locally compact abelian group $G$ on vector spaces over some fixed field. Am I right?</p> </blockquote> <p>and in my inexpert opinion, the answer is "yes". Why would it be 'just' a subtopic of the enterprise of classifying representations?</p> <hr> <p><b>Update:</b> to elaborate on my objections to the original questions, while not taking anything away from the informative comments and answers that other people have given: <em>there is more to Fourier analysis than constructing a Fourier transform between certain topological vector spaces and getting a Plancherel formula</em>. Hence being able to construct a generalization or analogue of the Fourier transform for nonabelian locally compact groups is not the be all and end all of the topic, unless the topic is "constructing a nonabelian Fourier transform". Looking in the literature on harmonic analysis, even in the abelian case, ought to bear this out.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/37071#37071 Answer by Theo Johnson-Freyd for Is Fourier analysis a special case of representation theory or an analogue? Theo Johnson-Freyd 2010-08-29T17:48:56Z 2010-08-30T03:08:03Z <p>This answer is essentially a comment, but slightly too long.</p> <p>As someone who is closer to representation theory than analysis, to me the word "Fourier analysis" means "Pontrjagin duality". You hint at this theorem in your question, but I will state (a version of) it for completeness:</p> <p><strong>Theorem:</strong> Let $G$ be a locally-compact topological abelian group. A <em>character</em> is a continuous homomorphism $G \to \mathbb S^1$ the circle. The set $G^\vee$ of characters is naturally an abelian group under $\otimes$, and has a canonical topological structure in which it is locally compact. The canonical pairing $G \times G^\vee \to \mathbb S^1$ induces a map $G \to (G^\vee)^\vee$, which is an isomorphism.</p> <p>A good reference is:</p> <ul> <li>André Joyal, Ross Street. An introduction to Tannaka duality and quantum groups. <em>Category Theory, Lecture Notes in Math</em>. 1991 vol. 1488 pp. 412–492.</li> </ul> <p>They describe the relationship between Pontrjagin duality and Fourier theory as a warm-up for various forms of Tannaka-Krein theory, which can be thought of as a "noncommutative" analogue of Pontrjagin duality.</p> <hr> <p>Incidentally, just as there are questions that Fourier analysts care about that aren't "just" representation theory of abelian groups, there are questions in the representation theory of abelian groups that aren't "just" Pontrjagin duality. For example, given a fixed vector space $V$, the collection of sets of $n$ commuting matrices $V \to V$ is naturally the same as the collection of representations of $\mathbb Z^n$ on $V$, i.e. $\operatorname{Hom}(\mathbb Z^n \to \operatorname{End}(V))$. Now, $\operatorname{GL}(V)$ acts on $\operatorname{End}(V)$ and hence on $\operatorname{Hom}(\mathbb Z^n \to \operatorname{End}(V))$ by conjugation. The corresponding moduli problem &mdash; find the moduli space of $n$ commuting matrices of fixed dimension &mdash; is hard, although I think it's solved.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/37078#37078 Answer by Dick Palais for Is Fourier analysis a special case of representation theory or an analogue? Dick Palais 2010-08-29T19:43:25Z 2010-08-29T20:06:26Z <p>First, I think it is better to restrict the term "Fourier Analysis" to refer to the process of expanding functions on a locally compact ABELIAN group $G$ as a "sum'' of the characters of the group. (I'll come back to that in a moment.) The generalization, when the group $G$ is not assumed to be abelian, should probably be better referred to as Harmonic Analysis". Regarding the latter, if the group $G$ is compact, then the Peter-Weyl Theorem gives an elegant and simple generalization to the theory of Fourier Series on the circle group---it shows how to write any $L^2$ function on $G$ as an series of (orthogonal) matrix elements of irreducible unitary representations of $G$. When $G$ is neither abelian nor compact, the theory becomes MUCH more complicated and sophisticated. BTW, note that when $G$ is abelian, then as you pointed out, the irreducble unitary representaions of $G$ are one-dimensional, so there is no difference between a matrix element and a character in this case and we are generalizing Fourier series on the circle group.</p> <p>OK, lets now restrict to the Fourier" case, where $G$ is locally compact and abelian. Note that an irreducible unitary character of $G$ is now just a group homomorphism of $G$ into the circle group $S= S^1$ (considered as the complex numbers of modulus one under multiplication). Since $G$ is abelian, the set $\hat G = Hom(G,S)$ is an abelian group, the character (or Pontrjagin dual) group of $G$, under pointwise multiplication. It is easy to see that $\hat G$ is locally compact (in the compact open topology) What Fourier analysis becomes in this case is a method for expressing an arbitrary element of $L^2(G)$ as an integral of the form $f(g) \sim \int \hat f(\chi)\chi(g) d\chi$, where $\hat f$, the Fourier transform of $f$ is defined dually by $\hat f(\chi) = \int f(g) \chi(g) dg$ (and the Haar measures on $G$ and $\hat G$ are suitably normalized). Note that if we take for $G$ the real line $R$ then this reduces to the classical Fourier transform. It is easy to show that the integral defining the Fourier transform $\hat f(\chi)$ is convergent when $f$ is in $L^1 \cap L^2$ and that then $||\hat f||_2 = ||f||_2^2$, and since $L^1 \cap L^2$ is dense in $L^2$ it follows that the Fourier transform extends uniquely to a unitary map of $L^2(G)$ onto $L^2(\hat G)$.</p> <p>Now lets restrict further to the compact case, where characters, being continuous, are bounded and so integrable. As one can prove in a couple of lines (using the invariance of Haar measure), if $\chi$ is any character of $G$ then $\int \chi(g)\, dg = 0$ unless $\chi$ is the identity character in which case the integral is one (using normalized Haar measure on $G$). Since the complex conjugate of a character is its inverse in $\hat G$, it now follows trivially that the elements of $\hat G$ are orthonormal. In fact they form an orthonormal basis for $L^2(G)$, and the Fourier transform of the preceding paragraph becomes a formula for expanding any element of $L^2(G)$ as the sum of an infinite series in the characters of $G$, a direct generalization of the theory of Fourier series (the case when $G = S$).</p> <p>A good place to see all the details is Lynn Loomis' "Absract Harmonic Analysis". </p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/37098#37098 Answer by Kimball for Is Fourier analysis a special case of representation theory or an analogue? Kimball 2010-08-29T23:42:14Z 2010-08-29T23:42:14Z <p>As a complement to the other answers, the (Selberg or Arthur-Selberg) trace formula can be viewed as a generalization of Poisson summation. Harish-Chandra also generalized the Plancherel formula. Both of these can be carried out for connected reductive Lie groups and are important in representation theory. </p> <p>From this point of view, it is perhaps more evident what one should expect of a generalized Fourier transform, and its role is played by the Harish-Chandra/Selberg transform. For the simplest (but not really so simple) non-abelian case, see Iwaniec's "Spectral Theory of Automorphic Forms." </p> <p>As for what other groups one might be able to do this for, one can at least do the trace formula for finite groups (which can be viewed as a generalization of Frobenius reciprocity, cf. Arthur's "Trace formula and Hecke operators"---Arthur also has a Notices article which discusses the general Plancherel formula and Langlands' program), and perhaps it's not too hard to see what a generalization of the Fourier transform should be in nonabelian cases, but I'd need to think about it.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/37189#37189 Answer by Emerton for Is Fourier analysis a special case of representation theory or an analogue? Emerton 2010-08-30T19:40:03Z 2010-08-31T14:28:48Z <p>I would like to elaborate slightly on my comment. First of all, Fourier analysis has a very broad meaning. Fourier introduced it as a means to study the heat equation, and it certainly remains a major tool in the study of PDE. I'm not sure that people who use it in this way think of it in a particularly representation-theoretic manner.</p> <p>Also, when one thinks of the Fourier transform as interchanging position space and frequency space, or (as in quantum mechanics) position space and momentum space, I don't think that a representation theoretic view-point necessarily need play much of a role.</p> <p>So, when one thinks about Fourier analysis from the point of view of group representation theory, this is just one part of Fourier analysis, perhaps the most foundational part, and it is probably most important when one wants to understand how to extend the basic statements regarding Fourier transforms or Fourier series from functions on $\mathbb R$ or $S^1$ to functions on other (locally compact, say) groups.</p> <p>As I noted in my comment, the basic question is: how to decompose the regular representation of $G$ on the Hilbert space $L^2(G)$. When $G$ is locally compact abelian, this has a very satisfactory answer in terms of the Pontrjagin dual group $\widehat{G}$, as described in Dick Palais's answer: one has a Fourier transform relating $L^2(G)$ and $L^2(\widehat{G})$. A useful point to note is that $G$ is discrete/compact if and only if $\widehat{G}$ is compact/discrete. So $L^2(G)$ is always described as the Hilbert space direct integral of the characters of $G$ (which are the points of $\widehat{G}$) with respect to the Haar measure on $\widehat{G}$, but when $G$ is compact, so that $\widehat{G}$ is discrete, this just becomes a Hilbert space direct sum, which is more straightforward (thus the series of Fourier series are easier than the integrals of Fourier transforms).</p> <p>I will now elide Dick Palais's distinction between the Fourier case and the more general context of harmonic analysis, and move on to the non-abelian case. As Dick Palais also notes, when $G$ is compact, the Peter--Weyl theorem nicely generalizes the theory of Fourier series; one again describes $L^2(G)$ as a Hilbert space direct sum, not of characters, but of finite dimensional representations, each appearing with multiplicity equal to its degree (i.e. its dimension). Note that the set over which one sums now is still discrete, but is not a group. And there is less homogeneity in the description: different irreducibles have different dimensions, and so contribute in different amounts (i.e. with different multiplicities) to the direct sum.</p> <p>When G is locally compact but neither compact nor abelian, the theory becomes more complex. One would like to describe $L^2(G)$ as a Hilbert space direct integral of matrix coefficients of irreducible unitary representations, and for this, one has to find the correct measure (the so-called Plancherel measure) on the set $\widehat{G}$ of irreducible unitary representations. Since $\widehat{G}$ is now just a set, a priori there is no natural measure to choose (unlike in the abelian case, when $\widehat{G}$ is a locally compact group, and so has its Haar measure), and in general, as far as I understand, one doesn't have such a direct integral decomposition of $L^2(G)$ in a reasonable sense.</p> <p>But in certain situations (when $G$ is of "Type I") there is such a decomposition, for a uniquely determined measure, so-called Plancherel measure, on $\widehat{G}$. But this measure is not explicitly given. Basic examples of Type I locally compact groups are semi-simple real Lie groups, and also semi-simple $p$-adic Lie groups.</p> <p>The major part of Harish-Chandra's work was devoted to explicitly describing the Plancherel measure for semi-simple real Lie groups. The most difficult part of the question is the existence of atoms (i.e. point masses) for the measure; these are irreducible unitary representations of $G$ that embed as subrepresentations of $L^2(G)$, and are known as "discrete series" representations. Harish-Chandra's description of the discrete series for all semi-simple real Lie groups is one of the major triumphs of 20th century representation theory (indeed, 20th century mathematics!).</p> <p>For $p$-adic groups, Harish-Chandra reduced the problem to the determination of the discrete series, but the question of explicitly describing the discrete series in that case remains open.</p> <p>One important thing that Harish-Chandra proved was that not all points of $\widehat{G}$ (when $G$ is a real or $p$-adic semisimple Lie group) are in the support of Plancherel measure; only those which satisfy the technical condition of being "tempered". (So this is another difference from the abelian case, where Haar measure is supported uniformly over all of $\widehat{G}$.) Thus in explicitly describing Plancherel measure, and hence giving an explicit form of Fourier analysis for any real semi-simple Lie group, he <em>didn't</em> have to classify all unitary representations of $G$.</p> <p>Indeed, the classification of all such reps. (i.e. the explicit description of $\widehat{G}$) remains an open problem for real semi-simple Lie groups (and even more so for $p$-adic semi-simple Lie groups, where even the discrete series are not yet classified).</p> <p>This should give you some sense of the relationship between Fourier analysis in its representation-theoretic interpretation (i.e. the explicit description of $L^2(G)$ in terms of irreducibles) and the general classification of irreducible unitary representations of $G$. They are related questions, but are certainly not the same, and one can fully understand one without understanding the other.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/46041#46041 Answer by Marc Palm for Is Fourier analysis a special case of representation theory or an analogue? Marc Palm 2010-11-14T13:42:34Z 2010-11-14T14:55:23Z <p>Fourier Analysis on $\mathbb{R}$ has several similiar interpretations. The most important one is it realizes the Functional calculus for the rightregular representation.</p> <p>I can only be really sketchy here:</p> <p>We can see it as the realization of the functional calculus for the operator $D= - \mathrm{i} \frac{\partial}{\partial x}$. Observe that $\mathcal{F} D = M_x \mathcal{F}$. Here $M_x$ is multiplication by $x$, which is much easier to understand than taking derivative. That is the main reason, why the Fourier transform is so important in the theory of differential operators. A great generalization of this is the Gelfand transform, which identifies certain commutative Algebras with functions over topological spaces. In this theory, we identify the algebra $D$ given by normal closed operator with the continouos function on the spectrum of $D$.</p> <p>Analogues ideas in algebraic geometry have been introduced by Grothendieck, who associated to varieties over a commutative unital ring R also a spectrum. In the case of an algebraic group this spectrum can be seen as a certain the group ring.</p> <p>Since taking derivatives commutes with the right translations, which are exactly the right regular representation of $\mathbb{R}$. The Fourier analysis also realizes the functional calculus for this family of operators.</p> <p>The analysis of noncommutative groups is of course much more difficult since the right translation do not commute here, hence there is no functional calculus, since this is not available for non commutative algebras.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/56600#56600 Answer by saghar for Is Fourier analysis a special case of representation theory or an analogue? saghar 2011-02-25T06:02:56Z 2011-02-25T06:02:56Z <p>If you want to know what is the dual of a nonabelian locally compact group, you have to study about locally compact quantum groups. Then you can see that even we can define the fourier transform here as well.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/115355#115355 Answer by paul garrett for Is Fourier analysis a special case of representation theory or an analogue? paul garrett 2012-12-04T04:09:27Z 2012-12-04T04:09:27Z <p>In addition to the many other interesting and useful answers, and as evidence for the fruitfulness of the question (!), I do think there are a few other (maybe-interesting and maybe-useful) points to be made. </p> <p>First, to limit the scope, let's say we're talking about "Type I" groups, that is, groups which more-or-less have a reasonable/tractable representation theory, in the sense that "factor representations" are sums/integrals of irreducibles. This assumption deserves comment: as in one of the earlier good answers, there are many reasonable groups which do not fall into this class. (Dang...) The good news is that it is possible to understand this failing (e.g., see Alain Robert's wonderful LMS book), and that for many critical applications (in my own purview, to number-theoretic things) this is not an issue. Whew.</p> <p>It is likewise certainly true (as observed and documented in earlier answers) that the "full question" of determination of details about various Plancherel theorems (for reductive p-adic groups...) is still open... but, also, sufficiently-many examples are known that "we" feel some confidence in advancing in a certain way. It is important to note that many literal Plancherel formulas do not (as noted in other answers!) involve <em>all</em> (unitary) irreducibles, but only a nice (a.k.a. "tempered", in some contexts) subclass.</p> <p>A very educational case is the Gelfand-Naimark story from the late 1940's, addressing more-or-less reductive complex Lie groups, essentially proving that the decomposition of $L^2(G)$ needed only unitary principal series... [sic]</p> <p>At best, such an assertion is about $L^2$, not about pointwise convergence, etc. </p> <p>Harish-Chandra showed in the 1950s and '60s that things are (stunningly) more complicated for "real" Lie groups <em>not</em> obtained by the forgetful functor complex-to-real Lie group.</p> <p>Nevertheless, ... for applications to analytic number theory (!?), one would desire sharp estimates on convergence of spectral expansions of automorphic forms. Maass and Selberg initiated this study, but/and this line of thought has not-so-often interacted with the Schwartz-Grothendieck modern-analysis thinking... to all our loss.</p> <p>As David Farmer aptly quipped in Oklahoma at a lovely conference in Sept of this year, "convergence is tricky". </p> <p>... but/and in many interesting cases, the convergence of "an eigenfunction expansion" is exactly what a serious problem wants.</p> <p>(Some schools of thought study the individual "eigenfunctions", e.g., automorphic forms, ... but/and many applications require those pesky convergence considerations.)</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/115358#115358 Answer by Will Sawin for Is Fourier analysis a special case of representation theory or an analogue? Will Sawin 2012-12-04T05:28:35Z 2012-12-04T05:28:35Z <p>Here is a very quick, overly simplified answer:</p> <p>Fourier analysis = The representation theory of S^1 + Peter-Weyl for S^1.</p> <p>So it's not a special case of representation theory, but it is a special case of ( representation theory + Peter-Weyl ).</p> <p>The reason this is only a rough schematic is that there is Fourier analysis that isn't just about the $L^2$ spaces. But you can think of it as having an $L^2$, algebraic core, with all the other functions between Banach spaces with various properties "glued" to the core, meaning they determine each other.</p> http://mathoverflow.net/questions/37021/is-fourier-analysis-a-special-case-of-representation-theory-or-an-analogue/115564#115564 Answer by Steve Huntsman for Is Fourier analysis a special case of representation theory or an analogue? Steve Huntsman 2012-12-06T00:36:58Z 2012-12-06T00:36:58Z <p>I just saw this and figured a more elementary and explicit answer discussing Fourier transforms on finite groups couldn't hurt, especially since it's a chance to use some of my notes.</p> <p>First, some scene-setting: harmonic analysis on a finite abelian group $G$ turns out to be a direct generalization of the theory of Fourier series. A function $f$ is decomposed according to</p> <p>$\hat f(\chi) := \lvert G \rvert^{-1/2} \sum_g f(g) \chi(g);$</p> <p>$f(g) = \lvert G \rvert^{-1/2} \sum_\chi \hat f(\chi) \chi(g^{-1}).$</p> <p>Here $\chi$ denotes a character. The factors of $\lvert G \rvert^{-1/2}$ are chosen for the sake of unitarity; the more general case of locally compact abelian $G$ is broadly similar.</p> <p>Nonabelian groups do not have enough unitary characters to enable a decomposition of the form above. Let $\rho: G \rightarrow GL(V)$ be a representation with dimension $d_\rho \equiv \dim V$; the corresponding character is $\chi_\rho(g) = \mbox{Tr} \rho(g)$.</p> <p>Two key identities express the orthogonality and completeness of representations, i.e.</p> <p><code>$\frac{d_\rho}{\lvert G \rvert} \sum_g \rho_{jk}(g^{-1}) \rho'_{\ell m}(g) = \delta_{\rho \rho'} \delta_{jm} \delta_{k \ell}$</code>; </p> <p>$\sum_\rho \frac{d_\rho}{\lvert G \rvert} \mbox{Tr} \left [ \rho(g^{-1}) \rho(g') \right ] = \delta_{gg'},$</p> <p>respectively, where straightforward generalizations of the usual Kronecker delta are indicated, $\rho_{jk}(g)$ denotes the $jk$ matrix element of $\rho(g)$, and the sum in the equality on the right is over inequivalent irreps (taking $g' = g$ shows also that $\sum_\rho d_\rho^2 = \lvert G \rvert$, in turn demonstrating that the irreps are all finite-dimensional). </p> <p>With this in mind it should not come as a surprise that Fourier analysis on a finite group essentially amounts to the prescription </p> <p>$\hat f(\rho) := (d_\rho/\lvert G \rvert)^{1/2} \sum_g f(g) \rho(g);$</p> <p>$f(g) = \lvert G \rvert^{-1/2} \sum_{\rho } \mbox{Tr}\left[ \hat f(\rho) \rho(g^{-1}) \right] d_\rho^{1/2}.$</p> <p>By the orthogonality and completeness of characters, the number of inequivalent irreps equals the number of conjugacy classes for $G$ finite. In fact a complete set of inequivalent irreps over $\mathbb{C}$ can be constructed classically in $poly(\lvert G \rvert)$ time, which makes the construction of FFTs feasible in general.</p>

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https://byjus.com/jee/jee-advance-physics-syllabus/

# JEE Advanced Physics Syllabus 2021 JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get the detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with the day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts. Many students rate JEE Advanced physics syllabus as difficult and vast, therefore, it is important to develop a clear understanding of concepts from the very beginning itself. Get the basics right and then move on to mastering advanced concepts. Besides, securing better marks in JEE Advanced 2021 demands a solid conceptual base with broad knowledge on its applications. Candidates can start their preparations from NCERT textbooks. These textbooks cover all the topics included in JEE Advanced physics syllabus and are one of the best resources to study productively. Once the basics are clear, focus on the important topics depending on their weightage. Additionally, students can also check the comprehensive list of all the chapters in IIT JEE Maths and Chemistry syllabus from the below links.

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https://physics.stackexchange.com/questions/75321/connection-between-particles-and-fields-and-spinor-representation-of-the-poincar

# Connection between particles and fields and spinor representation of the Poincare group Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}}$, which is equal to $\left( \frac{m}{2}, \frac{n}{2}\right)$ representation of the Lorentz group. There is the hard provable theorem: $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}}$ realizes irreducible representation of the Poincare group, if $$(\partial^{2} - m^{2})\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}} = 0,$$ $$\partial^{\alpha \dot {\beta}}\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}} = 0.$$ Can this theorem be interpreted as connection between fields and particles? The definition is that a particle in Minkowski space is a unitary irreducible representation of the Poincare group. So one needs to see how various P.D.E.s are related to the classification of unitary irreducible representations of $iso(3,1)$ or $iso(d-1,1)$ in the case of $d$-dimensions instead of $4$. Note that these are all the Poincare-invariant constraints that can be imposed on the given field without trivializing the solution space (one could imposed $\partial \psi=0$ (gradient), which is Poincare-invariant but too strong as the field must be a constant). The theorem is not hard to prove. One has to know how to construct irreducible representations of the Poincare group, see chapter 2 of the Weinberg's QFT textbook. Then one solves the equations by standard Fourier transform and shows that the solution space indeed equivalent to what is called a spin-$m$ particle in Minkowski space. There is nothing special about $4d$ in defining spin-$m$ field, so it is simpler to look at arbitrary dimension, where, say for bosons the above equations are equivalent to $(\square-m^2)\phi_{\mu_1...\mu_m}=0$ $\partial_\nu \phi^{\nu \mu_2...\mu_m}=0$ $\eta_{\nu\rho} \phi^{\nu\rho \mu_3...\mu_m}=0$ $\phi^{\mu_1...\mu_s}$ is totally symmetric in all indices. In $4d$ one can use $so(3,1)\sim sl(2,C)$ and the last algebraic constraint then trivializes - an irreducible spin-tensor is equivalent to an irreducible $so(3,1)$-tensor • "...The theorem is not hard to prove...", - I didn't read this part of Weinberg book and only used spinor representation of the Lorentz group (without using some equations). After completing the proof I can construct field equation from this equivalence for cases of arbitrary spin. – user8817 Aug 26 '13 at 19:16 • Just one comment, the correspondence between reasonable P.D.E.'s and particles is not one-to-one. One and the same particle can be desribed in many different ways. For example, a spin-one, photon, can be described with the help of gauge potential $A_\mu$ or field strength $F_{\mu\nu}$ – John Aug 27 '13 at 7:34 • Because there are three representations of the spin 1: $\left( 1, 0 \right), \left( 0, 1\right), \left( \frac{1}{2}, \frac{1}{2}\right)$. – user8817 Aug 27 '13 at 8:02 • it is even worse, there is infinitely many ways to describe a given particle, it can sit as a subrepresentation. I did not understand if I answered your question above or not? – John Aug 27 '13 at 18:00

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http://gfm.cii.fc.ul.pt/events/seminars/20111202-sanz-sole/view?set_language=pt

# GFM ##### Secções Você está aqui: Entrada Deterministic Sets Visited by Random Paths # Deterministic Sets Visited by Random Paths Seminário do GFM IIIUL, B1-01 2011-12-02 14:30 .. 15:30 Adicionar evento ao calendário:   vCal    iCal joint seminar CMAF/GFM, by Marta Sanz-Solé (Univ. Barcelona, Spain) We are interested in the geometric measure properties of deterministic sets reached by random fields. More specifically, we will analyze conditions which provide upper and lower bounds for hitting probabilities of random fields in terms of the Hausdorff measure and the Bessel-Riesz capacity, respectively. The role of the regularity of the sample paths, and of the properties of probability densities will be highlighted. As an illustration, we shall consider systems of stochastic wave equations in spatial dimension k > or = to 1. In the non-Gaussian case, k will be restricted to {1; 2; 3}, and we will apply Malliavin calculus. For the sake of completeness, a brief introduction to these techniques will be presented. Applications to other examples of stochastic partial differential equations will be mentioned. This is joint work with Robert Dalang (EPFL, Switzerland).

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http://moniker.name/worldmaking/

## Hierarchies of Spaces: Building From the Bottom Up One of the major challenges in building a system that can increase in complexity as it runs is figuring out how to transfer complex structures in a lower level space into simple structures in a higher level space while still maintaining the essential qualities that the complex lower level structure represents.  Without this jump in abstraction, the system will simply asymptotically approach a maximum level of complexity determined by available resources (energy, computation, memory, time, …). I’ve shown how particles can be modeled to form surfaces and surface patches by endowing them with local surface properties à la differential geometry and using that information to filter how particles connect to each other.  There still remains a question as to what happens next.  Given a million particles, the system (as described in a previous post) can be run in realtime on a decent laptop, which will likely produce beautiful images and structures, but still only reach a particular level of complexity that is all qualitatively the same.  Even with 100 million particles, the complexity threshold will only reach a level or two above where it currently sits.  To really jump ahead, a completely different spatial logic is required that operates on a higher, more abstract level. The differential particle system deals with local surface properties and local connectivity but can’t say anything about the overall topological properties of the surfaces it’s producing such as genus or 2-manifold-ness.  These kinds of properties are more efficiently calculated at the coarser level of the surface patch.  Thus, if each surface patch produced by the differential particles is itself turned into a “topological” particle, we can start to figure out how the next higher level might work. ## A Space for Topological Particles and Automata The differential particles exist in the usual Euclidean 3D space and interact with each other according to principles derived from this underlying geometry based on distance, local coordinate frames, and local surface properties.  They are discrete entities representing continuous properties.  Topological particles on the other hand are discrete entities representing discrete properties.  They interact with each other in a completely different manner than differential particles.  In the space that topological particles exist in, distance is backgrounded in favor of patterns of connectivity. In previous posts, I’ve talked about how hyperbolic tilings (particularly the (5,4) tiling) can be used to represent 2-manifold structures.  The structure of hyperbolic tilings provides a natural scaffolding for constructing surface from a topological perspective for a number of reasons.  First, all 2-genus and higher surfaces can be decomposed into pentagonal tiles.  Second, the structure that you get for free with hyperbolic tilings enables the efficient encoding of algorithms encoding how the topological particles interact. The particles themselves live on the vertices of the hyperbolic tiling and can only interact with other particles on edges that they are directly linked to.  As a result topological particles can only interact with four other particles.  Since topological particles are abstractions of surface patches, this means that surface patches should themselves be quadrilateral in nature.  But what kind of information do topological particles contain aside from connectivity and what rules govern their interactions? ### The  Role of Genus The essential property we’re after with the topological particles is genus.  Once we can talk about genus in an efficient and hierarchically consistent manner, we can start building the next level up from topological particles.  The genus of a network is determined by its Euler characteristic which is given by $\chi = V – E + F$.  Genus is related to the Euler characteristic by $\chi = 2 – 2*g$. If we look at a torus, which has a genus of 1, and Euler characteristic of 0, we see it can be divided up into 4 quadrilaterals.  The quadrilaterals on the outer shell have positive curvature while the inner ones have both positive and negative curvature in orthogonal directions.  By comparison, a sphere has positive curvature everywhere and a genus of 0. The fundamental different between a torus and a sphere is that some surface patches on the torus have negative curvature, inducing a change in genus.  For higher genus structures, it’s the patterns of connectivity between positive and negative curvature regions that determine genus.  All of this points to the idea that the topological properties simply need to know whether they represent surface patches with positive or negative curvature in their two principal directions. To sum up, topological particles can connect to 4 other particles along 2 principal directions.  Each principal direction has associated with it a value indicating either positive or negative curvature.  For simplicity, we will simply assign +1 for positive curvature and -1 for negative curvature. Now, if we think about how these particles interact at a very basic level, we can further constrain things by requiring particles that connect to each other to only connect if the principal directions linked by an edge have the same principal curvature.  While this limits a lot of possibilities in principal, it doesn’t actually limit what kinds of topological structures we can make and it vastly simplifies the way the particles operate to great benefit.  Under this constrain as well, there can be no particles with negative curvature in both directions since they would form an unbounded surface whose normals are solely on the interior.  Thus, we can only have particles with (+1, +1), (+1, -1) and (-1, +1) curvatures. The next concern is how a pattern of topological particles accumulate and transform into different structures.  The most basic structures are particle pairs, of which there are 4 kinds: (+1, +1) x (+1, +1), (+1, +1) x (+1, -1), and two different forms of (+1, -1) x (+1, -1).  These are represented in the image above with black indicating positive curvature and red negative curvature. When placed into the hyperbolic tiling, the particles look like the above image, which has 4 particles.  In the above image, it appears that there are only 3 edges linking the particles and it raises the question as to how the surface will close since the tiling doesn’t wrap around but continues infinitely in all directions.  The answer comes from looking at the particle pairs.  Whenever an edge is connected, the edge opposite it (in the same principal direction) must also be connected.  In the diagram above, the edges on the outside wrap around to the next particle on the same hyperbolic line.  It’s easiest to think of it as the tiles on a particular hyperbolic line as being cyclical with only one cycle shown in the image.  The one constraint is that there must be at least 2 particles since a particle cannot connect to itself. ### Rules of Interaction After many many hours of playing with topological particle tiles with the goal of having the particles interact in a way that is not deterministic but does favor an increase in genus, I come up with the following rules: 1. When a particle is place in the hyperbolic tiling, it marks its neighbors with a score indicating how strong a preference that location has for attaching to the next particle.  Neighbors with negative curvature are considered the most “reactive” and have a score of 2 while positive curvature gives a score of 1.  Scoring is only done for unconnected edges.  Edges that connect back around are left out. 2. All particles are attached to the highest scoring (most reactive) site that they can be matched to.  If there are sites which tie, one is chosen at random There are a lot of possibilities for further refinement, including using the location of the generators of genus and measures of local complexity to tweak the scoring of reactivity.  Also, there needs to be some rules for determining how things break apart.  Likely this will involve a combination of overall size and genus generators.  The only one of these I’ve explored so far is the measure of complexity The diagram above shows how this would work.  On the left is is a 4 tile setup.  On the right a 6 tile setup.  The blue lines indicate how the left-most tile/particle gets reflected through the tiling.  The pattern on the left is highly regular.  If the same diagram were made for each particle, they would be identical, indicating that the combinatorics around the tiling are symmetric.  On the right, once the two extra tiles are added, one of the branches projecting from the left-most tile is cut off, generating an asymmetrical combinatorial pattern.  One measure of complexity or asymmetry would be to look at a neighborhood around existing particles and determine their relative combinatorics, which could then be used as an input to determine reactivity.  The input could be used to regulate symmetry versus asymmetry. ### An Example Interaction So what does an example interaction between two networks of topological particles look like? Above are two pairs of topological particles with their reaction sites marked by circles.  Each pair of particles has four open sites that can react with each other.  Since they all have the same level of reactivity, one is chose at random.  One possible result is below: | | 1 Comment ## Valency (video) These are clips of how the particle systems described in previous posts move in space. It’s all very raw, but I wanted to get something out there. The larger structures suffer from convergence problems creating oscillations, twisting, foldings, and other distortions while the small networks converge almost immediately into their designated shapes. These appear around the 6:05 mark. ## Particle-Based Structure Formation In order to build a complex and dynamic spatial system, there need be entities operating at multiple temporal and spatial scales.  As mentioned in the previous post, the extremes of the spatial scale are local and global objects, which are typically particles and fields.  It’s straightforward to build something where particles are affected by fields, but without intermediate structure formation, there is no opportunity for more complex dynamics to emerge.  In morphogenetic processes, cells differentiate, cluster, striate, extend, etc. as interconnected and interwoven groups.  Such patterns can be represented by meshes or networks of particles connected with edges that impart some form of behavioral change in the particles.  The question is, how can the formation of such structures be described generally in terms of the patterns of formations but be given precise and specific behaviors that differentiate types?  In other words, what are the primitive events and conditions that can describe the formation of a wide range of network structures? ### Making Connections The primitive operation here is that of connecting two particles together. (image)  What is the condition that enables two particles to associate with each other?  For simplicity, let’s assume that all particles are of the same kind and that particle can connect to every other particle under the proper conditions.  Let’s further specify that the network structures that emerge should be surfaces and not volumetric in nature. There isn’t much literature out there on how to connect particles together.  Probably the best place to look is the point cloud research, which describes how data sets made up of particles in space can be turned into surfaces.  The problem with a lot of the point cloud techniques is that they are often expensive and rely on optimization techniques that don’t map well to a real-time dynamic system.  Typically, the first instinct when thinking about this problem is to make the capacity for particles to connect purely distance-based.  The problem with this approach is that particles can easily crowd around each other, producing overlapping edges and degenerate mesh faces.  Preferably, the particles would have a fairly regular spacing appropriate for the curvature of the surface. ### Filtering Connections To correct for this problem, a little bit of extra structure is needed to filter the conditions under which connections can be made.  For the case of surfaces, what’s needed is some kind of device that tracks connection density and will only allow connections if the density criteria are met.  This device could equally be called valency if it’s thought about like chemical bonds. If we define the connection density as determining how many connections can be made within a given interval and set the number of 1, we can represent the connection criteria by a set of intervals around the particle in the particles’ plane.  Each particle has a normal and two planar directions that uniquely determine its local coordinate system.  If we say each particle can have up to 5 connections that sets a minimum spacing of 72 degrees between each connection.  If a connection is attempted and it’s within 72 degrees of another connection, it will be rejected. ### Applying Connections Once connections are made, the new properties and forces are applied to the particles. When a connection is formed, the particles on either end are likely not in the ideal locations to form a coherent surfaces, so we use the connections between particles to move them into some sort of optimized position and orientation.  For example, in the simple case of forming a spherical shape, the particles will act on each other through the connections in order to form a surface of constant positive curvature. Probably the most widespread technique for optimizing the structure of a mesh network is some form of spring or spring-electric simulation where each edge is a spring and in the spring-electric case each node applies a repulsive electric field to every other node.  While this can give some interesting results, there is a certain uniformity to the shapes.  Instead, each particle is given principle curvature values that define the local surface patch the particle represents.  When particles are connected to each other, the attempt to place and orient the connected particle with the local surface patch. The particles started out unconnected but connected themselves according to the connection filtering process described above.  The light blue lines are the particle normals and the pink dots are the target locations the particles are trying to reach. Since each particle in this simulation has a curvature of (1, 1), they will attempt curve into a sphere-like shape. The corner and then edge particles move faster because they have anisotropic constraints. Currently, self-intersection is not prevented.  When the edges come within range of each other, they form new connections as seen in the middle of this image. The new connections further warp the form as it “inflates”. A view from the inside.  The pink lines show target movements.  The (black) particles on one end of the line are trying to reach the pink dots on the other end. ## Spatial Processes There are four broad categories of spatial processes 1. Purely Global 2. Global <-> Local 3. Local <-> Local 4. Purely Local and two general categories of spatial primitives 1. Field 2. Particle Of course, the spatial primitives can be organized into composite structures such as meshes where particles are linked together in a network. Fields represent global information over a defined N-dimensional range of space while particles represent local information located at an infinitesimal point in space.  Information moves from a local to global context when particles interact with a field.  For example, stigmergic behavior can be generated by having particles leave traces in a field that represents pheromone concentrations over an environment. In stigmergic systems, information flows in a positive feedback loop from local behavior to global concentrations, which in turn affect local behavior. ## Spatial Information Flows The simplest kinds of information flows are those that are internal to an object be it global as in the evolution of a field according to its dynamical equations or local as in the movement of a particle according to kinematics.  In both cases, the state of the spatial system is affected but not in a way that adds any new information or structure.  Existing information is simply transformed and displaced. The next level of complexity in terms of spatially directed pattern formation occurs when information transfers between local and global contexts.  In such instances, particles are essentially reading from and writing into fields and altering their internal state accordingly.  When information is written into a field by a particle, it loses its specificity (that of being attached to a particular entity) and becomes part of an intensive processes as opposed to an extensive one.  While limiting in the sense that once the information is in the field the actions that contributed to the state of the field can no longer be distinguished, it does open up an efficient communication channel between many local objects since each can read the aggregate state of the local entities as it is mediated by the field.  Communication between individual local objects is not possible through a field however because the number of channels required is prohibitive.  Instead, this has to be done through local to local flows. Local to local interactions provide the most fine grained spatial information flows but are also the most computationally intensive.  If there are N objects in a space, there are (N-1)^2 channels of interaction.  For local to global flows there are only N channels of interaction.  While incredibly useful in terms of composing complex spatial patterns, the computational cost of local to local interactions can make them impractical. The classic example of local to local interactions is the N-body problem, which occurs in gravitational and electric field simulations among others.  Both of these problems deal with particles generating fields that affect every other particle.  To simplify the computational complexity of the problem, the local fields of each particle are accumulated into a hierarchy of fields that can then be precisely applied to each particle such that the total runtime is N log(N).  This technique is called the Fast Multipole Method. While having every particle able to communicate efficiently with every other particle  might be desirable in the ideal case, practically speaking it’s often good enough to have particles communicate with each other within a particular range or with the nearest N particles.  Such a system can be implemented by binning particles according to their location and then operating over the binned particles to realize local to local communication channels.  The fastest algorithm I’ve found for spatial binning and neighborhood calculation is Query Sphere Indexing. ### Spatial Hashing Query sphere indexing is a form of spatial whereby a spatial location is given an integer value that can be used as a key to look up the position quickly from a table.  In the query sphere technique, the space is divided into a finite number of discrete cells and each cell is given an integer hash value based on its coordinate.  Any particle falling within the cell is binned to it and associated with the cell’s integer hash value. The speed of the query sphere technique comes from precomputing as much information as possible about neighborhoods.  When the data structure is created, a table of relative coordinates in terms of hash indices is calculated for all the possible distances and ordered according to nearest to furthest offset.  For example, if you want to know how many objects are within radius 1 of a point in space, the offset lookup table will provide a list of cell offsets that can be added to the query location efficiently and all of the cells within radius 1 retrieved for processing. The calculations in the Query Sphere paper are incredibly efficient since they’re all operating on integers using addition and bit manipulation.  In a version of the algorithm I’ve implemented for example, I can hash 302,500 (550×550) points at 33fps and query thousands of neighborhoods for nearest neighbors.  As a result, local to local communication is incredibly efficient and used judiciously can add a lot more detail and complex pattern formation to the evolution of a spatial system.  For instance, once local to local communication becomes efficient, it becomes to describe the formation of aggregate structures such as meshes in a straightforward manner, which can in turn introduce new behaviors and trajectories into the system. The cubes in the image above are the bins holding particles.  The pink dots are query locations with lines connecting the nearest 16 neighbors within a particular radius. Posted in Software Engineering, Space and Geometry | | 1 Comment ## Transversion and the Torus As a first test of the efficacy of the new Transversion Automaton design, I set it up to carve out a simple torus.  Since a torus only has two loops whose product generates the surface, it’s easy to model simply by mapping the two principle directions of the Transversion Automaton to the loops. The Transversion Automaton consists of a central unit sphere (in grey) whose center is a point on the surface being generated and two surface coordinate (UV-coordinate) generating lines.  At each step, the automaton inverts the lines through the central unit sphere to generate the UV osculating circles.  These circles represent the instantaneous curvature at the surface point in the principle directions.  Next, the automaton is diffused through space along both principle circles and the locations of the generating lines is adjusted to properly account for the curvature values at the next location. Above are frame capturing the automaton’s motion around one of the cycles of the torus.  The total movement through the nine frames is half a rotation (180 degrees) where the curvature of the direction given by the red line changes from 1 (spherical) on the outside to -1 (hyperbolic) on the inside.  Notice that in frame 5, the circle generated by inverting the red line into the central unit sphere is actually a line, or a circle of infinite radius.  This is because at the top of the torus, the lateral curvature is zero or Euclidean, which makes sense since for the curvature to change form 1 to -1 it has to pass through 0. These images show different points of view on the set of circles generated in one cycle of the torus.  Notice that there are two lines indicating the two locations of Euclidean curvature.  These images were generated simply by accumulating all of the circles and drawing them together. Overall, this iteration of the Transversion Automaton is much simpler to control and move through space.  The logic of its structure is now super clear.  One of the aspects I appreciate most is how its internal structure dictates its own transformation.  In other words, it’s a self-modifying spatial automaton.  All it does is read off a couple of curvature values and it’s able to move itself and adjust its relative weights accordingly.  The next step is to figure out how to get the Transversion Automaton to operate in a panelizing mode where it traces out surface patches instead of entire cycles.  This is the only way it will be able to generate more complex surfaces. ## Hyperbolic Tilings Again I’m revisiting a lot of the techniques I’ve implemented for working with hyperbolic geometry as I’m rebuilding the Transversion Automaton in order to make the simpler and clearer.  The most basic structure that underlies the topology of the surfaces generated by the Transversion Automaton is the hyperbolic tiling.  I recently found a much simpler derivation for the fundamental polygon that seeds the tiling and implemented it. In a regular hyperbolic tiling, each tile is exactly the same with the tile located at the center of the Poincaré disc called the fundamental polygon.  By virtue of the expansive nature of hyperbolic space, there are an infinite number of regular tilings of the hyperbolic plane since the polygons can simply be resized until the rate at which they fill space matches the rate at which the hyperbolic plane expands.  Thus, the key value to calculate when generating regular hyperbolic tilings is the radius of the fundamental polygon. The value that determines how big the radius is is the angle of parallelism of the edges of the fundamental polygon.  The angle of parallelism essentially says how close to Euclidean space a particular tiling is.  The closer to 90 degrees the angle of parallelism, the closer to Euclidean it is.  For example, in the image above, the fundamental polygon on the far left is for the (3, 7) tiling.  Notice how the radius of the pink circle is large and the arc that’s visible approaches a straight line.  The angle that the line tangent to vertex D makes with the horizontal axis is the angle of parallelism.  As D moves toward the top of the Poincaré disc circle, this angle approaches 90 degrees.  If we changed the tiling to (3, 6), we would in fact have a 90 degree angle of parallelism and a Euclidean tiling.  As the fundamental polygon increases in sides and number of polygons meeting at a vertex, the angle of parallelism decreases toward 0 as both values approach infinity. The diagrams above show how the angle of parallelism varies with the number if polygons incident to a vertex (left) and the number of sides (right).  Calculating the location of the fundamental polygon’s vertices is equivalent to calculating the location of the circles that the polygon’s arcs lie on.  Since they’re all equidistant from the origin, we just need to figure out how far away the circle is.  To do this, we use right triangles AEF and ABF along with the fact that angles $\angle{}BAF = \frac{\pi}{p}$ and $\angle{}ABF = \frac{\pi}{q}$ are known to derive the fact that: 1. $sin(\angle{}EBF) = \frac{\overline{EF}}{\overline{BF}}$ and $sin(\angle{}BAF) = \frac{\overline{EB}}{\overline{AF}}$ 2. $1+\overline{BF}^2 = \overline{AF}^2$ 3. $sin(\angle{}EBF) = \frac{\pi}{2} – \frac{\pi}{q}$ 4. $sin(\angle{}BAF) = \frac{\pi}{p}$ 5. $\sqrt{\overline{AF}^2-1} \dot{} sin(\frac{\pi}{2} – \frac{\pi}{q}) = \overline{AF} \dot{} sin(\frac{\pi}{2})$ 6. $\overline{AF} = \sqrt{\frac{sin^2(\frac{\pi}{2}- \frac{\pi}{q})}{sin^2(\frac{\pi}{2}- \frac{\pi}{q}) – sin^2(\frac{\pi}{p})}}$ ## Thoughts on the Original Design The motivation for constructing a transversion-based spatial automaton was to construct a surface in 3D Euclidean space from as little local geometric information as possible.  It was the automaton’s role to expand the information into a fully specified surface of arbitrary complexity.  Essentially, this is a problem of differential geometry with a little bit of analysis (particularly complex harmonic functions) thrown in. The original design was essentially a straight translation into (Geometric Algebra) GA elements of the standard approaches differential geometry uses to analyze local surface properties and particularly curvature.  The idea was to have two spheres, each representing one of the two principal surface coordinates and to relate the size of the spheres to instantaneous curvature.  By inverting a differential surface element into the two spheres, the Transversion Machine incrementally constructed patches of the surface. While the design worked, it was unwieldy and suffered from some interpolation issues that lead to closed paths not actually closing like they should.  The primary issue was figuring out how to update the automaton on each step.  Essentially, this involved rotating and translating the entire machine to be centered at the new surface point in order to continue extended the surface while simultaneously warping with a transversion operation the two spheres such that their radii corresponded to the new local curvature values.  In the end, there were just too many loosely connected transformations to keep in sync, so the mechanism felt cobbled together and inelegant.  Furthermore, it wasn’t at all clear how the input curvature values parameterizing the Transversion Machine mapped to its internal transformations. ## Hyperbolic Inspiration In the back of my mind, I kept thinking that there had to be another way to organize things such that it just worked, every element was tightly integrated, and the input parameters mapped in a straightforward manner to the controls of the machine.  Fortunately, inspiration struck while I was working on understanding hyperbolic translations. Hyperbolic translations are just like Euclidean translations in that they move along a line.  The difference is that lines in hyperbolic space are actually Euclidean circles when the Poincaré model of hyperbolic geometry is used.  The one exception is for lines that pass through the center of the unit disc.  These hyperbolic lines are circles of infinite radius and thus also Euclidean lines.  I then wondered how this fact could be used to redesign the Transversion Machine since it also needs to be able to smoothly move between rounds such as circles and spheres to flats such as lines and planes.  This kind of behavior allows it to smoothly model changes in curvature from positive to flat to negative curvature.  The only question is how to make such a mapping. ## Test 1: Real and Imaginary Spheres One of the unique features of GA is that many objects come in both real and imaginary forms.  For instance, spheres are called real if they have a positive radius and imaginary if they have a negative radius.  While it may seem strange for a sphere to have a negative radius, it has profound consequences for the interpretation of the geometry of a particular arrangement of geometry objects.  For instance, when two spheres intersect, they generate a real circle.  If they don’t intersect, they generate an imaginary circle.  Importantly, the magnitude of the imaginary circle indicates how far apart the two spheres are. Since the curvature of a surface varies from positive through zero to negative values, I wondered if some way of transforming spheres between real and imaginary states could be used to implement the Transversion Machine.  As a first test, I placed a line tangent to both a real and imaginary sphere colocated in space and with radii of the same magnitude but of opposite sign.  The two spheres are given by $S_{real} = o – \frac{\infty}{2}$ and $S_{imaginary} = o + \frac{\infty}{2}$. On the left is a single instance of inverting a line by a sphere.  The pink circle is generated by the real sphere while the blue is generated by the imaginary sphere.  The inversion is described by $Circle = SLS^{-1}$.  What’s curious is how the imaginary and real spheres result in exactly the same shape but on opposite sides of the center of the inversion sphere. When I saw this image, my first thought was that I could map the inversion sphere’s radius to surface curvature with the convenient mapping of imaginary spheres describing negative curvature (hyperbolic patches).  The only question then is how to smoothly vary the spheres. First, however, I did the easy thing and varied the position of the line.  The image on the right shows what happens when the line is varied from the center of the inversion sphere to the right.  When the line is in the center, the inversion is an identity operation mapping the line to itself.  As it moves to the right, the resulting circles vary in radius, smoothly shrinking to a point if the line was infinitely far away.  Notice that the is exclusively to the right hand side of the inversion sphere’s center.  If it was on the left, the real and imaginary circles would swap sides too.  This is the answer to the question as to how to vary the size of the curvature spheres.  We can simply move a plane (line) in space to generate the appropriate sized sphere.  What’s really nice about this setup is it’s basically a spatial slider for controlling curvature that generates exactly the kind of geometry we need and takes precisely the kind of input we have, a scalar curvature value.  We can map this curvature value to displacement along an axis running through the center of the inversion sphere.  As a further bonus, the current point on the surface that the Transversion Machine is operating from is located at the center of the inversion sphere. In the end, we don’t actually need the imaginary sphere, but it’s nice to know how it operates with respect to spherical inversion for future problems. ## Test 2: Circular Rigid Body Motion The second problem in the original design was interpolating the motion of the Transversion Machine according to how the surface bends at each point.  The transformation describing the motion is a rigid body motion through space that rotates the machine around a circle.  The transformation is given by $V = exp(\infty\rfloor{}\frac{L}{2})$. The image above show the action of the circular rigid body motion.  The diagrams are slightly skewed to show the axis of the circle since it comes out of the page.  The axis is a dual line, which is a bivector inducing the motions in the images.  Of course, the motion needed by the Transversion Machine is not arbitrary.  It needs to be scaled such that it moves the Transversion Machine around the circle in fixed number of steps.  To do this, we have to scale the circle such that its norm is equal to the distance travelled by each step around the circle.  The following algorithm generates a motion around the circle in N steps from a line $L$ and an inversion sphere $S$: • Generate the circle that will move the Transversion Machine: $C = SLS^{-1}$. • Normalize the circler: $C_n = \frac{C}{\sqrt{C*C}}$. • Calculate the versor representing the transformation and scale by the length of the circular arc: $V = exp(-\infty\rfloor{}\frac{C_n}{2}\frac{2\pi{}R}{N})$. • Transform the Transversion Machine inversion sphere and coordinate axis line: $S = VSV^{-1}, L = VSV^{-1}$. ## Hyperbolic Translations One of the crucial issues in the construction of the implementation of the transversion automaton is how it interpolate its geometric relationships (transversions and rigid body motions) through space to generate a surface in 3D.  The input data is pentagonal tiling of the surface unfolded into a (5, 4) hyperbolic tiling with the state of the transversion automaton defined at the vertices of the tiling. Interpolation the state of the automaton across the tiling is subject to the constraint that any given arc through the tiling represents a complete cycle around some part of the surface and must therefore be a harmonic function of the transversion state. Ideally, the interpolation scheme chosen will evenly sample the space over which the interpolation is performed in order describe the most surface for the least number of interpolation points.  In the case of the transversion automaton, the interpolation space is hyperbolic.  As a result, our familiar Euclidean intuition about what constitutes evenly spaced samples doesn’t apply.  The most straightforward way to interpolate hyperbolically is to work with a mapping of hyperbolic space into Euclidean space and develop the geometry of interpolation through that mapping.  In this case, the mapping is the Poincaré disc model of the hyperbolic plane. ## The Poincaré Disc in Geometric Algebra In the conformal model of Geometric Algebra (GA), the usual Euclidean axes are augmented with two additional axes representing the point at infinity and the point at the origin.  In other words, the point at infinity is explicitly represented in the model of Euclidean space.  As a result, new symmetries appear enable exotic transformations that smoothly interpolate between circles and lines or spheres and planes since lines are essentially circles of infinite radius and planes are spheres of infinite radius.  Furthermore, translations and rotations collapse into a single representation since translations are really just rotations about the infinite point. In GA, the particular representation of infinity is fungible and depending on which representation is chosen, a particular geometry will arise.  For Euclidean geometry, infinity is taken as a point.  For spherical and hyperbolic geometry, infinity is typically taken as the unit sphere where the only difference is that spherical geometry is given by the imaginary dual unit sphere and hyperbolic geometry by the real dual unit sphere.  Imaginary spheres have a negative radius while real spheres have a positive radius.  In the Poincaré disc model of hyperbolic space, infinity is also represented by a unit sphere in 3D and a 2D sphere (aka a circle) in 2D space.  The beauty of all this is that all of our previously acquired knowledge about working with spatial transformations in the conformal model of Euclidean space still apply to hyperbolic space.  All that needs to be done is to swap the usual $\infty$ with $o – \frac{\infty}{2}$. For example, given two points $p$ and $q$, the line through them is given by $L = p\wedge{}q\wedge{}\infty$.  The hyperbolic line through them is given by $L = p\wedge{}q\wedge{}(o – \frac{\infty}{2})$.  Of course, the hyperbolic line is not a line in the Euclidean sense but instead a circular arc. The reason for this difference is that hyperbolic space expands as you move away from the center, so the mapping to Euclidean space squishes it toward the unit circle, bending the line into a circle. ## Translations Translations in hyperbolic space also occur along circular arcs and from a Euclidean point of view move quickly through the center of the disc and slowly toward the perimeter.  In Euclidean space, translations along lines are described by $exp(-\infty{}\rfloor{}\frac{L}{2})$ with the equivalent hyperbolic expression being $exp(-e\rfloor{}\frac{L}{2})$ where $e = o – \frac{\infty}{2}$. The real trick with hyperbolic translations is how to get them into a form that is useful for interpolation purposes.  Essentially, we want to calculate a hyperbolic translation that will move between two points in a fixed number of steps.  The form of the translation given above won’t do this because the line is not normalized and thus scales the distance covered by translation by a factor.  To calculate a hyperbolic translation that moves between two points in N steps, the term $-e\rfloor{}L$ has to be normalized and then scaled by half the hyperbolic distance between the points. Hyperbolic distance can be calculated in GA by first normalizing the given points in terms of hyperbolic space.  The condition for normalization is $-e\dot{}p = -1$.  The distance between two points is then $d(p, q) = acosh(1 – \frac{-p}{e\dot{}p}\dot{}\frac{-q}{e\dot{}q})$.  The algorithm for computing the interpolating translation is: 1. Construct a translation bivector between $p$ and $q$ as $T = e\rfloor{}(p\wedge{}q\wedge{}e)$. 2. Normalize it $T_n = \frac{T}{\sqrt{T*T}}$. 3. Calculate the distance between $p$ and $q$ using $d(p, q) = acosh(1 – \frac{-p}{e\dot{}p}\dot{}\frac{-q}{e\dot{}q})$. 4. Scale the normalized bivector and exponentiate it $V = exp(T_n\frac{d}{2N})$ where N is the number of steps to take between the points. V is then the versor used to translate $p$ into $q$ over N steps. In the image above, the edges of the pentagon are drawn by interpolating between the vertices 20 steps.  The pink points are midpoints while the blue divide the edges into quarters.  The pink and blue points were calculated with a hyperbolic lerp constructed from the hyperbolic translation algorithm. ## Background The Meet operation in Geometric Algebra (GA) calculates the intersection of two subspaces. In set theoretical terms, the intersection is given by the relationship $M = A\cap{}B$ where M is the intersection (or Meet). Frequently in GA papers and books, you’ll find the elegant looking equation $M = A\cap{}B = (B^{*}\wedge{}A^{*})^{*}$ where $A^{*}$ indicates the dual of A. Unfortunately, calculating Meet is not so simple. Related to the intersection of two subspaces, we can define a second quantity that is the difference between their union and intersection, which is called the symmetric difference or delta product.  Using this product, the intersection can be rewritten as $A\cap{}B = \frac{A + B – A\Delta{}B}{2}$.  In Geometric Algebra, the delta product of blades is defined as the highest grade part of the geometric product of A and B $A\cap{}B = \langle{AB}\rangle{}_{max}$.  The grade operation in the delta product stems from the way the geometric product automatically eliminates dependent factors.  Furthermore, the grade of the Meet can equally be formulated in terms of the delta product as $grade(A\cap{}B) = \frac{grade(A) + grade(B) – grade(A\Delta{}B)}{2}$. ## The Algorithm* ### Approach Through the delta product, we now have a proper way of expressing how the two subspaces A and B relate to each other and can formulate an algorithm to compute it.  In the diagrams above, notice that the delta product includes both A and B but not their intersection while the dual of the delta product includes both the surrounding space as well as the intersection.  We can take advantage of this fact by computing the meet by projecting the dual of the delta product into the subspace A since whatever projects into A from the dual delta product is the intersection because the intersection is by definition a subspace of A. Since the grade of the meet is not necessarily equal to the grade of $(A\cap{}B)^{*}$, we must first factor it into an orthogonal basis before projecting it into A.  Factoring a blade essentially involves probing the blade with a candidate basis vector and iteratively taking the basis vectors out of the blade until only one is left.  In order to start the process, a good candidate basis vector must first be selected.  Since the specific factorization doesn’t matter, we can simply select the element of the blade with the largest magnitude and go from there.  Since we are dealing with a blade in this case, we can simply project the vectors of the element chosen into the blade and iteratively remove those projections.  The algorithm looks like this given a blade B of grade k: 1. Calculate the norm of B $s = \Vert{}B\Vert{}$ 2. Find the basis element E in B with the largest coordinate 3. Determine the vectors $e_{i}$ of E 4. Normalize B $B_{c} = B/s$ 5. For each $e_{i}$ except for 1 • Project $e_{i}$ onto $B_{c}$ : $f_{i} = (e_{i}\rfloor{}B_{c})B_{c}^{-1}$ • Normalize $f_{i}$ • Remove $f_{i}$ from $B_{c}$ : $B_{c} \leftarrow{} f_{i}^{-1}\rfloor{}B_{c}$ 6. The last $f_{i}$ factor is set to $B_{c}$ : $f_{k} = B_{c}$ and normalized. ### The Basic Meet Algorithm The meet can be taken between two blades A and B of different grades and here we’ll assume blade A is of equal or greater grade than blade B.  Given blades A and B: 1. Compute the dual delta product $S = (A\Delta{}B)^{*}$ 2. Apply the factoring algorithm to S to get the factors $s_{i}$ 3. Compute the grade of the meet $grade(A\cap{}B) = \frac{grade(A) + grade(B) – grade(A\Delta{}B)}{2}$ 4. Set the meet result M to 1: $M = 1$ 5. For each $s_{i}$ • Project $s_{i}$ into A: $p_{i} = (s_{i}\rfloor{}A)\rfloor{}A^{-1}$ • If the projection $p_{i}$ is not zero, accumulate it into M: $M \leftarrow{} M\wedge{}p_{i}$ • If $grade(M)$ is equal to that computed in step 3, break the loop ### Circle Intersection A simple example of the meet operation in use is the case of circle intersections.  If we define two circles.  If we take two circles C1 and C2 at (1, 0, 0) and (-1, 0, 0) respectively, each with a radius of 2, the meet operation will return a point pair.  In other words, the meet gives back a single object describing the two intersection points of the circle. • $C1 = oe_1e_2 – oe_2\infty + 1.5*e_1e_2\infty$ • $C2 = oe_1e_2 + oe2\infty + 1.5*e_1e_2\infty$ • $S = C1\Delta{}C2 = -2*oe_1 – 3*e_1\infty$ • $S^* = -2*oe_2e_3 – 3*e_2e_3\infty$ • $s_1 = e_2, s_2 = e_3, s_3 = – \frac{2}{\sqrt{12}}o – \frac{3}{\sqrt{12}}\infty$ • $A\cap{}B = \frac{2}{\sqrt{12}}oe_2 – \frac{3}{\sqrt{12}}e_2\infty$ The result of the meet as calculated above is a point pair.  The points can be extracted by a simple equation that extracts the point pair’s axis and then pushes out a distance along this axis from their center point.  The equation is given by: $P = p_{-}\wedge{}p_{+}$ where P is the point pair and $p_{\pm} = \frac{P\mp\sqrt{P^2}}{-\infty\rfloor{}P}$ are the points. For the case above, the points are located at $p_{\pm} = o \mp \sqrt{3}e_2 + 1.5*\infty$. * see Geometric Algebra for Computer Science by Dorst et al, p. 536 | Tagged , , | 2 Comments

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https://artofproblemsolving.com/wiki/index.php?title=1975_AHSME_Problems&oldid=64579

# 1975 AHSME Problems ## Problem 1 The value of ${\frac {1}{2 - \frac {1}{2 - \frac {1}{2 - \frac12}}}$ (Error compiling LaTeX. ! Missing } inserted.) is ## Problem 2 For which real values of m are the simultaneous equations y = mx + 3 \\ \[ y = (2m - 1)x + 4 (Error compiling LaTeX. ! LaTeX Error: \begin{equation*} on input line 20 ended by \end{document}.) satisfied by at least one pair of real numbers ? ## Problem 3 Which of the following inequalities are satisfied for all real numbers which satisfy the conditions , and ? ## Problem 4 If the side of one square is the diagonal of a second square, what is the ratio of the area of the first square to the area of the second? ## Problem 5 The polynomial is expanded in decreasing powers of . The second and third terms have equal values when evaluated at and , where and are positive numbers whose sum is one. What is the value of ? ## Problem 6 The sum of the first eighty positive odd integers subtracted from the sum of the first eighty positive even integers is ## Problem 7 For which non-zero real numbers is a positive integers? ## Problem 8 If the statement "All shirts in this store are on sale." is false, then which of the following statements must be true? I. All shirts in this store are at non-sale prices. II. There is some shirt in this store not on sale. III. No shirt in this store is on sale. IV. Not all shirts in this store are on sale. ## Problem 9 Let and be arithmetic progressions such that , and . Find the sum of the first hundred terms of the progression ## Problem 10 The sum of the digits in base ten of , where is a positive integer, is ## Problem 11 Let be an interior point of circle other than the center of . Form all chords of which pass through , and determine their midpoints. The locus of these midpoints is ## Problem 12 If , and , which of the following conclusions is correct? The equation has ## Problem 14 If the is when the is and the and is , what is the when the is , the and is and the is is two ( and are variables taking positive values)? ## Problem 15 In the sequence of numbers each term after the first two is equal to the term preceding it minus the term preceding that. The sum of the first one hundred terms of the sequence is ## Problem 16 If the first term of an infinite geometric series is a positive integer, the common ratio is the reciprocal of a positive integer, and the sum of the series is , then the sum of the first two terms of the series is ## Problem 17 A man can commute either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon; and if he comes home in the afternoon on the train, he took the bus in the morning. During a total of x working days, the man took the bus to work in the morning times, came home by bus in the afternoon times, and commuted by train (either morning or afternoon) times. Find . ## Problem 18 A positive integer with three digits in its base ten representation is chosen at random, with each three digit number having an equal chance of being chosen. The probability that is an integer is ## Problem 19 Which positive numbers satisfy the equation ? ## Problem 20 In the adjoining figure is such that and . If is the midpoint of and , what is the length of ? ## Problem 21 Suppose is defined for all real numbers ; for all , and for all and . Which of the following statements is true? ## Problem 22 If and are primes and has distinct positive integral roots, then which of the following statements are true? ## Problem 23 In the adjoining figure and are adjacent sides of square ; is the midpoint of ; is the midpoint of ; and and intersect at . The ratio of the area of to the area of is ## Problem 24 In , and , where . The circle with center and radius intersects at and intersects , extended if necessary, at and at ( may coincide with ). Then ## Problem 25 A woman, her brother, her son and her daughter are chess players (all relations by birth). The worst player's twin (who is one of the four players) and the best player are of opposite sex. The worst player and the best player are the same age. Who is the worst player? ## Problem 26 In acute the bisector of meets side at . The circle with center and radius intersects side at ; and the circle with center and radius intersects side at . Then it is always true that ## Problem 27 If and are distinct roots of , then equals ## Problem 28 In shown in the adjoining figure, is the midpoint of side and . Points and are taken on and , respectively, and lines and intersect at . If then equals ## Problem 29 What is the smallest integer larger than ? ## Problem 30 Let . Then equals

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http://scholarpedia.org/article/Talk:Hopfield_network

Notice: Undefined offset: 248 in /var/www/scholarpedia.org/mediawiki/includes/parser/Parser.php on line 5961 Talk:Hopfield network - Scholarpedia # Talk:Hopfield network This is an excellent summary, written with the author's usual succinctness. I have just one minor point to raise: For large networks, it makes a big difference whether the barriers confining a system to the neighborhood of a particular fixed point grow with the size of the network. For example, for the case with all T_jk = T_0 > 0, there are just two fixed points (all up and all down) and the barriers grow proportional to the size of the system. On the other hand, if the couplings have the opposite sign, there can be many fixed points, with small barriers between them. With finite noise, this difference is important: We are generally interested in large networks which are stabilized by their size (this is implicit in the notion of "collective computation"). This point seems worth mentioning, if space allows. This is a very pleasantly written, succinct review. Just two comments: 1) Would it be possible to include more precise citations in the text as to which article in the reference list discusses which issue (binary vs. continuous variables, optimization etc.)? 2) Also, one might consider including some reference to the related area of automata networks (e.g. Fogelman-Robert-Tchuente, "Automata Networks in Computer Science", Princeton UP 1987, or Goles-Martinez, "Neural and automata networks", Kluwer 1990). There very similar discrete-time dynamical models have been studied, starting from different considerations but concluding with quite analogous techniques and results. (Only with respect to analysis of the dynamics, of course, not for associative memory or optimization.)

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http://mathhelpforum.com/differential-geometry/193504-convergence-r.html

# Math Help - convergence in R 1. ## convergence in R Let $(x^{(n)})^\infty_{n=1}= ((x_k^{(n)})_{k=1}^{\infty})_{n=1}^{\infty}$be a sequence of elements of $l_1$. Prove that if $(x^{(n)})_{n=1}^{\infty}$ converges in $l_1$ to $x=(x_k)_{k=1}^{\infty}$, then for every $K \in N$, the sequence $(x_k^{(n)})_{n=1}^{\infty}$ converges in $R$ to $x_k$. Show by example that the converse is not true. 2. ## Re: convergence in R $|x_k^{(n)}-x_k|\leq |x^{(n)}-x|$ and taking $x^{(k)}=e^{(k)}$ where $e_n^{(k)}=\begin{cases}1&\mbox{ if }n=k\\0&\mbox{ otherwise}\end{cases}$ we get a counter-example for the converse.

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https://www.enotes.com/homework-help/find-values-h-that-makes-following-system-454757

# Find the values of h that makes the following system inconsistent: x + 2y + hz = hx + 3y + 4z = h2x + 4y + 5z = 5 Tibor Pejić | Certified Educator calendarEducator since 2012 starTop subjects are Math, Science, and History There are number of different ways to solve this: using Cramer's ruleRouché–Capelli theorem, some forms of matrix decomposition... But probably the best way for you would be to simply thy to solve the system and see what you get. `x+2y+hz=h` `x+3y+4z=h` `2x+4y+5z=5` Now 1) subtract first row from the second row and 2) subtract first row multiplied by 2 from the third row `x+2y+hz=h` `0+y+(4-h)z=0` `0+0+(5-2h)z=5-2h` Now, only way we would have some problem with solving this system of equations is if `5-2h=0=>h=5/2`  (then the last row would be only zeros). If we put that value of `h` back into our system we would get infinitely many solutions, to be exact solutions would be defined with `y=15/2-3x` `z=-5+2x,` `x in RR` In all the other cases the system has unique solution. And since a system of linear equations is inconsistent when it has no solution there exist no real number h for which this system is inconsistent. check Approved by eNotes Editorial

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https://search.datacite.org/works/10.17605/osf.io/8zupj

### Experiment 3b Matthias Raemaekers, Ian Hussey & Jan De Houwer A replication of Experiment 3, to which two changes were made: (1) participants only completed one phase, simply to shorten the experiment and reduce costs, and (2) the instructions for the one of the blocks were slightly altered to investigate whether this might have an effect on the results. This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.

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https://math-faq.com/chapter-14/section-14-1/

# The Substitution Method In Chapter 13, we reversed the derivative process for basic functions like power and exponential functions. By taking the antiderivative of a power function, we were able to find the original function we had taken the derivative of. In this question, we continue to find antiderivatives of function. For example, suppose we want to take the derivative Since the express is a composition of two functions, we must use the chain rule to take this derivative. Start by identifying the inside and outside functions of the composition, The derivatives of these functions are Using the chain rule, This derivative can also be written as the antiderivative, If we have already carried out the derivative, writing out the antiderivative is just the reverse process. However, it is rarely the case that we have the derivative available to help us evaluate the antiderivative. For integrands involving compositions, Substitution Method may help us to find the antiderivative.

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