119138353
Inner structure of Gauss-Bonnet-Chern Theorem and the Morse theory
We define a new one-form HA based on the second fundamental tensor , the Gauss–Bonnet–Chern form can be novelly expressed with this one-form. Using the ϕ-mapping theory we find that the Gauss–Bonnet–Chern density can be expressed in terms of the δ-function δ(ϕ) and the relationship between the Gauss–Bonnet–Chern theorem and Hopf–Poincare theorem is given straightforwardly. The topological current of the Gauss–Bonnet–Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.
119182413
NUCLEON SPIN IN QCD: OLD CRISIS AND NEW RESOLUTION
We clarify the on-going confusion on the long-standing gauge invariance problem of the nucleon spin decomposition to the spin and angular momentum of quarks and gluons. We provide two gauge-invariant decompositions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all (binding and valence) gluons contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it.
120706090
DECOMPOSITION OF THE SEMI-SIMPLE GROUP CONNECTION AND COSMIC STRINGS IN THE LORENTZ SPACETIME
In a previous paper, we addressed the method of Abelian decomposition to the case of SU(N) Yang–Mills theory. Here, we extend the decomposition method further to the general case. With the Cartan–Weyl basis we decompose semisimple group connection and discuss the SO(3,1) group in particular. In terms of the vierbein projection, we propose two two-forms as the U(1) gauge fields in the SO(3,1) gauge theory and show that these two-forms are just the different cosmic string tensors. Meanwhile, these two-forms indicate that the cosmic strings appear naturally in the Lorentz spacetime, i.e. the torsion in the Riemann–Cartan spacetime is not necessary for the cosmic strings.
9177547
TOPOLOGICAL STRUCTURE OF THE MANY VORTICES SOLUTION IN JACKIW–PI MODEL
By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw–Pi model. We obtain a new concrete self-dual equation and find relationship between Chern–Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Ψ-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw–Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.
121146051
The single vortex in the FFLO state
In this Letter, we study the generalized Ginzburg-Landau (GL) functional near the tricritical temperature, and obtain the vortex solution of the FFLO state. Furthermore, we investigate the structure of the vortex and find that the vortices shrink when the Zeeman effect is weaken or temperature is lowered. (C) 2010 Elsevier B.V. All rights reserved.
117181910
Exotic Hill problem: Hall motions and symmetries
Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical value of the angular velocity, the only allowed motions follow the Hall law. Translations and generalized boosts span two independent Heisenberg algebras with different central parameters. In the critical case, the symmetry reduces to a single Heisenberg algebra.
55581636
A Study of Beam Position Diagnostics with Beam-excited Dipole Higher Order Modes using a Downconverter Test Electronics in Third Harmonic 3.9 GHz Superconducting Accelerating Cavities at FLASH
Beam-excited higher order modes (HOM) in accelerating cavities contain transverse beam position information. Previous studies have narrowed down three modal options for beam position diagnostics in the third harmonic 3.9 GHz cavities at FLASH. Localized modes in the beam pipes at approximately 4.1 GHz and in the fifth cavity dipole band at approximately 9 GHz were found, that can provide a local measurement of the beam position. In contrast, propagating modes in the first and second dipole bands between 4.2 and 5.5 GHz can reach a better resolution. All the options were assessed with a specially designed test electronics built by Fermilab. The aim is to define a mode or spectral region suitable for the HOM electronics. Two data analysis techniques are used and compared in extracting beam position information from the dipole HOMs: direct linear regression and singular value decomposition. Current experiments suggest a resolution of 50 {\mu}m accuracy in predicting local beam position using modes in the fifth dipole band, and a global resolution of 20 {\mu}m over the complete module. Based on these results we decided to build a HOM electronics for the second dipole band and the fifth dipole band, so that we will have both high resolution measurements for the whole module, and localized measurements for individual cavity. The prototype electronics is being built by Fermilab and planned to be tested in FLASH by the end of 2012.
118557906
Type Ia supernovae as speed sensors at intermediate redshifts
Large scale peculiar velocity (LSPV) is a crucial probe of dark matter, dark energy, and gravity at cosmological scales. However, its application is severely limited by measurement obstacles. We show that fluctuations in type Ia supernovae fluxes induced by LSPV offer a promising approach to measure LSPV at intermediate redshifts. In the 3D Fourier space, gravitational lensing, the dominant systematical error, is well suppressed, localized, and can be further corrected effectively. Advances in supernova observations can further significantly reduce shot noise induced by supernova intrinsic fluctuations, which is the dominant statistical error. Robust mapping on the motion of the dark universe through type Ia supernovae is thus feasible to z similar to 0.5.
44301996
BEAM-BASED HOM STUDY IN THIRD HARMONIC SC CAVITIES FOR BEAM ALIGNMENT AT FLASH*
An electron beam entering an accelerator cavity excites higher order modes (HOM). These are radiated to HOM couplers and subsequently damped. They can also be used to facilitate beam position monitoring. The modes excited by off-axis beams are the focus of this study. Results are presented on the first analysis of HOM dependency on the beam position for the third harmonic cavities at FLASH. The analysis is based on the beampipe and cavity dipole modes. Various analysis methods are used and compared to satisfy the needs emerging from the characteristics of those modes. The electric center of each mode is observed by looking for the minima of the HOM signals of different beam positions. A single electron bunch per RF pulse is used.
13832368
A new method of measuring the peculiar velocity power spectrum
We show that by directly correlating the cluster kinetic Sunyaev Zeldovich (KSZ) flux, the cluster peculiar velocity power spectrum can be measured to $\sim 10%$ accuracy by future large sky coverage KSZ surveys. This method is almost free of systemics entangled in the usual velocity inversion method. The direct correlation brings extra information of density and velocity clustering. We utilize these information to construct two indicators of the Hubble constant and comoving angular distance and propose a novel method to constrain cosmology.
15003877
SELF-CALIBRATION OF GRAVITATIONAL SHEAR-GALAXY INTRINSIC ELLIPTICITY CORRELATION IN WEAK LENSING SURVEYS
The galaxy intrinsic alignment is a severe challenge to precision cosmic shear measurement. We propose self-calibrating the induced gravitational shear-galaxy intrinsic ellipticity correlation (the GI correlation) in weak lensing surveys with photometric redshift measurements. (1) We propose a method to extract the intrinsic ellipticity-galaxy density cross-correlation (I-g) from the galaxy ellipticity-density measurement in the same redshift bin. (2) We also find a generic scaling relation to convert the extracted I-g correlation to the necessary GI correlation. We perform a concept study under simplified conditions and demonstrate its capability to significantly reduce GI contamination. We discuss the impact of various complexities on the two key ingredients of the self-calibration technique, namely the method for extracting the I-g correlation and the scaling relation between the I-g and the GI correlation. We expect that none of them will likely be able to completely invalidate the proposed self-calibration technique.