Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles

A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space (which includes energy and time as independent coordinates) for all three adiabatic invariants. First, the guiding-center equations of motion for a relativistic particle are derived from the particle Lagrangian. Covariant aspects of the resulting relativistic guiding-center equations of motion are discussed and contrasted with previous works. Next, the second and third invariants for the bounce motion and drift motion, respectively, are obtained by successively removing the bounce phase and the drift phase from the guiding-center Lagrangian. First-order corrections to the second and third adiabatic invariants for a relativistic particle are derived. These results simplify and generalize previous works to all three adiabatic motions of relativistic magnetically-trapped particles.Comment: 20 pages, LaTeX, to appear in Physics of Plasmas (Aug, 2007

Difference of optical conductivity between one- and two-dimensional doped nickelates

We study the optical conductivity in doped nickelates, and find the dramatic difference of the spectrum in the gap ($\omega$\alt4 eV) between one- (1D) and two-dimensional (2D) nickelates. The difference is shown to be caused by the dependence of hopping integral on dimensionality. The theoretical results explain consistently the experimental data in 1D and 2D nickelates, Y$_{2-x}$Ca$_x$BaNiO$_5$ and La$_{2-x}$Sr$_x$NiO$_4$, respectively. The relation between the spectrum in the X-ray aborption experiments and the optical conductivity in La$_{2-x}$Sr$_x$NiO$_4$ is discussed.Comment: RevTeX, 4 pages, 4 figure

Soliton with a Pion Field in the Global Color Symmetry Model

We calculate the property of the global color symmetry model soliton with the pion field being included explicitly. The calculated results indicate that the pion field provides a strong attraction so that the eigen-energy of a quark and the mass of a soliton reduce drastically, in contrast to those with only the sigma field.Comment: 15 pages, 2 figure

Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field

We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed form analytical formulas for the one point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulas allows us to analyze the ensemble averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulas of combustion in the thin reaction zone limit and show that these approximate formulas can either underestimate or overestimate average concentrations when reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in space due to random advection induced diffusion; and that the level curves of ensemble averaged concentration undergo diffusion about mean locations.Comment: 18 page

Atomic scale elastic textures coupled to electrons in superconductors

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov-de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation-- the elasticity propagates the electronic response over long distances. In particular, it is possible for the trapping of low-lying quasiparticle states around the defects. These predictions could be directly tested by STM experiments in superconducting materials.Comment: Proceeding paper for "Conference on Dynamic Inhomogeneities in Complex Oxides" (to appear in J. Superconductivity

Interplay between Superconductivity and Antiferromagnetism in a Multi-layered System

Based on a microscopic model, we study the interplay between superconductivity and antiferromagnetism in a multi-layered system, where two superconductors are separated by an antiferromagnetic region. Within a self-consistent mean-field theory, this system is solved numerically. We find that the antiferromagnetism in the middle layers profoundly affects the supercurrent flowing across the junction, while the phase difference across the junction influences the development of antiferromagnetism in the middle layers. This study may not only shed new light on the mechanism for high-$T_{c}$ superconductors, but also bring important insights to building Josephson-junction-based quantum devices, such as SQUID and superconducting qubit.Comment: 4+ pages, 5 figures, Accepted for publication in Phys. Rev.

Automatic recognition of lactating sow behaviors through depth image processing

Manual observation and classification of animal behaviors is laborious, time-consuming, and of limited ability to process large amount of data. A computer vision-based system was developed that automatically recognizes sow behaviors (lying, sitting, standing, kneeling, feeding, drinking, and shifting) in farrowing crate. The system consisted of a low-cost 3D camera that simultaneously acquires digital and depth images and a software program that detects and identifies the sow’s behaviors. This paper describes the computational algorithm for the analysis of depth images and presents its performance in recognizing the sow’s behaviors as compared to manual recognition. The images were acquired at 6 s intervals on three days of a 21-day lactation period. Based on analysis of the 6 s interval images, the algorithm had the following accuracy of behavioral classification: 99.9% in lying, 96.4% in sitting, 99.2% in standing, 78.1% in kneeling, 97.4% in feeding, 92.7% in drinking, and 63.9% in transitioning between behaviors. The lower classification accuracy for the transitioning category presumably stemmed from insufficient frequency of the image acquisition which can be readily improved. Hence the reported system provides an effective way to automatically process and classify the sow’s behavioral images. This tool is conducive to investigating behavioral responses and time budget of lactating sows and their litters to farrowing crate designs and management practices

Ultra-high energy cosmic rays threshold in Randers-Finsler space

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space