Vector and Spinor Decomposition of SU(2) Gauge Potential, their quivalence and Knot Structure in SU(2) Chern-Simons Theory

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the $\phi$--mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping.Comment: 10 pages, ni figur

Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind forcing and the $\beta$ parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical system

Topological Excitation in Skyrme Theory

Based on the $\phi$-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes (splitting, merging and intersection) during the evolution of the monopoles.Comment: 10 pages, 0 figure

Self-Dual Vortices in the Fractional Quantum Hall System

Based on the $\phi$-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It is revealed that there exist self-dual vortices in the system. We investigate the inner topological structure of the self-dual vortices and show that the topological charges of the vortices are quantized by Hopf indices and Brouwer degrees. Furthermore, we study the branch processes in detail. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field $\vec\phi$.Comment: 13 pages 10 figures. accepted by IJMP

Synchronization of dissipative dynamical systems driven by non-Gaussian Lévy noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation, and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under a class of Lévy noises is considered. After discussing cocycle property, stationary orbits, and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in some asymptotic sense

Modeling Space-Time Data Using Stochastic Differential Equations

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio

Topological Properties of Spatial Coherence Function

Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.Comment: 9 page

Superfluidity of fermions with repulsive on-site interaction in an anisotropic optical lattice near a Feshbach resonance

We present a numerical study on ground state properties of a one-dimensional (1D) general Hubbard model (GHM) with particle-assisted tunnelling rates and repulsive on-site interaction (positive-U), which describes fermionic atoms in an anisotropic optical lattice near a wide Feshbach resonance. For our calculation, we utilize the time evolving block decimation (TEBD) algorithm, which is an extension of the density matrix renormalization group and provides a well-controlled method for 1D systems. We show that the positive-U GHM, when hole-doped from half-filling, exhibits a phase with coexistence of quasi-long-range superfluid and charge-density-wave orders. This feature is different from the property of the conventional Hubbard model with positive-U, indicating the particle-assisted tunnelling mechanism in GHM brings in qualitatively new physics.Comment: updated with published version