Rigorous Derivation and Analysis of Coupling of Kinetic Equations and Their Hydrodynamic Limits for a Simplified Boltzmann Model

In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.     

Similarity Solutions for a Nonlinear Model of the Heat Equation

Abstract

The Hilbert space representations of a class of commutation relations associated with a Möbius transformation is studied using results on convergence of continued fractions.     

Towards the Automatic Study of the Vocal Tract From Magnetic Resonance Images

Over the last few decades, researchers have been investigating the mechanisms involved in speech production. Image analysis can be a valuable aid in the understanding of the morphology of the vocal tract. The application of magnetic resonance imaging to study these mechanisms has been proven to be reliable and safe. We have applied deformable models in magnetic resonance images to conduct an automatic study of the vocal tract; mainly, to evaluate the shape of the vocal tract in the articulation of some European Portuguese sounds, and then to successfully automatically segment the vocal tract's shape in new images. Thus, a point distribution model has been built from a set of magnetic resonance images acquired during artificially sustained articulations of 21 sounds, which successfully extracts the main characteristics of the movements of the vocal tract. The combination of that statistical shape model with the gray levels of its points is subsequently used to build active shape models and active appearance models. Those models have then been used to segment the modeled vocal tract into new images in a successful and automatic manner. The computational models have thus been revealed to be useful for the specific area of speech simulation and rehabilitation, namely to simulate and recognize the compensatory movements of the articulators during speech production.     

Experimental Investigation of the Nonlinear Coupling Strength of a Photorefractive Crystal

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Analysis and Experiments for a Computational Model of a Heat Bath

A question of some interest in computational statistical mechanics is whether macroscopic quantities can be accurately computed without detailed resolution of the fastest scales in the problem. To address this question a simple model for a distinguished particle immersed in a heat bath is studied (due to Ford and Kac). The model yields a Hamiltonian system of dimension 2N+2 for the distinguished particle and the degrees of freedom describing the bath. It is proven that, in the limit of an infinite number of particles in the heat bath (N), the motion of the distinguished particle is governed by a stochastic differential equation (SDE) of dimension 2. Numerical experiments are then conducted on the Hamiltonian system of dimension 2N+2 (N1) to investigate whether the motion of the distinguished particle is accurately computed (i.e., whether it is close to the solution of the SDE) when the time step is small relative to the natural time scale of the distinguished particle, but the product of the fastest frequency in the heat bath and the time step is not small—the underresolved regime in which many computations are performed. It is shown that certain methods accurately compute the limiting behavior of the distinguished particle, while others do not. Those that do not are shown to compute a different, incorrect, macroscopic limit.     

Effects Due to a Scalar Coupling on the Particle-Antiparticle Production in the Duffin-Kemmer-Petiau Theory

The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used to point out a few misconceptions diffused in the literature. It is explicitly shown that the scalar coupling makes the DKP formalism not equivalent to the Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of the DKP theory looks formally like the spin-0 sector. With proper boundary conditions, scattering of massive bosons in an arbitrary mixed vector-scalar square step potential is explored in a simple way and effects due to the scalar coupling on the particle-antiparticle production and localization of bosons are analyzed in some detail.     

存在Kerr介质的广义Jaynes-Cummings模型非线性耦合强度对光场量子相位特性的影响

研究了由于Jaynes-Cumming模型和非谐振子模型构成的组合模型中光场的量子相位特性,计算了光场-Kerr介质非线性耦合常数与光场-原子耦合常数的比值在弱(-ng-2>>-n2x2).中性(-ng-2 ～-n2χ2)和强(-ng2<<-n2χ2)非线性耦合情形对光场相位分布、相位平均值和相位涨落的影响,并将结果与Jaynes-Cummings模型和非谐振子模型的结果进行了比较.     

Localization for a Nonlinear Sigma Model in a Strip Related to Vertex Reinforced Jump Processes

We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin–Wagner type argument and a transfer operator approach.