相关论文: Integrability propagation for a Boltzmann system d…

In this article we develop Poincar\'e ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that…

This paper constitutes a step in the direction of developing integer lattice gas methods as an attractive alternative to lattice Boltzmann methods. Here we show that to Boltzmann limit the one dimensional Blommel integer lattice gas is very…

We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the…

This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium…

Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…

The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with…

We prove quantitative growth estimates for large data solutions to the 1D Boltzmann equation, for a collision kernel with angular cutoff and relative velocity cutoff. We present proofs for the global well-posedness results presented in the…

For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…

The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…

We consider the non-cutoff Boltzmann equation in the spatially inhomogeneous, soft potentials regime, and establish decay estimates for large velocity. In particular, we prove that pointwise algebraically decaying upper bounds in the…

The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bounded domain with the Cercignani-Lampis boundary condition,…

For different models of the electron-phonon interaction, the asymptotic behaviour of the moments of the stationary homogeneous solution of the linear Boltzmann equation is determined in the limit of a high external field. For…

A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the…

This paper is to study the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the solution to the initial value problem is established for the Maxwellian molecules in a space of…

Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…

In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…

The phenomena of diffusion in multicomponent (more than two components) mixtures are very universal in both science and engineering, and from mathematical point of view, they are usually described by the Maxwell-Stefan (MS) based continuum…

A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal…