Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Gué...

We present recent results [4, 28, 29] about the quantitative study of the linearized Boltzmann collision operator, and its application to the study of the trend to equilibrium for the spatially homogeneous Boltzmann equation for hard spheres.

The paper considers initial boundary value problems for the non-linear Boltzmann equation with large L 1 initial data and for the lin-earised Bolzmann equation with L 2 initial data. Particular problems under analysis describe ows in a domain consisting of two subdomains connected through a joint part ? of the boundary which can have a complicated fractal geometry. The presence of interaction b...

The understanding of thermal conductance in both classical and quantum mechanical systems is one of the fundamental problems of non-equilibrium statistical mechanics. A particular aspect that has attracted much interest is the observation that autonomous translation invariant systems in dimensions one and two exhibit anomalously large conductivity. The canonical example here is a chain of anhar...

Recently, a lot of progress has been made on the study for the spatially homogeneous Boltzmann equation without angular cutoff, cf. [2, 3, 8, 22] and references therein, which shows that the singularity of collision cross-section yields some gain of regularity in the Sobolev space frame on weak solutions for Cauchy problem. That means, this gives the C regularity of weak solution for the spatia...

The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural coordinates.

We provide a simple method for obtain boundary asymptotics of the Poisson kernel on a domain in R . 0 Introduction Let Ω ⊆ R be a connected open set—called a domain. It is a matter of considerable interest to estimate the size of the Poisson kernel PΩ(x, t) = P (x, t) of Ω. Here, and throughout this paper, x ∈ Ω and t ∈ ∂Ω. In case Ω has a large group of symmetries, then it is often possible to...

In this paper lattice-Boltzmann equation method is used to simulate non-Darcy flow in porous media. 2-D in-line and staggered arrangements of uniform cylinders have been considered. The results of a comprehensive computational evaluation are reported: the range of validity of Darcy-Forchheimer equation is investigated and correlations for macroscopic transport properties are presented (i. e., f...

It is well known that Poisson binomial distribution can be approximated by Poisson distribution. In this paper, we give a nonuniform bound of this approximation by using Stein-Chen method.