On the distribution of free-path lengths for the periodic Lorentz gas III

In a flat 2-torus with a disk of diameter $r$ removed, let $\Phi_r(t)$ be the distribution of free-path lengths (the probability that a segment of length larger than $t$ with uniformly distributed origin and direction does not meet the disk). We prove that $\Phi_r(t/r)$ behaves like $\frac{2}{\pi^2 t}$ for each $t>2$ and in the limit as $r\to 0^+$, in some appropriate sense. We then discuss the implications of this result in the context of kinetic theory.Comment: 26 pages, 5 figures, to be published in Commun. Math. Phy

On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of Gases

Correction published 22 March 2021: DOI: 10.1007/s00205-021-01644-5 (ISI: 000631321100001)</p

A Numerical Method for Computing Asymptotic States and Outgoing Distributions for Kinetic Linear Half-Space Problems

Linear half space problems can be used to solve domain decomposition problems between Boltzmann and aerodynamic equations. A new fast numerical method computing the asymptotic states and outgoing distributions for a linearized BGK half-space problem is presented. Relations with the so-called variational methods are discussed. In particular, we stress the connection between these methods and Chapman-Enskog type expansions. 1 Introduction The Boltzmann equation and the more classical gas dynamics equations (such as Euler or Navier-Stokes equations) are used to model hypersonic gas flows. Numerical simulations of such flows are useful in the design of space vehicles, especially in understanding the behavior of the early phases of reentry flights. Such flows are usually far from any kind of local equilibrium states: real gas effects (and the so many different degrees of freedom involved such as rotational and vibrational energies) as well as the importance of chemical reactions in the ene..

Numerical study of a domain decomposition method for a two-scale linear transport equation, Netw

Abstract. We perform a numerical study on a domain decomposition method proposed in [13] for the linear transport equation between a diffusive and a non-diffusive region. This method avoids iterating the diffusion and transport solutions as in a typical domain decomposition method. Our numerical results, in both one and two space dimensions, confirm the theoretical analysis of [13]. We also provide an improved second order method that provides a more accurate numerical solution than that proposed in [13]

Analyse asymptotique de l'equation de Poisson couplee a la relation de Boltzmann quasi neutralite des plasmas

Available at INIST (FR), Document Supply Service, under shelf-number : RP 12161 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc