On the distribution of free-path lengths for the periodic Lorentz gas III - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Physics Année : 2003

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

Emanuele Caglioti
  • Fonction : Auteur
François Golse

Résumé

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.

Dates et versions

hal-00119070 , version 1 (07-12-2006)

Identifiants

Citer

Emanuele Caglioti, François Golse. On the distribution of free-path lengths for the periodic Lorentz gas III. Communications in Mathematical Physics, 2003, 236 numéro 2, pp.199-221. ⟨hal-00119070⟩
40 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More