Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles

Abstract : We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of atoms with the rigid body: these collisions, due to the geometry of the rigid body, require developing a new type of trajectory analysis.
Liste complète des métadonnées

Littérature citée [18 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01609594
Contributeur : Isabelle Gallagher <>
Soumis le : mercredi 4 octobre 2017 - 15:04:34
Dernière modification le : mardi 10 octobre 2017 - 13:44:12

Fichiers

bigparticle.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01609594, version 1
  • ARXIV : 1710.01610

Citation

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond. Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles. 2017. 〈hal-01609594〉

Partager

Métriques

Consultations de
la notice

41

Téléchargements du document

6