Eur. Phys. J. E 5, 161-170

Heated granular fluids: The random restitution coefficient approach

A. Barrat¹, E. Trizac¹ and J.-N. Fuchs<sup>2

1</sup>  Laboratoire de Physique Théorique ( Unité Mixte de Recherche UMR 8627) , Bâtiment 210, Université de Paris-Sud, 91405 Orsay, France
²  Laboratoire Kastler-Brossel ( Unité Mixte de Recherche UMR 8552) , Département de Physique de l'E.N.S, 24 rue Lhomond, 75231 Paris, France

Alain.Barrat@th.u-psud.fr

(Received 24 November 2000 and Received in final form 8 February 2001)

Abstract
We introduce the model of inelastic hard spheres with random restitution coefficient , in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the energy injected vertically is transferred to the horizontal degrees of freedom through collisions only, which leads to heating through collisions, i.e. to inelastic horizontal collisions with an effective restitution coefficient that can be larger than 1. This allows the system to reach a non-equilibrium steady state, where we focus, in particular, on the single-particle velocity distribution f(v) in the horizontal plane, and on its deviation from a Maxwellian. Molecular Dynamics simulations and Direct Simulation Monte Carlo (DSMC) show that, depending on the distribution of , different shapes of f(v) can be obtained, with very different high-energy tails. Moreover, the fourth cumulant of the velocity distribution quantifying the deviations from Gaussian statistics is obtained analytically from the Boltzmann equation and successfully tested against the simulations.

PACS
45.70.-n - Granular systems.
51.10.+y - Kinetic and transport theory of gases.
45.10.-b - Computational methods in classical mechanics.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001