Eur. Phys. J. E 5, 161-170
Heated granular fluids: The random restitution coefficient approach
A. Barrat1, E. Trizac1 and J.-N. Fuchs21 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.
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
