INELASTIC HARD SPHERES WITH RANDOM RESTITUTION COEFFICIENT: A NEW MODEL FOR HEATED GRANULAR FLUIDS

Abstract

We consider a vertically shaken granular system interacting elastically with the vibrating boundary, so that the energy injected vertically is transferred to the horizontal degrees of freedom through inter-particle collisions only. This leads to collisions which, once projected onto the horizontal plane, become essentially stochastic and may have an effective restitution coefficient larger than unity. We therefore introduce the model of inelastic hard spheres with random restitution coefficient α (larger or smaller than unity) to describe granular systems heated by vibrations. In the non-equilibrium steady state, we focus in particular on the single particle velocity distribution f(v) in the horizontal plane, and on its deviation from a Maxwellian. We use Molecular Dynamics simulations and Direct Simulation Monte Carlo (DSMC) to show that, depending on the distribution of α, different shapes of f(v) can be obtained, with very different high energy tails. Moreover, the fourth cumulant of the velocity distribution (which quantifies the deviations from Gaussian statistics) is obtained analytically from the Boltzmann equation and successfully tested against the simulations.