Heated granular fluids: The random restitution coefficient approach

We introduce the model of inelastic hard spheres with random restitution co efficient ct, in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the e nergy injected vertically is transferred to the horizontal degrees of freed om through collisions only, which leads to heating through collisions, i.e. to inelastic horizontal collisions with an effective restitution coefficie nt that can be larger than 1. This allows the system to reach a nonequilibr ium steady state, where we focus, in particular, on the single-particle vel ocity distribution f(v) in the horizontal plane, and on its deviation from a Maxwellian. Molecular Dynamics simulations and Direct Simulation Monte Ca rlo (DSMC) show that, depending on the distribution of ct, 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 equat ion and successfully tested against the simulations.