Brownian motion in a granular gas

Abstract

The dynamics of a heavy particle in a gas of much lighter particles is studied via the Boltzmann-Lorentz equation with inelastic collisions among all particles. A formal expansion in the ratio of gas to tagged particle mass transforms the Boltzmann-Lorentz equation into a Fokker Planck equation. The predictions of the latter are tested here using direct Monte Carlo simulation of the Boltzmann-Lorentz equation. Excellent agreement is obtained for the approach to a homogeneous cooling state, the temperature of that state, approach to diffusion, and the dependence of the diffusion constant on dissipation parameters. Some results from molecular-dynamics simulations are also presented and shown to agree with the theoretical predictions.