Exponential velocity tails in a driven inelastic Maxwell model

Abstract

The problem of the steady-state velocity distribution in a driven inelastic Maxwell model of shaken granular material is revisited. Numerical solution of the master equation and analytical arguments show that the model has bilateral exponential velocity tails ($P(v)\sim e^{-|v|/\sqrt D}$), where $D$ is the amplitude of the noise. Previous study of this model predicted Gaussian tails ($P(v)\sim e^{-av^2}$).