Exponential velocity tails in a driven inelastic Maxwell model

TL;DR

This paper demonstrates that a driven inelastic Maxwell model exhibits bilateral exponential velocity tails, contrasting previous predictions of Gaussian tails, through numerical and analytical methods.

Contribution

It provides the first analytical and numerical confirmation that the velocity distribution has exponential tails in this model, revising earlier Gaussian tail predictions.

Findings

Velocity distribution has bilateral exponential tails.

Numerical solutions confirm analytical predictions.

Contrasts with previous Gaussian tail predictions.

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 ($P(v)\sim e^{-av^2}$).