Velocity Distribution of Inelastic Granular Gas in Homogeneous Cooling State

TL;DR

This study uses molecular dynamics simulations to analyze the velocity distribution in a two-dimensional inelastic granular gas, revealing that velocity correlations invalidate the Boltzmann equation's assumptions during homogeneous cooling.

Contribution

It demonstrates that velocity correlations cause deviations from Boltzmann predictions in inelastic granular gases, challenging the molecular chaos assumption.

Findings

Velocity distribution initially matches Boltzmann prediction.

Velocity correlations cause distribution to deviate over time.

Boltzmann equation predictions fail due to correlations.

Abstract

The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after a several inelastic collisions per particle, the system falls in the state that the Boltzmann equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time-independent, but is gradually returning to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction by the Boltzmann equation fails.