Universal reference state in a driven homogeneous granular gas

TL;DR

This paper demonstrates that a driven homogeneous granular gas exhibits a universal transient state characterized by a two-parameter scaling, differing from the traditional single-parameter cooling models, with theoretical and simulation agreement.

Contribution

It introduces a universal reference state in driven granular gases that depends on both velocity and temperature, extending the understanding beyond cooling phenomenology.

Findings

Universal state depends on velocity and temperature

Excellent agreement between theory and simulations

Velocity statistics require two-parameter scaling

Abstract

We study the dynamics of a homogeneous granular gas heated by a stochastic thermostat, in the low density limit. It is found that, before reaching the stationary regime, the system quickly "forgets" the initial condition and then evolves through a universal state that does not only depend on the dimensionless velocity, but also on the instantaneous temperature, suitably renormalized by its steady state value. We find excellent agreement between the theoretical predictions at Boltzmann equation level for the one-particle distribution function, and Direct Monte Carlo simulations. We conclude that at variance with the homogeneous cooling phenomenology, the velocity statistics should not be envisioned as a single-parameter, but as a two-parameter scaling form, keeping track of the distance to stationarity.