Random inelasticity and velocity fluctuations in a driven granular gas

TL;DR

This paper investigates velocity distributions in driven granular gases, showing that simple models are incompatible with experiments, and proposes a refined random restitution coefficient model that aligns well with observed data.

Contribution

The study refines a random restitution coefficient model to accurately describe experimental velocity distributions in driven granular gases.

Findings

Simple stochastic thermostat models are incompatible with experimental data.

Refined random restitution coefficient model fits experimental velocity distributions well.

Provides insights into the universality of velocity statistics in granular gases.

Abstract

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the ``stochastic thermostat'' model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high velocity stretched exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.