Velocity distribution of driven granular gases

TL;DR

This paper derives microscopic models for driven granular gases, revealing two universal velocity distribution regimes: a Gaussian decay with logarithmic corrections for typical driving, and an exponential decay contradicting kinetic theory predictions.

Contribution

It provides the first microscopic derivation of velocity distribution tails in driven granular gases, challenging existing kinetic theory assumptions.

Findings

Velocity distribution is Gaussian with logarithmic corrections under typical driving.

In a less generic regime, the distribution decays exponentially, contradicting kinetic theory.

Microscopic model results necessitate re-examining kinetic theory assumptions.

Abstract

The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of the velocity distribution of a driven granular gas is a stretched exponential that, counterintuitively, decays slower than that of the corresponding elastic gas in equilibrium. However, a derivation of this result starting from a microscopic model is lacking. Here, we obtain analytical results for a microscopic model for a granular gas where particles with two-dimensional velocities are driven homogeneously and isotropically by reducing the velocities by a factor and adding a stochastic noise. We find two universal regimes. For generic physically relevant driving, we find that the tail of the velocity distribution is a Gaussian with additional logarithmic corrections. Thus, the velocity distribution decays faster than the corresponding equilibrium gas. The second universal regime is less generic and corresponds to the scenario described by kinetic theory. Here, the velocity distribution is shown to decay as an exponential with additional logarithmic corrections, in contradiction to the predictions of the phenomenological kinetic theory, necessitating a re-examination of its basic assumptions.