The Granular Phase Diagram

TL;DR

This paper develops an analytical and numerical study of the kinetic energy distribution in granular systems, constructing a phase diagram that distinguishes between different instability regimes and validating findings with molecular dynamics simulations.

Contribution

It introduces a comprehensive phase diagram for granular systems based on kinetic theory and simulations, highlighting stability regions and novel fluctuation effects.

Findings

Analytical form of energy distribution function for inelastic spheres

Identification of stability regions in the phase diagram

Observation of fluctuational breakdown of mean-field theories

Abstract

The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems, and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions.