Stationary Probability Distribution in Granular Media

TL;DR

This paper explores a statistical mechanics framework for granular media, analyzing a mean field model to derive phase diagrams and segregation patterns, thus advancing understanding of non-thermal systems.

Contribution

It applies Edwards' theory to a mean field model of granular mixtures, providing analytical insights into phase behavior and segregation.

Findings

Derived the phase diagram of the model

Predicted segregation pattern features

Validated Edwards' theory in this context

Abstract

We discuss recent developments in the formulation of a Statistical Mechanics approach to non thermal systems, such as granular media. We review a few important numerical results on the assessment of Edwards' theory and, in particular, we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity, which can be fully analytically investigated. As a consequence, we derive the rich phase diagram and predict the features of segregation patterns of the mixture.