An invariant distribution in static granular media

TL;DR

This paper identifies a universal invariant distribution for local packing configurations in static granular media, consistent across different packing fractions and environments, derived from statistical mechanics principles.

Contribution

It introduces a universal distribution function for granular media based on elementary cell subdivision, analogous to Maxwell-Boltzmann distribution.

Findings

Distribution holds across various packing fractions

Consistent in air and water environments

Derived from statistical mechanics

Abstract

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses.