Elegance of disordered granular packings: a validation of Edwards' hypothesis

TL;DR

This paper validates Edwards' hypothesis by analyzing the density of states in static granular packings, showing good agreement with empirical data and revealing underlying structural insights.

Contribution

It introduces a method to analyze Edwards' density of states for frictionless granular packings, validating the statistical mechanics approach in this context.

Findings

Good agreement between theory and empirical data

Coordination number influences discrepancies

Insights into the structure of granular packings

Abstract

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly related to the coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states.