Equivalence between random close packing in granular matter and freezing in the hard sphere model

TL;DR

This paper demonstrates that random close packings in granular matter are fundamentally equivalent to the freezing transition in the hard sphere model, providing a geometric explanation based on recent experiments and simulations.

Contribution

It establishes a geometric equivalence between random close packing and the freezing transition in the hard sphere model, clarifying their relationship.

Findings

Random close packings can be explained geometrically.

Recent experiments support the equivalence.

Theoretical insights unify granular matter and phase transition behaviors.

Abstract

The notion of random close packings of a bulk static collection of ball bearings or sand grains was introduced in the 1960's by G.D. Scott and J.D. Bernal. There have been numerous attempts to understand the packings. We give a short argument, based on recent experiments and simulations, which explains the packings in purely geometric terms.