Jamming in two-dimensional packings

TL;DR

This paper explores the limits of random close and loose packings in 2D disk systems using a statistical mechanics framework, revealing potential density thresholds linked to jammed states and glass transition phenomena.

Contribution

It introduces a statistical mechanics model to predict packing limits in 2D disk packings, connecting density thresholds with coordination number and compactivity.

Findings

Existence of limiting densities for jammed packings

Correlation between packing density and coordination number

Implications for glass transition in 2D systems

Abstract

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution of volumes-- suggests the existence of the limiting densities of the jammed packings according to their coordination number and compactivity. This result has implications for the understanding of disordered states in the disk packing problem as well as the existence of a putative glass transition in two dimensional systems.