Spatial correlations in polydisperse, frictionless two-dimensional packings

TL;DR

This study reveals counter-intuitive spatial correlations in contact numbers of polydisperse, frictionless 2D packings, showing that particles with few contacts tend to contact those with many, explained via an analogy to cellular structures.

Contribution

It introduces an empirical relation analogous to the Aboav-Weaire law for contact number correlations in polydisperse packings, with a sum rule constraint.

Findings

Discs with few contacts contact those with many.

No radius correlations between neighboring particles.

Empirical relation satisfying sum rule constraints.

Abstract

We investigate next nearest neighbor correlations of the contact number in simulations of polydisperse, frictionless packings in two dimensions. We find that discs with few contacting neighbors are predominantly in contact with discs that have many neighbors and vice versa at all packing fractions. This counter-intuitive result can be explained by drawing a direct analogy to the Aboav-Weaire law in cellular structures. We find an empirical one parameter relation similar to the Aboav-Weaire law that satisfies an exact sum rule constraint. Surprisingly, there are no correlations in the radii between neighboring particles, despite correlations between contact number and radius.