Random close packing revisited: How many ways can we pack frictionless disks?

TL;DR

This study investigates the distribution of jammed packings of frictionless disks in 2D, revealing that the packing fraction distribution's peak in large systems can serve as a protocol-independent measure of random close packing.

Contribution

The paper introduces a method to nearly exhaustively identify all collectively jammed states in small 2D disk systems and decomposes the packing fraction distribution into geometric and algorithm-dependent components.

Findings

The density of CJ packing fractions is sharply peaked.

The frequency distribution depends exponentially on packing fraction.

In the large system limit, the packing fraction distribution's peak is determined by geometric factors.

Abstract

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in 2d using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2d and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability $P(\phi)$ for obtaining a collectively jammed state at a particular packing fraction $\phi$ into two composite functions: 1) the density of CJ packing fractions $\rho(\phi)$, which only depends on geometry and 2) the frequency distribution $\beta(\phi)$, which depends on the particular algorithm used to create them. We find that the function $\rho(\phi)$ is sharply peaked and that $\beta(\phi)$ depends exponentially on $\phi$. We predict that in the infinite system-size limit the behavior of $P(\phi)$ in these systems is controlled by the density of CJ packing fractions--not the frequency distribution. These results suggest that the location of the peak in $P(\phi)$ when $N \to \infty$ can be used as a protocol-independent definition of random close packing.