Statistics of Conserved Quantities in Mechanically Stable Packings of Frictionless Disks Above Jamming

TL;DR

This study numerically investigates the statistical properties of conserved quantities in mechanically stable, frictionless disk packings above jamming, revealing differences based on cluster definitions and informing maximum entropy models.

Contribution

It provides a detailed numerical analysis of conserved quantities in jammed packings, highlighting the impact of cluster definitions on their statistical behavior.

Findings

Significant differences in conserved quantities depending on cluster definition.

Quantitative relationships between cluster size and conserved quantity fluctuations.

Implications for maximum entropy models of jammed packings.

Abstract

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $\phi_J$. For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress $\Gamma_{\cal C}$, force-tile area $A_{\cal C}$, Voronoi volume $V_{\cal C}$, number of particles $N_{\cal C}$, and number of small particles $N_{s{\cal C}}$) on compact subclusters of particles ${\cal C}$, as a function of the cluster size and the global system stress. We find several significant differences depending on whether the cluster ${\cal C}$ is defined by a fixed radius $R$ or a fixed number of particles $M$. We comment on the implications of our findings for maximum entropy models of jammed packings.