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

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $ϕ_J$. For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress $Γ_{\cal C}$, 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.

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