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Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA

Phys. Rev. E 91, 022207 – Published 26 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022207

Abstract

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 $Γ_{C}$ , force-tile area $A_{C}$ , Voronoi volume $V_{C}$ , number of particles $N_{C}$ , and number of small particles $N_{s C}$ ) on compact subclusters of particles $C$ , as a function of the cluster size and the global system stress. We find several significant differences depending on whether the cluster $C$ 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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References (26)

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See http://math.lbl.gov/voro++/.
The correlation of stress $Γ$ has been computed numerically, within the same model we study here, by G. Lois, J. Zhang, T. S. Majmudar, S. Henkes, B. Chakraborty, C. S. O'Hern, and R. P. Behringer, Phys. Rev. E 80, 060303(R) (2009); they indeed find that for isotropic systems the correlation length, for systems with total stress $Γ_{N} / N$ similar to what we consider here, is smaller than a particle diameter.
We thank C. E. Maloney for this observation.
Given the rather limited range of $\tilde{p}$ that we study, the exact numerical values of the exponents reported here should not be taken as too definitive; they should not be viewed as critical exponents describing the true critical behavior as $ϕ \to ϕ_{J}$ .
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Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

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