Estimating angoricity and granular equations of state for monodisperse packings of frictional hard spheres in a wide range of densities.

Abstract

In this paper, we study the granular equation of state (EOS) for computer-generated three-dimensional mechanically stable packings of frictional monodisperse particles over a wide range of densities (packing fractions), φ=0.56-0.72. As a statistical physics framework, we utilize the statistical ensemble for granular matter, specifically the "angoricity" ensemble, where the compressional component Σ_{p} of the force-moment tensor serves as granular energy and angoricity A_{p} is the corresponding granular "temperature." We demonstrate that the systems under study conform well to this statistical description, and the simple equation of state Σ_{p}=2.8NA_{p} holds very well, where N is the number of particles. We show that granular temperature exhibits a rapid drop around the random-close packing (RCP) limit φ≈0.64-0.65, and, hence, one can say that granular packings "freeze" at the RCP limit. We repeat these calculation for shear angoricity A_{sh} and shear component Σ_{sh} of the force-moment tensor and obtain a similar EOS, Σ_{sh}=0.85NA_{sh}. Additionally, we measure the so-called keramicity, an inverse temperature variable corresponding to the determinant of the force-moment tensor, while pressure angoricity corresponds to its trace. We show that inverse keramicity κ^{-1} and angoricity A_{p} conform to an EOS 1/A_{p}Σ_{p}/N+0.11κ(Σ_{p}/N)^{3}=1.2, whose form is predicted by mean-field theory. Finally, we demonstrate that the alternative statistical ensemble where Voronoi volumes serve as granular energy (and so-called compactivity serves as temperature) does not describe the systems under study well.