Force balance in canonical ensembles of static granular packings

Abstract

We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.

9 pages, 9 figures, submitted to JSTAT

References in corpus (5)

• Critical scaling in linear response of frictionless granular packings near jamming
• Entropy and Temperature of a Static Granular Assembly
• Entropy maximization in the force network ensemble for granular solids
• The tail of the contact force distribution in static granular materials
• Ensemble Theory for Force Networks in Hyperstatic Granular Matter

Cited by in corpus (8)

• The Statistical Physics of Athermal Materials
• Field theory for amorphous solids
• Laws of Granular Solids. Geometry and Topology
• Edwards field theory for glasses and granular matter
• Corrigendum to "Thermodynamical instabilities of perfect fluid spheres in General Relativity"
• Maximum Entropy and the Stress Distribution in Soft Disk Packings Above Jamming
• Statistics of Conserved Quantities in Mechanically Stable Packings of Frictionless Disks Above Jamming
• Contact force measurements and local anisotropy in ellipses and disks