Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions
arXiv:cond-mat/0511551 · doi:10.1140/epje/e2006-00014-7
Abstract
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling the identification of a phase space and making it possible to take account of geometrical correlations systematically. Case studies are presented for which explicit calculations of the mean vertex density and porosity fluctuations are given as functions of compactivity. The formalism applies equally well to two- and three-dimensional granular assemblies.
14 pages, 4 figures, to appear in The European Physical Journal E - Soft Matter
References in corpus (2)
Cited by in corpus (22)
- A deductive statistical mechanics approach for granular matter
- A statistical mechanics framework for static granular matter
- Entropy and Temperature of a Static Granular Assembly
- An invariant distribution in static granular media
- Void statistics and compactivity measurement in an experimental granular pile
- Edwards entropy and compactivity in a model of granular matter
- Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems
- Friction-controlled entropy-stability competition in granular systems
- On universal structural characteristics of granular packs
- Application of Edwards' statistical mechanics to high dimensional jammed sphere packings
- Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation
- Scaling Theory for the Frictionless Unjamming Transition
- Edwards thermodynamics for a driven athermal system with dry friction
- Effects of particle angularity on granular self-organization
- A Tiling Approach to Counting Inherent Structures in Hard Potential Systems
- Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media
- Affine and topological structural entropies in granular statistical mechanics: explicit calculations and equation of state
- Generalized Edwards thermodynamics and marginal stability in a driven system with dry and viscous friction
- Interacting jammed granular systems
- Theory of strains in auxetic materials
- Statistical physics of frictional grains: some simple applications of Edwards statistics
- Topological Analysis of Foams and tetrahedral structures