Statistical theory of correlations in random packings of hard particles

Abstract

A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the $n$-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom-up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply the formalism to hard disks and predict the density of two-dimensional random close packing (RCP), ${\varphi }_{\mathrm{rcp}}=0.85\pm 0.01$, and random loose packing (RLP), ${\varphi }_{\mathrm{rlp}}=0.67\pm 0.01$. Our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data.

arXiv comment9 pages, 6 figures, to appear in PRE

References in corpus (16)

• Is Random Close Packing of Spheres Well Defined?
• Mean field theory of hard sphere glasses and jamming
• Random Packings of Frictionless Particles
• Jamming versus Glass Transitions
• A Landscape Analysis of Constraint Satisfaction Problems
• Mean-field theory of random close packings of axisymmetric particles
• Fundamental challenges in packing problems: from spherical to non-spherical particles
• A first-order phase transition at the random close packing of hard spheres
• Equilibrating temperature-like variables in jammed granular subsystems
• Granular dynamics in compaction and stress relaxation
• Model of random packings of different size balls
• Jamming in two-dimensional packings
• A Model for Granular Texture with Steric Exclusion
• Application of Edwards' statistical mechanics to high dimensional jammed sphere packings
• On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition
• Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders

Cited by in corpus (5)

• Explicit Analytical Solution for Random Close Packing in d=2 and d=3
• A geometric probabilistic approach to random packing of hard disks in a plane
• Random Close Packing of Semi-Flexible Polymers in Two Dimensions: Emergence of Local and Global Order
• Non-monotonic dependence of the friction coefficient on heterogeneous stiffness
• Chain structure of head-on collisions in boundary driven granular gases