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.

9 pages, 6 figures, to appear in PRE

References in corpus (4)

• Jamming versus Glass Transitions
• A Landscape Analysis of Constraint Satisfaction Problems
• 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

Cited by in corpus (2)

• Explicit Analytical Solution for Random Close Packing in d=2 and d=3
• Random Close Packing of Semi-Flexible Polymers in Two Dimensions: Emergence of Local and Global Order