Document Type
Article
Publication Date
5-2014
Department 1
Physics
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), φrcp = 0.85 ± 0.01, and random loose packing (RLP), φrlp = 0.67 ± 0.01. Our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data.
Copyright Note
This is the publisher's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
DOI
10.1103/PhysRevE.89.052207
Recommended Citation
Jin, Yuliang, James G. Puckett and Hernan A. Makse. "Statistical Theory of Correlations in Random Packings of Hard Particles." Physical Review E 89:052207 (May 2014).
Required Publisher's Statement
Original version is available from the publisher at: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.052207