Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.

Journal Article (Journal Article)

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension d using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling ϕ∼d2(-d) is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

Full Text

Duke Authors

Cited Authors

  • Jin, Y; Charbonneau, P; Meyer, S; Song, C; Zamponi, F

Published Date

  • November 18, 2010

Published In

Volume / Issue

  • 82 / 5 Pt 1

Start / End Page

  • 051126 -

PubMed ID

  • 21230456

Electronic International Standard Serial Number (EISSN)

  • 1550-2376

International Standard Serial Number (ISSN)

  • 1539-3755

Digital Object Identifier (DOI)

  • 10.1103/physreve.82.051126


  • eng