The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics 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 ∼d 2 -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.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Nov 18 2010|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics