Nearest-neighbor statistics for packings of hard spheres and disks

Journal Article · Sat Apr 01 04:00:00 EST 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.51.3170· OSTI ID:27840

Torquato, S ^[1]

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1. Princeton Materials Institute and Department of Civil Engineering Operations Research, Princeton University, Princeton, New Jersey 08540 (United States)

The probability of finding a nearest neighbor at some radial distance from a given particle in a system of interacting particles is of fundamental importance in a host of fields in the physical as well as biological sciences. A procedure is developed to obtain analytical expressions for nearest-neighbor probability functions for random isotropic packings of hard {ital D}-dimensional spheres that are accurate for all densities, i.e., up to the random close-packing fraction. Using these results, the mean nearest-neighbor distance {lambda} as a function of the packing fraction is computed for such many-body systems and compared to rigorous bounds on {lambda} derived here. Our theoretical results are found to be in excellent agreement with available computer-simulation data.

• OSTI ID: 27840
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 51; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANALYTICAL SOLUTION
DENSITY
DISTRIBUTION FUNCTIONS
HARD-SPHERE MODEL
RANDOMNESS
SOLIDS
STATISTICS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS