Nearest-neighbor distribution functions in many-body systems

Journal Article · Thu Feb 15 04:00:00 EST 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.2059· OSTI ID:7102276

Torquato, S ^[1]; Lu, B ^[2]; Rubinstein, J ^[3]

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1. Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (USA)
2. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (USA)
3. Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 (Israel)

The probability of finding a nearest neighbor at some given distance from a reference point in a many-body system of interacting particles is of importance in a host of problems in the physical as well as biological sciences. We develop a formalism to obtain two different types of nearest-neighbor probability density functions ({ital void} and {ital particle} probability densities) and closely related quantities, such as their associated cumulative distributions and conditional pair distributions, for many-body systems of {ital D}-dimensional spheres. For the special case of impenetrable (hard) spheres, we compute low-density expansions of each of these quantities and obtain analytical expressions for them that are accurate for a wide range of sphere concentrations. Using these results, we are able to calculate the mean nearest-neighbor distance for distributions of {ital D}-dimensional impenetrable spheres. Our theoretical results are found to be in excellent agreement with computer-simulation data.

• OSTI ID: 7102276
• Journal Information: Physical Review, A (General Physics); (USA), Journal Name: Physical Review, A (General Physics); (USA) Vol. 41:4; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DENSITY
DISTANCE
DISTRIBUTION FUNCTIONS
FUNCTIONS
INTERACTION RANGE
MANY-BODY PROBLEM
PARTICLES
PHYSICAL PROPERTIES
PROBABILITY