Computer simulations of nearest-neighbor distribution functions and related quantities for hard-sphere systems

One of the fundamental quantities which statistically characterizes a random system of interacting particles is the nearest-neighbor distribution function. We present computer-simulation results for two different types of nearest-neighbor distribution functions for random distributions of identical impenetrable (hard) spheres. We also report, for such systems, computer-simulation data for closely related quantities such as the associated cumulative distributions. From this information, we calculate the “mean nearest-neighbor distance” between particles. Our computer-simulation results are compared to the various sets of theoretical expressions derived recently by Torquato, Lu and Rubinstein. One of these sets of expressions is shown to be in excellent agreement with the simulation data.