Clustering of randomly placed spheres

Abstract

Spheres of radius R are randomly situated in a homogeneous medium. Results are reported for computer calculations of cluster size distributions as a function of the average number of spheres per unit volume, λ. The results are compared with previous calculations of the same kind performed by Roberts and Storey. A concentration parameter, t, is denned as t =λR3. The value of the critical concentration at which the mean cluster size diverges is tc = 0.070, in some disagreement with the Roberts and Storey value of tc = 0.0889.