Measure of clustering in continuum percolation: Computer-simulation of the two-point cluster function

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Abstract
The two-point cluster function C2(r1,r2) is determined for a D-dimensional interpenetrable-sphere continuum model from Monte Carlo simulations. C2(r1,r2) gives the probability of finding two points, at positions r1 and r2, in the same cluster of particles, and thus provides a measure of clustering in continuum-percolation systems. A pair of particles are said to be ‘‘connected’’ when they overlap. Results are reported for D=1,2, and 3 at selected values of the sphere number density ρ and of the impenetrability index λ, 0≤λ≤1. The extreme limits λ=0 and 1 correspond, respectively, to the cases of fully penetrable spheres (‘‘Swiss-cheese’’ model) and totally impenetrable spheres.