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

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.