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We present computer simulation results of the pair-connectedness function and the two-point cluster function for random media, consisted of equisized particles of adhesive sphere model. The pair-connectedness function P(r1,r2) is defined as that the quantity ρ2 P(r1,r2)dr1 dr2 represents the probability of finding two particles centered in the volume elements dr1 and dr2 about r1 and r2, respectively, and are physically connected. On the other hand, the two-point cluster function C2(r1,r2) gives the probability of finding two points at positions r1 and r2, in the same cluster of one of the phases. Data are compared with the analytical results from the Percus–Yevick (PY) approximation. In low densities, Monte Carlo data reasonably agree with the PY approximation results, while in high densities near percolation thresholds, data significantly deviate from the analytical results. [ABSTRACT FROM AUTHOR]

We devise a new algorithm to obtain the pair-connectedness function P(r) for continuum-percolation models from computer simulations. It is shown to converge rapidly to the infinite-system limit, even near the percolation threshold, thus providing accurate estimates of P(r) for a wide range of densities. We specifically consider an interpenetrable-particle model (referred to as the penetrable-concentric-shell model) in which D-dimensional spheres (D=2 or 3) of diameter σ are distributed with an arbitrary degree of impenetrability parameter λ, 0≤λ≤1. Pairs of particles are taken to be ‘‘connected’’ when the interparticle separation is less than σ. The theoretical results of Xu and Stell for P(r) in the case of fully penetrable spheres (λ=0) are shown to be in excellent agreement with our simulations. We also compute the mean cluster size as a function of density and λ for the case of 2D, and, from these data, estimate the respective percolation thresholds. [ABSTRACT FROM AUTHOR]

Computer-simulation results are reported for the porosity of a model of two-phase random media composed of identical D-dimensional spheres (D=2 or 3) distributed with an arbitrary degree of impenetrability λ, 0≤λ≤1; λ=0 corresponding to randomly centered or ‘‘fully penetrable’’ particles and λ=1 corresponding to totally impenetrable particles. We specifically consider the D-dimensional penetrable-concentric-shell model in which each sphere of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable concentric shell of thickness (1-λ)σ/2. We develop two independent techniques to sample for the porosity. Simulation results agree with known exact results for the extreme limits of λ=0 and λ=1 up to three significant figures. The results for intermediate λ are new and compare favorably with approximate analytical expressions obtained by Rikvold and Stell. [ABSTRACT FROM AUTHOR]

We test accuracies of the Percus-Yevick (PY) approximation for percolation thresholds and long-range correlated probability functions for continuum media of the adhesive sphere model. We clarify the universality of the continuum percolation of such a model and estimate the percolation thresholds for selected values of the adhesiveness parameter τ. We then calculate the pair-connectedness function and the two-point cluster function at percolation point and compare them with the analytical predictions by the PY approximation. We find that the PY approximation yields the pecolation points overestimated for τ>0.161 and underestimated for τ<0.161. The analytical calculations of the probability functions exhibit fairly good agreement with the Monte Carlo data for τ=0.161. However, for other values of τ, the analytical results show marked deviations from the Monte Carlo data. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]