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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]

An apparatus has been developed that enables one to investigate the conservation of a linear momentum in a two-dimensional collision experiment. It was found that a cycloidal slide yields a constant rolling time of the ball, independent of the release position on the slide. The two balls, released on two slides of the same size at any desired angle, produce a two-dimensional collision. The initial velocity of the ball before the collision is determined by the height of the release position, and the final velocity after collision is determined from the height of the collision point from the ground and the horizontal distance that the ball travels before it reaches the ground. With this apparatus, the performance of a high precision experiment for momentum conservation during the collision process was achieved. [DOI: 10.1119/1.1397454]