Monte Carlo Simulations of Pair Distribution Functions of Dense Discrete Random Media With Multiple Sizes of Particles

Abstract

In a dense discrete random medium, the propagation and scattering of waves are affected by the statistics of the particle positions. For the case of particles of finite size, the positions of the particles relative to each other in the presence of other particles are correlated and the second order statistics are described by the pair distribution functions. In this paper, we perform Monte Carlo simulations of pair distribution functions of dense discrete random media consisting of particles of multiple sizes. The Metropolis technique and the sequential random addition of particles methods are used to generate a series of configurations through random processes. The pair distribution functions are calculated by counting the average occurrence of pair separation of particles. The Monte Carlo results of the particle pair distribution functions are illustrated and are compared with the results of the Percus-Yevick approximation. The results from the two Monte Carlo methods are found to be in good agreement.