Monte Carlo calculations of cluster statistics in continuum models of composite morphology

We describe a simple and efficient algorithm for sampling physical cluster statistics in Monte Carlo simulations of continuum morphology models. The algorithm produces a variety of information including the pair connectedness function, cluster size distribution, and mean cluster size. The approach can be applied to any system, given a definition of a physical cluster for that system. Results are presented for two types of models commonly used in studies of percolation phenomena; randomly centered spheres and the concentric shell (extended sphere) model. The simulation results are used to assess the accuracy of the predictions of the Percus-Yevick closure of the Ornstein-Zernike equation for the pair connectedness function.