Measures of clustering in systems of overlapping particles

Abstract

This paper reviews several advances in the measurement of clustering properties in the Boolean model, a prototypical model for many classes of random materials. First, we discuss and evaluate the lineal-path function, a microstructure function which provides a partial signature of clustering. We present a new expression for the lineal-path function of a Boolean model which suggests that novel bounds on the effective properties of random materials cannot be generated using this function. Second, we review various simulation and computational techniques that have recently been used to evaluate the percolation threshold of Boolean models.