LINEAL MEASURES OF CLUSTERING IN OVERLAPPING PARTICLE-SYSTEMS

The lineal-path function L(z) gives the probability of finding a Line segment of length z entirely in one of the phases of a disordered mult iphase medium. We develop an exact methodology to determine L(z) for t he particle phase of systems of overlapping particles, thus providing a measure of particle clustering in this prototypical model of continu um percolation. We describe this procedure for systems of overlapping disks and spheres with a polydispersivity of sizes and for randomly al igned equal-sized overlapping squares. We also study the effect of pol ydispersivity on the range of the lineal-path function. We note that t he lineal-path function L(z) is a rigorous lower bound on the two-poin t cluster function C-2(z), which is not available analytically for ove rlapping particle models for spatial dimension d greater than or equal to 2. By evaluating the second derivative of L(z), we then evaluate t he chord-length distribution function for the particle phase. Computer simulations that we perform are in excellent agreement with our theor etical results.