Lineal measures of clustering in overlapping particle systems

J. Quintanilla, S. Torquato

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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 multiphase medium. We develop an exact methodology to determine L(z) for the particle phase of systems of overlapping particles, thus providing a measure of particle clustering in this prototypical model of continuum percolation. We describe this procedure for systems of overlapping disks and spheres with a polydispersivity of sizes and for randomly aligned equal-sized overlapping squares. We also study the effect of polydispersivity on the range of the lineal-path function. We note that the lineal-path function L(z) is a rigorous lower bound on the two-point cluster function [Formula Presented](z), which is not available analytically for overlapping particle models for spatial dimension d⩾2. By evaluating the second derivative of L(z), we then evaluate the chord-length distribution function for the particle phase. Computer simulations that we perform are in excellent agreement with our theoretical results.

Original languageEnglish (US)
Pages (from-to)4027-4036
Number of pages10
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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