Clustering properties of d -dimensional overlapping spheres

J. Quintanilla, S. Torquato

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38 Scopus citations


Various clustering properties of d-dimensional overlapping (i.e., Poisson distributed) spheres are investigated. We evaluate nk, the average number of connected clusters of k particles (called k-mers) per unit particle, for k = 2,3,4 and vk, the expected volume of a k-mer, for k = 2,3,4 by using our general expressions for these quantities for d = 1, 2, or 3. We use these calculations to obtain low-density expansions of various averaged cluster numbers and volumes, which can be obtained from the nk and vk. We study the behavior of these cluster statistics as the percolation threshold is approached from below, and we rigorously show that two of these averaged quantities do not diverge for d≥2.

Original languageEnglish (US)
Pages (from-to)5331-5339
Number of pages9
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
StatePublished - 1996

All Science Journal Classification (ASJC) codes

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


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