Percolation of disordered jammed sphere packings

Robert M. Ziff, Salvatore Torquato

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44 Scopus citations


We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato-Jiao algorithm. For the site threshold, which gives the fraction of conducting versus non-conducting spheres necessary for percolation, we find pc = 0.3116(3), consistent with the 1979 value of Powell 0.310(5) and identical within errors to the threshold for the simplecubic lattice, 0.311 608, which shares the same average coordination number of 6. In terms of the volume fraction φ, the threshold corresponds to a critical value φc = 0.199. For the bond threshold, which apparently was not measured before, we find pc = 0.2424(3). To find these thresholds, we considered two shape-dependent universal ratios involving the size of the largest cluster, fluctuations in that size, and the second moment of the size distribution; we confirmed the ratios universality by also studying the simple-cubic lattice with a similar cubic boundary. The results are applicable to many problems including conductivity in random mixtures, glass formation, and drug loading in pharmaceutical tablets.

Original languageEnglish (US)
Article number085001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
StatePublished - Jan 20 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • filling factor
  • jammed spheres
  • percolation


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