“Percolation of disordered jammed sphere packings” was published in Journal of Physics A: Mathematical and Theoretical

Read the full paper: here

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 \(p_c = 0.3116(3)\), 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 \(\phi \), the threshold corresponds to a critical
value \(\phi_c = 0.199\). For the bond threshold, which apparently was not measured
before, we find \(p_c = 0.2424(3)\). 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.