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Packing fraction and measures of disorder of ultradense irregular packings of equal spheres. I. Nearly ordered packing

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Packing densities, φ, from 0.74047 to 0.700 are obtained by randomly moving the spheres in a simulated face-centred cubic (f.c.c.) lattice and using the force-biased algorithm (FBA) to remove overlaps. The Hausdorff distance, h, between the disordered packing and its lattice parent is one measure of disorder. Both φ and h are random variables which are functions of the distribution of the initial perturbations and the parameters of the FBA. Using h and other measures, we show that density varies continuously downward from the density of f.c.c. packing while the associated disorder varies continuously upward from zero. The reduction in density is roughly linear in h for h « 1. Furthermore, the disorder for a given reduction in density is much more than expected.

Affiliations: 1: Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick EOA 3C0, Canada


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