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Emergence of Gamma distributions in granular materials and packing models T. Aste and T. Di Matteo

Summary: Emergence of Gamma distributions in granular materials and packing models
T. Aste and T. Di Matteo
Department of Applied Mathematics, The Australian National University, 0200 Canberra, ACT, Australia
Received 19 June 2007; revised manuscript received 3 December 2007; published 29 February 2008
We study the distribution of volume fluctuations in experiments and numerical simulations concerning
equal-sized sphere packings prepared with different techniques. We show that the distribution of the local
volumes Voronoļ cells and also the distributions of the global volumes whole samples follow remarkably
well a shifted and rescaled Gamma distribution that we name a k-Gamma distribution. Such agreement is
robust over a broad range of packing fractions and it is observed for several distinct systems. This distribution
is characterized by the average packing fraction and a shape parameter "k" which is very sensitive to changes
in the structural organization. A statistical mechanics approach predicts such k-Gamma distribution at statistical
equilibrium and it links the parameter k with the number of elementary cells which are exchanging volume
during the system preparation. The thermodynamical equivalent of k and its relation with the "granular tem-
perature" are also discussed.
DOI: 10.1103/PhysRevE.77.021309 PACS number s : 45.70. n, 45.70.Cc, 81.05.Rm
Granular materials are central in a very wide range of
domains from agriculture to the pharmaceutical industry, but,
despite such a relevance in most fields of human activity and
their ubiquitous presence in scientific research areas, their


Source: Aste, Tomaso - Department of Applied Mathematics, Australian National University
Di Matteo, Tiziana - Department of Mathematics, King's College London


Collections: Materials Science; Mathematics; Physics