McNamara Sean, Richard Patrick, de Richter Sébastien Kiesgen, Le Caër Gérard, Delannay Renaud
Institut de Physique de Rennes, UMR UR1-CNRS 6251, Université de Rennes I, Bât 11A, 35042 Rennes Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031301. doi: 10.1103/PhysRevE.80.031301. Epub 2009 Sep 10.
Recently, Dean and Lefèvre [Phys. Rev. Lett. 90, 198301 (2003)] developed a method for testing the statistical mechanical theory of granular packings proposed by Edwards and co-workers [Physica A 157, 1080 (1989); Phys. Rev. E 58, 4758 (1998)]. The method relies on the prediction that the ratio of two overlapping volume histograms should be exponential in volume. We extend the method by showing that one can also calculate the entropy of the packing and also that the method can yield false positive results when the histograms are Gaussians with nearly identical variances. We then apply the method to simulations and experiments of granular compaction. The distribution of global volumes (the volume of the entire packing) is nearly Gaussian and it is difficult to conclude if the theory is valid. On the other hand, the distribution of Voronoï volumes clearly obeys the theoretical prediction.
