Distribution of volumes and coordination numbers in jammed matter: mesoscopicensemble

Abstract

We investigate the distribution of the volume and coordination number associated to eachparticle in a jammed packing of monodisperse hard spheres using the mesoscopic ensembledeveloped in Song et al (2008 Nature 453 606). Theory predicts an exponentialdistribution of the orientational volumes for random close packings (RCP) and randomloose packings (RLP). A comparison with computer generated packings revealsdeviations from the theoretical prediction in the volume distribution, which can bebetter modeled by a compressed exponential function. On the other hand, theaverage of the volumes is well reproduced by the theory, leading to good predictionsof the limiting densities of RCP and RLP. We discuss a more exact theory tocapture the volume distribution in its entire range. Finally, we consider an extendedensemble to calculate the coordination number distribution which is shown tobe of an exponential and inverse exponential form for coordinations larger andsmaller than the average, respectively, in reasonable agreement with the simulateddata.