Distribution of volumes and coordination numbers in jammed matter: Mesoscopic ensemble

Ping Wang, Chaoming Song, Yuliang Jin, Kun Wang, Hernán A. Makse

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard spheres using the mesoscopic ensemble developed in Song et al (2008 Nature 453 606). Theory predicts an exponential distribution of the orientational volumes for random close packings (RCP) and random loose packings (RLP). A comparison with computer generated packings reveals deviations from the theoretical prediction in the volume distribution, which can be better modeled by a compressed exponential function. On the other hand, the average of the volumes is well reproduced by the theory, leading to good predictions of the limiting densities of RCP and RLP. We discuss a more exact theory to capture the volume distribution in its entire range. Finally, we consider an extended ensemble to calculate the coordination number distribution which is shown to be of an exponential and inverse exponential form for coordinations larger and smaller than the average, respectively, in reasonable agreement with the simulated data.

Original languageEnglish (US)
Article numberP12005
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number12
StatePublished - Dec 2010
Externally publishedYes


  • Jamming and packing

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Distribution of volumes and coordination numbers in jammed matter: Mesoscopic ensemble'. Together they form a unique fingerprint.

Cite this