Properties of chord length distributions across ordered and disordered packing of hard disks.

Chord length distributions across packings--random or not--of equal hard disks have a universal divergence which is proportional to n(c)/square root of l for small chords, where n(c) is the mean number of contacts. A similar behavior is derived for a population of polydisperse disks. Monte Carlo simulations across various kinds of regular and random packings are in full agreement with the theoretical predictions.

[1]  Alain Mazzolo,et al.  On the properties of the chord length distribution, from integral geometry to reactor physics , 2003 .

[2]  Y. Pomeau,et al.  Contacts in random packings of spheres , 1985 .

[3]  Yaron Danon,et al.  Application of Monte Carlo Chord-Length Sampling Algorithms to Transport through a Two-Dimensional Binary Stochastic Mixture , 2003 .

[4]  Talbot,et al.  Restructuring effects in irreversible deposition of spheres on a plane. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Paul Meakin,et al.  Geometrical properties of a random packing of hard spheres , 1991 .

[6]  Thomas M Truskett,et al.  Is random close packing of spheres well defined? , 2000, Physical review letters.

[7]  A. Gervois,et al.  Geometrical properties of disordered packings of hard disks , 1986 .

[8]  T. I. Quickenden,et al.  Random packing in two dimensions and the structure of monolayers , 1974 .

[9]  S. Torquato,et al.  Lineal-path function for random heterogeneous materials. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[10]  W. Visscher,et al.  Random Packing of Equal and Unequal Spheres in Two and Three Dimensions , 1972, Nature.

[11]  S. Torquato,et al.  Multiplicity of Generation, Selection, and Classification Procedures for Jammed Hard-Particle Packings † , 2001 .

[12]  Alain Mazzolo,et al.  Properties of chord length distributions of nonconvex bodies , 2003 .

[13]  S. Torquato,et al.  Chord-length distribution function for two-phase random media. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.