Statistical Geometry of Random Heaps of Equal Hard Spheres

The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

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Statistical geometry of some dense random packing of hard spheres model structures

Journal of Non-Crystalline Solids ◽

10.1016/0022-3093(86)90255-3 ◽

1986 ◽

Vol 81 (1-2) ◽

pp. 13-28 ◽

Cited By ~ 3

Author(s):

L. Takács

Keyword(s):

Hard Spheres ◽

Random Packing ◽

Statistical Geometry ◽

Model Structures

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Random packings and the structure of simple liquids. I. The geometry of random close packing

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1970.0189 ◽

1970 ◽

Vol 319 (1539) ◽

pp. 479-493 ◽

Cited By ~ 1075

Keyword(s):

Hard Spheres ◽

Real Space ◽

Close Packing ◽

Topological Properties ◽

Statistical Geometry ◽

Science And Engineering ◽

Simple Liquids ◽

Structure Of Simple Liquids ◽

Structural Descriptions ◽

Random Packings

In his Bakerian Lecture, Bernal (1964) discussed those ideas of restricted irregularity which are physically realized in random packings of equal hard spheres, with particular reference to the structure of simple liquids. He stressed the need for a science of ‘statistical geometry ’, and took the first steps himself by proposing possible ways of describing such arrays. In this paper, these and other associated ideas are briefly described and extended by deriving an equivalent set of polyhedral subunits essentially inverse to the packing in real space. Examination of two independent high density arrays demonstrates the repro-ducibility of certain metrical and topological properties of these polyhedra, and their correlations over larger elements of volume. As a result, several possible ‘descriptive parameters’ are proposed. Although these essentially ‘numerical’ characteristics facilitate sensitive structural descriptions of any assembly of micro- and macroscopic subunits, we are still unable to characterize an irregular array in formal mathematical terms. Such a formulation of statistical geometry could be a powerful tool for tackling important problems in many branches of science and engineering.

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