Close to close packing

Oliver Penrose; George Stell

doi:10.1023/A:1018679309775

Close to close packing

Oliver Penrose, George Stell

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/m_cp= 1 -const · (N_cp/N - 1), where N is the number of occupied sites, m_cp is the value of m at close packing, and N_cp is the value of N at close packing. An analogous result exists for hard disks in the plane.

Original language	English
Pages (from-to)	89-95
Number of pages	7
Journal	Journal of Statistical Physics
Volume	100
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1018679309775
Publication status	Published - 1 Jul 2000

Keywords

Close packing
Hard disks
Inequalities
Lattice models
Nearest neighbor exclusion

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N2 - For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/mcp= 1 -const · (Ncp/N - 1), where N is the number of occupied sites, mcp is the value of m at close packing, and Ncp is the value of N at close packing. An analogous result exists for hard disks in the plane.

AB - For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/mcp= 1 -const · (Ncp/N - 1), where N is the number of occupied sites, mcp is the value of m at close packing, and Ncp is the value of N at close packing. An analogous result exists for hard disks in the plane.

KW - Close packing

KW - Hard disks

KW - Inequalities

KW - Lattice models

KW - Nearest neighbor exclusion

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JF - Journal of Statistical Physics

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Close to close packing

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Keywords

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