Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T17:26:53.285Z Has data issue: false hasContentIssue false
  • English
  • Français

A constraint on the random packing of disks

Part of: Discrete geometry

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Hong Kong
*
∗ Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper addresses random packing of equal-sized disks in a manner such that no disk has a gap on its circumference large enough to accommodate an extra touching neighbour. This structure generalises the deterministic packing models discussed in classical geometry (Coxeter (1961), Hilbert and Cohn-Vossen (1952)). Relationships with the dual mosaic formed by joining the centres of touching disks are established. Constraints on the neighbourhood of disks and on the packing density are established.

Keywords

TESSELLATIONSMOSAICS

MSC classification

Primary: 52C15: Packing and covering in $2$ dimensions
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 263 - 268
Copyright
Copyright © Applied Probability Trust 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cowan, R. (1978) The use of the ergodic theorems in random geometry. Suppl. Adv. Appl. Prob. 10, 47–57.CrossRefGoogle Scholar
Cowan, R. (1980) Properties of ergodic random mosaic processes. Math. Nachr. 97, 89–102.CrossRefGoogle Scholar
Cowan, R. (1984) A model for the random packing of disks in the neighbourhood of one disk. SIAM J. Appl. Math. 44, 839–853.CrossRefGoogle Scholar
Coxeter, H. S. M. (1961) Introduction to Geometry. Wiley, New York.Google Scholar
Hilbert, D. and Cohn-Vossen, S. (1952) Geometry and the Imagination. Chelsea, New York.Google Scholar
Matschinski, M. (1954) Considérations statistiques sur les polygones et les polyèdres. Publ. Inst. Statist. Univ. Paris 3, 179–201.Google Scholar
Mecke, J. (1980) Palm methods for stationary random mosaics. In Combinational Principles in Stochastic Geometry, ed. Ambartzumian, R. V., pp. 124–132, Armenian Academy of Sciences, Erevan.Google Scholar
Stoyan, D. and Mecke, J. (1983) Stochastische Geometrie. Akademie-Verlag, Berlin.Google Scholar
Stoyan, D., Kendall, W. S. and Mecke, J. (1987) Stochastic Geometry and Its Applications. Wiley, New York; Akademie-Verlag, Berlin.Google Scholar