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Approximate variances associated with random configurations of hard spheres

Published online by Cambridge University Press:  14 July 2016

A. J. Girling
A. J. Girling*
Affiliation:
University of Birmingham
*
∗Postal address: Department of Statistics, The University of Birmingham, P.O. Box 363, Birmingham B15 2TT, U.K.
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Abstract

The Percus–Yevick approximation of classical liquid theory is employed to obtain variances associated with random configurations of equal spheres in ℝ3. The idea is illustrated by considering the number of spheres, and also the amount of hard material, contained within a fixed cylinder — an application of some practical value.

Keywords

GEOMETRICAL PROBABILITYHARD SPHERESSTATISTICAL MECHANICSPERCUSYEVICK APPROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 588 - 596
Copyright
Copyright © Applied Probability Trust 1982 

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References

Croxton, C. A. (1974) Liquid State Physics. Cambridge University Press, London.Google Scholar
Hammersley, J. M. (1951) On a certain type of integral associated with circular cylinders. Proc. R. Soc. London A 210, 98–110.Google Scholar
Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
Ornstein, L. S. and Zernike, F. (1914) Accidental deviations of density and opalescence at the critical point of a single substance. Proc. Akad. Sci. (Amsterdam) 17, 793–806. (Reprinted in The Equilibrium Theory of Classical Fluids , ed. Frisch, H. L. and Lebowitz, J. L., Benjamin, New York (1964).) Google Scholar
Percus, J. K. and Yevick, G. J. (1958) Analysis of classical statistical mechanics by means of collective co-ordinates. Phys. Rev. 110, 1–13.CrossRefGoogle Scholar
Thiele, E. (1963) Equation of state for hard spheres. J. Chem. Phys. 39, 474–479.CrossRefGoogle Scholar
Wertheim, M. S. (1963) Exact solution of the Percus–Yevick integral equation for hard spheres. Phys. Rev. Letters 10, 321–323.CrossRefGoogle Scholar
Wertheim, M. S. (1964) Analytic solution of the Percus–Yevick equation. J. Math. Phys. 5, 643–651.CrossRefGoogle Scholar
Yates, G. J. and Jones, R. C. (1979) The excitations of ferromagnets with liquid-like disorder. J. Phys. C Sol. Stat. Phys. 12, 1725–1753.CrossRefGoogle Scholar