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Probability models for liberation

Published online by Cambridge University Press:  14 July 2016

Pamela J. Davy
Pamela J. Davy*
Affiliation:
The Australian National University
*
∗ Postal address: Department of Statistics, 1AS, The Australian National University, P.O. Box 4, Canberra, ACT 2600, Australia.
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Abstract

An index lying between 0 and 1 is presented to describe the degree of liberation (or separation) of one component of a particulate material. It is shown how the index is related to the covariance function of the material, the distribution of shapes and sizes of the particles and to the interaction between fracture surfaces and the structure of the material. The variation of the index with the extent of crushing is investigated, together with the problem of stereological estimation. The index is evaluated for some particular probability models.

Keywords

RANDOM SETSTOCHASTIC PROCESSIMAGE ANALYSISSTEREOLOGY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 260 - 269
Copyright
Copyright © Applied Probability Trust 1984 

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References

Davy, P. J. (to appear) Inequalities for moment ratios of secant length.Google Scholar
Davy, P. J. (1983) Liberation of points, fibres and sheets. Proc. Conf. Stochastic Geometry, Geometric Statistics, and Stereology, Oberwolfach 1983. Teubner-Verlag, Leipzig.Google Scholar
Efron, B. (1982) The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF regional conference series in applied mathematics, No. 38, Society for Industrial and Applied Mathematics, Philadelphia.CrossRefGoogle Scholar
Enns, E. G. and Ehlers, P. F. (1978) Random paths through a convex region. J. Appl. Prob. 15, 144–152.Google Scholar
Gilbert, E. N. (1962) Random subdivisions of space into crystals. Ann. Math. Statist. 33, 958–972.CrossRefGoogle Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Miles, R. E. (1972) The random division of space. Suppl. Adv. Appl. Prob., 243–266.CrossRefGoogle Scholar
Serra, J. (1982) Image Analysis and Mathematical Morphology. Academic Press, New York.Google Scholar
Stoyan, D. (1979) Proofs of some fundamental formulas of stereology for non-Poisson grain models. Math. Operationsforsch. Statist. Ser. Optimization 10, 575–583.Google Scholar