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Random patterns of nonoverlapping convex grains

Part of: Stochastic processes Geometric probability and stochastic geometry Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Marianne Månsson  and
Mats Rudemo
Marianne Månsson*
Affiliation:
Chalmers University of Technology
Mats Rudemo*
Affiliation:
Chalmers University of Technology
*
∗ Postal address: Department of Mathematical Statistics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden.
∗ Postal address: Department of Mathematical Statistics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden.
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Abstract

Generalizing Matérn's (1960) two hard-core processes, marked point processes are considered as models for systems of varying-sized, nonoverlapping convex grains. A Poisson point process is generated and grains are placed at the points. The grains are supposed to have varying sizes but the same shape as a fixed convex grain, with spheres as an important special case. The pattern is thinned so that no grains overlap. We consider the thinning probability of a ‘typical point’ under various thinning procedures, the volume fraction of the resulting system of grains, the relation between the intensity of the point processes before and after thinning, and the corresponding size distributions. The study is inspired by problems in material fatigue, where cracks are supposed to be initiated by large defects.

Keywords

Germ-grain processnonoverlapping grainsradius distributionPoisson processvolume fractionmaterial fatigueMatérn's hard-core processes

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 718 - 738
Copyright
Copyright © Applied Probability Trust 2002 

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