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Title: Bernoulli cluster field: Voronoi tessellations (English)
Author: Saxl, Ivan
Author: Ponížil, Petr
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 47
Issue: 2
Year: 2002
Pages: 157-167
Summary lang: English
Category: math
Summary: A new point process is proposed which can be viewed either as a Boolean cluster model with two cluster modes or as a $p$-thinned Neyman-Scott cluster process with the retention of the original parent point. Voronoi tessellation generated by such a point process has extremely high coefficients of variation of cell volumes as well as of profile areas and lengths in the planar and line induced tessellations. An approximate numerical model of tessellation characteristics is developed for the case of small cluster size; its predictions are compared with the results of computer simulations. Tessellations of this type can be used as models of grain structures in steels. (English)
Keyword: cluster point process
Keyword: Voronoi tessellation
Keyword: induced tessellation
Keyword: coefficients of variation of cell size characteristics
MSC: 60D05
MSC: 60G55
MSC: 60–04
idZBL: Zbl 1090.60500
idMR: MR1894667
DOI: 10.1023/A:1021737219136
Date available: 2009-09-22T18:09:30Z
Last updated: 2020-07-02
Stable URL:
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