Iterated Boolean random varieties and application to fracture statistics models
Applications of Mathematics (2016)
- Volume: 61, Issue: 4, page 363-386
- ISSN: 0862-7940
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topJeulin, Dominique. "Iterated Boolean random varieties and application to fracture statistics models." Applications of Mathematics 61.4 (2016): 363-386. <http://eudml.org/doc/283400>.
@article{Jeulin2016,
abstract = {Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in $ \mathbb \{R\}^\{2\}$ and $\mathbb \{R\} ^\{3\}$ and on random planes in $ \mathbb \{R\}^\{3\}$. The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set $K$ and the Choquet capacity $T(K)$ are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results on the probability of fracture of convex specimens in the framework of the weakest link assumption are derived, and used to compare geometrical effects on the sensitivity of materials to fracture.},
author = {Jeulin, Dominique},
journal = {Applications of Mathematics},
keywords = {Boolean model; Boolean varieties; Cox process; weakest link model; fracture statistics; mathematical morphology; Boolean model; Boolean varieties; Cox process; weakest link model; fracture statistics; mathematical morphology},
language = {eng},
number = {4},
pages = {363-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Iterated Boolean random varieties and application to fracture statistics models},
url = {http://eudml.org/doc/283400},
volume = {61},
year = {2016},
}
TY - JOUR
AU - Jeulin, Dominique
TI - Iterated Boolean random varieties and application to fracture statistics models
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 363
EP - 386
AB - Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in $ \mathbb {R}^{2}$ and $\mathbb {R} ^{3}$ and on random planes in $ \mathbb {R}^{3}$. The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set $K$ and the Choquet capacity $T(K)$ are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results on the probability of fracture of convex specimens in the framework of the weakest link assumption are derived, and used to compare geometrical effects on the sensitivity of materials to fracture.
LA - eng
KW - Boolean model; Boolean varieties; Cox process; weakest link model; fracture statistics; mathematical morphology; Boolean model; Boolean varieties; Cox process; weakest link model; fracture statistics; mathematical morphology
UR - http://eudml.org/doc/283400
ER -
References
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