Bernoulli cluster field: Voronoi tessellations
Applications of Mathematics (2002)
- Volume: 47, Issue: 2, page 157-167
- ISSN: 0862-7940
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topSaxl, Ivan, and Ponížil, Petr. "Bernoulli cluster field: Voronoi tessellations." Applications of Mathematics 47.2 (2002): 157-167. <http://eudml.org/doc/33110>.
@article{Saxl2002,
abstract = {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.},
author = {Saxl, Ivan, Ponížil, Petr},
journal = {Applications of Mathematics},
keywords = {cluster point process; Voronoi tessellation; induced tessellation; coefficients of variation of cell size characteristics; cluster point process; Voronoi tessellation; induced tessellation; coefficients of variation of cell size characteristics},
language = {eng},
number = {2},
pages = {157-167},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bernoulli cluster field: Voronoi tessellations},
url = {http://eudml.org/doc/33110},
volume = {47},
year = {2002},
}
TY - JOUR
AU - Saxl, Ivan
AU - Ponížil, Petr
TI - Bernoulli cluster field: Voronoi tessellations
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 2
SP - 157
EP - 167
AB - 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.
LA - eng
KW - cluster point process; Voronoi tessellation; induced tessellation; coefficients of variation of cell size characteristics; cluster point process; Voronoi tessellation; induced tessellation; coefficients of variation of cell size characteristics
UR - http://eudml.org/doc/33110
ER -
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