Bernoulli cluster field: Voronoi tessellation

Ponížil, Petr; Saxl, Ivan

dc.title	Bernoulli cluster field: Voronoi tessellation	en
dc.contributor.author	Ponížil, Petr
dc.contributor.author	Saxl, Ivan
dc.relation.ispartof	Applications of Mathematics
dc.identifier.issn	0862-7940 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2002
utb.relation.volume	47
utb.relation.issue	2
dc.citation.spage	157
dc.citation.epage	167
dc.type	article
dc.language.iso	en
dc.publisher	Matematický ústav Akademie věd České republiky (MÚ)	cs
dc.identifier.doi	10.1023/A:1021737219136
dc.relation.uri	http://www.springerlink.com/content/n166602621p12662/
dc.subject	shlukový bodový proces	cs
dc.subject	Voronoiova teselace	cs
dc.subject	indukovaná teselace	cs
dc.subject	variační koeficient velikosti buněk	cs
dc.subject	cluster points process	en
dc.subject	Voronoi tesselllation	en
dc.subject	induced tesselation	en
dc.subject	coefficients of variation of cell size characteristics	en
dc.description.abstract	Proposed new point process (p-thinned Neymann-Scott process with the retention of the parent point) generates 3D Voronoi tessellations with extremely high variance of the original and induced (in sectional linear flats) tessellations. An approximate numerical model is presented.	en
utb.faculty	Faculty of Technology
dc.identifier.uri	http://hdl.handle.net/10563/1000086
utb.identifier.rivid	RIV/70883521:28110/02:63500516
utb.identifier.obdid	11052332
utb.identifier.scopus	2-s2.0-84867966735
utb.source	j-riv
utb.contributor.internalauthor	Ponížil, Petr
utb.fulltext.affiliation	Ivan Saxl, Praha, Petr Ponížil, Zlín Authors’ addresses: I. Saxl, Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, CZ 115 67 Praha 1, Czech Republic, e-mail: saxl@math.cas.cz; P. Ponížil, Tomas Bata University in Zlin, Náměstí TGM 275, CZ 762 72 Zlín, Czech Republic, e-mail: ponizil@ft.utb.cz.
utb.fulltext.dates	-
utb.fulltext.references	[1] V. Horálek: ASTM grain size model and related random tessellation models. Materials Characterization 25 (1990), 263–284. [2] J. Møller: Random Johnson-Mehl tessellations. Adv. in Appl. Probab. 24 (1992), 814–844. [3] J. Møller: Lectures on Random Voronoi Tessellations. Lecture Notes in Statistics 87. Springer-Verlag, New York, 1994. [4] A. Okabe, B. Boots and K. Sugihara: Spatial Tessellations. J. Wiley & Sons, Chichester, 1992. [5] P. Ponížil, I. Saxl: Grain size estimation II: Other models, variances. In: STERMAT’2000, Proceedings of the Sixth Int. Conf. “Stereology and Image Analysis in Materials Science” (L. Wojnar, K. Ro´zniatowski, eds.). Polish Society for Stereology, Cracow, 2000, pp. 379–384. [6] I. Saxl, P. Ponížil: 3D Voronoi tessellations of cluster fields. Acta Stereol. 17 (1998), 237–246. [7] I. Saxl, P. Ponížil: 3D Voronoi tessellations generated by Poisson and lattice of cluster fields. Acta Stereol. 17 (1998), 247–252. [8] I. Saxl, P. Ponížil: Random tessellations: Stochastic simulations and applications. Proceedings of the workshop “Programs and Algorithms of Numerical Mathematics”, Libverda 2000. Mathematical Institute of the Academy of Sciences of the Czech Republic, Praha, 2000, pp. 150–161. [9] I. Saxl, K. Sülleiová and P. Ponížil: 3D simulations of intergranular fracture. In: Proceedings of the International Conference “Fractography 2000”, Vysoké Tatry, 15–18. 10. 2000 (L. Parilák, ed.). Inst. Mat. Res., Slovak Acad. Sci., Košice, 2000, pp. 94–107. [10] I. Saxl, K. Sülleiová and P. Ponížil: Simulating grain size estimation. Metallic Materials 39 (2001), 396–409. [11] D. Stoyan, W. S. Kendall and J. Mecke: Stochastic Geometry and its Applications. J. Wiley & Sons, New York, 1995. [12] D. Stoyan, H. Stoyan: Fractals, Random Shapes and Point Fields. J. Wiley & Sons, Chichester, 1994. [13] A. Ševčík, K. Sülleiová, M. Besterci, I. Kohútek and I. Saxl: Grain size estimation in steels. Metallic Materials 40 (2002), in press. [14] G. F. Vander Voort: Grain size measurement. In: Practical Applications of Quantitative Metallography. ASTM STP 839, ASTM, Philadelphia, 1982, pp. 85–131. [15] O. Velgosová, I. Saxl and M. Besterci: Microstructural characteristics of dispersion strengthned Cu-based system. In: Proc. 3rd International Conference “Materials Structure & Micromechanics of Fracture” (P. Šandera, ed.). Vutim, Brno University of Technology, 2001, pp. 223–231, CD ROM.
utb.fulltext.sponsorship	This work was supported by the Grant No. 201/99/0269 of the Grant Agency of the Czech Republic (the first author) and by the Grant No. 96108 of the Ministry of Education of the Czech Republic (the second author).
utb.fulltext.projects	GACR 201/99/0269
utb.fulltext.projects	MSM 96108