| 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:
|
http://hdl.handle.net/10338.dmlcz/134492 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] A. Okabe, B. Boots and K. Sugihara: Spatial Tessellations.J. Wiley & Sons, Chichester, 1992. MR 1210959 |
| Reference:
|
[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. Roźniatowski (eds.), Polish Society for Stereology, Cracow, 2000, pp. 379–384. |
| Reference:
|
[6] I. Saxl, P. Ponížil: 3D Voronoi tessellations of cluster fields.Acta Stereol. 17 (1998), 237–246. |
| Reference:
|
[7] I. Saxl, P. Ponížil: 3D Voronoi tessellations generated by Poisson and lattice of cluster fields.Acta Stereol. 17 (1998), 247–252. |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[10] I. Saxl, K. Sülleiová and P. Ponížil: Simulating grain size estimation.Metallic Materials 39 (2001), 396–409. |
| Reference:
|
[11] D. Stoyan, W. S. Kendall and J. Mecke: Stochastic Geometry and its Applications.J. Wiley & Sons, New York, 1995. MR 0895588 |
| Reference:
|
[12] D. Stoyan, H. Stoyan: Fractals, Random Shapes and Point Fields.J. Wiley & Sons, Chichester, 1994. MR 1297125 |
| Reference:
|
[13] A. Ševčík, K. Sülleiová, M. Besterci, I. Kohútek and I. Saxl: Grain size estimation in steels.Metallic Materials 40 (2002), in press. |
| Reference:
|
[14] G. F. Vander Voort: Grain size measurement.In: Practical Applications of Quantitative Metallography, ASTM STP 839, ASTM, Philadelphia, 1982, pp. 85–131. |
| Reference:
|
[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. |
| . |
