Random patterns of nonoverlapping convex grains

Advances in Applied Probability

Volumn 34, Issue 4, 2002, Pages 718-738

  Månsson, Marianne ^a   Rudemo, Mats ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Germ grain process; Mat rn's hard core processes; Material fatigue; Nonoverlapping grains; Poisson process; Radius distribution; Volume fraction

Indexed keywords

FATIGUE OF MATERIALS; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; POISSON DISTRIBUTION; VOLUME FRACTION;

NONOVERLAPPING GRAINS;

RANDOM PROCESSES;

EID: 0036955144     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1037990950     Document Type: Article

References (32)

1. BERWALD, L. AND VARGA, O. (1937). Integralgeometrie XXIV. Über die Schiebungen im Raum. Math. Z. 42, 710-736.
2. BETKE, U. (1992). Mixed volumes of polytopes. Arch. Math. 58, 388-391.
3. BLASCHKE, W. (1937). Integralgeometrie XXI. Über Schiebungen. Math. Z. 42, 399-410.
4. BONNESEN, T. AND FENCHEL, W. (1948). Theorie der Konvexen Körper. Chelsea, New York.
5. DALEY, D. J., STOYAN, H. AND STOYAN, D. (1999). The volume fraction of a Poisson germ model with maximally non-overlapping spherical grains. Adv. Appl. Prob. 31, 610-624.
6. EGGLESTON, H. G. (1963). Convexity. Cambridge University Press.
7. EMBRECHTS, P., KLÜPPELBERG, C. AND MIKOSCH, T. (1997). Modelling Extremal Events. Springer, Berlin.
8. HÄGGSTRÖM, O. AND MEESTER, R. (1996). Nearest neighbour and hard sphere models in continuum percolation. Random Structures Algorithms 9, 295-315.
9. JEULIN, D. (1989). Morphological modeling of images by sequential random functions. Signal Process. 16, 403-431.
10. JEULIN, D. (1993). Random models for morphological analysis of powder. J. Microscopy 172, 13-21.
11. JEULIN, D. (1998). Probabilistic models of structures. In PROBAMAT-21st Century: Probabilities and Materials, ed. G. N. Frantziskonis, Kluwer, Dordrecht, pp. 233-257.
12. MASE, S. (1985). On the possible form of size distributions for Gibbsian processes of mutually non-intersecting discs. J. Appl. Prob. 23, 649-659.
13. MATÉRN, B. (1960). Spatial Variation (Meddelanden Statens Skogsforskningsinst. 49). Statens Skogsforskningsinstitut, Stockholm. Second edition: Springer, Berlin, 1986.
14. MATHERON, G. (1975). Random Sets and Integral Geometry. John Wiley, New York.
15. MEAKIN, P. AND JULLIEN, R. (1992a). Random-sequential adsorption of disks of different sizes. Phys. Rev. A 46, 2029-2038.
16. MEAKIN, P. AND JULLIEN, R. (1992b). Random sequential adsorption of spheres of different sizes. Physica A 187, 475-488.
17. 3. Biometrika 52, 636-639.
18. MURAKAMI, Y. AND BERETTA, S. (1999). Small defects and inhomogeneities in fatigue strength: experiments, models and statistical implications. Extremes 2, 123-147.
19. RÉISS, H., FRISCH, H. L. AND LEBOWITZ, J. (1959). Statistical mechanics of rigid spheres. J. Chem. Phys. 31, 369-380.
20. SANTALÓ, L. A. (1976). Integral Geometry and Geometric Probability. Addison-Wesley, Reading, MA.
21. SCHNEIDER, R. (1993). Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press.
22. STIENEN, H. (1982). Die Vergroeberung von Karbiden in reinen Eisen-Kohlenstoff Staehlen. Dissertation, RWTH Aachen.
23. STOYAN, D. (1990). Stereological formulae for a random system of non-overlapping spheres. Statistics 22, 449-462.
24. STOYAN, D. (1998). Random sets: models and statistics. Internat. Statist. Rev. 66, 1-27.
25. STOYAN, D. AND SCHLATER, M. (2000). Random sequential adsorption: relationship to dead leaves and characterization of variability. J. Statist. Phys. 100, 969-979.
26. STOYAN, D. AND STOYAN, H. (1985). On one of Matérn's bard-core point process models. Math. Nachr. 122, 205-214.
27. STOYAN, D., KENDALL, W. S. AND MECKE, J. (1995). Stochastic Geometry and Its Applications, 2nd edn. John Wiley, Chichester.
28. TALBOT, J., TARJUS, G., VAN TASSEL, P. R. AND VIOT, P. (2000). From car parking to protein adsorption: an overview of sequential adsorption processes. Colloids Surfaces A 165, 287-324.
29. TORQUATO, S. (1995). Nearest neighbor statistics for packings of hard spheres and disks. Phys. Rev. E 51, 3170-3182.
30. WEIL, W. (1990). Iterations of translative formulae and non-isotropic Poisson processes of particles. Math. Z. 205, 531-549.
31. WELL, W. AND WIEACKER, J. (1993). Stochastic geometry. In Handbook of Convex Geometry, Vol. B, eds P. M. Gruber and J. M. Wills, North-Holland, Amsterdam, pp. 1391-1438.
32. ZOUGHI, R. et al. (1997). Real-time and on-line microwave inspection of surface defects in rolled steel. In Proc. Asia-Pacific Microwave Conf. (Hong Kong, December 1997), IEEE, New York, pp. 1081-1084.