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Generation of Johnson-Mehl crystals and comparative analysis of models for random nucleation

  • Jesper Møller (a1)

Abstract

Simulation procedures for typical Johnson-Mehl crystals generated under various models for random nucleation are proposed. These procedures include algorithms for simulating spatio-time-inhomogeneous Poisson processes. Empirical results for a particular class of Johnson-Mehl tessellations in two and three dimensions show remarkably different crystals.

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* Postal address: Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, DK-8000 Aarhus C, Denmark.

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The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain, on 21–24 September 1993.

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References

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Daley, D. J. and Vere-Jones, D. (1988) An Introduction to the Theory of Point Processes. Springer-Verlag, New York.
Devroye, L. (1986) Non-uniform Random Variate Generation. Springer-Verlag, New York.
Frost, H. J. and Thompson, C. V. (1987) The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures. Acta Metall. 35, 529540.
Mahin, K. W., Hanson, K. and Morris, J. W. (1980) Comparative analysis of the cellular and Johnson-Mehl microstructures through computer simulation. Acta Metall. 28, 443453.
Møller, J. (1989) Random tessellations in. Adv. Appl. Prob. 21, 3773.
Møller, J. (1992) Random Johnson-Mehl tessellations. Adv. Appl. Prob. 24, 814844.
Møller, J. (1994) Lectures on Random Voronoi Tessellations. Lecture Notes in Statistics. Springer-Verlag, New York.
Quine, M. P. and Watson, D. F. (1984) Radial generation of n-dimensional Poisson processes. J. Appl. Prob. 21, 548557.
Ripley, B. D. (1987) Stochastic Simulation. Wiley, New York.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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