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Cellular automaton explosion models

  • Plasma And Gravitation
  • Conference paper
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Part of the book series: Lecture Notes in Physics ((LNP,volume 518))

Abstract

We translate a standard approach of Field Theory into the framework of Cellular Automata (CA) to construct a parametrised class of stochastic 2D CA models simulating general explosion phenomena. The models exhibit morphological instabilities and phase transitions from bounded to unbounded growth.

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References

  • Bak, P., Tang, C., Wiesenfeld, K. (1987): Self organized criticality: an expansion of 1/f noise. Phys. Rev. Lett. 59, 381–384

    Article  ADS  MathSciNet  Google Scholar 

  • Boccara, N., Cheong, K., Oram, M. (1994): A probabilistic automata network epidemic model with births and deaths exhibiting cyclic behavior. J. Phys. A27, 1585–1597

    ADS  Google Scholar 

  • Erzan, A., Pietronero, L., Vespignani, A. (1995): The fixed-scale transformation of fractal growth. Rev. Mod. Phys. 67, 545–604

    Article  ADS  Google Scholar 

  • Fryxell, B., Arnett, D., Müller, E. (1991): Instabilities and clumping in SN 1987A. Ap. J. 367, 619–634

    Article  ADS  Google Scholar 

  • Langer, J.S. (1980): Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52, 1–28

    Article  ADS  Google Scholar 

  • Meakin, M. (1995): Progress in DLA research. Physica D86, 104–112

    Google Scholar 

  • Packard, N.H., Wolfram, S. (1985): Two dimensional cellular automata. J. Stat. Phys. 38, 901–946

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Packard, N.H. (1986): Theory and Applications of Cellular Automata, Wolfram, S. ed. (World Scientific, Singapore)

    Google Scholar 

  • Pandey, R.B. (1991): Cellular automata approach to interacting cellular network models for the dynamics of cell population in an early HIV infection. Physica A179, 442–470

    ADS  Google Scholar 

  • Perdang, J. (1993): The cellular automaton framework: A new tool for astrophysical modelling. Cellular Automata: Prospects in Astrophysical Applications (World Scientific, Singapore), 3–83

    Google Scholar 

  • Perdang, J. (1995): Chaos and stellar evolution. Stellar Evolution: What Should Be Done, Proceedings of the 32nd Liège International Astrophysical Colloquium, Noels, A. ed. (Durouaux-Ordina, Liège), 147–167

    Google Scholar 

  • Perdang, J. (1996): Cloudy, filamentary, and knotty structures: Simulating diffusive growth dynamics. Proceedings on Knowledge Transfer, Behrooz, A. ed. (Pace, London), 8–15

    Google Scholar 

  • Seiden, P.E., Schulman, L.S. (1990): Percolation model of galactic structure. Adv. Phys. 39 1, 1–54

    Article  ADS  MathSciNet  Google Scholar 

  • Stanley, H.S., Ostrowski, N. (1986): On Growth and Form, (Nijhoff, Dordrecht)

    MATH  Google Scholar 

  • Stauffer, D. (1985): Introduction to Percolation Theory, (Taylor & Francis, London)

    Book  MATH  Google Scholar 

  • Stauffer, D., Pandey, R.B. (1992): Immunology motivated simulations of cellular automata. Comp. Phys. 6, 404–410

    Google Scholar 

  • Todo, Y. (1991): Num. Astrophys. (Japan) 2, 193

    Google Scholar 

  • Uchida, Y. (1991): Num. Astrophys. (Japan) 2, 219

    Google Scholar 

  • Wolfram, S. (1983): Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644

    Article  ADS  MathSciNet  MATH  Google Scholar 

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P. G. L. Leach S. E. Bouquet J.-L. Rouet E. Fijalkow

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© 1999 Springer-Verlag

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Perdang, J. (1999). Cellular automaton explosion models. In: Leach, P.G.L., Bouquet, S.E., Rouet, JL., Fijalkow, E. (eds) Dynamical Systems, Plasmas and Gravitation. Lecture Notes in Physics, vol 518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105927

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  • DOI: https://doi.org/10.1007/BFb0105927

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65467-4

  • Online ISBN: 978-3-540-49251-1

  • eBook Packages: Springer Book Archive

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