Parallel Simulation of Asynchronous Cellular Automata Evolution

  • Olga Bandman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)

Abstract

For simulating physical and chemical processes on molecular level asynchronous cellular automata with probabilistic transition rules are widely used being sometimes referred to as Monte-Carlo methods. The simulation requires huge cellular space and millions of iterative steps for obtaining the CA evolution representing the real scene of the process. This may be achieved by allocating the CA evolution program onto a multiprocessor system. As distinct from the synchronous CAs which is extremely efficient, the asynchronous case of parallel implementation is stiff. To improve the situation we propose a method for approximating asynchronous CA by a superposition of a number of synchronous ones, each being applied to locally separated blocks forming a partition of the cellular array.

References

  1. 1.
    Neizvestny, I.G., Shwartz, N.L., Yanovitskaya, Z.S., Zverev, A.V.: 3D-model of epitaxial growth on porous {111} and {100} Si surfaces. Computer Physics Communications 147, 272–275 (2002)MATHCrossRefGoogle Scholar
  2. 2.
    Ziff, R.M., Gulari, E., Bershad, Y.: Kinetic phase transitions in irreversible surface-reaction model. Physical Review Letters 56, 2553–2558 (1986)CrossRefGoogle Scholar
  3. 3.
    Choppard, B., Droz, M.: Cellular automata approach to nonequilibrium phase transition in a surface reaction model; static and and dynamic propereties. Journ.of Physics. A Mathenatical and General 21, 205–211 (1988)CrossRefGoogle Scholar
  4. 4.
    Elokhin, V.I., Latkin, E.I., Matveev, A.V., Gorodetskii, V.V.: Application of Statistical Lattice Models to the Analysis of Oscillatory and Autowave Processes on the Reaction of Carbon Monoxide Oxidation over Platinum and Palladium Surfaces. Kinetics and Catalysis 5, 672–700 (2003)Google Scholar
  5. 5.
    Makeev, A.G.: Coarse bifurcation analysis of kinetic Monte Carlo simulations: a lattice-gas model with lateral interactions. Journal of chemical physics 18, 8229–8240 (2002)CrossRefGoogle Scholar
  6. 6.
    Nedea, S.V., Lukkien, J.J., Jansen, A.P.J., Hilbers, P.A.J.: Methods for parallel simulations of surface reactions. arXiv:physics/0209017, vol. 1(4), pp. 1–8 (2002)Google Scholar
  7. 7.
    Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champain (2002)MATHGoogle Scholar
  8. 8.
    Achasova, S., Bandman, O., Markova, V., Piskunov, S.: Parallel Substitution Algorithm. Theory and Application. World Scientific, Singapore (1994)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Olga Bandman
    • 1
  1. 1.Supercomputer Software Department, ICMMGSiberian Branch Russian Academy of SciencesNovosibirskRussia

Personalised recommendations