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Growth Of Surfaces Generated By A Probabilistic Cellular Automation

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  • PRATIP BHATTACHARYYA

    (Low Temperature Physics Division, Saha Institute of Nuclear Physics, Sector – 1, Block – AF, Bidhannagar, Calcutta 700 064, India)

Abstract

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in(1+1)dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called Model A in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called Model B, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, Model B shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.

Suggested Citation

  • Pratip Bhattacharyya, 1999. "Growth Of Surfaces Generated By A Probabilistic Cellular Automation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 165-181.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:01:n:s0129183199000115
    DOI: 10.1142/S0129183199000115
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