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Scaling In A Simple Model For Surface Growth In A Random Medium

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  • AMNON AHARONY

    (School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;
    Department of Physics, University of Oslo, POB 1048 Blindern, N-0316 Oslo, Norway)

  • DIETRICH STAUFFER

    (School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;
    Institute for Theoretical Physics, Cologne University, D-50923 Köln, Euroland)

Abstract

Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradientmon the surface heights, and the latter by site-dependent random growth probabilities. Here we consider the limitm → ∞, where the surface grows at the site with minimal random number,independentof its neighbors. The resulting height distribution obeys a simple scaling law, which is destroyed when local surface tension is included. Our model is equivalent to Yee's simplification of the Bak–Sneppen model for the extinction of biological species, where the height represents the number of times a biological species is exchanged.

Suggested Citation

  • Amnon Aharony & Dietrich Stauffer, 2002. "Scaling In A Simple Model For Surface Growth In A Random Medium," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 603-612.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:05:n:s0129183102003383
    DOI: 10.1142/S0129183102003383
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    Cited by:

    1. Berx, Jonas & Bervoets, Evi & Giuraniuc, Claudiu V. & Indekeu, Joseph O., 2021. "Coastlines and percolation in a model for hierarchical random deposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).

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    Keywords

    Surface growth; Monte Carlo simulation;

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