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Scaling properties and height distributions of persisting roughness in the discrete growth models in the presence of the angle of repose

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  • Wang, Chuan
  • Xia, Hui

Abstract

Inspired by the modified Langevin-type growth equations for persisting roughness when deposition stops, we perform extensive simulations on the modified versions of typical discrete growth models including random deposition with surface relaxation (RDSR) and the restricted solid-on-solid (RSOS). Our results show that, when the angle of repose γ is introduced, the stable surface always presents persisting roughness in the process of surface flattening after deposition ceases, and sand dune-like morphology could gradually appear with different angles of repose. The height distributions and nontrivial scaling properties of these modified growth systems are investigated to provide deeper insights into the surface flattening dynamics. The comparisons between these two modified discrete models and the corresponding continuum growth equations belonging to the same universality classes are also discussed in the presence of the angle of repose.

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  • Wang, Chuan & Xia, Hui, 2024. "Scaling properties and height distributions of persisting roughness in the discrete growth models in the presence of the angle of repose," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001498
    DOI: 10.1016/j.chaos.2024.114598
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    3. Grevenstette, Michael & Linz, Stefan J., 2009. "Model for pattern formation of granular matter on vibratory conveyors," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1896-1902.
    4. Vicsek, Tamás & Cserző, Miklós & Horváth, Viktor K., 1990. "Self-affine growth of bacterial colonies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(2), pages 315-321.
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