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Extensive numerical study of the anomalous dynamic scaling of the Wolf–Villain model

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  • Xun, Zhipeng
  • Tang, Gang
  • Han, Kui
  • Xia, Hui
  • Hao, Dapeng
  • Yang, Xiquan
  • Zhou, Wei

Abstract

In order to study the microscopic physical mechanisms of roughness surfaces exhibiting the anomalous scaling behavior, the Wolf–Villain model in 1+1 and 2+1 dimensions is investigated by the kinetic Monte-Carlo simulation on long time and large length scale (the growth time and the system size are respectively extended to t=229, L=400000 for 1+1 dimensions, and t=221, L×L=512×512 for 2+1 dimensions). In the 2+1-dimensional simulations, the noise reduction technique is employed so as to eliminate the crossover effects in the growth process. Our calculations show that the Wolf–Villain model in 1+1 dimensions very probably exhibits intrinsic anomalous scaling behavior in the time and length simulation range of this paper, and the 2+1-dimensional Wolf–Villain model leads to a pyramidal mounded morphology. Some properties of the mounded pattern in the 2+1-dimensional Wolf–Villain model are discussed in the final part of this presentation.

Suggested Citation

  • Xun, Zhipeng & Tang, Gang & Han, Kui & Xia, Hui & Hao, Dapeng & Yang, Xiquan & Zhou, Wei, 2010. "Extensive numerical study of the anomalous dynamic scaling of the Wolf–Villain model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2189-2197.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:11:p:2189-2197
    DOI: 10.1016/j.physa.2010.01.051
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    Cited by:

    1. Chen, Yili & Tang, Gang & Xun, Zhipeng & Zhu, Lei & Zhang, Zhe, 2017. "Schramm–Loewner evolution theory of the asymptotic behaviors of (2+1)-dimensional Wolf–Villain model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 613-620.

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    Keywords

    Anomalous scaling; Wolf–Villain model;

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