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A Monte Carlo method for simulating fractal surfaces

Author

Listed:
  • Zou, Mingqing
  • Yu, Boming
  • Feng, Yongjin
  • Xu, Peng

Abstract

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.

Suggested Citation

  • Zou, Mingqing & Yu, Boming & Feng, Yongjin & Xu, Peng, 2007. "A Monte Carlo method for simulating fractal surfaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 176-186.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:176-186
    DOI: 10.1016/j.physa.2007.07.058
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    References listed on IDEAS

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    1. H. W. Zhou & H. Xie, 2003. "Direct Estimation of the Fractal Dimensions of a Fracture Surface of Rock," Surface Review and Letters (SRL), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 751-762.
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    Cited by:

    1. Kolyukhin Dmitriy, 2020. "Statistical modeling of three-dimensional fractal point sets with a given spatial probability distribution," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 245-252, September.
    2. Feng Feng & Meng Yuan & Yousheng Xia & Haoming Xu & Pingfa Feng & Xinghui Li, 2022. "Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal," Mathematics, MDPI, vol. 10(7), pages 1-17, March.

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