Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 10503-010503.doi: 10.1088/1674-1056/23/1/010503

• GENERAL • 上一篇    下一篇

Surface structures of equilibrium restricted curvature model on two fractal substrates

宋丽建, 唐刚, 张永伟, 韩奎, 寻之朋, 夏辉, 郝大鹏, 李炎   

  1. Department of Physics, China University of Mining and Technology, Xuzhou 221116, China
  • 收稿日期:2013-04-12 修回日期:2013-06-28 出版日期:2013-11-12 发布日期:2013-11-12
  • 基金资助:
    Project support by the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 2013XK04).

Surface structures of equilibrium restricted curvature model on two fractal substrates

Song Li-Jian (宋丽建), Tang Gang (唐刚), Zhang Yong-Wei (张永伟), Han Kui (韩奎), Xun Zhi-Peng (寻之朋), Xia Hui (夏辉), Hao Da-Peng (郝大鹏), Li Yan (李炎)   

  1. Department of Physics, China University of Mining and Technology, Xuzhou 221116, China
  • Received:2013-04-12 Revised:2013-06-28 Online:2013-11-12 Published:2013-11-12
  • Contact: Tang Gang E-mail:gangtang@cumt.edu.cn
  • Supported by:
    Project support by the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 2013XK04).

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摘要： With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension df, but possess different dynamic exponents of random walk zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk zrw. The ERC model growing on the two substrates follows the well-known Family–Vicsek scaling law and satisfies the scaling relations 2α+df ≈ z ≈ 2zrw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.

关键词: equilibrium restricted curvature model, Sierpinski arrowhead, crab fractal substrate, dynamic scaling

Abstract: With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension df, but possess different dynamic exponents of random walk zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk zrw. The ERC model growing on the two substrates follows the well-known Family–Vicsek scaling law and satisfies the scaling relations 2α+df ≈ z ≈ 2zrw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.

Key words: equilibrium restricted curvature model, Sierpinski arrowhead, crab fractal substrate, dynamic scaling

中图分类号:  (Fluctuation phenomena, random processes, noise, and Brownian motion)

  • 05.40.-a
02.50.-r (Probability theory, stochastic processes, and statistics) 64.60.Ht (Dynamic critical phenomena)