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分形基底上受限固-固模型动力学性质的数值模拟研究

杨毅 唐刚 宋丽建 寻之朋 夏辉 郝大鹏

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分形基底上受限固-固模型动力学性质的数值模拟研究

杨毅, 唐刚, 宋丽建, 寻之朋, 夏辉, 郝大鹏

Numerical simulations of dynamic properties of the restricted solid-on-solid model on fractal substrates

Yang Yi, Tang Gang, Song Li-Jian, Xun Zhi-Peng, Xia Hui, Hao Da-Peng
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  • 为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid,RSOS)模型的生长过程进行了大量的数值模拟研究. 通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析. 结果表明,分形基底结构对生长表面的动力学行为具有显著的影响. 尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同. 饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull,Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布.
    In order to investigate the effect of the structure of a non-complete substrate on the dynamic behaviors of a growing surface, the restricted solid-on-solid model on Sierpinski arrowhead and Crab fractal substrates, which have the same fractal dimensions but of different spectrum dimensions, are extensively studied by means of numerical simulations. The surface width and the maximal height of the saturated surface are calculated. It is found that the microscopic structure of the substrates affects significantly the dynamic properties of the surfaces. Although the restricted solid-on-solid model evolving on two kinds of fractal substrates exhibits dynamic scaling behavior, the standard Family-Vicsek scaling is still satisfied for different dynamic scaling exponents. The maximal height of the width of saturated surface can be fitted by Asym2Sig distribution, not by the three kinds of usual extreme statistical distribution, i.e. Weibull, Gumbel, and Frechet distributions.
    • 基金项目: 中央高校基本科研业务费(批准号:2013XK04)和国家自然科学基金(批准号:11304377,11247249)资助的课题.
    • Funds: Projects supported by the Fundamental Research Funds for the Central Universities (Grant No. 2013XK04), and the National Natural Science Foundation of China (Grant Nos. 11304377, 11247249).
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    Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)

    [2]

    Barabsi A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)

    [3]
    [4]
    [5]

    Tang G, Ma B K 2002 Acta Phys. Sin. 51 0994 (in Chinese) [唐刚, 马本堃 2002 物理学报 51 0994]

    [6]

    Xun Z P, Tang G, Han K, Hao D P, Xia H, Zhou W, Yang X Q, Wen R J, Chen Y L 2010 Chin. Phys. B 19 070516

    [7]
    [8]

    Kim J M, Kim D H 2008 J. Stat. Phys. 133 1179

    [9]
    [10]
    [11]

    Zhang Y W, Tang G, Han K, Xun Z P, Xie Y Y, Li Y 2012 Acta Phys. Sin. 61 020511 (in Chinese) [张永伟, 唐刚, 韩奎, 寻之朋, 谢裕颖, 李炎 2012 物理学报 61 020511]

    [12]

    Family F, Vicsek T 1985 J. Phys. A 18 L75

    [13]
    [14]
    [15]

    Foltin G, Oerding K, Racz Z, Workman R L, Zia R K P 1994 Phys. Rev. E 50 639

    [16]
    [17]

    Derrida B, Lebowitz J L 1998 Phys. Rev. Lett. 80 209

    [18]

    Raychaudhuri S, Cranston M, Przybyla C, Shapir Y 2001 Phys. Rev. Lett. 87 136101

    [19]
    [20]

    Majumdar S N, Comtet A 2004 Phys. Rev. Lett. 92 225501

    [21]
    [22]
    [23]

    Xun Z P, Tang G, Han K, Xia H, Hao D P, Li Y 2012 Phys. Rev. E 85 041126

    [24]
    [25]

    Meakin P, Ramanlal P, Sander L M, Ball R C 1986 Phys. Rev. A 34 5091

    [26]

    Julien R, Boter R 1985 Phys. Rev. Lett. 54 2055

    [27]
    [28]
    [29]

    Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889

    [30]

    Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 64 2289

    [31]
    [32]
    [33]

    Lee S B, Jeong H C, Kim J M 2008 J. Stat. Mech. p12013

    [34]

    Tang G, Xun Z P, Wong R J, Han K, Xia H, Hao D P, Zhou W, Yang X Q, Chen Y L 2010 Physica A 389 4552

    [35]
    [36]
    [37]

    Lee S B, Kim J M 2009 Phys. Rev. E 80 021101

    [38]
    [39]

    Xun Z P, Zhang Y W, Li Y, Xia H, Hao D P, Tang G 2012 J. Stat. Mech. p10014

    [40]

    Kim D H, Kim J M 2010 J. Stat. Mech. p08008

    [41]
    [42]

    Huynh H N, Chew L Y, Pruessner G 2010 Phys. Rev.E 82 042103

    [43]
    [44]
    [45]

    Fisher R A, Tippett L H C 1928 Proc. Cambridge Philos. Soc. 24 180

    [46]
    [47]

    Bramwell S T, Christensen K, Fortin J, Holdsworth P C W, Jensen H J, Lise S, Lpez J M, Nicodemi M, Pinton J F, Sellitto M 2000 Phys. Rev. Lett. 84 3744

    [48]
    [49]

    Antal T, Droz M, Gyrgyi G, Rcz Z 2001 Phys. Rev. Lett. 87 240601

    [50]

    Lee D S 2005 Phys. Rev. Lett. 95 150601

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    [52]
    [53]

    Wen R J, Tang G, Han K, Xia H, Hao D P, Xun Z P, Chen Y L 2011 Chinese J Comput. Phys. 28 933

    [54]

    Oliveira T J, Aaro Reis F D A 2008 Phys. Rev. E 77 041605

    [55]
    [56]

    Cui L J, Zhang Y, Zhang M Y, Li W, Zhao X S, Li S G, Wang Y F 2012 J. Environ. Mont. 14 3037

    [57]
    [58]

    Brar J 2011 Photoluminescence Spectroscopy of CdSe/Cd 0.5Zn 0.5S Core/Shell Colloidal Quantum Dots MS Thesis (Ottawa: University of Ottawa)

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出版历程
  • 收稿日期:  2014-03-04
  • 修回日期:  2014-04-15
  • 刊出日期:  2014-08-05

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