科赫分形基底上受限固-固模型动力学标度行为的数值研究

杨毅; 唐刚; 张哲; 寻之朋; 宋丽建; 韩奎

doi:10.7498/aps.64.130501

摘要

为分析基底结构对离散生长模型动力学性质的影响, 本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究. 通过分析表面宽度和饱和表面极值高度的统计行为发现: 随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献. 尽管分形基底具有不同的分形维数和谱维数, 但是在两种分形基底上得到了在误差范围内相同的粗造度指数. 两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起, 且很好的满足Asym2Sig函数分布.

关键词:

Abstract

In order to investigate the influence of structures of substrates on the dynamic properties of a discrete growth model, the restricted solid-on-solid model for Koch lattice and Koch curve fractal substrates, which have different fractal dimensions and spectrum dimensions but the same walk dimensions, is studied by means of numerical simulations. Surface width and distribution of the extremal height of the saturated surface are calculated. Results show that the random walk exponent plays the determinative part in the saturated regime. Although the fractal substrates have different fractal dimensions and spectral dimensions, the value of roughness exponents for the two substrates are almost the same within the error. The data of maximal height distributions (minmal height distribution) on the width of the saturated surface for the two fractal substrates can be well collapsed together and fitted by Asym2Sig distribution.

Keywords:

作者及机构信息

1.
中国矿业大学理学院物理系, 徐州 221116

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:11304377,11247249,11447123)资助的课题.

Authors and contacts

1.
Department of Physics, China University of Mining and Technology, Xuzhou 221116, China

Funds: Projects supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2013XK04) and the National Natural Science Foundation of China (Grant Nos. 11304377, 11247249, 11447123).

参考文献

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[7]	Family F, Vicsek T 1985 J. Phys. A 18 L75
[8]	Foltin G, Oerding K, Racz Z, Workman R L, Zia R K P 1994 Phys. Rev. E 50 639
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[11]	Majumdar S N, Comtet A 2004 Phys. Rev. Lett. 92 225501
[12]	Fisher R A, Tippett L H C 1928 Proc. Cambridge Philos. Soc. 24 180
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[14]	Antal T, Droz M, Györgyi G, Rácz Z 2001 Phys. Rev. Lett. 87 240601
[15]	Lee D S 2005 Phys. Rev. Lett. 95 150601
[16]	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
[17]	T. J. Oliveira, F. D. A. Aarāo Reis 2008 Phys. Rev. E 77 041605
[18]	Yang Y, Tang G, Song L J, Xun Z P, Xia H, Hao D P 2014 Acta Phys. Sin. 63 150501 (in Chinese) [杨毅, 唐刚, 宋丽建, 寻之朋, 夏辉, 郝大鹏 2014 物理学报 63 150501]
[19]	Xun Z P, Tang G, Han K, Xia H, Hao D P, Li Y 2012 Phys. Rev. E 85 041126
[20]	Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[21]	Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 64 2289
[22]	Lee S B, Jeong H C, Kim J M 2008 J. Stat. Mech. P12013
[23]	Xun Z P, Zhang Y W, Li Y, Xia H, Hao D P, Tang G 2012 J. Stat. Mech. P10014
[24]	Huynh H N, Gunnar P 2012 Phys. Rev. E 85 061133
[25]	Essex C, Davison M 2001 J. Phys. A 34 8397

施引文献

[1]	Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)
[2]	Barabási A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[3]	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]
[4]	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
[5]	Kim J M, Kim D H 2008 J. Stat. Phys. 133 1179
[6]	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]
[7]	Family F, Vicsek T 1985 J. Phys. A 18 L75
[8]	Foltin G, Oerding K, Racz Z, Workman R L, Zia R K P 1994 Phys. Rev. E 50 639
[9]	Derrida B, Lebowitz J L 1998 Phys. Rev. Lett. 80 209
[10]	Raychaudhuri S, Cranston M, Przybyla C, Shapir Y 2001 Phys. Rev. Lett. 87 136101
[11]	Majumdar S N, Comtet A 2004 Phys. Rev. Lett. 92 225501
[12]	Fisher R A, Tippett L H C 1928 Proc. Cambridge Philos. Soc. 24 180
[13]	Bramwell S T, Christensen K, Fortin J, Holdsworth P C W, Jensen H J, Lise S, López J M, Nicodemi M, Pinton J F, Sellitto M 2000 Phys. Rev. Lett. 84 3744
[14]	Antal T, Droz M, Györgyi G, Rácz Z 2001 Phys. Rev. Lett. 87 240601
[15]	Lee D S 2005 Phys. Rev. Lett. 95 150601
[16]	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
[17]	T. J. Oliveira, F. D. A. Aarāo Reis 2008 Phys. Rev. E 77 041605
[18]	Yang Y, Tang G, Song L J, Xun Z P, Xia H, Hao D P 2014 Acta Phys. Sin. 63 150501 (in Chinese) [杨毅, 唐刚, 宋丽建, 寻之朋, 夏辉, 郝大鹏 2014 物理学报 63 150501]
[19]	Xun Z P, Tang G, Han K, Xia H, Hao D P, Li Y 2012 Phys. Rev. E 85 041126
[20]	Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[21]	Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 64 2289
[22]	Lee S B, Jeong H C, Kim J M 2008 J. Stat. Mech. P12013
[23]	Xun Z P, Zhang Y W, Li Y, Xia H, Hao D P, Tang G 2012 J. Stat. Mech. P10014
[24]	Huynh H N, Gunnar P 2012 Phys. Rev. E 85 061133
[25]	Essex C, Davison M 2001 J. Phys. A 34 8397

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