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

doi:10.7498/aps.63.150501

Abstract

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.

Keywords:

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 (Grant No. 2013XK04), and the National Natural Science Foundation of China (Grant Nos. 11304377, 11247249).

References

[1]	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 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 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
[51]
[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)
[59]
[60]
[61]
[62]
[63]
[64]
[65]
[66]
[67]
[68]
[69]
[70]
[71]
[72]
[73]
[74]
[75]
[76]
[77]
[78]
[79]
[80]
[81]
[82]
[83]
[84]
[85]
[86]
[87]
[88]
[89]
[90]
[91]
[92]
[93]
[94]
[95]
[96]
[97]
[98]
[99]
[100]
[101]
[102]
[103]
[104]
[105]
[106]
[107]
[108]
[109]
[110]
[111]
[112]
[113]
[114]
[115]
[116]
[117]

Cited By

[1]	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 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 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
[51]
[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)
[59]
[60]
[61]
[62]
[63]
[64]
[65]
[66]
[67]
[68]
[69]
[70]
[71]
[72]
[73]
[74]
[75]
[76]
[77]
[78]
[79]
[80]
[81]
[82]
[83]
[84]
[85]
[86]
[87]
[88]
[89]
[90]
[91]
[92]
[93]
[94]
[95]
[96]
[97]
[98]
[99]
[100]
[101]
[102]
[103]
[104]
[105]
[106]
[107]
[108]
[109]
[110]
[111]
[112]
[113]
[114]
[115]
[116]
[117]

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Vol. 63, Issue 15 - 2014-08-05

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