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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.
[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 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 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 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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[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 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 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 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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