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采用Kinetic Monte Carlo方法对1+1维抛射沉积(BD) 模型内部结构的动力学行为进行了大量的数值模拟研究. 分别分析了空洞密度和内部界面的动力学行为. 研究表明, 空洞密度呈高斯型分布, 其平均值首先随生长时间快速增长, 然后达到一个与基底尺寸无关的饱和值.除表面宽度, 还引入了新的极值统计方法来分析该模型内部界面的动力学行为, 分析结果显示, 1+1维BD模型内部界面的演化满足标准的Family-Vicsek标度规律, 并且属Kardar-Parisi-Zhang方程所描述的普适类. 最后对表面宽度和极值统计两种理论方法的有限尺寸效应进行了比较.
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关键词:
- 抛射沉积模型 /
- 动力学行为 /
- Family-Vicsek标度
In this paper, the dynamic behavior of internal structure of 1+1-dimensional ballistic deposition model is simulated by means of Kinetic Monte Carlo. The dynamic behaviors of the porosity and internal interface are investigated. It is found that the porosity, with the standard Gaussian distribution, increases very fast at the initial times and reaches a saturation valve, which is independent of the linear substrates. In addition to the surface width, the new method of extreme statistics is also employed to analyze the dynamic behavior of internal interface. The results show that the evolution of the internal interface of 1+1-dimensional ballistic deposition model satisfies the standard Family-Vicsek scaling, and belongs to the universality class described by the Kardar-Parisi-Zhang equation. Finally, the finite-size effects obtained by the two theoretical methods, i.e., surface width and extreme statistics are compared.-
Keywords:
- ballistic deposition model /
- dynamic behavior /
- Family-Vicsek scaling
[1] Barabási A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)
[3] Tang G, Ma B K 2002 Acta Phys. Sin. 51 994 (in Chinese) [唐刚, 马本堃 2002 51 994]
[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] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19 100508
[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] Raychaudhuri S, Cranston M, Przybyla C, Shapir Y 2001 Phys. Rev. Lett. 87 136101
[9] Majumdar S N, Comtet A 2004 Phys. Rev. Lett. 92 225501
[10] Schehr G, Majumdar S N 2006 Phys. Rev. E 73 056103
[11] Oliveira T J, Aarao Reis F D A 2008 Phys. Rev. E 77 041605
[12] Sutherland D N 1966 J. Colloid. Interface Sci. 22 300
[13] Vold M J 1959 J. Colloid Sci. 14 168
[14] Vold M J 1959 J. Phys. Chem. 63 1608
[15] Meakin P, Jullien R 1987 SPIE 821 45
[16] Baiod R, Kessler D, Ramanlal P, Sander L, Savit R 1988 Phys. Rev. A 38 3672
[17] Meakin P, Ramanlal P, Sander L M, Ball R C 1986 Phys. Rev. A 34 5091
[18] Meakin P 1993 Phys. Rep. 235 189
[19] Katzav E, Schwartz M 2004 Phys. Rev. E 70 061608
[20] Nagatani T 1998 Phys. Rev. E 58 700
[21] Aarao Reis F D A 2001 Phys. Rev. E 63 056116
[22] Farnudi B, Vvedensky D D 2011 Phys. Rev. E (R) 83 020103
[23] Hao D P, Tang G, Xia H, Han K, Xun Z P 2011 Acta Phys. Sin. 60 038102 (in Chinese) [郝大鹏, 唐刚, 夏辉, 韩奎, 寻之朋 2011 60 038102]
[24] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[25] Yu J G, Amar J G 2002 Phys. Rev. E(R) 65 060601
[26] Katzav E, Edwards S F, Schwartz M 2006 Europhys. Lett. 75 29
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[1] Barabási A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)
[3] Tang G, Ma B K 2002 Acta Phys. Sin. 51 994 (in Chinese) [唐刚, 马本堃 2002 51 994]
[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] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19 100508
[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] Raychaudhuri S, Cranston M, Przybyla C, Shapir Y 2001 Phys. Rev. Lett. 87 136101
[9] Majumdar S N, Comtet A 2004 Phys. Rev. Lett. 92 225501
[10] Schehr G, Majumdar S N 2006 Phys. Rev. E 73 056103
[11] Oliveira T J, Aarao Reis F D A 2008 Phys. Rev. E 77 041605
[12] Sutherland D N 1966 J. Colloid. Interface Sci. 22 300
[13] Vold M J 1959 J. Colloid Sci. 14 168
[14] Vold M J 1959 J. Phys. Chem. 63 1608
[15] Meakin P, Jullien R 1987 SPIE 821 45
[16] Baiod R, Kessler D, Ramanlal P, Sander L, Savit R 1988 Phys. Rev. A 38 3672
[17] Meakin P, Ramanlal P, Sander L M, Ball R C 1986 Phys. Rev. A 34 5091
[18] Meakin P 1993 Phys. Rep. 235 189
[19] Katzav E, Schwartz M 2004 Phys. Rev. E 70 061608
[20] Nagatani T 1998 Phys. Rev. E 58 700
[21] Aarao Reis F D A 2001 Phys. Rev. E 63 056116
[22] Farnudi B, Vvedensky D D 2011 Phys. Rev. E (R) 83 020103
[23] Hao D P, Tang G, Xia H, Han K, Xun Z P 2011 Acta Phys. Sin. 60 038102 (in Chinese) [郝大鹏, 唐刚, 夏辉, 韩奎, 寻之朋 2011 60 038102]
[24] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[25] Yu J G, Amar J G 2002 Phys. Rev. E(R) 65 060601
[26] Katzav E, Edwards S F, Schwartz M 2006 Europhys. Lett. 75 29
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