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为了更全面、有效地研究刻蚀模型（etching model）涨落表面的统计性质，基于Schramm Loewner Evolution（SLE）理论，对2+1维刻蚀模型饱和表面的等高线进行了数值模拟分析. 研究表明，2+1维刻蚀模型饱和表面的等高线是共形不变曲线，可用Schramm Loewner Evolution理论进行描述，且扩散系数=2.70 0.04，属= 8/3普适类. 相应的等高线分形维数为df =1.34 0.01.
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关键词:
- 刻蚀模型 /
- Schramm Loewner Evolution理论 /
- 共形不变性
In order to study the statistical properties of the surface fluctuations in the Etching model more comprehensively and effectively, based on the Schramm Loewner evolution (SLE) theory, the contour lines of the saturated surface in the (2+1)-dimensional Etching model are investigated by means of numerical simulations. Results show that the isoheight lines of the (2+1)-dimensional Etching surfaces are conformally invariant and can be described in the frame work of the SLE theory with diffusivity =2.70 0.04, which belongs to the =8/3 universality class. The corresponding fractal dimensions of the isoheight lines are df =1.34 0.01.[1] Barabsi A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2] [3] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)
[4] [5] Meakin P 1998 Fractals, Scaling and Growth Far from Equilibrium (Cambridge: Cambridge University Press)
[6] Halpin-Healy T, Zhang Y C 1995 Phys. Rep. 254 215
[7] [8] Family F, Vicsek T 1985 J. Phys. A: Math. Gen. 18 L75
[9] [10] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19 100508
[11] [12] [13] 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]
[14] [15] Xun Z P, Tang G, Xia H, Hao D P 2013 Acta Phys. Sin. 62 010503 (in Chinese) [寻之朋, 唐刚, 夏辉, 郝大鹏 2013 62 010503]
[16] [17] Schramm O 2000 Isr. J. Math. 118 221
[18] [19] Cardy J 2005 Ann. Phys. 318 81
[20] [21] Bauer M, Bernard D 2006 Phys. Rep. 432 115
[22] [23] Gruzberg I A 2006 J. Phys. A: Math. Gen. 39 12601
[24] [25] Bernard D, Boffetta G, Celani A, Falkovich G 2006 Nat. Phy 2 124
[26] Bernard D, Boffetta G, Celani A, Falkovich G 2007 Phys. Rev. Lett. 98 024501
[27] [28] Amoruso C, Hartmann A K, Hastings M B, Moore M A 2006 Phys. Rev. Lett. 97 267202
[29] [30] Bernard D, LeDoussal P, Middleton A A 2007 Phys. Rev. B 76 020403
[31] [32] [33] Keating J P, Marklof J, Williams G 2006 Phys. Rev. Lett. 97 034101
[34] [35] Bogomolny E, Dubertrand R, Schmit C 2007 J. Phys. A: Math. Theor. 40 381
[36] [37] Saberi A A, Rajabpour M A, Rouhani S 2008 Phys. Rev. Lett. 100 044504
[38] Saberi A A, Niry M D, Fazeli S M, Rahimi Tabar M R, Rouhani S 2008 Phys. Rev. E 77 051607
[39] [40] Schramm O, Sheffield S 2009 Acta Math. 202 21
[41] [42] Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 62 2289
[43] [44] [45] Wolf D E, Villain J 1990 Europhys. Lett. 13 389
[46] Zhou W, Tang G, Han K, Xia H, Hao D P, Xun Z P, Yang X Q, Chen Y L, Wen R J 2011 Mod. Phys. Lett. B 25 255
[47] [48] Chen Y L, Tang G, Han K, Xia H, Hao D P, Xun Z P, Wen R J 2011 J. Stat. Phys. 143 501
[49] [50] Saberi A A, Dashti-Naserabadi H, Rouhani S 2010 Phys. Rev. E 82 020101
[51] [52] [53] Mello B A 2001 Phys. Rev. E 63 041113
[54] Aaro Reis F D A 2004 Phys. Rev. E 69 021610
[55] [56] Tang G, Xun Z P, Wen R J, Han K, Xia H, Hao D P, Zhou W, Yang X Q, Chen Y L 2010 Physica A 389 4552
[57] [58] Xun Z P, Zhang Y W, Li Y, Xia H, Hao D P, Tang G 2012 J. Stat. Mech: Theory and Experiment p10014
[59] -
[1] Barabsi A L, Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2] [3] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific Press)
[4] [5] Meakin P 1998 Fractals, Scaling and Growth Far from Equilibrium (Cambridge: Cambridge University Press)
[6] Halpin-Healy T, Zhang Y C 1995 Phys. Rep. 254 215
[7] [8] Family F, Vicsek T 1985 J. Phys. A: Math. Gen. 18 L75
[9] [10] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19 100508
[11] [12] [13] 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]
[14] [15] Xun Z P, Tang G, Xia H, Hao D P 2013 Acta Phys. Sin. 62 010503 (in Chinese) [寻之朋, 唐刚, 夏辉, 郝大鹏 2013 62 010503]
[16] [17] Schramm O 2000 Isr. J. Math. 118 221
[18] [19] Cardy J 2005 Ann. Phys. 318 81
[20] [21] Bauer M, Bernard D 2006 Phys. Rep. 432 115
[22] [23] Gruzberg I A 2006 J. Phys. A: Math. Gen. 39 12601
[24] [25] Bernard D, Boffetta G, Celani A, Falkovich G 2006 Nat. Phy 2 124
[26] Bernard D, Boffetta G, Celani A, Falkovich G 2007 Phys. Rev. Lett. 98 024501
[27] [28] Amoruso C, Hartmann A K, Hastings M B, Moore M A 2006 Phys. Rev. Lett. 97 267202
[29] [30] Bernard D, LeDoussal P, Middleton A A 2007 Phys. Rev. B 76 020403
[31] [32] [33] Keating J P, Marklof J, Williams G 2006 Phys. Rev. Lett. 97 034101
[34] [35] Bogomolny E, Dubertrand R, Schmit C 2007 J. Phys. A: Math. Theor. 40 381
[36] [37] Saberi A A, Rajabpour M A, Rouhani S 2008 Phys. Rev. Lett. 100 044504
[38] Saberi A A, Niry M D, Fazeli S M, Rahimi Tabar M R, Rouhani S 2008 Phys. Rev. E 77 051607
[39] [40] Schramm O, Sheffield S 2009 Acta Math. 202 21
[41] [42] Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 62 2289
[43] [44] [45] Wolf D E, Villain J 1990 Europhys. Lett. 13 389
[46] Zhou W, Tang G, Han K, Xia H, Hao D P, Xun Z P, Yang X Q, Chen Y L, Wen R J 2011 Mod. Phys. Lett. B 25 255
[47] [48] Chen Y L, Tang G, Han K, Xia H, Hao D P, Xun Z P, Wen R J 2011 J. Stat. Phys. 143 501
[49] [50] Saberi A A, Dashti-Naserabadi H, Rouhani S 2010 Phys. Rev. E 82 020101
[51] [52] [53] Mello B A 2001 Phys. Rev. E 63 041113
[54] Aaro Reis F D A 2004 Phys. Rev. E 69 021610
[55] [56] Tang G, Xun Z P, Wen R J, Han K, Xia H, Hao D P, Zhou W, Yang X Q, Chen Y L 2010 Physica A 389 4552
[57] [58] Xun Z P, Zhang Y W, Li Y, Xia H, Hao D P, Tang G 2012 J. Stat. Mech: Theory and Experiment p10014
[59]
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