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为探讨含关联噪声的空间分数阶随机生长方程的动力学标度行为, 本文利用Riesz分数阶导数和Grmwald-Letnikov分数阶导数定义方法研究了关联噪声驱动下 的空间分数阶Edwards-Wilkinson (SFEW)方程在1+1维情况下的数值解, 得到了不同噪声关联因子和分数阶数时的生长指数、粗糙度指数、动力学指数等, 所求出的临界指数均与标度分析方法的结果相符合. 研究表明噪声关联因子和分数阶数均影响到SFEW方程的动力学标度行为,且表现为连续变化的普适类.
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关键词:
- 关联噪声 /
- 空间分数阶 /
- Edwards-Wilkinson方程 /
- 表面粗糙度
In order to study the dynamic scaling behavior of the space-fractional stochastic growth equation with correlated noise, we simulate numerically the space-fractional Edwards-Wilkinson (SFEW) equation driven by correlated noise in (1+1)-dimensional case based on the Riesz-and the Grmwald-Letnikov-type fractional derivatives. The scaling exponents including growth exponent, roughness exponent and dynamic exponent with different noise correlation factors and fractional orders are obtained, which are consistent with the corresponding scaling analysis. Our results show that the noise correlation factors and fractional orders affect the dynamic scaling behavior of the SFEW equation, which displays a continuous changing universality class.-
Keywords:
- correlated noise /
- space-fractional derivative /
- Edwards-Wilkinson equation /
- surface roughness
[1] Podlubny I 1999 Fractional Differential Equations (New York and London: Academic Press)
[2] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific)
[3] Chang F X, Chen J, Huang W 2005 Acta Phys. Sin. 54 1113 (in Chinese) [常福宣, 陈进, 黄薇 2005 54 1113]
[4] Torvik P J, Bagley R L 1984 Transaction of the ASME 51 294
[5] Liu F W, Anh V, Turner I, Zhang P H 2004 ANZIAM Journal 45 461
[6] Leith J R 2003 Signal Processing 83 2397
[7] Burov S, Barkai E 2008 Phys. Rev. Lett. 100 070601
[8] Mann J A, Woyczynski W A 2001 Physica A 291 159
[9] Katzav E 2003 Phys. Rev. E 68 031607
[10] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[11] Xia H, Tang G, Han K, Hao D P, Xun Z P 2009 Eur. Phys. J. B 71 237
[12] Xia H, Tang G, Ma J J, Hao D P, Xun Z P 2011 J. Phys. A 44 275003
[13] Tang G, Ma B K 2001 Acta Phys. Sin. 50 851 (in Chinese) [唐刚, 马本堃 2001 50 851]
[14] Hao D P, Tang G, Xia H, Chen H, Zhang L M, Xun Z P 2007 Acta Phys. Sin. 56 2018 (in Chinese) [郝大鹏, 唐刚, 夏辉, 陈华, 张雷明, 寻之朋 2007 56 2018]
[15] Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 2239
[16] Wu M, Billah K Y R, Shinozuka M 1995 Phys. Rev. E 51 995
[17] Li M S 1997 Phys. Rev. E 55 1178
[18] Edwards S F, Wilkinson D R 1982 Proc. R. Soc. London, Ser. A 381 17
[19] Family F, Vicsek T 1985 J. Phys. A 18 75
[20] Meerschaert M M, Tadjeran C 2004 J. Comp. Appl. Math. 172 65
[21] Katzav E, Schwartz M 2004 Phys. Rev. E 69 052603
-
[1] Podlubny I 1999 Fractional Differential Equations (New York and London: Academic Press)
[2] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific)
[3] Chang F X, Chen J, Huang W 2005 Acta Phys. Sin. 54 1113 (in Chinese) [常福宣, 陈进, 黄薇 2005 54 1113]
[4] Torvik P J, Bagley R L 1984 Transaction of the ASME 51 294
[5] Liu F W, Anh V, Turner I, Zhang P H 2004 ANZIAM Journal 45 461
[6] Leith J R 2003 Signal Processing 83 2397
[7] Burov S, Barkai E 2008 Phys. Rev. Lett. 100 070601
[8] Mann J A, Woyczynski W A 2001 Physica A 291 159
[9] Katzav E 2003 Phys. Rev. E 68 031607
[10] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[11] Xia H, Tang G, Han K, Hao D P, Xun Z P 2009 Eur. Phys. J. B 71 237
[12] Xia H, Tang G, Ma J J, Hao D P, Xun Z P 2011 J. Phys. A 44 275003
[13] Tang G, Ma B K 2001 Acta Phys. Sin. 50 851 (in Chinese) [唐刚, 马本堃 2001 50 851]
[14] Hao D P, Tang G, Xia H, Chen H, Zhang L M, Xun Z P 2007 Acta Phys. Sin. 56 2018 (in Chinese) [郝大鹏, 唐刚, 夏辉, 陈华, 张雷明, 寻之朋 2007 56 2018]
[15] Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 2239
[16] Wu M, Billah K Y R, Shinozuka M 1995 Phys. Rev. E 51 995
[17] Li M S 1997 Phys. Rev. E 55 1178
[18] Edwards S F, Wilkinson D R 1982 Proc. R. Soc. London, Ser. A 381 17
[19] Family F, Vicsek T 1985 J. Phys. A 18 75
[20] Meerschaert M M, Tadjeran C 2004 J. Comp. Appl. Math. 172 65
[21] Katzav E, Schwartz M 2004 Phys. Rev. E 69 052603
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