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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.
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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
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[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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