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Effects of memory on scaling behaviour of Kardar–Parisi–Zhang equation |
Tang Gang(唐刚)†, Hao Da-Peng(郝大鹏), Xia Hui(夏辉), Han Kui(韩奎), and Xun Zhi-Peng(寻之朋) |
Department of Physics, China University of Mining and Technology, Xuzhou 221116, China |
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Abstract In order to describe the time delay in the surface roughing process the Kardar–Parisis–Zhang (KPZ) equation with memory effects is constructed and analysed using the dynamic renormalization group and the power counting mode coupling approach by Chattopadhyay [2009 Phys. Rev. E 80 011144]. In this paper, the scaling analysis and the classical self-consistent mode-coupling approximation are utilized to investigate the dynamic scaling behaviour of the KPZ equation with memory effects. The values of the scaling exponents depending on the memory parameter are calculated for the substrate dimensions being 1 and 2, respectively. The more detailed relationship between the scaling exponent and memory parameter reveals the significant influence of memory effects on the scaling properties of the KPZ equation.
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Received: 11 January 2010
Revised: 02 April 2010
Accepted manuscript online:
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PACS:
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02.30.Mv
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(Approximations and expansions)
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05.45.Df
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(Fractals)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10674177), and the Youth Foundation of China University of Mining & Technology (Grant No. 2008A035). |
Cite this article:
Tang Gang(唐刚), Hao Da-Peng(郝大鹏), Xia Hui(夏辉), Han Kui(韩奎), and Xun Zhi-Peng(寻之朋) Effects of memory on scaling behaviour of Kardar–Parisi–Zhang equation 2010 Chin. Phys. B 19 100508
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[1] |
Kardar M, Parisi G and Zhang Y C 1986 Phys. Rev. Lett. 56 889
|
[2] |
Barab'asi A L and Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
|
[3] |
Family F and Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore: World Scientific)
|
[4] |
Mukherji S and Bhattacharjee S M 1997 Phys. Rev. Lett. 79 2502
|
[5] |
Tang G and Ma B K 2001 Physica A 298 257
|
[6] |
Hu B and Tang G 2002 Phys. Rev. E 66 026105
|
[7] |
Hao D P, Tang G, Xia H, Chen H, Zhang L M and Xun Z P 2007 Acta Phys. Sin. 56 2018 (in Chinese)
|
[8] |
Chattopadhyay A K 2009 Phys. Rev. E 80 011144
|
[9] |
Hentschel H G E and Family F 1991 Phys. Rev. Lett. 66 1982
|
[10] |
Tang G and Ma B K 2001 Int. J. Mod. Phys. B 15 2275
|
[11] |
Zhang L P, Tang G, Xia H, Hao D P and Chen H 2004 Physica A 338 431
|
[12] |
Tang G and Ma B K 2002 Acta Phys. Sin. 51 994 (in Chinese)
|
[13] |
Xia H, Tang G, Han K, Hao D P, Chen H and Zhang L M 2006 Mod. Phys. Lett. 20 1935
|
[14] |
G"otze W and Sj"ogren L 1992 Rep. Prog. Phys. 55 241
|
[15] |
Frey E and Schwabl F 1994 Adv. Phys. 43 577
|
[16] |
Kawasaki K 1976 Phase Transitions and Critical Phenomena (New York: Academic Press) Vol. 5a
|
[17] |
Frey E, Tauber U C and Hwa T 1996 Phys. Rev. E 53 4424
|
[18] |
Tu Y 1994 Phys. Rev. Lett. 73 3109
|
[19] |
Colaiori F and Moore M A 2001 Phys. Rev. Lett. 86 3946
|
[20] |
Colaiori F and Moore M A 2001 Phys. Rev. E 63 057103
|
[21] |
Doherty J P, Moore M A, Kim J M and Bray A J 1994 Phys. Rev. Lett. 72 2041
|
[22] |
Hwa T and Frey E 1991 Phys. Rev. A 44 R7873
|
[23] |
Jung Y K and Kim I M 2000 Phys. Rev. E 62 2949
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