Effects of memory on scaling behaviour of Kardar–Parisi–Zhang equation

doi:10.1088/1674-1056/19/10/100508

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.

Keywords: memory effect scaling analysis self-consistent mode coupling theory

Received: 11 January 2010
Revised: 02 April 2010
Accepted manuscript online:

PACS:	02.30.Mv	(Approximations and expansions)
	05.45.Df	(Fractals)

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).

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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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Effects of memory on scaling behaviour of Kardar–Parisi–Zhang equation

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