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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100508-100508.doi: 10.1088/1674-1056/19/10/100508

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

唐刚, 郝大鹏, 夏辉, 韩奎, 寻之朋

Department of Physics, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2010-01-11 修回日期:2010-04-02 出版日期:2010-10-15 发布日期:2010-10-15
基金资助:
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).

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

Received:2010-01-11 Revised:2010-04-02 Online:2010-10-15 Published:2010-10-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: memory effect, scaling analysis, self-consistent mode coupling theory

中图分类号: (Approximations and expansions)

02.30.Mv

05.45.Df (Fractals)

唐刚, 郝大鹏, 夏辉, 韩奎, 寻之朋. Effects of memory on scaling behaviour of Kardar–Parisi–Zhang equation[J]. 中国物理B, 2010, 19(10): 100508-100508.

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[J]. Chin. Phys. B, 2010, 19(10): 100508-100508.

参考文献 23

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

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

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