Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

L. Zhang, G. Tang (), Z. Xun, K. Han, H. Chen and Baiding Hu ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2008, vol. 63, issue 2, 227-234

Abstract: The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d=1 and d=2, respectively. In the case of d=1, we arrive at the critical exponents z=1.5 and α=0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d=2, we find a fixed point with the dynamic exponents z=2.866 and α=-0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Keywords: 05.70.Ln Nonequilibrium and irreversible thermodynamics, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 68.35.Fx Diffusion; interface formation, (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1140/epjb/e2008-00228-4

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