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The European Physical Journal B

, Volume 63, Issue 2, pp 227–234 | Cite as

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

Statistical and Nonlinear Physics

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.

PACS.

05.70.Ln Nonequilibrium and irreversible thermodynamics 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 68.35.Fx Diffusion; interface formation 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  • L. Zhang
    • 1
  • G. Tang
    • 1
    • 2
  • Z. Xun
    • 1
  • K. Han
    • 1
  • H. Chen
    • 1
  • B. Hu
    • 2
    • 3
  1. 1.Department of PhysicsChina University of Mining and TechnologyXuzhouP.R. China
  2. 2.Department of Physics, Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems. (Hong Kong)Hong Kong Baptist UniversityHong KongP.R. China
  3. 3.Department of PhysicsUniversity of HoustonHoustonUSA

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