Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation

Abstract

We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability occurring in the system, the large-distance and long-time behavior of this equation is the same as for the Kardar-Parisi-Zhang equation in one and two spatial dimensions. For the $d=2$ case the agreement is only qualitative. On the other hand, when coarse-graining on larger scales the asymptotic flow depends on the initial values of the parameters.

arXiv comment8 pages, 5 figures, revtex

References in corpus (2)

• Dynamic Scaling of Ion-Sputtered Surfaces
• Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos

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