Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation

TL;DR

This paper applies dynamic renormalization group analysis to a noisy Kuramoto-Sivashinsky equation, revealing its large-scale behavior aligns with the KPZ equation in certain dimensions, with scale-dependent asymptotic flows.

Contribution

It provides a detailed RG analysis of the noisy Kuramoto-Sivashinsky equation, connecting its large-scale behavior to the KPZ universality class in one and two dimensions.

Findings

Large-distance behavior matches KPZ in 1D and 2D.

Qualitative agreement for 2D case.

Asymptotic flow depends on initial parameters at larger scales.

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.