Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1+1 dimensions

TL;DR

This paper demonstrates that the noisy Kuramoto-Sivashinsky equation in 1+1 dimensions shares the same universality class as the KPZ equation, confirmed through renormalization group analysis and numerical simulations showing similar scaling behavior.

Contribution

It establishes the universality class of the noisy KS equation as KPZ using RG analysis and numerical simulations, highlighting the approach to KPZ fixed point with increasing noise.

Findings

Noisy KS equation belongs to KPZ universality class.

RG flow approaches KPZ fixed point with stronger noise.

Numerical simulations confirm KPZ scaling behavior.

Abstract

The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1+1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents in the long-wavelength limit. The RG analysis reveals that the RG flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed point with increasing the strength of the noise. This is supplemented by the numerical simulations of the KS equation with a stochastic noise, in which the scaling behavior of the KPZ equation can be easily observed even in the moderate system size and time.