State selection in the noisy stabilized Kuramoto-Sivashinsky equation

TL;DR

This paper investigates how stochastic noise influences state selection in the 1D stabilized Kuramoto-Sivashinsky equation, revealing a narrowed stable band and connections to out-of-equilibrium phenomena.

Contribution

It demonstrates the narrowing of the Eckhaus stable band under noise and links this to phase diffusion, providing new insights into state selection mechanisms.

Findings

Eckhaus stable band narrows near the center due to noise

Phase diffusion constants decrease in the narrowed band

Connections established between noise effects and out-of-equilibrium state selection

Abstract

In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.