# The most effective model for describing the universal behavior of unstable surface growth

## TL;DR

This paper investigates whether the universal long-wavelength behavior of a noisy Kuramoto-Sivashinsky equation, modeling unstable surface growth, can be effectively described by a Kardar-Parisi-Zhang equation through renormalization-group analysis.

## Contribution

It uniquely identifies the KPZ parameters that best capture the universal behavior of the noisy KS equation, advancing understanding of surface growth models.

## Key findings

- KPZ effectively describes the universal behavior of the noisy KS equation
- Renormalization-group analysis determines optimal KPZ parameters
- Supports conjecture linking KS and KPZ universality classes

## Abstract

We study a noisy Kuramoto-Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar-Parisi-Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.