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

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