Noise and dynamical pattern selection

Abstract

In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will be realized in a given experiment appears to depend on unobservable details of the system's initial conditions. We show, however, that weak, Gaussian white noise drives such a system toward a preferred wave number which depends only on the system parameters and is independent of initial conditions. We give a prescription for calculating this wave number, analytically near the onset of instability and numerically otherwise.

12 pages, REVTEX, no figures. Submitted to Phys. Rev. Lett

References in corpus (2)

• Domain Coarsening in Systems Far from Equilibrium
• Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation

Cited by in corpus (5)

• State selection in the noisy stabilized Kuramoto-Sivashinsky equation
• Pattern Selection in a Phase Field Model for Directional Solidification
• Observation of stochastic coherence in coupled map lattices
• Wavenumber Selection in Pattern Forming Systems
• Effect of noise on coupled chaotic systems