Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinksy equation

Details Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinksy equation Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinksy equation

2010-11-05

arxiv.org/abs/1011.1481v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, 4 figures. Submitted to PRL

Scientific paper

We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both the KS and the noisy Burgers equation belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.

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