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 [sic] equation

Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1 + 1 dimensions.

The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1 + 1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents...

Study of the noise-induced transition and the exploration of the phase space for the Kuramoto–Sivashinsky equation using the minimum action method

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddl...

State selection in the noisy stabilized Kuramoto-Sivashinsky equation.

In this work, we study the one-dimensional 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 o...

Minimum-action paths for wave-number selection in nonequilibrium systems.

The problem of wave-number selections in nonequilibrium pattern-forming systems in the presence of noise is investigated. The minimum-action method is proposed to study the noise-induced transitions between the different spatiotemporal states by generalizing the traditional theory previously applied in low-dimensional dynamical systems. The scheme is shown as an example in the stabilized Kuramo...