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State selection in the noisy stabilized Kuramoto-Sivashinsky equation
D Obeid1, J M Kosterlitz, B Sandstede
1Department of Physics, Brown University, Providence, Rhode Island 02912, USA. dina_obeid@brown.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We investigated the one-dimensional stabilized Kuramoto-Sivashinsky equation with stochastic noise. The study found that the Eckhaus stable band collapses, consistent with phase diffusion behavior in driven systems.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Partial differential equations
Background:
- The Kuramoto-Sivashinsky equation models phenomena like surface growth and fluid dynamics.
- Understanding the influence of noise on deterministic systems is crucial for predicting real-world behavior.
- State selection in driven, out-of-equilibrium systems is a complex phenomenon with broad implications.
Purpose of the Study:
- To analyze the one-dimensional stabilized Kuramoto-Sivashinsky equation with additive uncorrelated stochastic noise.
- To investigate the behavior of the Eckhaus stable band under stochastic forcing.
- To explore connections between the observed dynamics and state selection in driven systems.
Main Methods:
- Numerical simulations of the one-dimensional stabilized Kuramoto-Sivashinsky equation.
- Analysis of the Eckhaus stable band properties.
- Calculation and examination of phase diffusion constants.
Main Results:
- The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center.
- Observed collapse is consistent with the behavior of phase diffusion constants.
- The findings suggest a mechanism for state selection in driven, out-of-equilibrium systems.
Conclusions:
- Stochastic noise significantly impacts the stability of solutions to the Kuramoto-Sivashinsky equation.
- The collapse of the Eckhaus stable band provides insights into pattern formation and selection.
- This research contributes to understanding complex systems driven far from equilibrium.
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