Nonequilibrium statistics of a reduced model for energy transfer in waves

We study energy transfer in a “resonant duet”—a resonant quartet where symmetries support a reduced subsystem with only 2 degrees of freedom—where one mode is forced by white noise and the other is damped. We consider a physically motivated family of nonlinear damping forms and investigate their eff...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2007-03, Vol.60 (3), p.439-461
Main Authors: DeVille, R. E. Lee, Milewski, Paul A., Pignol, Ricardo J., Tabak, Esteban G., Vanden-Eijnden, Eric
Format: Article
Language:English
Subjects:
Differential equations
Energy
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Ordinary differential equations
Partial differential equations
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic models
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We study energy transfer in a “resonant duet”—a resonant quartet where symmetries support a reduced subsystem with only 2 degrees of freedom—where one mode is forced by white noise and the other is damped. We consider a physically motivated family of nonlinear damping forms and investigate their effect on the dynamics of the system. A variety of statistical steady states arise in different parameter regimes, including intermittent bursting phases, states highly constrained by slaving among amplitudes and phases, and Gaussian and non‐Gaussian quasi‐equilibrium regimes. All of this can be understood analytically using asymptotic techniques for stochastic differential equations. © 2006 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.20157