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Resonant Wave Interaction with Random Forcing and Dissipation

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A new model for studying energy transfer is introduced. It consists of a “resonant duo”—a resonant quartet where extra symmetries support a reduced subsystem with only two degrees of freedom—where one mode is forced by white noise and the other is damped. This system has a single free parameter: the quotient of the damping coefficient to the amplitude of the forcing times the square root of the strength of the nonlinearity. As this parameter varies, a transition takes place from a Gaussian, high-temperature, near equilibrium regime, to one highly intermittent and non-Gaussian. Both regimes can be understood in terms of appropriate Fokker–Planck equations.
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Document Type: Original Article

Affiliations: 1: University of Wisconson, Madison, 2: Courant Institute of Mathematical Sciences,

Publication date: January 1, 2002

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