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Resonant Wave Interaction with Random Forcing and Dissipation
Author(s) -
Milewski Paul A.,
Tabak Esteban G.,
VandenEijnden Eric
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01427
Subject(s) - forcing (mathematics) , dissipation , amplitude , physics , white noise , nonlinear system , gaussian , mathematics , degrees of freedom (physics and chemistry) , square root , normal mode , statistical physics , mathematical analysis , classical mechanics , quantum mechanics , vibration , geometry , statistics
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.