منابع مشابه
Parametric autoresonance in Faraday waves.
We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite a steadily growing wave via parametric autoresonance. The method of averaging is employed to derive the governing equations for the primary mode....
متن کاملAsymptotic analysis of a model of autoresonance
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the phenomenon is that the nonlinear oscillator selfadjusts to the varying external conditions so that it remains in resonance with the driver for a long time. This long ...
متن کاملLaser-driven Cyclotron Autoresonance Accelerator*
Theory is developed for the cyclotron autoresonance acceleration of electrons in a gently-focused Gaussian laser beam and a gently tapered axial magnetic field. Numerical simulation shows, for example, acceleration from 50 MeV to 178 MeV over a distance of 148 cm, using a 10.6 μm CO2 laser with a minimum spot size of 0.1 cm.
متن کاملAutoresonance of coupled nonlinear waves
Adiabatic passage of weakly coupled nonlinear waves with space-time varying parameters through resonance is investigated. Slow evolution equations describing this wave interaction problem are obtained via Whitham’s averaged variational principle. Autoresonant solutions of these equations are found and, locally, comprise adiabatically varying quasiuniform wave train solutions of the decoupled pr...
متن کاملAutoresonance: A universal amplification mechanism in nature
A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. The theory is applied to Duffing-like systems to obtain exact analytical expressions for autoresonance e...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2001
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.64.036619