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Nonlinear Landau Damping—The Spectrum
The Physics of Fluids, 1970The spatial damping of large-amplitude electrostatic waves in a collisionless plasma is derived. The theory leads to differential equations which describe the nonlinear oscillation of the electric field amplitude, the broadening of the frequency spectrum, and the growth of sidebands.
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The Stochastic Nonlinear Damped Wave Equation
Applied Mathematics and Optimization, 2002The authors investigate the following stochastic wave equation in a bounded subset \(D\) of \({\mathbb R}^n, n \leq 3\) with smooth boundary \(\partial D\): \[ dY_t +(AY + Y_t +g(Y)) dt= \sqrt{Q} dW(t)\;\text{in }[0,\infty)\times D, \] \[ Y(0) = y\in H_0^1(D), \quad Y_t(0)=z\in L^2(D), \] \[ Y=0\;\text{ on }[0,\infty)\times\partial D, \] where (1) \(W\)
Barbu, Viorel, Da Prato, Giuseppe
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Deconvolution of damping forces with a nonlinear microresonator
Review of Scientific Instruments, 2011We report a fully electrical microcantilever device that utilizes capacitance for both actuation and detection and show that it can characterize various gases with a bare silicon microcantilever. We find the motion of the cantilever as it rings down when the oscillating force is removed, by measuring the voltage induced by the oscillating capacitance ...
Bevan, Elliott +5 more
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Physical Review Letters, 1997
We present a new description of nonlinear Landau damping, applicable to wave propagation in a weakly collisional as well as a collisionless plasma. We derive a set of equations with a simple energy conservation law which is useful for understanding the evolution of the system.
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We present a new description of nonlinear Landau damping, applicable to wave propagation in a weakly collisional as well as a collisionless plasma. We derive a set of equations with a simple energy conservation law which is useful for understanding the evolution of the system.
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Nonlinear Oscillations of Nonlinear Damping Gyros: Resonances, Hysteresis and Multistability
International Journal of Bifurcation and Chaos, 2020This paper addresses the issues on the dynamics of nonlinear damping gyros subjected to a quintic nonlinear parametric excitation. The fixed points and their stability are analyzed for the autonomous gyros equation. The number of fixed points of the system varies from one to six.
C. H. Miwadinou +5 more
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Nonlinear Vibrations of Fractionally Damped Systems
Nonlinear Dynamics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Padovan, Joe, Sawicki, Jerzy T.
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Perturbation Theory for Damped Nonlinear Oscillations
Journal of Mathematical Physics, 1970A perturbation theory has been worked out for the decay of autonomous, nonlinear oscillations in the case where there is large linear damping. The solution reduces to a solution obtained by Kryloff and Bogoliuboff for small damping and to the perturbation solution for periodic oscillations for vanishing damping.
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2015
In this chapter we consider the effects of linear and nonlinear absorption (damping) on collapsing solutions.
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In this chapter we consider the effects of linear and nonlinear absorption (damping) on collapsing solutions.
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ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS
International Journal of Bifurcation and Chaos, 2000This paper reports on the effect of nonlinear damping on certain nonlinear oscillators, where analytical estimates provided by the Melnikov theory are obtained. We assume general nonlinear damping terms proportional to the power of velocity. General and useful expressions for the nonlinearly damped Duffing oscillator and for the nonlinearly damped ...
José L. Trueba +2 more
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On the Stochastic Wave Equation with Nonlinear Damping
Applied Mathematics and Optimization, 2007This article considers a wave equation with nonlinear damping, driven by Brownian noise. Existence and pathwise uniqueness of solution to the initial-boundary value problem is established. For the special case of pure nonlinear damping, existence of an invariant measure is also established.
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