DISSIPATIVE INSTABILITIES AND SUPERRADIATION REGIMES (CLASSIC MODELS)

The generation of an electromagnetic field by oscillators in an open resonator is discussed in a one-dimensional approximation. In this case, the development of the so-called dissipative instability  the dissipative generation regime. Such an instability with the generation of electromagnetic oscillations arises when the decrement of oscillations in an open resonator in the absence of oscillators turns out to be greater than the increment of the resulting instability of the system of oscillators placed in this resonator. It is assumed that the oscillators do not interact with each other, and only the resonator field affects their behavior. If the resonator field is absent or small, the superradiance regime is possible, when the radiation of each oscillator is essential and the field in the system is the sum of all the eigenfields of the oscillators. In the dissipative regime of instability generation, the system of oscillators is synchronized by the induced resonator field. The synchronization of the oscillators in the superradiance mode owes its existence to the integral field of the entire system of oscillators. With a weak nonlinearity of the oscillators, a small initiating external field is required to excite the generation regime. It is noteworthy that the maximum value of the superradiance field is approximately two times less than the maximum field that the same particles could generate if they were at the same point. In all cases, for a given open resonator, the superradiance field turned out to be somewhat larger than the resonator field. Nevertheless, for the same resonator, the increments and attainable field amplitudes in both cases are of the same order of magnitude.

Internal wave shoaling in nearly linear stratifications

<div> <div> <div> <p>In the theory of internal waves in the coastal ocean, linear stratification plays an exceptional role. This is because the nonlinearity coefficient in KdV theory vanishes, and in the case of large amplitude waves, the DJL theory linearizes and fails to give solitary wave solutions. We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth. We demonstrate that the DJL equation does yield exact internal solitary waves in this case. These waves are long due to the weak nonlinearity, and we explore how this weak nonlinearity manifests during shoaling.</p> </div> </div> </div>

Harmonic Generation at a Nonlinear Imperfect Joint of Plates by the S0 Lamb Wave Incidence

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity.