Resonance Enhancement by Suitably Chosen Frequency Detuning

The theory of exact resonances (kinematics and dynamics) is well developed while even the very concept of detuned resonance is ambiguous and only studies of their kinematic characteristics (that is, those not depending on time) are available in the literature. In this paper, we report novel effects enforced by the resonance detuning on solutions of the dynamical system describing interactions of three spherical planetary waves. We establish that the energy variation range can significantly exceed the range of the exact resonance for suitably chosen values of the detuning. The asymmetry of system’s solutions with respect to the sign of the detuning parameter is demonstrated. Finally, a non-monotonic dependence of the energy oscillation period with respect to detuning magnitude is discovered. These results have direct implications in physics of atmosphere, e.g., for prediction of weather extremes in the Northern Hemisphere midlatitudes (Proc. Nat. Acad. Sci. USA 2016, 133(25), 6862–6867). Moreover, similar study can be conducted for a generic three-wave system taken in the Hamiltonian form which makes our results applicable for an arbitrary Hamiltonian three-wave system met in climate prediction theory, geophysical fluid dynamics, plasma physics, etc.

Resonance Enhancement by Suitably Chosen Frequency Detuning

In this manuscript we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for exact resonance. Moreover, the range of energy variation is not symmetric with respect to the sign of the detuning. Finally, the period of the energy oscillation exhibits non-monotonic dependency on the magnitude of detuning. These results have important theoretical implications where nonlinear resonance analysis is involved, such as geophysics, plasma physics, fluid dynamics. Numerous practical applications are envisageable e.g. in energy harvesting systems.

К теории плазмон-экситонов: оценка константы взаимодействия и оптический спектр

The structure of the optical spectra related to the resonant interaction of quasi-two-dimensional excitons and localized plasmons is investigated theoretically. The constant of plasmon–exciton coupling is estimated in a model considering a semiconductor quantum well close to a layer of metal nanoparticles in an adjacent dielectric medium. Numerical calculations carried out for GaAs/Ag and ZnO/Al nanosystems indicate that near the plasmon–exciton resonance the spectrum features a double-peak structure which exhibits the plasmon-excitonic anticrossing behavior upon detuning from exact resonance.

On the existence of steady-state resonant waves in experiments

This paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction

The nonlinear triad interaction of two opposing gravity waves with almost identical frequencies and one much longer acoustic-gravity wave is studied for non-resonance, as well as for exact resonance conditions. For non-resonance conditions the previously known results for a ‘bound’ acoustic-gravity wave are recovered. For resonance, or near-resonance conditions, where all three waves are ‘free waves’, the interaction is recurrent and the amplitude of the free acoustic-gravity wave turns out to be much larger than that known for the bound wave. The results for the recurrent evolution are given analytically, in terms of Jacobian elliptic functions and elliptic integrals.

On the Planetary Orbital Period Ratio Distribution In Multiple Planet Systems

Many multiple planet systems have been found by both radial velocity (RV) and transit surveys, such as the Kepler mission. Period ratio distribution of these planet candidates show that they do not prefer to be in or near Mean Motion Resonance (MMR). Nevertheless, there are small but significant excesses of candidate pairs both spaced slightly exterior to exact resonance, particular near the first order of MMR, such as 2:1 and 3:2. Here, we first review recent observational constraints on these multiple transiting systems and theoretical models, which attempt to understand their period ratio distributions. Then we identify a statistical effect based on an intrinsic asymmetry associated with MMR, and find it play an important role in shaping the period ratio distribution near MMR. Last but least, we also find such an intrinsic asymmetry is existing in asteroids of our solar system.