Resonant Interaction Research Articles

Solitons and lumps in the cylindrical Kadomtsev-Petviashvili equation. II. Lumps and their interactions.

We study solitary waves in the cylindrical Kadomtsev-Petviashvili equation designated to media with positive dispersion (the cKP1 equation). By means of the Darboux-Matveev transform, we derive exact solutions that describe two-dimensional solitary waves (lumps), lump chains, and their interactions. One of the obtained solutions describes the modulation instability of outgoing ring solitons and their disintegration onto a number of lumps. We also derive solutions describing decaying lumps and lump chains of a complex spatial structure-ripplons. Then, we study normal and anomalous (resonant) interactions of lump chains with each other and with ring solitons. Results obtained agree with the numerical data presented in Part I of this study [Hu et al., Chaos (2024)].

Design of metamaterial perfect absorbers in the long-wave infrared region.

We designed a narrow-band metamaterial absorber (NMA) and an ultra-broadband metamaterial perfect absorber (UMPA) based on the impedance matching theory. The narrow-band metamaterial absorber mainly consists of Si3N4 cylinders with Si3N4 and Ti substrates. Numerical analysis shows that the absorption peak of the NMA is about 99.9% and the absorption bandwidth with more than 90% absorption is about 4.8 μm (9.5-14.3 μm). To further extend the absorption bandwidth, an ultra-broadband absorber was designed by integrating a Ti hyperbolic rectangle into the Si3N4 cylinder of the NMA. Numerical analysis shows that the absorption bandwidth of the UMPA is up to 10 μm (7-17 μm) with an average absorption rate of 96.6%. The designed UMPA has polarization insensitive properties with wide-angle absorption characteristics, and the average absorption can reach 85% and 76% in transverse magnetic (TM) and transverse electric (TE) modes, respectively, at 60° oblique incidence. The high absorption and wide band are mainly dominated by localized surface plasmon resonance, Fabry-Perot resonance and inter-resonance interactions. The designed absorber achieves excellent absorption in the long infrared wavelength band, which has potential applications in energy absorption, infrared sensing and other fields.

SIMULATION OF CAPILLARY WAVE TURBULENCE ON THE BASIS OF FULLY NONLINEAR PLANE-SYMMETRIC MODEL

A new model for the direct numerical simulation of capillary wave turbulence arising at a free surface of deep incompressible fluid is proposed in the work. The plane-symmetric model based on the time-dependent conformal transform is fully nonlinear and takes into account the effects of surface tension, external random forcing and dissipation of energy. The simulation results show that the system of nonlinear capillary waves can go into a quasi-stationary state (wave turbulence regime), when the action of an external force is compensated by the viscosity. In this regime, the fluid motion demonstrates quite complex and irregular behavior. The spatial and frequency spectra of surface perturbations acquire a power-law dependence in the quasi-stationary state. The exponents of the spectra do not coincide with the classical Zakharov-Filonenko spectrum obtained for isotropic capillary turbulence. In the case of anisotropic quasi-1D geometry, five-wave resonant interactions become the dominant process. The numerical results agree with high accuracy with the corresponding analytical spectra obtained on the basis of dimensional analysis of weak turbulence spectra.

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

NOVEL INVESTIGATION OF FRACTIONAL LONG- AND SHORT-WAVE INTERACTION SYSTEM

In ocean engineering, the long- and short-wave interaction system represents a crucial nonlinear evolution equation that elucidates the resonant interaction phenomenon between ocean waves. In this study, we describe the fractional long and short-wave interaction (FLSWI) system employing the M-truncated derivative. Subsequently, we employ the extended fractional [Formula: see text] and the fractional [Formula: see text] methods to address the FLSWI system. These two approaches yields novel and intriguing soliton solutions. To further elucidate the derived soliton solutions, three-dimensional visualizations are constructed and analyzed.

Dielectric coated conductive rod resonantly coupled with a cut transmission line as a tunable microwave bandstop filter and sensor

The resonant interaction of a dielectric-coated conductive rod with the X-band microwave field is investigated. The magnetic field distribution of the Goubau standing radial surface waves was experimentally visualized by using a thermo-elastic optical indicator microscope, and the corresponding electric field distribution was determined via numerical simulations. These field distributions are characterized by a certain pattern of antinodes distinctive for standing waves. An analysis of these field distributions allows one to couple a coated rod with a cut Goubau line. A rod placed in the gap region perpendicular to the Goubau line results in a sharp rejection band in the transmission spectrum which is extremely sensitive to the changes in the surrounding media. The shifting rate of the resonance as a function of the dielectric shell thickness is approximately 1.4 GHz/mm. The Q-factor of copper rods depends on their size and dielectric shell thickness. Longer rods with more energy localization areas have higher Q-factors, typically 1.7 times higher (12.7 vs. 7.5). Moreover, incorporating a dielectric shell enhances energy confinement and can elevate the Q-factor by as much as 22 %. When a 25 mm Cu rod is situated inside a cut Goubau line system, the Q-factor values are significantly higher, with a ratio of 275 to 13. With the addition of a dielectric shell, the Q-factor can be elevated by 58 %. The versatility of the proposed controllable system makes it possible to tune the operating spectrum towards higher GHz and THz frequencies.

Mathematical Modeling of Resonance Interaction of the Microwave and Terahertz Electromagnetic Radiation with 3D Arrays of Magnetically Functionalized Carbon Nanotubes

Mathematical Modeling of Resonance Interaction of the Microwave and Terahertz Electromagnetic Radiation with 3D Arrays of Magnetically Functionalized Carbon Nanotubes

Enhanced X and Ku band microwave absorption powered by a magnetic–dielectric synergistic effect in Pr-doped M/W composite hexaferrites

Pr-doped M/W composite hexaferrites exhibit satisfactory microwave absorption performance due to high magnetic loss and dielectric loss caused by strong resonance interaction and multiple polarization mechanisms.

Properties of Intense H‐Band Electromagnetic Ion Cyclotron Waves: Implications for Quasi‐Linear, Nonlinear, and Nonresonant Wave‐Particle Interactions

AbstractResonant interactions between relativistic electrons and electromagnetic ion cyclotron (EMIC) waves provide an effective loss mechanism for this important electron population in the outer radiation belt. The diffusive regime of electron scattering and loss has been well incorporated into radiation belt models within the framework of the quasi‐linear diffusion theory, whereas the nonlinear regime has been mostly studied with test particle simulations. There is also a less investigated, nonresonant regime of electron scattering by EMIC waves. All three regimes should be present, depending on the EMIC waves and ambient plasma properties, but the occurrence rates of these regimes have not been previously quantified. This study provides a statistical investigation of the most important EMIC wave‐packet characteristics for the diffusive, nonlinear, and nonresonant regimes of electron scattering. We utilize 3 years of observations to derive distributions of wave amplitudes, wave‐packet sizes, and rates of frequency variations within individual wave‐packets. We demonstrate that EMIC waves typically propagate as wave‐packets with ∼10 wave periods each, and that ∼3–10% of such wave‐packets can reach the regime of nonlinear resonant interaction with 2–6 MeV electrons. We show that EMIC frequency variations within wave‐packets reach 50–100% of the center frequency, corresponding to a significant high‐frequency tail in their wave power spectrum. We explore the consequences of these wave‐packet characteristics for high and low energy electron precipitation by H‐band EMIC waves and for the relative importance of quasi‐linear and nonlinear regimes of wave‐particle interactions.

Sensitivity of radio-frequency electric field sensor based on Rydberg Stark effect

Rydberg atoms hold special attraction in electric applications due to their large transition electric dipole moments and huge polarization, which leads to a strong response of atom to electric fields. In radio-frequency (RF) fields, the Rydberg levels are AC Stark shift and splitting, which can realize the study of high-sensitivity electric field sensor of Rydberg atoms. In this work, we use the simpler Shirley’s time-independent Floquet Hamiltonian model to calculate the AC Stark energy spectrum of Cs Rydberg atoms. This model can reduce the basic Hamiltonian into such a Hamiltonian that includes only those Rydberg states that have direct dipole-allowed transitions with the target state, thereby significantly improving the speed of computation. The accuracy of the calculation is proved by fitting with the calculated frequency shift of DC Stark energy levels in the weak fields, and the polarizability of 60D<sub>5/2</sub> and 70D<sub>5/2</sub> Rydberg atomic states are obtained by fitting with the measured ion spectra of DC Stark Cs ultra-cold Rydberg atoms in magneto-optical trap. In addition, we calculate the AC Stark shift of Cs Rydberg atom <inline-formula><tex-math id="M2">\begin{document}$ \left| {60{{\text{D}}_{5/2}},{m_j} = 1/2} \right\rangle $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20240162_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20240162_M2.png"/></alternatives></inline-formula> state in electric fields with different frequencies with <i>ε</i> = 100 mV/m. Rydberg atoms provide a structured spectrum of sensitivity to electric fields due to strong resonant interaction and off-resonant interaction with many dipole-allowed transitions to nearby Rydberg states. This kind of the frequency response structure is of significance to a broadband sensor. And we calculate the sensitivity and the scaling of the signal-to-noise ratio (SNR), <i>β</i>, varying with detuning from the <inline-formula><tex-math id="M3">\begin{document}$ \left| {60{{\text{D}}_{5/2}}} \right\rangle \to \left| {61{{\text{P}}_{3/2}}} \right\rangle $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20240162_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20240162_M3.png"/></alternatives></inline-formula> transition. The value of <i>β</i> allows one to use the result for any Rydberg state sensor to determine the SNR for any <i>Ε</i> in a 1 s measurement. Therefrom, Rydberg sensor can preferentially detect many RF frequencies spreading across its carrier spectral range without modification while effectively rejecting large portions where the atom response is significantly weaker, and the signal depends primarily on the detuning of the RF field to the nearest resonance which does not convey the RF frequency directly.

Energy Spectra of Nonlocal Internal Gravity Wave Turbulence.

Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws for the spatial and temporal energy spectra of internal wave turbulence which are consistent with typical scaling exponents observed in the oceans. The keystone of our description is the assumption that the energy transfers are dominated by a class of nonlocal resonant interactions, known as the "induced diffusion" triads, which conserve the ratio between the wave frequency and vertical wave number. Our analysis remarkably shows that the internal wave turbulence cascade is associated to an apparent constant flux of wave action.

Wave energy conversion by an array of oscillating water columns deployed along a long-flexible floating breakwater

Large-scale spatial configurations combining Wave Energy Converters (WECs) and coastal attenuating-wave facilities have the potential to exploit marine renewable energy sustainably. In this study, an integrated concept of multiple Oscillating Water Columns (OWCs) and a very long floating breakwater is introduced. Associated energy extraction, gap resonance and hydroelastic interaction problems are examined. A coupled numerical simulation methodology consisting of a Finite Volume Method (FVM)based solver and a Finite Element Method (FEM) solver, is developed to investigate the strong fluid and structure coupled problem. The fluid-structure information is matched in real-time and the flexible modes of the floating breakwater are obtained by imposing a restrained beam inside the pontoon. The accurate time-domain model is validated against both simulated and measured data. Extensive parametric studies indicate that the energy conversion has a conflict with the wave attenuation in terms of determining the along-shore number of OWCs. The highest energy conversion in medium-period and long-period waves are observed in the OWCs near the end and middle locations, respectively. Besides, the constructive resonant gap effect between OWCs and the breakwater can amplify the peaks of energy conversion efficiency, leads to a sudden collapse in transmission coefficient curves. With an increased sidewall draft, OWCs closer to oblique incident direction generate stronger piston-type and sloshing oscillations. Additionally, compared with a rigid breakwater, the elastic deformation of the breakwater plays a destructive role in wave energy conversion, which is attributed to the out-of-phase interference of multi-mode radiated waves.

Electron precipitation caused by intense whistler-mode waves: combined effects of anomalous scattering and phase bunching

Resonant interactions with whistler-mode waves are a crucial mechanism that drives the precipitation of energetic electrons. Using test particle simulations, we investigated the impact of nonlinear interactions of whistler-mode waves on electron precipitation across a broad energy range (10 keV- 1 MeV). Specifically, we focused on the combined effects of conventional phase bunching and anomalous scattering, which includes anomalous trapping and positive bunching. It is shown that anomalous scattering transports electrons away from the loss cone and the only process directly causing precipitation in the nonlinear regime is the phase bunching. We further show that their combined effects result in a precipitation-to-trapped flux ratio lower than the quasilinear expectations in a quasi-equilibrium state. Additionally, we calculated the diffusion and advection coefficients associated with the nonlinear trapping and bunching processes, which are vital for understanding the underlying mechanisms of the precipitation. Based on these coefficients, we characterized the phase bunching boundary, representing the innermost pitch angle boundary where phase bunching can occur. A further analysis revealed that electrons just outside this boundary, rather than near the loss cone, are directly precipitated, while electrons within the boundary are prevented from precipitation due to anomalous scattering. Moreover, we demonstrated that the regime of dominant nonlinear precipitation is determined by the combination of the phase bunching boundary and the inhomogeneity ratio. This comprehensive analysis provides insights into the nonlinear effects of whistler-mode waves on electron precipitation, which are essential for understanding physical processes related to precipitation, such as microbursts, characterized by intense and bursty electron precipitation.

Superradiant Detection of Microscopic Optical Dipolar Interactions.

The interaction between light and cold atoms is a complex phenomenon potentially featuring many-body resonant dipole interactions. A major obstacle toward exploring these quantum resources of the system is macroscopic light propagation effects, which not only limit the available time for the microscopic correlations to locally build up, but also create a directional, superradiant emission background whose variations can overwhelm the microscopic effects. In this Letter, we demonstrate a method to perform "background-free" detection of the microscopic optical dynamics in a laser-cooled atomic ensemble. This is made possible by transiently suppressing the macroscopic optical propagation over a substantial time, before a recall of superradiance that imprints the effect of the accumulated microscopic dynamics onto an efficiently detectable outgoing field. We apply this technique to unveil and precisely characterize a density-dependent, microscopic dipolar dephasing effect that generally limits the lifetime of optical spin-wave order in ensemble-based atom-light interfaces.

Velocity-space Signatures of Resonant Energy Transfer between Whistler Waves and Electrons in the Earth’s Magnetosheath

Wave–particle interactions play a crucial role in transferring energy between electromagnetic fields and charged particles in space and astrophysical plasmas. Despite the prevalence of different electromagnetic waves in space, there is still a lack of understanding of fundamental aspects of wave–particle interactions, particularly in terms of energy flow and velocity-space characteristics. In this study, we combine a novel quasilinear model with observations from the Magnetospheric Multiscale mission to reveal the signatures of resonant interactions between electrons and whistler waves in magnetic holes, which are coherent structures often found in the Earth’s magnetosheath. We investigate the energy transfer rates and velocity-space characteristics associated with Landau and cyclotron resonances between electrons and slightly oblique propagating whistler waves. In the case of our observed magnetic hole, the loss of electron kinetic energy primarily contributes to the growth of whistler waves through the n = −1 cyclotron resonance, where n is the order of the resonance expansion in linear Vlasov–Maxwell theory. The excitation of whistler waves leads to a reduction of the temperature anisotropy and parallel heating of the electrons. Our study offers a new and self-consistent understanding of resonant energy transfer in turbulent plasmas.

Simulation of the Wave Turbulence of a Liquid Surface Using the Dynamic Conformal Transformation Method

The dynamic conformal transformation method has been generalized for the first time to numerically simulate the capillary wave turbulence of a liquid surface in the plane symmetric anisotropic geometry. The model is strongly nonlinear and involves effects of surface tension, as well as energy dissipation and pumping. Simulation results have shown that the system of nonlinear capillary waves can pass to the quasistationary chaotic motion regime (wave turbulence). The calculated exponents of spectra do not coincide with those for the classical Zakharov–Filonenko spectrum for isotropic capillary turbulence but are in good agreement with the estimate obtained under the assumption of the dominant effect of five-wave resonant interactions.

In Silico, SwissADME, and DFT Studies of Newly Synthesized Oxindole Derivatives Followed by Antioxidant Studies

The compounds were synthesized by refluxing 6-chlorooxindole with 2,3-dichlorobenzaldehyde and 2,6-dichlorobenzaldehyde in the presence of piperidine as a catalyst and characterized by spectroscopic analysis using 1H NMR, 13C NMR, and mass spectrometry as (E)-3-(2,3-dichlorobenzylidene)-6-chloroindolin-2-one (C-1) and (E)-3-(2,6-dichlorobenzylidene)-6-chloroindolin-2-one (C-2). Additionally, in silico ADME studies indicated that C-1 and C-2 with 1,1 rotatable bonds could have moderate water solubility and therefore could have the potential ability to cross the blood-brain barrier. Both showed high GI absorption, indicating that they are suitable for intestinal absorption while the compounds showed CYP1A2, CYP2C19, and CYP2C9 inhibition. The five drug-likeness criteria, which were Lipinski, Muegge, Ghose, Veber, and Egan, and the principles of drug-likeness are not violated by compounds C-1 and C-2. Also, the DFT computations were performed at the B3LYP level and at 6-311++G ∗ ∗ basis set to evaluate and support the obtained results from the experiment. The FMO results revealed that C-1 could likely prefer the intramolecular interactions rather than the intermolecular interactions, and vice versa for C-2. In addition, the NBO results indicated that the resonance interaction, especially the shift of electron to empty orbitals from lone pair electrons of nitrogen, would contribute to the stabilization of both compounds greatly. In DPPH assay, the compounds showed IC50 values of 37.390 and 34.676 μM, respectively. Similarly, in ABTS assay, the calculated IC50 values for the compounds were 25.381 and 33.706 μM, respectively. In short, these results provided a solid ground for further preclinical studies in quest of new effective therapeutic agents.

Analysis of Short Video Communication Mode of City Image under Cross-cultural Threshold: Taking Chengdu on Tiktok as an Example

Cities are carriers of culture, and the process of shaping and disseminating city image is also the process of exporting Chinese culture to foreign countries and attracting audiences. TikTok, as an overseas short-video sharing platform with the characteristics of fragmentation, interactivity, and fast dissemination, has attracted widespread attention from overseas audiences for its short videos about Chinese city image and culture, which has become an important channel for cross-cultural communication. This paper takes the international image shaping and dissemination model of the popular Chinese city Chengdu on TikTok as the research object and uses the 5W model and the encoding decoding theory as the theoretical basis to explore the strategies and effects of Chinese city image and culture dissemination on TikTok from a cross-cultural perspective. The study shows that Chengdus communication on TikTok is characterized by self-media as the major communication body, young travelers as the target audience, the use of city branding and other shaping perspectives as the content communication strategy, and the use of emotional resonance and cultural interactions to enhance the appeal and communication effect of the city, which provides some references and guidance to Chinas external communication of its city image.

Electron resonant interaction with whistler-mode waves around the Earth's bow shock I: The probabilistic approach

Adiabatic heating of solar wind electrons at the Earth's bow shock and its foreshock region produces transversely anisotropic hot electrons that, in turn, generate intense high-frequency whistler-mode waves. These waves are often detected by spacecraft as narrow-band, electromagnetic emissions in the frequency range of [0.1, 0.5] of the local electron gyrofrequency. Resonant interactions between these waves and electrons may cause electron acceleration and pitch-angle scattering, which can be important for creating the electron population that seeds shock drift acceleration. The high intensity and coherence of the observed whistler-mode waves prohibit the use of quasi-linear theory to describe their interaction with electrons. In this paper, we aim to develop a new theoretical approach to describe this interaction, which incorporates nonlinear resonant interactions, gradients of the background density and magnetic field, and the fine structure of the waveforms that usually consist of short, intense wave-packet trains. This is the first of two accompanying papers. It outlines a probabilistic approach to describe the wave–particle interaction. We demonstrate how the wave-packet size affects electron nonlinear resonance at the bow shock and foreshock regions, and how to evaluate electron distribution dynamics in such a system that is frequented by short, intense whistler-mode wave-packets. In the Paper II, this probabilistic approach is merged with a mapping technique, which allows us to model systems containing short and long wave-packets.

Energy Transfer Between Various Electron Populations Via Resonant Interaction With Whistler Mode Wave

AbstractElectron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi‐monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave‐particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles.