Dispersion Relation For Waves Research Articles

Influence of nonlinearity on the Bragg resonances in coupled magnon crystals

Purpose. The purpose of this paper is to investigate the effect of nonlinearity on formation mechanism and characteristics of Bragg resonances in vertically coupled magnon crystals with periodic groove system on the surface. In this paper a wave model is constructed, a nonlinear dispersion relation for surface magnetostatic waves in such a structure is obtained and the characteristics of each of the Bragg resonances are numerically studied with increasing input signal power. Methods. Theoretical methods of investigation of spin-wave excitations in a wide class of structures with ferromagnetic layers have been used. In particular, the following theoretical models have been used: coupled wave method, long-wave approximation. Results. This paper presents the results of a theoretical investigation of the effect of magnetic nonlinearity on Bragg resonances in a sandwich structure based on magnon crystals with periodic grooves on the surface separated by a dielectric layer. A mechanism for the formation of band gaps at the Bragg resonance frequencies in the presence of media nonlinearity has been revealed. It is shown that with increasing input power the frequency interval between the band gaps decreases. With increasing magnetization difference of magnon crystals, the effect of nonlinear convergence is more pronounced. Conclusion. The identified features extend the capabilities of sandwich structures based on magnon crystals for frequency selective signal processing by controlling the frequency selectivity, both via static coupling parameters, periodicity and layer magnetisation, and dynamically via the input signal power.

Breggovskie rezonansy v mul'tiferroidnom kristalle s dvoynoy nelineynost'yu

The influence of double (electrical and magnetic) nonlinearity on the Bragg resonances of the hybrid electromagnetic-spin waves in a multiferroic crystal has been theoretically and experimentally revealed. The multiferroic crystal consists of an yttrium iron garnet layer with a periodic system of grooves on the surface and a ferroelectric strontium–barium titanate layer. A dispersion relation for the hybrid waves is obtained, and the mechanism of formation of main and hybrid band gaps, namely, suppression bands, is revealed. It is shown that taking into account the magnetic nonlinearity leads to frequency rearrangement of both band gaps and taking into account the electrical nonlinearity leads to frequency rearrangement of only the hybrid band gap. In the general case, the effects of the electrical and magnetic nonlinearities on the hybrid band gap can be compensated.

Graphene-based phononic crystal lenses: Machine learning-assisted analysis and design

The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing.

Dispersion Engineering by Hybridizing the Back-Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes.

In many cases, the hybridization of two or more excitation modes in solids has led to new and useful dispersion relations of waves. Well-studied examples are phonon polaritons, plasmon polaritons, particle-plasmon polaritons, cavity polaritons, and magnetic resonances at optical frequencies. In all of these cases, the lowest propagating mode couples to a finite-frequency localized resonance. Herein, the unusual metamaterial phonon dispersion relations arising from the hybridization of an ordinary acoustical phonon mode with a back-folded soft or easy phonon mode of a monomode elastic metamaterial are discussed. Conceptually, the single easy mode can have strictly zero wave velocity. In reality, its wave velocity is very much smaller than that of all other modes. Considering polymeric three-dimensional printed elastic monomode metamaterials at ultrasound frequencies, it is shown theoretically and experimentally that the resulting pronounced avoided crossing, with a frequency splitting comparable to the mid-frequency, leads to backward-wave behavior for the lowest band over a broad frequency range, conceptually at zero loss.

Instability of Ion Cyclotron Waves (ICWS) at the Expense of Lower Hybrid Drift Waves (LHDWS) Turbulence Energy

Instability of ion cyclotron waves(ICWs) is investigated in presence of lower hybrid drift waves(LHDWs) turbulence. Plasma inhomogeneity in the Earth’s magnetopause region supports a range of low frequency drift wave turbulent fields due to gradients in density in different regions of the media. One of these drift phenomena is identified as lower hybrid drift waves (LHDWs) which satisfies resonant conditions ω − k · v = 0. We have considered a nonlinear wave-particle interaction model where the resonant wave that accelerates the particle in magnetopause may transfer its energy to ion cyclotron waves through a modulated field. In spite of the frequency gaps between the two waves, energy can be transferred nonlinearly to generate unstable ion cyclotron waves which always do not satisfy the resonant condition Ω−K · v ≠ 0 and the nonlinear scattering condition Ω − ω − (K − k) · v ̸= 0. Here, ω and Ω are frequencies of the resonant and the nonresonant waves respectively and k and K are the corresponding wave numbers. We have obtained a nonlinear dispersion relation for ion cyclotron waves(ICWs) in presence of lower hybrid drift waves(LHDWs)turbulence. The growth rate of the ion cyclotron waves using space observational data in the magnetopause region has been estimated.

Non-ideal magnetohydrodynamics on a moving mesh II: Hall effect

ABSTRACT In this work, we extend the non-ideal magnetohydrodynamics (MHD) solver in the moving-mesh code arepo to include the Hall effect. The core of our algorithm is based on an estimation of the magnetic field gradients by a least-squares reconstruction on the unstructured mesh, which we also used in the companion paper for Ohmic and ambipolar diffusion. In an extensive study of simulations of a magnetic shock, we show that without additional magnetic diffusion our algorithm for the Hall effect becomes unstable at high resolution. We can however stabilize it by artificially increasing the Ohmic resistivity, ηOR, so that it satisfies the condition ηOR ≥ ηH/5, where ηH is the Hall diffusion coefficient. Adopting this solution, we find second-order convergence for the C-shock and are also able to accurately reproduce the dispersion relation of the whistler waves. As a first application of the new scheme, we simulate the collapse of a magnetized cloud with constant Hall parameter ηH and show that, depending on the sign of ηH, the magnetic braking can either be weakened or strengthened by the Hall effect. The quasi-Lagrangian nature of the moving-mesh method used here automatically increases the resolution in the forming core, making it well suited for more realistic studies with non-constant magnetic diffusivities in the future.

Surface Properties of Double-Fin Generated Shock-Wave/Boundary-Layer Interactions

Shock-Wave/Boundary-Layer Interaction (SBLI) is ubiquitous in high-speed air vehicles. SBLI surface flowfield properties of crossing shocks induced by symmetric Double-Fins (DFs) at fin angles of 8° and 10° at Mach 2 are experimentally investigated; a 10° Single-Fin (SF) is also explored as a comparison. Surface visualization is used to capture distinct flowfield structures such as separation and upstream influence. Steady and unsteady Pressure-Sensitive Paints (PSPs) are used to obtain global surface pressure fields. Characteristics of DF-SBLI surface topology are discussed by comparing the corresponding SF-SBLI. The effect of fin angle on DF-SBLI is characterized, and unsteady dynamics of the pressure field are examined. Spectral Proper Orthogonal Decomposition (SPOD) is performed on unsteady PSP, and traveling surface pressure waves and their frequency-dependent behavior are discussed. Dispersion relation of surface pressure waves is revealed by performing two-dimensional space–time Fourier transform on unsteady PSP, and the results are compared with the phase velocity distributions obtained from SPOD. Accompanying group velocity behavior is examined for distinct SBLI regions wherein wave propagation is found dependent on its frequency. Steady surface pressures along the centerline are compared with previous experimental data. Fin-tip spacing is found to be an essential parameter for scaling of upstream influence length.

Design and evaluation of an efficient high-precision ocean surface wave model with a multiscale grid system (MSG_Wav1.0)

Abstract. Ocean surface waves induced by wind forcing and topographic effects are a crucial physical process at the air–sea interface, which significantly affect typhoon development, ocean mixing, etc. Higher-resolution wave modeling can simulate more accurate wave states but requires a huge number of computational resources, making it difficult for Earth system models to include ocean waves as a fast-response physical process. Given that high-resolution Earth system models are in demand, efficient high-precision wave simulation is necessary and urgent. Based on the wave dispersion relation, we design a new wave modeling framework using a multiscale grid system. It has the fewest number of fine grids and reasonable grid spacing in deep-water areas. We compare the performance of wave simulation using different spatial propagation schemes, reveal the different reasons for wave simulation differences in the westerly zone and the active tropical cyclone region, and quantify the matching of spatial resolutions between wave models and wind forcing. A series of numerical experiments show that this new modeling framework can more precisely simulate wave states in shallow-water areas without losing accuracy in the deep ocean while costing a fraction of the price of traditional simulations with uniform fine-gridding space. With affordable computational expenses, the new ocean surface wave modeling can be implemented into high-resolution Earth system models, which may significantly improve the simulation of the atmospheric planetary boundary layer and upper-ocean mixing.

Dispersion Relation and Dynamic Properties of Pendulum-Type Waves Caused by Low-Frequency Vibrations in Blocky Rock Masses with Complex Block-Hierarchical Structures

Dispersion Relation and Dynamic Properties of Pendulum-Type Waves Caused by Low-Frequency Vibrations in Blocky Rock Masses with Complex Block-Hierarchical Structures

A test of gravity with Pulsar Timing Arrays

A successful measurement of the Stochastic Gravitational Wave Background (SGWB) in Pulsar Timing Arrays (PTAs) would open up a new window through which to test the predictions of General Relativity (GR). We consider how these measurements might reveal deviations from GR by studying the overlap reduction function — the quantity that in GR is approximated by the Hellings-Downs curve — in some sample modifications of gravity, focusing on the generic prediction of a modified dispersion relation for gravitational waves. We find a distinct signature of such modifications to GR — a shift in the minimum angle of the angular distribution — and demonstrate that this shift is quantitatively sensitive to any change in the phase velocity. In a given modification of gravity, this result can be used, in some regions of parameter space, to distinguish the effect of a modified dispersion relation from that due to the presence of extra polarization modes.

Suppression of the hydroelastic responses of a composite very large floating structure by a submerged elastic ring

With the aid of the method of matched eigenfunction expansions, the hydroelastic dynamics of a composite very large floating structure on a two-layer fluid is analytically investigated in the framework of linear potential flow theory. The composite structure consists of a semi-immersed rigid cylinder fixed with a floating elastic ring and protected by a submerged flexible ring for mitigating the hydroelastic responses. A new dispersion relation for the hydroelastic waves in the two-layer fluid containing a submerged plate is derived to obtain the wave numbers with a given frequency. The coupling effect among the oscillation of rigid cylinder, the deformation of the floating and submerged plates and the motion of wave is considered by dividing the problem into scattering and radiation parts. An inner product is introduced to deduce the unknown expansion coefficients of the velocity potentials. The amplitudes of heave and pitch motions for the rigid cylinder are obtained and shown graphically. The effects of the physical parameters are explored to confirm the mitigative effect of the submerged ring on the response of the composite very large floating structure. A submerged porous ring can also eliminate the amplitudes of waves in the surrounding water region.

Analysis and Application of the Electromagnetic Wave Propagation, Fields, and Dispersion Relation in an Elliptical Chiro Plasma Waveguide Immersed in Magnetized Plasma

AbstractThis research proposes and investigates an elliptical waveguide filled with chiro plasma as its core and magnetized plasma as its clad region. The clad region is in the constant infinite magnetic field, and its direction is the same as the wave propagation in the chiro plasma elliptical waveguide. The electromagnetic wave propagation in the considered waveguide is studied. The expressions for electromagnetic field components in the chiro plasma core and magnetized plasma cladding are derived. The dispersion relations for the hybrid modes are calculated considering appropriate boundary conditions at the chiro plasma and magnetized plasma interface. The behavior of the energy flux and the dispersion curves are numerically and graphically studied. It is seen that the magnitude of the power density decreases with the increase of the cyclotron frequency and it increases with the increase of the plasma frequency and supports power flow in the backward direction for the considered mode. Furthermore, it is shown higher values of the chirality parameter cause the magnitude of the power flux to increase in the backward direction.

Doppler effect and Rossby waves in the ocean: A brief history and new approaches

The review is devoted to Rossby waves in the ocean. Currently, there are many monographs and scientific articles on this topic, in which the authors approach the presentation of the material in different ways. For researchers who have not delved too deeply into this topic, the analysis of these sources is often perceived as a collection of disparate and often contradictory information that does not allow an adequate understanding of the subject. The review is based on the analysis of the main publications on this topic, and it systematizes the main ideas in various aspects. We also give the readers a comparison of different approaches in this area. Particular attention is paid to the review of the dispersion relations of Rossby waves in the presence of a background flow with an emphasis on the presence or absence of a Doppler additive to the frequency. Although the problem statements and variance ratios under consideration are generally well-known, however, they are presented in significantly different ways by many authors, which often leads to misunderstanding and confusion. We draw the reader’s attention to the key controversial points and bring various approaches into a single coherent system. If long Rossby waves do not “feel” the flow, then this is true for the “shallow water” model and is a consequence of the Galilean non-invariance of the dispersion relation. Considering various approaches, we show that there is no strict dispersion relation for the Galilean-non-invariant dispersion relation. Some not quite strict assumptions and assumptions are always added, such as the formal existence of vertical boundaries or the dependence of the barotropic radius on the variable transverse coordinate. The derivation of the dispersion relation with the Doppler shift also contains some asymptotic expansions, accompanied by an analysis of the theory of dimensions. Using common terminology, we combine the main analytical results on the topic and present them in a single logic.

Screened plasmons of graphene near a perfect electric conductor

Screened plasmon properties of graphene near a perfect electric conductor (PEC) are investigated taking into account the retardation effects. A detailed discussion of the dispersion relation of the mentioned screened plasmonic waves is presented and illustrated graphically using classical electrodynamics and a linearized hydrodynamic model that includes Fermi correction. The result indicates that for realistic wavenumbers, the dispersion relation of plasmonic waves of isolated graphene is almost unaffected by the Fermi correction, while this correction is an important factor for the screened plasmons of graphene near a PEC, where it increases the frequency of surface waves. The results show that near the graphene neutrality point, the surface wave has linear dispersion with a universal speed close to vF/2. Such linear dispersion for surface waves (also known as energy waves) appears to be a common occurrence when splitting of plasma frequencies occurs, e.g., in the electron–hole plasma of graphene [Zhao et al., Nature 614, 688 (2023)]. Furthermore, analytical expressions for the energy parameters (the power flow, energy density, and energy velocity) of screened plasmons of the system are derived. Also, the analytical expressions are derived and analyzed for the damping function and surface plasmon and electromagnetic field strength functions of surface waves of the system with small intrinsic damping.

Inferring neutral winds in the ionospheric transition region from atmospheric-gravity-wave traveling-ionospheric-disturbance (AGW-TID) observations with the EISCAT VHF radar and the Nordic Meteor Radar Cluster

Abstract. Atmospheric gravity waves and traveling ionospheric disturbances can be observed in the neutral atmosphere and the ionosphere at a wide range of spatial and temporal scales. Especially at medium scales, these oscillations are often not resolved in general circulation models and are parameterized. We show that ionospheric disturbances forced by upward-propagating atmospheric gravity waves can be simultaneously observed with the EISCAT very high frequency incoherent scatter radar and the Nordic Meteor Radar Cluster. From combined multi-static measurements, both vertical and horizontal wave parameters can be determined by applying a specially developed Fourier filter analysis method. This method is demonstrated using the example of a strongly pronounced wave mode that occurred during the EISCAT experiment on 7 July 2020. Leveraging the developed technique, we show that the wave characteristics of traveling ionospheric disturbances are notably impacted by the fall transition of the mesosphere and lower thermosphere. We also demonstrate the application of using the determined wave parameters to infer the thermospheric neutral wind velocities. Applying the dissipative anelastic gravity wave dispersion relation, we obtain vertical wind profiles in the lower thermosphere.

Experimental investigation on tip vortex cavity deformation and flow dynamics using high-speed imaging and laser Doppler velocimetry measurements

Cavitation affects engineering applications relating to aquatic operations. Tip vortex cavitation (TVC) leads to several technical problems, such as efficiency loss and noise. Hence, there is a need for a comprehensive understanding of the formation mechanism, shape distortions, and underlying physical phenomena of TVC. The dispersion relation of inertial waves on inviscid cavitating vortices is a valuable tool for predicting various TVC shapes. This study explains the patterns of flow around the tip of an elliptical foil and the cavity shape deformations under different flow conditions through experimental analysis. Experiments are conducted using a National Advisory Committee for Aeronautics hydrofoil in the cavitation tunnel at Chungnam National University. The appearance, development, and shapes of vortex cavitation are closely examined using high-speed imaging technology. There is good agreement between the vortex cavity shapes captured by this high-speed imaging and those derived in previous studies. Using laser Doppler velocimetry (LDV) measurements and analysis through image processing of high-speed images, we compare the vortex core trajectories in cavitating and non-cavitating conditions. There is a good match between the two, demonstrating the feasibility of predicting the flow behaviors around vortex cavities using LDV data. As the noise from the TVC is considered a significant source of underwater radiated noise we also measured sound pressure level, which exhibits abrupt changes at specific cavitation numbers, supporting the occurrence of the singing vortex phenomenon and highlighting its sensitivity to small variations in flow conditions. Furthermore, we obtain precise measurements of the instantaneous TVC diameter under different cavitation numbers, allowing the physical functionality of distinct TVC shapes to be determined. Our results significantly extend the scientific understanding of the flow around TVC and the fundamental causes of TVC distortions.

Closed-Form Wave Dispersion Relationships for Ordinary State-Based Peridynamics

Peridynamics (PD) is a new continuum mechanics formulation introduced to overcome limitations of classical continuum mechanics (CCM). This is mainly achieved by using integro-differential equations rather than partial differential equations. Another important difference of PD is its nonlocal nature with respect to local characteristic of CCM. Moreover, it has a length scale parameter, horizon, defining the range of nonlocal interactions between material points. This nonclassical behaviour also shows itself for dispersion relationships. As opposed to linear dispersion relationships for CCM, PD dispersion relationships are non-linear similar to the observed in experiments. In this study, closed-form dispersion relationships are provided for ordinary state-based peridynamics which is one of the most common PD formulations. Finally, derived closed-form solutions are used to demonstrate the dispersion relationships for various material systems including copper, gold, silver and platinum.

Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Based on Mindlin’s theory and the plane wave expansion method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.

PHYSICS-INFORMED DEEP LEARNING OF NEARSHORE WAVE PROCESSES

The paper introduces the NWnets, a physics-informed deep learning model for reconstructing nearshore wave fields and mapping bathymetry. The physics encoded into the deep neural networks are the wave energy balance equation and dispersion relation. Insights into the model capability are gained through application of the NWnets to a laboratory experiment of wave transformation over a circular shoal. If the bathymetry and discrete measurements of wave height are available, the NWnets model is capable of simulating nearshore wave transformation. Moreover, the extended NWnets can be used for depth inversion if the bathymetry is unknown. Two methods for simultaneously estimating water depths and surface waves are presented. If surface wave number and limited wave height measurements are available from remote sensing platforms, the first method employs wave numbers and scarce measurements of wave height as training data. The second method utilizes scarce wave height and limited water depth measurements as training points to reconstruct bathymetry and wave fields. The results show that both methods are capable of simultaneously mapping the bathymetry and waves when the locations of training points are appropriately distributed.

Polarization and properties of low-frequency waves in warm magnetized two-fluid plasma

This paper presents the derivation of a general wave dispersion relation for warm magnetized plasma under the two-fluid formalism. The discussion is quite general except for the assumption of low frequency and slow phase speed, for which the displacement current is negligible, under the implicit assumption that the plasma is sufficiently dense to satisfy the condition ωpe>ωce, where ωpe and ωce denote the plasma oscillation frequency and electron gyro frequency, respectively. The present discussion does not invoke charge neutrality associated with the fluctuations although it is implicitly satisfied. The resulting dispersion relation that includes the fluid thermal effects shows that there are three eigen modes, which include those corresponding to ideal MHD, namely, fast, slow, and kinetic Alfvén waves, as well as higher-frequency modes including the ion and electron cyclotron and lower-hybrid resonances. The fluid effects in the ideal MHD wave branches are influenced by the finite Larmor radius scales, and when the wave number in the cross field direction is comparable to these values, the fluid effects become significant. It is found that the Larmor radius should be interpreted in the sense as ion-acoustic gyro-radius instead of ion thermal gyro radius only. That is, it is found that the electrons also contribute to the non-ideal effect associated with the kinetic Alfvén wave. A comprehensive explanation of the polarization of each mode is also presented. The present findings indicate that the polarity may change its sign only for the kinetic Alfvén mode branch and that such a transition is based on the propagation angle. When such a change does take place, it is found that the kinetic Alfvén wave transits to an ion-acoustic mode. For each branch, it is also found that the electric field along the ambient magnetic field is purely transverse.