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The present study analyzes the propagation of surface waves on a strongly inhomogeneous loaded bi-elastic cylindrical tube with variable material constituents. More precisely, due to the number of related physical applications, the exerted load is considered to be in favor of the Winkler elastic foundation. Further, analytical and approximation procedures of solution are beseeched to examine the model. The revealed results by two approaches are then graphically portrayed, which are then found to possess a high level of conformity. Finally, both the external load due to Winkler foundation d, and the internal material property b are found to oppose the propagation of surface waves in the media. In fact, the opposition deteriorates when both the dimensionless parameters d and b are greater than 0.5.

Elastic metamaterials are man-made materials engineered with the purpose of inducing atypical bulk elastic properties. To model a type of elastic metamaterial with local rotational effects, a new two-dimensional continuum model which incorporates local rotation as a scalar field superposed on the translational displacement fields is utilized. This paper provides a comprehensive study of surface wave propagation in this new continuous medium. Unlike the classical Rayleigh wave, the surface wave in this new medium is dispersive. An explicit dispersion relation is obtained, and a closed-form solution of the dispersion curve is derived. The dispersion relation is then used to evaluate the general behaviour of the surface wave. It is found that even for the cases where the effect of local rotation is relatively weak, the surface wave still clearly shows dispersion. The phase velocity of the surface wave falls mostly between the classical Rayleigh wave and the shear wave, especially for cases where the effect of local rotation is weak. In addition to the classical Rayleigh wave, there exists another surface wave which possesses a wavespeed depending only on local rotational parameters. It was also found that particles residing on the free surface of the material move in an elliptical fashion similar to that of classical Rayleigh wave propagation. [ABSTRACT FROM AUTHOR]

The effects of poloidally inhomogeneous heat sources are investigated through a gyrokinetic formula in collisionless toroidal plasmas. A gyrokinetic dispersion relation is newly derived under the assumption that equilibrium parallel heat flows are generated to remove the injected poloidally nonuniform heat source. The dispersion relation is numerically solved, considering both inboard and outboard heat source injections. In the case of the inboard source injection, both Stringer spin-up and geodesic acoustic mode (GAM) are excited. Conversely, outboard injection leads to the emergence of a heat source-driven GAM (referred to as Q-GAM), featuring a frequency around half that of the standard GAM. Various physical quantities of the Q-GAM, such as mode frequency and source threshold, are analyzed through parametric scans. The Q-GAM exhibits similarities with the energetic-particle-driven GAM (EGAM), particularly in its frequency range, and both belong to one of the strong Landau damped poles. Despite having distinct driving mechanisms and structural differences in parallel velocity and poloidal coordinates, the response function of the perturbed parallel pressure to the potential, mainly contributing to the destabilization of each mode around half of the GAM frequency, is derived to have a similar form for both the Q-GAM and EGAM cases.

This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are mathematically derived. Then, based on these basic equations and the transfer matrix method, two equivalent mathematical models are established concerning the propagation of radially propagated cylindrical surface acoustic waves in this piezoelectric semiconductor semi-infinite medium. Based on the surface and interface effect theory, the homo- or hetero-junction is theoretically treated as a two-dimensional electrically imperfect interface in the first mathematical model. To legitimately confirm the interface characteristic lengths that appear in the electrically imperfect interface conditions, the homo- or hetero-junction is equivalently treated as a functional gradient thin layer in the second mathematical model. Finally, based on these two mathematical models, the dispersion and attenuation curves of radially propagated cylindrical surface acoustic waves are numerically calculated to discuss the influence of the homo- and hetero-junctions on the dispersion and attenuation characteristics of radially propagated cylindrical surface acoustic waves. The interface characteristic lengths are legitimately confirmed through the comparison of dispersion and attenuation curves calculated using the two equivalent mathematical models. As piezoelectric semiconductor energy harvesters usually work under elastic deformation, the establishment of mathematical models and the revelation of physical mechanisms are both fundamental to the analysis and optimization of micro-scale surface acoustic wave resonators, energy harvesters, and acoustic wave amplification based on the propagation of surface acoustic waves.

The gray model simplifies calculations by ignoring phonon polarization, but sacrifices a certain level of computational accuracy. In effect, the frequency and wavevector of phonons form complex polarization patterns, which means their propagation modes and vibrational directions have different influences. Therefore, based on the phonon dispersion relations in silicon, the lattice Boltzmann method is used to analyze the phonon transport characteristics in nano-silicon films under ultrafast laser excitation. The results show that the total energy density distribution obtained by superimposing acoustic and optical branches exhibits multiple wave-like behaviors. Among them, the acoustic branch has excellent transfer capability, dominating the rate at which the total energy density reaches a steady state distribution, while the optical branch has stronger heat capacity characteristics, with a greater impact on the peak value of the total energy density. When the heat transfer approaches a steady state, the longitudinal optical branch surprisingly contributes up to 52.73%. This indicates that the often-neglected optical phonons should also receive sufficient attention. Additionally, compared to the results of the gray model, it is found that the dispersion model is preferred when more attention is paid to the propagation characteristics during phonon transport.

Abstract There is an increasing interest in the study of metamaterials and periodic materials across disciplines. These are anisotropic and their properties present directionality. For example, the wave speed depends on the propagation direction. Furthermore, they are heterogeneous, and their directionality depends on their spectra. Common approaches to describe anisotropy have been used in the large-wavelength approximation corresponding to static properties. Here we present an anisotropy measure based on the dynamic behavior. It receives dispersion surfaces from Bloch analyses and outputs a curve/surface with bulk directionality encoded on it. We present results for elastodynamics, but it is applicable to other phenomena. [ABSTRACT FROM AUTHOR]

The present paper investigates the band structure of an axially moving belt resting on a foundation with periodically varying stiffness. It is concluded that the band gaps appear when the divergence of the eigenvalue occurs and the veering phenomenon of mode shape begins. The bifurcation of eigenvalues and mode shape veering lead to wave attenuation. Hence, the boundary stiffness modulation can be designed to manipulate the band gap where the vibration is suppressed. The contribution of the system parameters to the band gaps has been obtained by applying the method of varying amplitudes. By tuning the stiffness, the desired band gap can be obtained and the vibration for specific parameters can be suppressed. The current study provides a technique to avoid vibration transmission of the axially moving material by designing the foundation stiffness. [ABSTRACT FROM AUTHOR]

• Novel mathematical model for wave-particle drag effects in semiconductor plates. • Extended Mindlin method for coupled flexoelectric semiconductor plates. • Explicit coupling mechanisms in different waves (extensional, thickness-stretch, bending, and thickness-shear). • New 3D dispersion relations for Lamb waves in flexoelectric semiconductor plates. • New analytical and simple solutions with high accuracy at small wavenumbers. In this paper, the infinite power series of two-dimensional (2D) differential equations for flexoelectric semiconductor plates are derived by extending the Mindlin method. The zeroth-order and first-order theories are systematically presented and applied to the plate made of cubic crystals of class m3m, identifying explicitly the coupling among wave modes and charge distributions. More specifically, it is observed that the extensional and thickness-stretch waves are coupled with axial motions of free carriers; bending and fundamental shear are coupled with the thickness motions of free carriers, showing the dynamic phenomena of the flexoelectric electronic (flexoelectronic) effect; and the shear-horizontal waves, such as face-shear and thickness-twist, are decoupled. Furthermore, when comparing with the three-dimensional (3D) dispersion relations in the flexoelectric semiconductor plate which are also derived for the first time in this paper, the simple 2D theory is shown to be amazingly accurate. For instance, for an infinite plate of thickness 2 h = 0.2 µm, the extension, bending, and shear modes predicted from the present 2D theory agree well with the 3D benchmarks when the actual wavelength is larger than 1.26 µm, i.e., wavelength is at least more than six times of the thickness. To illustrate the flexoelectricity-based wave-particle drag effects, the wave modes and charge distributions are plotted. Due to its simplicity and computational efficiency, the present 2D theory provides us a powerful tool in understanding the physical mechanism of wave-particle drag in flexoelectric semiconductor plates and analyzing acoustoelectric devices when the flexoelectric effect is involved. [ABSTRACT FROM AUTHOR]

The numerical study of surface plasmon polaritons in a chiroplasma–graphene planar structure is presented. The Kobo formulism is utilized for modeling of graphene's conductivity, and certain type of boundary conditions is employed to obtain the dispersion relation for the proposed waveguide structure. The electromagnetic wave theory is used to solve the numerical problem. The effective mode index is studied for the different values of chiroplasma features (i.e., plasma frequency, cyclotron frequency, and chirality are studied in a certain frequency region). It is concluded that chirality has strong influence on attenuation phase constant against incident wave frequency. Furthermore, the normalized field distributions of the graphene medium are also presented for the proposed waveguide. Graphene layer offers additional degree of freedom as compared to conventional plasmonic materials to fabricate the compact nanophotonic circuits. [ABSTRACT FROM AUTHOR]

Ion beam‐dusty plasma interaction leads to significant changes in the dispersion relation of shear Alfven wave depending on the beam, dust grain, and plasma parameters. Hydrogen ion beam particles interact with the shear Alfven wave via cyclotron interaction when they counter‐propagate with the wave and they can also interact with the co‐propagating wave via Cerenkov interaction. The interaction causes beam as well as plasma density fluctuations and gives rise to perpendicular currents. We have analytically obtained the dispersion relation and the growth/damping rate expressions for obliquely propagating shear Alfven waves in dusty plasma. The effect of beam velocity, magnetic field, wave number, dust particle density, and dust charge fluctuations are discussed. It is shown that both the wave frequency and the maximum growth rate decrease with an increase in beam velocity and the variations are different for parallel and perpendicular wave numbers. The dust particles enhance the frequency and maximum growth rate while the dust charge fluctuations induce damping. The results are in good agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

In this paper, using the hydrodynamic model, the Jeans gravitational instability in a dusty plasma with q-nonextensive velocity distributions is investigated. The change in the Jeans instability criterion and growth rate due to the effects of the dust-ion collision, polarization force, and nonextensivity parameters are analyzed in the dust acoustic frequency range. It is shown that by increasing the nonextensivity and polarization parameters, the threshold condition and growth rate of the instability enhance. Furthermore, it is represented that the dust-ion collisions have a stabilizing influence on the growth rate of the instability and drive the system toward thermal equilibrium. These results can be applied to astrophysical phenomena such as the collapse of interstellar gas clouds and subsequent star formation, and also, in the laboratory dusty plasmas. [ABSTRACT FROM AUTHOR]

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Properties of dispersion relations for two new fully nonlinear weakly dispersive shallow water models are studied. For these models, it is possible to use certain parameters to obtain the fourth, sixth, or eighth order of accuracy of phase velocity approximation of the three-dimensional potential flow model. For the hierarchy of shallow water models, with the assumption of slight changes in the bottom shape, formulas are obtained that establish a relationship between the variation rate of the wave amplitude and that of the fluid layer thickness; also, the dependences of the amplitude and length of an incoming wave on the water region depth are derived. It is shown that the new model of the fourth-order long-wave approximation with the eighth order of accuracy of the dispersion relation provides the best approximation of considered characteristics in the case of bottoms of both horizontal and variable shape. [ABSTRACT FROM AUTHOR]

A family , , of the Generalized Friedrichs models with the perturbation of rank one is considered. An absolutely convergent expansion for eigenvalue at the coupling constant threshold is obtained. The expansion largely depends on whether the lower bound of the essential spectrum is a threshold resonance or a threshold eigenvalue. [ABSTRACT FROM AUTHOR]

We construct a two-particle discrete Schrödinger-type operator , associated to a system of two fermions on the two-dimensional cubic lattice interacting via short-range potential, where the non-perturbed part is a convolution type operator with dispersion relation defined on the torus and having a degenerate minimum at . The existence of eigenvalues below the essential spectrum of the operator is proved in the following two cases: in the case for all and in the case of for large . [ABSTRACT FROM AUTHOR]

The Two-stream Instability (TSI) generation is studied analytically in the lunar ionosphere. The TSI is a tiny perturbation in the electron plasma density, due to which an electric field grows with time and this growth is facilitated by the electron plasma in the background. In lunar ionosphere, the TSI comes into existence when the solar wind interacts unhindered with the tenuous lunar electron plasma in the surface bound exosphere. In this study, the conditions which allow the TSI to form and the subsequent instability growth with time i.e. the growth factor, is estimated. Initially, the threshold condition for the TSI to take place is determined. Thereafter, the solar wind and lunar plasma parameter contribution to trigger TSI is investigated along with the effect of these parameters in the evolution of TSI. The plasma TSI evolution with the passage of time is also depicted in phase space diagram with Particle-In-Cell simulations. [ABSTRACT FROM AUTHOR]

Noble metal nanoparticles have attracted attention in recent years due to a number of their exciting applications in plasmonic applications, e.g., in sensing, high-gain antennas, structural colour printing, solar energy management, nanoscale lasing, and biomedicines. The report embraces the electromagnetic description of inherent properties of spherical nanoparticles, which enable resonant excitation of Localized Surface Plasmons (defined as collective excitations of free electrons), and the complementary model in which plasmonic nanoparticles are treated as quantum quasi-particles with discrete electronic energy levels. A quantum picture including plasmon damping processes due to the irreversible coupling to the environment enables us to distinguish between the dephasing of coherent electron motion and the decay of populations of electronic states. Using the link between classical EM and the quantum picture, the explicit dependence of the population and coherence damping rates as a function of NP size is given. Contrary to the usual expectations, such dependence for Au and Ag NPs is not a monotonically growing function, which provides a new perspective for tailoring plasmonic properties in larger-sized nanoparticles, which are still hardly available experimentally. The practical tools for comparing the plasmonic performance of gold and silver nanoparticles of the same radii in an extensive range of sizes are also given. [ABSTRACT FROM AUTHOR]

The quasi-magnetostatic (briefly, magnetostatic) microwaves propagation in a long, circular cross-section waveguide made of an anisotropic uniaxial μ -negative medium (here, a metamaterial consisting of split-ring resonators) is studied by using the quasi-static Maxwell's equations. Such waves do not exist in a circular dielectric waveguide made of an isotropic μ -negative medium. A Laplace equation for the magnetostatic potential of the system is obtained and solved. We derive the dispersion relation for the modes and present numerical solutions. Also, general expressions are derived and illustrated graphically for the power flow and the energy density of the different magnetostatic modes. Physically, these magnetostatic waves owe their existence to the anisotropic property of the system, where in the absence of this property, they disappear. [ABSTRACT FROM AUTHOR]

The present paper uses mathematical analysis to investigate Rayleigh wave transference in an orthotropic layer. The considered model comprises an orthotropic layer covering a homogeneous isotropic micropolar half-space. The surface of the layer and the interface of the two media are taken to be corrugated. The dispersion relation is obtained in the determinant form, which describes the reliance of Rayleigh wave velocity on wave number. Some particular cases have also been deduced and are found to match existing results. The primary outcome of the present study is that the corrugation present in the structure has an influential impact on the velocity of the propagating wave. This impact has been presented through graphs. Moreover, the dynamic response of the layer's height, elastic constant, material density of the orthotropic material, and micropolarity associated with the half-space on the phase velocity of Rayleigh waves have also been shown with the aid of graphs. The present paper finds its applications in the theoretical study of surface wave transference in anisotropic elastic structures. [ABSTRACT FROM AUTHOR]

Scattering-type near-field scanning optical microscopy (s-NSOM) has been beneficial for observing various nano-optical phenomena by overcoming the spatial resolution diffraction limit, creating optical dispersion, and investigating optoelectronic systems. We used s-NSOM on mono-crystalline silver nanoflakes to selectively decompose tip-launched surface plasmon polariton (SPP) signals and suppress the undesired geometrical effects arising from the silver nanoflakes and s-NSOM tips. Comparing the Fourier transform analysis data from all the edges of silver nanoflakes, we successfully identified the momentum of tip-launched SPPs. We have conducted energy spectral measurements on mono-crystalline silver nanoflakes and applied a geometry-independent factor: tip-launched SPP. We neglected the additional complex contribution from various shapes of the nanoflakes in the visible-near infrared regime. These experimentally obtained momentums of SPPs have a good agreement with analytical calculations. We observed that the propagation of the SPP increases with a decrease in excitation energy even without additional destructive fabrications on the surface, although the surface quality of silver nanoflakes is affected by dirt and oxidation. This study provides a precise interpretation of the experimental studies on the various polariton studies using s-NSOM. [ABSTRACT FROM AUTHOR]

Using the method of different scales, formulas for the hydrodynamic fields of acoustic-gravity waves (AGWs) with vertical wavelengths that are small compared to the scales of changes in the background temperature and wind fields are derived. These formulas are equivalent to the conventional WKB approximation, but explicitly include the vertical gradients of the background fields. The conditions for the applicability of the formulas for describing the propagation of AGWs from the troposphere to the thermosphere are formulated and analyzed. The absence of singular points (critical levels) in the equations for wave modes in the analyzed height range is one of the conditions for the applicability of approximate formulas. For the wind from the empirical HWM model, singular points are often located below 200 km and are typical for internal gravity waves (IGWs) with lengths on the order of 10 km. As the wavelength increases, the number of singular points decreases. For IGWs with scales on the order of 300 km or more, there are usually no singular points. It is shown that IGWs with periods of less than 20 min propagating upward from tropospheric heights usually have one turning point in the altitude range from 100 to 130 km. The formulas are useful, in particular, for parametrizing the effects of AGWs in numerical models of atmospheric dynamics and energy. [ABSTRACT FROM AUTHOR]

With the development of composite materials, especially metamaterials, spatiotemporal nonlocal continuum models for overall dynamics of composites have made enormous progress in recent years, which naturally contain intrinsic space and time scales, and provide a favorable platform to explore the microstructural effects. In this paper, the microstructural effects on the overall dynamics of unidirectional composites are investigated via a mechanism-based spatiotemporal nonlocal model. We first identify the intermediate quantities including the intrinsic length and nonlocal attenuation function and explore their correlations to the microstructural parameters. Then analytical solutions of the mechanism-based spatiotemporal nonlocal model are derived to manifest the overall dynamics of composites. Finally, the microstructural effects on the dispersion relation, the dynamic Green's functions and the dynamic responses in the space-time domain are quantitatively depicted by explicit expressions. Since the intrinsic length and nonlocal attenuation function have always been two fundamental issues in nonlocal continuum theories, the results give some insights into their physical mechanisms in the context of composites. [ABSTRACT FROM AUTHOR]

• A constructive link between Willis' method and the two-scale asymptotic method. • Effective impedance tensor characterizing Willis' effective elastodynamic law. • Recursion formula for solving the hierarchical motion equations issuing from asymptotic analysis. Two-scale asymptotic method and Willis' method are jointly examined for the elastodynamic homogenization of periodic composites. The effective elastodynamic constitutive law given by Willis' method, non-local both in time and space, is first reformulated so as to make appear a compact expression for the effective impedance tensor characterizing it. The two-scale asymptotic method is then revisited by exploiting the fact that the results obtained by it constitute an approximation to the general ones delivered by Willis' method. The solutions for the hierarchical motion equations issuing from asymptotic analysis are shown to admit a compact recursive representation. A generic compact expression is derived for the effective impedance tensor associated with the n th-order approximation of asymptotic analysis. Remarkably, this expression turns out to be formally identical to the one of the effective impedance tensor obtained via Willis' method. As an example of illustration, the elastodynamic homogenization of a layered composite undergoing anti-plane shear is investigated in detail. [ABSTRACT FROM AUTHOR]

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Synthetic aperture radar (SAR) imagers are active microwave sensors that could overcome many challenges of passive optical bathymetry inversion, yet their capacity to yield accurate high-resolution bathymetric mapping is not studied sufficiently. In this study, we evaluate the feasibility of applying fast Fourier transform (FFT) to SAR data in coastal nearshore bathymetry derivation in Florida’s coastal waters. The study aims to develop a robust SAR bathymetry inversion framework across extensive spatial scales to address the dearth of bathymetric data in deeper nearshore coastal regions. By leveraging the Sentinel-1 datasets as a rich source of training data, our method yields high-resolution and accurate depth extraction up to 80 m. A comprehensive workflow to determine both the wavelength and peak wave period is associated with the proposed automated model compilation. A novel contour geometry-based spectral analysis technique for wavelength retrieval is presented that enables an efficient and scalable SAR bathymetry model. Multi-date SAR images were used to assess the robustness of the proposed depth-retrieval model. An accuracy assessment against the GMRT data demonstrated the high efficacy of the proposed approach, achieving a coefficient of determination (R2) above 0.95, a root-mean-square error (RMSE) of 1.56–10.20 m, and relative errors of 3.56–11.08% in automatically extracting the underwater terrain at every 50 m interval. A sensitivity analysis was conducted to estimate the uncertainty associated with our method. Overall, this study highlights the potential of SAR technology to produce updated, cost-effective, and accurate bathymetry maps of high resolution and to fill bathymetric data gaps worldwide. The code and datasets are made publicly available.

The paper shows the importance of the dispersion relation in characterizing the capillary waves seen on liquid jets. Several theoretical models are given to better understand the stability of cylindrical interfaces when various parameters are considered, such as confinement, bulk elasticity, or the viscosity ratio between the two liquid phases. Theoretical predictions are compared with experimental data in terms of the fastest-growing mode for several liquid-in-air systems. Capillary-wave decay factors are also investigated, for stationary wave trains created at the impact of a liquid jet on a horizontal liquid bath, via the dispersion relation.

The acoustic characteristics of a cylindrical viscoelastic tube of finite length with a radially fixed outer surface replacing the hexagonal unit cell of a segment of a micro-inhomogeneous medium with cylindrical channels are calculated. The least-action principle and the hypothesis of plane sections are applied. A dispersion relation for longitudinal sound waves in a tube is found, which coincides with the approximations of the exact dispersion relation and has a form typical of micro-inhomogeneous resonant media. From a suitable approximation of the results of known measurements of the reduced input conductance of "semi-infinite" samples, the frequency dependence of the complex shear modulus of the rubber used is found. [ABSTRACT FROM AUTHOR]

Vertical tilt of mesoscale eddies has been frequently observed in world oceans. The observations of composite eddies, individual eddies from an oceanic reanalysis product, and idealized numerical experiments of mesoscale eddies all show that the eddy vertical tilt is gradually increased with time in eddy mature stage, implying that the eddy translation speed changes with depth. However, eddy vertical tilt cannot be explained by the classic linear Rossby wave dispersion relation, since the classic zonal translation speed (Cx ${C}_{x}$) of linear Rossby waves is depth‐independent from the quasi‐geostrophic potential vorticity (QGPV) equation. To deduce a depth‐dependent linear Rossby wave dispersion relation, we solved the QGPV equation by assuming that the stratified water column in oceans can be separated into a number of fine layers with constant stratification in each layer, whereas the stratification changes among layers. A multi‐layer linear Rossby wave (MLRW) dispersion relation in stratified oceans is then deduced. The MLRW dispersion relation shows that Cx ${C}_{x}$ changes with depth. In each layer, Cx ${C}_{x}$ is proportional to stratification and layer thickness but inversely proportional to Earth's rotation. The estimated Cx ${C}_{x}$ structure from the MLRW dispersion relation is consistent with the Cx ${C}_{x}$ structure of eddies in numerical experiments and the observed composite eddies. Noticeably, there are some discrepancies between the theoretical estimates and those from observations and numerical simulations, primarily due to the sensitivity of the theoretical estimates to layer thickness. The study attempts to provide an approach to describe and predict mesoscale eddy vertical tilt. Plain Language Summary: Vertical tilt of mesoscale eddies has been frequently observed in world oceans. We found that the vertical tilt of mesoscale eddies is gradually increased with time in eddy mature stage from composite observed eddies, individual eddies from an oceanic reanalysis product and idealized numerical experiments. We proposed that eddy vertical tilt can be attributed to different translation speed of eddies/waves at depth. The classic linear Rossby wave theory, however, shows that the phase speed of long waves is constant with depth. To deduce depth‐dependent phase speeds of long waves, we assumed that the water column consists of a finite number of layers with constant stratification within each layer while the stratification changes among layers. A new long wave dispersion relation is deduced. The translation speed of eddies/waves from the new relation and the predicted structure of eddy vertical tilt agree well with the estimates from the composite analysis and the numerical experiments. So, the new dispersion relation is promising in predicting vertical tilt of mesoscale eddies in oceans. Key Points: The vertical tilt features of mesoscale eddies can be explained by vertical changes of translation speeds of eddies (Rossby waves)Based on the quasi‐geostrophic potential vorticity equation, a multi‐layer linear Rossby wave (MLRW) dispersion relation is deducedThe MLRW dispersion relation agrees well with the vertical tilt features of eddies in observations and numerical simulations [ABSTRACT FROM AUTHOR]

Solitons are known to play the role of elementary excitations for one-dimensional ordered systems, like atomic chains with charge or spin ordering. The main characteristic of solitons is their dispersion relation, dependence of soliton energy on the linear momentum. Topological kink-type solitons are the simplest and most important for the description of many physical properties of one-dimensional magnets. Here we provide a detailed analysis of solitons in some general class of magnets, ferrimagnets with the spin compensation point. The nonlinear spin dynamics of ferrimagnets are examined using a nonlinear sigma-model for the antiferromagnetic vector, which is a generalization of the Landau-Lifshitz equation for ferromagnets and sigma-model for the antiferromagnets. The characteristic features of this equation are governed by the value of the compensation parameter, describing the rate of compensation of spins of sublattices. The dispersion relation for kink-type solitons appears to be quite nontrivial, including periodic dispersion law for continuum model of magnet or the presence of ending point for kink spectrum. [ABSTRACT FROM AUTHOR]

Linear localized waves evolution in a discrete mass-in-mass lattice is studied. The presence of the attached mass in the model contributes to dispersion giving rise to appearance of both the acoustic and optic wave modes. Important features of the waves are described using the dispersion relation, which is obtained in a continuum limit of the original discrete equations using a harmonic wave solutions. We study numerically the localized initial perturbations evolution and compare the features of the numerical solutions with those obtained for the analytical harmonic wave ons. We have found differences in the wave dynamics depending on the parameters of the initial conditions. One scenario describes almost permanent shape and velocity counterpart localized waves propagation with oscillating standing wave around the position of the initial pulse. Another wave evolution accounts for a decrease in the moving wave amplitude with the developing oscillating tail behind the localized wave. Contrary to the periodic analytical solution, no evidence of a band gap is found in the simulations of localized waves. [ABSTRACT FROM AUTHOR]

We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion relation for general frequencies and show that there are exceptional frequencies for which the solution is a cluster of waves propagating in different directions with different frequencies so that the dispersion relation cannot be defined uniquely. Examples are provided for the spherical inclusions. [ABSTRACT FROM AUTHOR]

A class of problems of wave propagation in waveguides consisting of one or several layers that are characterized by linear variation of the squared refractive index along the normal to the interfaces between them is considered in this paper. In various problems arising in practical applications, it is necessary to efficiently solve the dispersion relations for such waveguides in order to compute horizontal wavenumbers for different frequencies. Such relations are transcendental equations written in terms of Airy functions, and their numerical solutions may require significant computational effort. A procedure that allows one to reduce a dispersion relation to an ordinary differential equation written in terms of elementary functions exclusively is proposed. The proposed technique is illustrated on two cases of waveguides with both compact and non-compact cross-sections. The developed reduction method can be used in applications such as geoacoustic inversion. [ABSTRACT FROM AUTHOR]

Bounded plasma occur in waveguide of nanodevices with dielectric boundaries and the dimension of nanodevices control the frequency of oscillation and particle acceleration. A system with cylindrical bounded quantum plasma is used to study the electrostatic wave instability in the presence of magnetic field. Bohm potential, exchange-correlation potential and Fermi pressure significantly affect the characteristic frequency of oscillation of particle in bounded plasma. Using quantum hydrodynamic model, basic equations of cylindrical bounded quantum plasma are constructed and linearized under the effect of ionization rate. Dispersion relation for growing waves is obtained, which shows dependence on ionization rate, magnetic field, number density, wave vector and geometry of cylindrical waveguide. We investigated that growth rate increases with magnetic field, ionization rate, number density and poles of Bessel’s function, whereas it decreases with wave vector and radius of waveguide. The present investigation is performed on the basis of numerical parameters of astrophysical plasma. [ABSTRACT FROM AUTHOR]

A unified theory of dust ionization waves (DIW) found in the recent experiment and dust acoustic waves (DAW) is proposed. DIW arise due to oscillations in the rate of electron–ion recombination on the surface of dust grains. The theoretical approach is based on the equations of motion and continuity for dust grains, the balance equation for cold ions, the Boltzmann distribution for hot electrons, and the Poisson equation. A unified dispersion relation is derived, which provides an interpretation of the DIW and DAW regularities observed experimentally. [ABSTRACT FROM AUTHOR]

Rayleigh waves are widely used in the nondestructive testing of structures due to the energy concentrating nature. Nevertheless, the wave characteristics become dispersive and complicated when the waveguide is consist of different layers. This may lead to the dispersion and multimodal characteristics of the Rayleigh waves, which is difficult to obtain the dispersion relation accurately. In this study, the dispersion relation of Rayleigh waves in a double-layer material is studied analytically, which allows to localize near-surface cracks more accurately than the classical non-dispersive Rayleigh waves. Firstly, the dispersion characteristic equation of Rayleigh waves in a double-layer material is formulated based on the plane wave expansion method, where the numerical singularity problem in solving the equation is avoided by transforming the characteristic matrix into the non-dimensional form. Based on this, the relations between the wavenumber, the phase velocity, the group velocity and the frequency are obtained and are verified by a refined spectral element model. The detectability of subsurface damages has been investigated based on the wave structure. Lastly, the wave responses simulated by the spectral element analysis are used for case studies. It has been shown that the explicit dispersion characteristic equation obtained in this study can be used to localize near-surface cracks in double-layer materials with high accuracy, having potential value for refined detection of near-surface cracks in practices. [Display omitted] • Characteristic equation is derived analytically in dimensionless formulation. • Quantitative investigation is performed on detectability of hidden damages. • Damage localization becomes more accurate by using proposed model as a reference. [ABSTRACT FROM AUTHOR]

• The influence of flexoelectricity, micro-stiffness and micro-inertia effects on the Rayleigh wave propagation is studied. • The micro-stiffness increases Rayleigh wave velocity, while the micro-inertia and flexoelectricity decrease its value. • The effect of material microstructure and flexoelectricity is important for short wavelengths. • The dispersion curve profile depends on the ratios between flexoelectric coefficients and material lengths scale parameters. A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials. [ABSTRACT FROM AUTHOR]

• Large ferromagnetic transition temperature is observed. • The ferromagnetic transition temperature increases nearly linearly with an increase in Mn ion concentration. • The dispersion relation of (In,Mn)As increases with an increase in the manganese ion concentration. Diluted magnetic semiconductors are a recent research area due to their ability to enhance ferromagnetic properties and facilitate the electrical detection of magnetoresistance and polarization. (In, Mn)As dilute magnetic semiconductor has potential application in the field of spintronic devices, such as spin field-effective transistors, spin laser light-emitted diodes, modern technology, multi-functional devices, green technology, and nanotechnology. For this study, we have considered the RKKY interaction between Mn2+ spins via delocalized carriers. The effect of manganese ion concentration and applied magnetic field on ferromagnetic diluted magnetic semiconductor properties such as dispersion relation, Curie temperature, and reduced magnetization of (In, Mn)As are studied. We have developed a spin-wave model using the Holstein-Primakaff transformation. Based on the developed model, the number of ferromagnetic magnons, dispersion relations, and Curie temperatures were calculated with or without an applied magnetic field. The reduced magnetization is also calculated. The graph of Curie temperature and magnetization of (In,Mn)As versus temperature with applied field up to 6 T and manganese ion concentration from 0.01 to 0.1 are plotted. The graph of spin wave dispersion of (In,Mn)As versus a wave vector with varying manganese ion concentration with and without an applied magnetic field up to 6 T. In this study, an InMnAs Curie temperature of 290.68 K is found without an applied magnetic field with a 0.1 manganese ion concentration, which is near room temperature. Moreover, with an applied magnetic field of 6 T at 0.1 manganese ion concentration, a Curie temperature of 342.466 K is found, which is above room temperature. Hence, these temperatures are suitable for the field of next-generation spintronic new technology. [ABSTRACT FROM AUTHOR]

We study the propagation of bending waves along the free edge of a semi-infinite piezoelectric plate within the framework of two-variable refined plate theory (TVPT, a high-order plate theory), Reissner-Mindlin refined plate theory (RMPT, a first-order plate theory), and the classical plate theory (CPT). The piezoelectric plate has macroscopic symmetry of orthogonal mm2 The governing equations are derived using Hamilton principle. The dispersion relations for electrically open and shorted boundary conditions at the free edge are obtained analytically. The difference in dispersion property between the three plate theories is analyzed. The numerical results show that the dispersion curves predicted by TVPT and RMPT are similar and have small difference over the complete frequency range, which means both the two theories are valid for the analysis of edge waves in a piezoelectric plate. But the wave velocity calculated by CPT is much larger than the two theories above and is no longer valid for high frequency and thick plate. The electrical boundary condition at the free edge has an insignificant effect on phase velocity and group velocity which can be ignored for the analysis of edge waves in a piezoelectric plate governed by bending deformation. The velocity of bending edge waves in a semi-infinite piezoelectric plate is positively related to that of Rayleigh surface wave in a traction-free piezoelectric half-space. The edge wave velocity can be enhanced when the piezoelectric plate is considered as one with weaker anisotropy.

A mathematical analysis of wave propagation along an elastic cylindrical tube is presented, with the aim of determining the range of Poisson's ratio for which backward wave propagation (i.e. at negative group velocity) can occur near the ring frequency. This range includes zero Poisson's ratio and a surrounding interval of positive and negative values, whose width depends on the thickness of the tube. The whole range of Poisson's ratio is considered, so that the work applies to modern materials, e.g. composites. All results are presented in simple analytic form by means of a dominant balance in parameter space. The identification of this balance, which is unique, is a main new result in the paper, which makes possible a new type of shell theory based on 'Poisson scaling'. The mathematical approach is deductive from the equations of motion, rather than being based on kinematic hypotheses. A key finding, accessible via the Poisson scaling, is that the regime of negative group velocities extends to high wavenumbers, while being confined to a narrow band of frequencies. Thus responses localized in space are possible for near-monochromatic forcing, an important fact for nonlinear theories of tube dynamics near the ring frequency. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'. [ABSTRACT FROM AUTHOR]

The local-resonance bandgap performance of piezoelectric metastructures could be deteriorated by the inherent resistance existing in the piezoelectric patches and the inductors of shunting circuits. In this article, we propose to use negative-resistance circuits to cancel the inherent electrical resistance and therefore enhance vibration reduction performance in the bandgap. The physical model of the piezoelectric metastructure with negative-resistance shunting circuits is firstly illustrated, followed by analyzing its wave dispersion relations and frequency response functions. The enhanced bandgap performance of the piezoelectric metastructure facilitated by negative-resistance circuits is verified with the analytical results. Last, an experimental setup of the piezoelectric metastructure is built. The experimental results demonstrate that the vibration suppression performance in the bandgap is significantly increased by using negative-resistance circuits, and a higher value of negative resistance could lead to larger vibration reduction. Overall, the results of this article provide a novel means to enhance the local-resonance bandgap performance of piezoelectric metastructures. [ABSTRACT FROM AUTHOR]

The dispersion relation and the speed of linear magnetosonic wave are given in the present paper. Furthermore, an arbitrary amplitude nonlinear magnetosonic solitary wave is studied. It is found that the amplitude of the magnetosonic solitary wave cannot be larger than a critical value. It is found that the maximum speed of the magnetosonic solitary wave is about 1.24 times that of the Alfvén wave speed when the magnetic field is sufficiently strong so that the magnetic pressure is much larger than the fluid pressure. On the other hand, the maximum perturbed magnetic field is just equal to the external magnetic field if the magnetic pressure is much larger than the fluid pressure. It suggest that the variation regime of the perturbed magnetic field is (0 , B 0) , while the variation regime of the speed of magnetosonic solitary wave is (v A , 1.24 v A) in the upstream and downstream regions of the Venusian bow shock. Here B 0 and v A represent the background magnetic field and the Alfvén wave speed, respectively. [ABSTRACT FROM AUTHOR]

A system of mathematical equations was developed for the calculation of the natural frequencies of helical springs, its predictions being compared with finite element simulation with ANSYS®. Authors derive the general equations governing the helical spring vibration relative to the Frenet trihedral representing the normal, binormal and tangent unit vectors to the spring medium line. The dispersion relation ω = f (k) has been obtained to model a wave traveling along the axis of the wire. [ABSTRACT FROM AUTHOR]