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The finite-difference time-domain (FDTD) method is widely used for numerical simulations of electromagnetic waves and acoustic waves. It is known, however, that the Courant condition is restricted in higher dimensions and with higher order differences in space. Although it is possible to relax the Courant condition by utilizing the third-degree difference in space, there remains a large anisotropy in the numerical dispersion at large Courant numbers. This study aims to reduce the anisotropy in the numerical dispersion and relax the Courant condition simultaneously. A new third-degree difference operator including the Laplacian is introduced to the time-development equations of FDTD(2,4) with second- and fourth-order accuracies. The present numerical simulations have demonstrated that numerical oscillations due to the anisotropic dispersion relation are reduced with the new operator. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 ( R 2 ) 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. [ABSTRACT FROM AUTHOR]

In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers. [ABSTRACT FROM AUTHOR]

In this work, the analytical properties of dispersion relations of the equation of internal gravity waves with benchmark and arbitrary distributions of buoyancy frequency are investigated. To solve the problem analytically, the benchmark distribution of the buoyancy frequency is used, which is known from applied oceanological calculations in the presence of seasonal thermocline. Implicit forms of dispersion dependences are obtained; they are expressed through the Bessel function of real index. For nonzero wave numbers, an asymptotic method of studying the dispersion relation is proposed based on constructing uniform asymptotics of the Bessel functions for large values of real index and argument, expressed through the Airy functions. For an arbitrary distribution of buoyancy frequency, the asymptotic representations of dispersions relationships at small wavenumbers are obtained by means of the perturbation method and the WKB method. The solutions constructed in this work allow further computing the amplitude-phase characteristics for the fields of internal gravity waves with benchmark and arbitrary distributions of the buoyancy frequency. [ABSTRACT FROM AUTHOR]

A gradient-type theory with flexomagnetic/flexoelectric and micro-inertia effects is used to study Love wave propagation in the layered magneto-electro-elastic structures. Two waveguide structures are considered: flexo-piezoelectric layer deposited on the piezomagnetic half-space and flexo-piezomagnetic layer resting on the piezoelectric half-space. The dispersion equations are numerically investigated for the magneto-electrically open and short circuit conditions. It is concluded that the profile of dispersion curves depends on the material composition of the waveguide structure, the guiding layer thickness, and the relative values of flexomagnetic/flexoelectric coefficients and the micro-inertia length-scale parameter. The obtained results are helpful for mathematical modeling of new small-sized acoustic devices. [ABSTRACT FROM AUTHOR]

It is shown that the continuum limit of the metamaterial mass-in-mass model with additional attached mass describes not only the appearance of the additional band gap but also variations in the width and the position of the band gaps. These variations are governed by the key parameter—the stiffness ratio of the attached masses. Numerical study of periodic boundary excitation of the harmonic waves reveals suppression of the harmonic waves for the frequencies lying inside the both band gap areas. Also it is found that harmonic waves recover differently for the frequencies below and above the band gap values. The control mechanism is developed based on the abrupt variation of the stiffness ratio. It gives rise to the arising of phase shift of the wave, its suppression or recovery of the previously suppressed harmonic wave. Nonlinear long wavelength generalization of the model results in obtaining the model equation whose coefficients differ from those of the usual nonlinear mass-in-mass model. It gives rise to propagation of the localized wave with another amplitude and velocity. [ABSTRACT FROM AUTHOR]

New results of experiments on studying the influence of a floating thin plate on regularization of a standing gravity Faraday wave on the free water surface in a rectangular vessel are given. It is shown that an increase in the thickness of the floating plate significantly affects both the natural frequency of oscillations of the hydroelastic system and the shape of the profiles of the observed standing flexural-gravity waves. When the plate thickness is below the critical value, the waveform is described by the theory of non-linear gravity waves; at large thicknesses, the "dry beam" approximation should be used as approximating dependencies. [ABSTRACT FROM AUTHOR]

Collective bulk excitation propagating in the medium of a quark‐gluon plasma are studied. The quark‐gluon plasma medium is described with two different models to investigate the effect of binary collisions and shear viscosity to account for damping and non‐ideality. To find the dispersion relation the longitudinal dielectric functions of the quark‐gluon plasma are used within quantum hydrodynamics and transport equation approaches. The results were obtained numerically by finding the roots of the dispersion relations. Both models are compared with the hard thermal loop approximation as the ideal case for both models. [ABSTRACT FROM AUTHOR]

The linear temporal instability of the confined curved liquid film formed by a liquid jet impinging on a curved wall has been investigated. The corresponding dispersion relation between the non-dimensional wave growth rate and wave number was derived. The dispersion relation further involves the influences of the local radius of curvature and the azimuthal angle of the liquid film. The dispersion relation could be verified with previous researches, and the optimal wavelength has been verified with experiments. Temporal stability analysis shows that the effects of gas-to-liquid velocity ratio, gas-to-liquid density ratio, the relative thickness of the liquid phase to the gas phase, and azimuthal wave number are similar to previous researches, but the unstable ranges are smaller than that in previous researches. This paper further studied the effects of the local radius of curvature and azimuthal angle of the liquid film. As the local radius of curvature decreases, the instability of confined curved films increases for the given conditions. And both the growth rate and instability range increase with the increase of the azimuthal angle. The solutions would be helpful to understand the atomization process of the liquid film formed by a liquid jet impinging on a curved wall. • The dispersion relation involves the influences of the local radius of curvature and azimuthal angle of the film. • The dispersion relation has been verified with experiments. • As the local radius of curvature decreases, the instability of films increases. • Both the growth rate and instability range increase with the increase of the azimuthal angle. [ABSTRACT FROM AUTHOR]

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]

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]

• 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]

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]

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]

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]

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]

Abstract This study uses an analytical method to examine the scattering of a Love wave from an interfacial crack in a thin lossy media (viscoelastic material) that serves as a waveguide layer attached to an unbounded loss-less media (piezoelectric material). The viscoelastic material is modeled using the Kelvin–Voigt equation. Phase velocity and attenuation have been calculated by equating the real and imaginary parts of the dispersion relation to zero, respectively, due to the complex wave number of viscoelastic material. Using the integral transform approach and the dislocation density function, the scattering field close to the crack tip is determined, resulting in a Cauchy singular integral equation of the first type. It has been transformed into a system of linear algebraic equations using Gauss-Chebyshev numerical integration. It has been investigated how frequency, waveguide layer thickness, and viscoelastic material loss factor affect phase velocity and Love wave attenuation. The mode-III dynamic stress intensity factor at the left and right crack-tip is investigated for various thicknesses of the waveguide layer and loss factor of viscoelastic material. The outcomes were verified using numerical data from the COMSOL Multiphysics 5.6 FEA software. The findings are fundamental and could be used in the design of particular sensors. [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]

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 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]

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]

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]

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]

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]

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 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 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]

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]

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]

Exploring the wave propagation in nano-waveguides enables the development of on-chip nano-resonators, leading innovative capabilities that enhance acoustics and micro-mechanics. This paper conducts a numerical investigation into the dynamic properties of periodic nano-waveguides. The Second Strain Gradient (SSG) elasticity, which captures the size effects, is used in the determination of the constitutive relations. The weak form including the element matrices is deduced by the Hamilton's principle. Furthermore, a finite element method, based on the periodic structure theory, is introduced to explore the free wave propagation by solving the eigenvalue problems. The stiffness hardening phenomenon manifested in the dispersion curves, band structures, and energy flow vector fields is discussed. The sensitivity of higher order parameters existing in the SSG theory is analyzed. The numerical investigation for wave propagation in the periodic nano-waveguides through the SSG theory is an innovative work, highlighting the significance of the proposed methodology in explaining the special dynamic characteristics of complex nano-waveguides. • Modeling of 3D nano-waveguides by second strain gradient theory. • Eigenvalue problems within 2D wave finite element method framework. • 2D wave motion properties in two different nano-waveguides. • Sensitivity of higher order parameters existing in second strain gradient elasticity. [ABSTRACT FROM AUTHOR]

This study investigates the comprehensive control of sound energy through a acoustic metamaterial. The unit cell is composed of a main waveguide periodically loaded with labyrinthine tubes that may feature a different number of coiled channels. A theoretical approach employs the four-pole transfer matrix, taking into account visco-thermal effects, to explore the behavior of the metamaterial. Furthermore, experimental tests were conducted in an impedance tube for normal incidence waves. The results of the reflection problem showed that an effective sound energy control (α ≥ 85 % at 520 Hz and ≥ 99 % at 1287 Hz) only exists outside the bandgap regions and that accumulation of absorption peaks is possible by increasing the periodicity of the structure. On the other hand, in the transmission problem, high sound transmission loss (70 dB at 750 Hz and 30 dB at 465 Hz) was obtained. This result is primarily due to the bandgap property, as the behavior of the transmission coefficient is strongly attributed to the wide stopband property in the structure. Therefore, the proposed metamaterial can manipulate sound waves in a wide frequency domain and enables broadband and low-frequency sound insulation. A method for retrieving parameters was used from the experimental reflection and transmission coefficients to obtain the effective parameters of the structure. The effective bulk modulus and the effective mass density exhibited negative values at specific frequencies, providing a better understanding of the physical mechanisms of the metamaterial. Finally, this work contributes to advances in the area of control and manipulation of sound energy through periodic structures as well as understanding the dual properties revealed by the structure. • A acoustic metamaterial for broad sound energy control is proposed. • Periodic labyrinthine structure controls low-frequency noise reduction. • The bandgap property allows for high values of sound transmission loss. • Sound absorption contributes to sound transmission loss in the structure. • Effective structure parameters are achieved with negative values at specific frequencies. [ABSTRACT FROM AUTHOR]

• Demonstration of the efficacy of FT-IR in characterizing materials. • Usage of FT-IR considering of thickness and absorption coefficient effects. • Explanation of dipolar electric moment, overtone bands, and Fermi resonance. • Vibrational modes in 1D, 2D, and 3D systems and IR spectrum representation. • Criteria for the correct FT-IR band identification. This paper investigates the application of Fourier-transform infrared (FT-IR) spectroscopy by analyzing a commercially available plastic bag as an example. The study investigates the vibrational modes, mechanical properties, and structural changes of a bare sample during a tensile test. By measuring the absorption bands and their intensities, valuable information about the chemical composition and the concentration of certain components in the plastic bag is obtained. The behavior of vibrational modes in one, two, and three-dimensional systems is studied, with a focus on their representation in the IR spectrum. The concept of the dipolar electric moment and phenomena such as overtone bands and Fermi resonance are also explained. The X-ray patterns of the bag show talc and polyethylene crystalline phases. Scanning electron microscopy (SEM) determines the thickness of the sample. Tensile tests are performed to investigate the mechanical behavior of the plastic bags. This study demonstrates the informative and educational capabilities of FT-IR spectroscopy in studying the vibrational, mechanical, and structural properties of materials, with an emphasis on the correct application of this technique. The study highlights the importance of considering the effects of thickness and absorption coefficient and applying the Beer-Lambert law to understand the changes in vibrational modes during tensile testing. The results contribute to a deeper understanding of the structural behavior of plastic bags and demonstrate the effectiveness of FT-IR spectroscopy in characterizing such materials. [Display omitted] [ABSTRACT FROM AUTHOR]

In this manuscript, numerical investigations at the chiroplasma-metal planar interface have been performed to explore some features of surface plasmon polaritons (SPPs). Based on the electromagnetic wave theory, we derive a dispersion relation. The effect of tensorial permittivity parameters on effective mode index and propagation loss is analyzed in detail. Numerical results show that chiroplasma parameters, i.e., chirality, cyclotron frequency, and plasma frequency, have a significant impact on effective mode index and propagation loss in the THz frequency spectrum. The presented results of chiroplasma-metal SPPs provide new possibilities to fabricate compact nanophotonic devices in the THz frequency regime. [ABSTRACT FROM AUTHOR]

The linear equations of motion are solved to obtain dispersion diagrams with Rayleigh friction (− γ u) and Laplacian friction (ν ∂ x x u), the latter being solved numerically. Laplacian friction is more efficient at eliminating the short-wavelength Rossby waves, whereas Rayleigh friction is more effective at dissipating long-wavelength Rossby waves. For Rayleigh friction, short-wavelength Rossby waves do not exist at periods longer than the damping time scale (1 / γ); for Laplacian friction, they do not exist for wavenumbers less than 3 / (2 ν 3). For both damping forms, the imaginary wavenumber (k i) no longer separates the upper branch (gravity waves) from the lower branch (Rossby waves) of the real wavenumber (k r), and the waves are damped at all frequencies. The two solutions of k r do not overlap, and for Rayleigh damping, they meet at 0. 5 − γ 2 , which roughly corresponds to ∼ 13.7 days for very low friction. For very high Rayleigh damping, which is an unrealistic scenario, only gravity waves exist in the dispersion diagram. The consequence of adding friction, even if negligible, is that the discontinuity evident in the inviscid solution at the critical latitude no longer holds, or the critical latitude ceases to exist. • Examining dispersion relations for viscid waves in equatorial ocean. • Dispersion diagrams with varied Rayleigh and Laplacian friction coefficients shown. • Minimal influence of damping choice on low-friction long Rossby and gravity waves. • Predominant impact of both damping forms on short Rossby Waves. • Disappearance of critical latitude with addition of damping. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlocal optical response of surface-plasmon polaritons (SPPs) in an asymmetric insulator-metal-insulator (A-IMI) waveguide, in which the two insulator materials have different permittivities. A nonlocal dispersion relation of SPPs in A-IMI waveguides is derived based on the generalized nonlocal response (GNOR) model including quantum pressure effects and induced charge diffusion kinetics in metal film, from which one can see that the nonlocal effects result in not only the disappearance of double-peak and step-like behaviors in the dispersion relation of A-IMI waveguides occurring at local response approximation, but also an obvious frequency blueshift and a loss enhancement. Furthermore, the influence of electron diffusion on the dispersion relation under different diffusion constants in the GNOR model as well as the variation in propagation length and penetration depth of SPPs with metal film thickness and frequency are provided, which are helpful to the future development of plasmonic waveguides. • A nonlocal dispersion relation of SPPs in A-IMI waveguides has been derived based on the GNOR model including quantum pressure effects and induced charge diffusion kinetics in metal film. • The nonlocal effects result in not only the disappearance of double-peak and step-like behaviors in the dispersion relation of A-IMI waveguides occurring at local response approximation, but also an obvious frequency blueshift and a loss enhancement. • The influence of electron diffusion on the dispersion relation under different diffusion constants in the GNOR model as well as the variation in propagation length and penetration depth of SPPs with metal film thickness and frequency are provided, which are helpful to the development of ultra-compact plasmonic waveguides. [ABSTRACT FROM AUTHOR]

• Dispersion relation for discrete heat equation is analyzed. • Real and imaginary parts of the wave vector are obtained as functions of frequency. • Analytical expressions for the phase and group velocities are derived and analyzed. • Continuum limit leads to either Fourier equation or hyperbolic heat equation. • On ultra-short time and space scales the discrete approach is preferable. The dispersion relation in ω-k space has been derived and analyzed for discrete heat conduction equation (DE). The DE is inherently nonlocal both in time and space and can be used to describe non-Fourier heat transport occurring on ultrashort time and length scales. An important distinction between the DE and the continuum description is that the frequencies and wave numbers available to the discrete system are limited, whereas in the continuum description there are no such limitations. Analytical expressions for the attenuation distance, group and phase velocities have been obtained and analyzed as functions of frequency. In the continuum limit, depending on the basic invariant of the continualization procedure, the dispersion relation for the DE reduces to either dispersion relation for the classical Fourier parabolic equation (PE) or to dispersion relation for the hyperbolic heat equation (HE). However, at the moderate and high frequencies the spectrum of the DE differs significantly from the spectra of the PE and HE. This implies that the continuum-based approaches, including both the PE and HE, unable to describe high-frequency and short-wavelength processes and the DE is preferable. This work provides a relatively simple analytical tool to interpret the transient wave-like behavior of heat transport on ultrashort space and time scales. [Display omitted] [ABSTRACT FROM AUTHOR]

We consider the propagation of acoustic time-harmonic waves in homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the radius a of inclusions is small. A new approach is suggested to derive the complete asymptotic expansions of the dispersion relations in two- and three-dimensional cases as a → 0 and first several terms of the expansions are evaluated explicitly. Our method is based on the reduction of the original singularly perturbed (by inclusions) problem to the regular one. The Dirichlet, Neumann, and transmission boundary conditions are considered. In the former case, we estimate the cutoff wavelength λ max supported by the periodic medium in two and three dimensions. The effective wave speed is obtained as a function of the wave frequency, the filling fraction of the inclusions, and the physical properties of the constituents of the mixture. Dependence of the asymptotic formulas obtained in the paper on geometric and material parameters is illustrated by graphs. [ABSTRACT FROM AUTHOR]

The governing equations for fluid flows, i.e. Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) model equations represent a water wave model. These model equations describe the bidirectional propagating water wave surface. In this paper, an auto-Bäcklund transformation is being generated by utilizing truncated Painlevé expansion method for the considered equation. This paper determines the new bright soliton solutions for (2 + 1) and (3 + 1) -dimensional nonlinear KP-BBM equations. The simplified version of Hirota's technique is utilized to infer new bright soliton solutions. The results are plotted graphically to understand the physical behavior of solutions. [ABSTRACT FROM AUTHOR]

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency. [ABSTRACT FROM AUTHOR]

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. Capillarywave 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. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic behavior of material strength due to the traction and propagation of torsional surface waves. Dynamic behavior of material strength depends on non-homogeneity, aeolotropy, irregularity, porosity, and internal prestress in an elastic body. The geometry of the model is constructed by a local-elastic, highly non-homogeneous finite thickness layer over a trigonometric variation of non-homogeneous aeolotropic porous half-space. The surface boundaries of both the free surface and interface are considered corrugated boundaries. The separation variable technique is used to solve the equation of motions (hyperbolic type PDEs), and the Bessel function is adopted in the displacement components of torsional waves for both the media. Because of highly non-homogeneity in the upper layer, the equation of motion comprises a special form of differential equation called Whittaker differential equation, and the solution (as displacement) of the equation is obtained in the form of Whittaker functions. The quantitative prediction of a differential equation is one of the significant tasks in the study of wave propagation, thus, the dispersion equation of the torsional surface waves is introduced analytically with the help of traction-free and continuity conditions. The validity of the final dispersion equation is described using several particular cases. To study the intensity of the torsional surface waves in the model, traction components have been computed along the coordinate axes, which helps to detect the material fracture in the medium. MATLAB software is used to study the dynamic behavior of the phase velocity, under the influence of prestressing irregular boundary surface, non-homogeneity, and porosity parameters in the media. By the numerical simulations, some marvelous changes in the propagation of the torsional surface waves due to the irregularity at the interface and free surface are obtained. The work may be useful to study the behavior of torsional surface waves in the micro-structure material and smart material composite structures used in the aerospace industry and seismology. [ABSTRACT FROM AUTHOR]

For the Vlasov equation with a self-consistent field, a connection is established between the dispersion relation and the Schur algebraic complement of the generator of the corresponding dynamical system. An estimate of the instability index is obtained in terms of the Hankel transform of the background distribution of electrons, the sign of which is determined using the saddle point method. [ABSTRACT FROM AUTHOR]

• Dispersion characteristics of shear wave propagation in an anisotropic dry sandy spherical layered structure is studied. • Structure is composed of isotropic sandy medium covered by a concentric transversely isotropic sandy layer of finite width. • Analytical treatment with contour integration and Fourier-Legendre Expansion theorem is used to achieve dispersion relation. • Debye Asymptotic Expansion is employed to obtain exact closed form dispersion relation and matched with classical result. • Numerical computations are carried out to illustrate the influence of affecting parameters on dispersion curves graphically. An analytical study on the propagation characteristics of shear wave in a spherical layered structure comprising of an isotropic sandy material medium covered by a concentric spherical transversely isotropic sandy material layer of finite thickness has been carried out in the present work. The source of excitation for wave propagation is considered in the outer layer and the analytical treatment with contour integration and Fourier-Legendre Expansion theorem is utilized to accomplish closed form of dispersion relation. Further, Debye Asymptotic Expansion analysis is used to deal the complication caused by the inclusion of Bessel's function, Hankel's function and their derivatives in the solution procedure. With help of Debye Asymptotic Expansion analysis, the obtained dispersion relation converts in the form of elementary functions and found to be in well-agreement with pre-established and classical results through the particular cases. Numerical computations are done to illustrate the influence of the affecting parameters (anisotropy, sandiness and radii ratio) on dispersion curves graphically. Moreover, to expose the impact of anisotropy, numerical data of three distinct transversely isotropic materials (Magnesium, Zinc and Beryl) are taken into the account to establish the comparative study with isotropic material which serves the major highlights of the present study. [ABSTRACT FROM AUTHOR]