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This paper presents a study of wave propagation through an infinite periodic structure that consists of elastic Timoshenko beams interconnected with rigid bodies. This is a generalized approach in which the beams are not coaxial and the centre of mass of each rigid body is placed away from the intersection of their neutral axes. An analytical approach is used by applying the transfer matrix method (TMM), along with the Floquet–Bloch theorem for elastic wave propagation. Subsequent parametric analysis is performed with visualization of resulting band diagrams of a representative structure. These results are verified through comparison with solutions obtained using the finite-element method (FEM). In this manner, a comprehensive dynamical analysis of tailored metastructures is provided. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

In this work, we investigate the dynamics of Scholte–Stoneley waves (SSWs) travelling along elastic metasurfaces, e.g. thin resonant structures embedding mechanical oscillators, placed at the interface between solid and fluid. To this purpose, an analytical dispersion law, valid in the long-wavelength regime, is derived and used to reveal the hybridization of SSWs with the collective resonance of the mechanical oscillators and the conversion of SSWs into leaky modes within the fluid. The analytical predictions are validated through numerical simulations that include both dispersive and harmonic analysis. Our findings disclose the capabilities of elastic metasurfaces in filtering, trapping and converting SSWs along fluid–solid interfaces, thus supporting the design of novel devices for solid–fluid interaction across various engineering applications, including microfluidics. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'. [ABSTRACT FROM AUTHOR]

Magnetosonic (MS) waves with frequencies above the proton gyrofrequency can be locally generated by ring‐beam protons in the Martian heavy ion‐rich ionosphere. In this study, we conduct a parametric analysis to investigate the effects of heavy ion concentrations, energy (Erb), and angle (αrb) of ring‐beam protons, and wave normal angle on the excitation features of Martian ionospheric MS waves. We find the growth rates and frequency range of MS waves decrease by including O+ and O2+ ions but are insensitive to their relative concentrations. With increasing Erb or αrb, the growth rates of MS waves show a general dropping tendency. Meanwhile, their frequency and wavenumber range are almost unaffected by increasing Erb but shrink to a narrower range mainly distributed in high frequencies by increasing αrb. Unstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique. Plain Language Summary: Magnetosonic (MS) waves are highly compressible electromagnetic emissions in space. Generally, they are locally excited by ring‐like hot protons in plasmas that lack heavy ions. However, a recent study reveals that they can also be locally excited by ring‐beam protons in the Martian heavy ion‐rich ionosphere. Motivated by these differences, we conduct a detailed parametric analysis to investigate how the heavy ion concentrations, the energy and angle of ring‐beam protons, and the wave normal angle affect the dispersion relation and growth rate of Martian MS wave. We find that O+ and O2+ ions lower the growth rates and frequency range of MS waves but the effects of their relative concentrations are insignificant. In addition to the heavy ions, the excitation features of MS waves strongly depend on the wave normal angle and the distribution properties of ring‐beam protons. These results deepen our understanding of the MS wave excitation features in the unmagnetized planet environment with plentiful heavy ions. Key Points: O+ and O2+ ions lower the growth rates and frequency range of Magnetosonic (MS) waves but the effects of their relative concentrations are insignificantThe growth rates of MS waves show a general dropping tendency with increasing ring‐beam energy or angleUnstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique [ABSTRACT FROM AUTHOR]

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 paper analyzes a three-layer waveguide made of chiral metamaterials separated by the graphene interface. The interface consists of three graphene monolayers with a thickness 0.34 nm, so the interface thickness is 1.02 nm. Mathematical formulas are derived for dispersion relations and power flux of guided waves for hybrid odd and even modes at right and left circular polarizations. Power profiles in the waveguide regions are potted and discussed. The work aims to investigate changes that occur due to the graphene presence as an interface in the chiral slab waveguide. It is shown that graphene properties affect the light propagation, which, in turn, provides a disappearance of the fundamental odd mode. The power flux through the waveguide shows a significant effect due to the presence of graphene and chirality. [ABSTRACT FROM AUTHOR]

The dispersion error is currently the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit examples of interior \alpha -dispersion-relation-preserving schemes, of interior order of accuracy 4, 5, 6, and 7, with a complete methodology to construct them. These are dual-pair finite-difference schemes for systems of hyperbolic partial differential equations which satisfy the summation-by-parts principle and preserve the dispersion relation of the continuous problem uniformly to an \alpha \% error tolerance for their interior stencil. We give a general framework to design provably stable finite-difference operators whose interior stencil preserves the dispersion relation for hyperbolic systems such as the elastic wave equation. The operators we derive here can resolve the highest frequency (π-mode) present on any equidistant grid at a tolerance of % lessapprox 5% maximum error within the interior stencil, with minimal extra stencil points. As standard finite-difference schemes have a 100\% dispersion error for high-frequency components, fine meshes must be used to resolve these components. Our derived schemes may compute solutions with the same accuracy as traditional schemes on far coarser meshes, which in high dimensions significantly improves the computational cost. [ABSTRACT FROM AUTHOR]

Multilayered van der Waals (vdW) materials have attracted increasing interest because of the manipulability of their superior optical, electrical, thermal, and mechanical properties. A mass-spring model (MSM) for elastic wave propagation in multilayered vdW metamaterials is reported in this paper. Molecular dynamics (MD) simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials. The results show that the graphene/MoS2 metamaterials have an elastic wave bandgap in the terahertz range. The MSM for the multilayered vdW metamaterials is proposed, and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials. The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional (2D) materials. The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors. [ABSTRACT FROM AUTHOR]

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In this paper, we investigate two-dimensional capillary-gravity water waves of small amplitude, which propagate over a flat bed. We prove the existence of a local curve of solutions by using the Crandall–Rabinowitz local bifurcation theory, and show the uniqueness for the capillary-gravity water waves. Furthermore, we recover the dispersion relation for the constant vorticity setting. Moreover, we present a formal stability result for the bifurcation of the laminar solution. In addition, we prove the analyticity of the free surface. [ABSTRACT FROM AUTHOR]

In this work, we study the propagation of plane acoustic waves in a uniformly moving monodispersed gas suspension. A mathematical model was constructed and the dispersion relation was obtained. [ABSTRACT FROM AUTHOR]

Abstract Magnetosonic (MS) waves with frequencies above the proton gyrofrequency can be locally generated by ring‐beam protons in the Martian heavy ion‐rich ionosphere. In this study, we conduct a parametric analysis to investigate the effects of heavy ion concentrations, energy (Erb), and angle (αrb) of ring‐beam protons, and wave normal angle on the excitation features of Martian ionospheric MS waves. We find the growth rates and frequency range of MS waves decrease by including O+ and O2+ ions but are insensitive to their relative concentrations. With increasing Erb or αrb, the growth rates of MS waves show a general dropping tendency. Meanwhile, their frequency and wavenumber range are almost unaffected by increasing Erb but shrink to a narrower range mainly distributed in high frequencies by increasing αrb. Unstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique.

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 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. Graphical Abstract

Background. Guiding properties of waveguiding structures with graphene are of great importance for various applications and have been studied in many papers. In all such studies, graphene was characterized, as a rule, by linear surface conductivity. However, if the intensity of an electromagnetic wave is large enough, the interaction of graphene with the electromagnetic wave becomes nonlinear; in this case, it is more correct to describe graphene by nonlinear conductivity. Aim. This work is aimed at studying the influence of cubic nonlinearity of graphene, corresponding to the so-called self-action effects (not affecting the frequency of the incident wave), on the propagation of TE- and TM-polarized waves in the structure, which is a plain dielectric layer covered on one side by graphene. Methods. In this study, the guiding properties of the waveguide are studied using primarily an analytical approach. Thus, from Maxwell's equations, material equations and boundary conditions, a couple of dispersion equations for TE-and TM-polarized waves is derived and then its solvability is studied. In addition, some numerical experiments are carried out in the study. Results. The dispersion equations of the studied waveguiding structure for TE- and TM-polarized waves are derived in explicit form. Studying analytically obtained equations, conditions for waveguide parameters are found, providing the existence of a given number of waveguide modes. In addition, some numerical results are obtained in the paper, which give an idea of the influence of nonlinear effects on the electromagnetic waves propagating in the structure. Conclusion. The results obtained in this paper reveal two effects related to the cubic nonlinearity of graphene. Firstly, in a plain dielectric layer with graphene coating in the strong nonlinear regime TE-waves with longer wavelength and TM-waves with shorter wavelength propagate compared to electromagnetic waves that propagate in the same structure in the linear regime. Secondly, the strong cubic nonlinearity leads to a greater localization of the electromagnetic wave within the waveguiding structure.

Purpose: This article concentrates on the block-hierarchical structures of rock masses and investigates the dynamic problem and dispersion relation of pendulum-type waves caused by the low-frequency vibrations of rock blocks in blocky rock masses, and determines the effect of block-hierarchical structures. Methods: The blocky rock masses composed of granite blocks and rubber interlayers are simplified into the block–spring model and the wave motion model. Based on Bloch theorem and d'Alembert's principle, the dispersion relation and equations of motion of blocky rock masses with complex block-hierarchical structures are determined, respectively. Conclusion: With the increase of the rock size and geomechanical invariant, the initial frequency of the first attenuation zone gradually decreases, and only the low-frequency waves lower than that frequency can propagate in the blocky rock masses, which reveals the mechanism of low-frequency characteristics of pendulum-type waves theoretically. Research on the two models with different block-hierarchical structures indicates that the equivalent substitution of the two models is not universal and unconditional. The larger the stiffness ratio, or the higher the order of block-hierarchical structures, the smaller is the effect of ignoring the high-order hierarchical structures. Applications: The research will be of interest to a wide range of experts in the fields of stress wave propagation, earthquake engineering and rock bursts, as well as those working to reduce the engineering vibrations of underground structures and process monitored wave packet data for structures. [ABSTRACT FROM AUTHOR]

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]

In this paper, the Surface Plasmon Polariton (SPP) dispersion relation in the TM polarization for the plane interface between a homogeneous dielectric medium (with constant εd) and a gradedpermittivity (i.e. nonhomogeneous) plasmonic medium (with dielectric function εp(z)) is obtained where ‘z’ is normal coordinate to the interface. For small variation of εp(z) it is revealed that the dispersion relation is related to the derivative of εp(z) at the interface and when εp becomes constant or when its derivative at the interface is zero the well-known dispersion relation for homogeneous plasmonic medium is obtained. For the case where εp(z) depends linearly on z, the dispersion relation is obtained. It is seen that two branches appear. The upper branch has a free-space-like behavior at small wavenumbers. Inclusion of frequency dependence in the εp(z) through Drude model, reveals that the upper branch has negative-value group velocity at intermediate wavenumbers. The results show that non-homogeneity of the plasmonic medium offers a good tunability to control dispersion relation and SPP group velocity. [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]

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]

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]

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 FROM AUTHOR]

We investigate the system of non-stationary one-dimensional equations consisting of a parabolic Burgers equation for the velocity of a viscous gas and a hyperbolic Hopf equation for the velocity of solid particles. The Burgers and Hopf equations are connected into a system due to relaxation terms simulating the momentum transfer between the carrier phase (gas) and the dispersed phase (particles). The momentum transfer intensity is inversely proportional to the relaxation time of the particle velocity to the gas velocity (stopping time). A dispersion relation is constructed for this system. A particular solution corresponding to the damping of a low-amplitude sound wave is found. For an infinitely short velocity relaxation time, the effective viscosity of the gas-dust medium is derived, which is determined by the viscosity of the gas and the mass fraction of particles in the mixture. The Lie algebra of symmetries of Burgers–Hopf system is found. Invariant submodels with respect to the basis operators of the symmetry algebra are derived. These submodels are explicitly integrated, except for one that defines stationary motion. For this submodel, a code has been developed for the numerical generation of particular solutions of the system. It is shown that the invariant solution determined by this submodel, in the asymptotic case of infinitely short velocity relaxation time also makes it possible to obtain the effective viscosity of the gas-dust mixture. Moreover, this effective viscosity coincides with the viscosity value determined from the dispersion relation. [ABSTRACT FROM AUTHOR]

Although an accurate description of wave propagation and absorption in plasmas requires complicated full-wave solutions or kinetic simulations, local dispersion analysis can still be helpful to capture the main physics of wave properties. Plasma wave propagation conditions or accessibility informs whether a wave can propagate to a region, which usually depends on the wave frequency, wave vector, the local plasma density, and magnetic field. We demonstrate a warm multi-fluid eigenvalue model and a matrix approach to rapidly calculate plasma wave accessibility diagrams, where thermal effects are also included via an isotropic pressure term. All cold plasma waves, from high-frequency electron cyclotron waves, intermediate-frequency lower hybrid waves, to low-frequency ion cyclotron waves, are presented. By comparing with the kinetic model, it is interesting to find that the warm multi-fluid model, though incapable of reproducing the Bernstein modes, can provide a quick way to determine whether thermal effects are important.

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.

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]

Foraging for resources is an essential process for the daily life of an ant colony. What makes this process so fascinating is the self-organization of ants into trails using chemical pheromone in the absence of direct communication. Here we present a stochastic lattice model that captures essential features of foraging ant dynamics inspired by recent agent-based models while forgoing more detailed interactions that may not be essential to trail formation. Nevertheless, our model's results coincide with those presented in more sophisticated theoretical models and experiments. Furthermore, it captures the phenomenon of multiple trail formation in environments with multiple food sources. This latter phenomenon is not described well by other more detailed models. We complement the stochastic lattice model by describing a macroscopic PDE which captures the basic structure of lattice model. The PDE provides a continuum framework for the first-principle interactions described in the stochastic lattice model and is amenable to analysis. Linear stability analysis of this PDE facilitates a computational study of the impact various parameters impart on trail formation. We also highlight universal features of the modeling framework that may allow this simple formation to be used to study complex systems beyond ants., (© 2024. The Author(s).)

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]

• 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]

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]

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]

We investigate a one-dimensional plasmonic crystal (1D PlC) using momentum-resolved electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) techniques, which are complementary in terms of available optical information. The PlC sample is fabricated from large aluminum grains through the focused ion beam (FIB) method. This approach allows curving nanostructures with high crystallinity, providing platforms for detailed analysis of plasmonic nanostructures using both EELS and CL. The momentum-resolved EELS visualizes dispersion curves outside the light cone, confirming the existence of the surface plasmon polaritons (SPP) and local modes, while the momentum-resolved CL mapping analysis identified these SPP and local modes. Such synergetic approach of two electron-beam techniques offers full insights into both radiative and non-radiative optical properties in plasmonic or photonic structures., (© The Author(s) 2024. Published by Oxford University Press on behalf of The Japanese Society of Microscopy.)

• A nonlocal dispersion relation of GPs in asymmetric MIM waveguides is derived. • The derivation is based on the GNOR model including quantum pressure and charge diffusion kinetics. • The nonlocal effects induce frequency blueshift and loss increment of dispersion relation. • The GPs-guiding performance of asymmetric MIM waveguides is sensitive to the nonlocal effects. In this paper, we combine the classical electrodynamics theory with the generalized nonlocal optical response (GNOR) model to theoretically investigate the propagation behaviors of gap plasmons (GPs) in an asymmetric metal-insulator-metal (A-MIM) waveguide. The nonlocal dispersion relation of GPs is derived, and the computational analysis is conducted for three different types of A-MIM waveguides. The results show that, compared with the local response, the introduction of the nonlocal effects induces not only frequency blueshift and loss increment, but also changes in field distribution, electron density distribution, and propagation length of GPs. [ABSTRACT FROM AUTHOR]

Smoothed Particle Hydrodynamics (SPH) is a numerical method to solve dynamical partial differential equations (PDE). The basis of the method is a ¡¡kernel-based¿¿ way to compute the spatial derivatives of a function whose values are given in moving irregularly located nodes (Lagrangian particles). Accuracy of the SPH is determined by independent parameters — the shape of the kernel, the kernel size h , the distance between the particles Δ x. Constructing high-order SPH-schemes for different types of PDE is a state-of-the-art problem of computational mathematics. For the classical SPH-approximation of one-dimensional hyperbolic equations (isothermal gas dynamics) we found that the order of approximation of smooth solution correlates to the dispersion properties of the method. To this end we analyzed the dispersion relation for the approximation and found analytical representation of the numerical wave phase velocity. Moreover, for the first time, the order of approximation with respect to Δ x / h was confirmed in computational experiments on a dynamic problem of sound wave propagation. For two kernels with 2 and 4 continuum derivatives, the second and the fourth order of approximation, respectively, was found. This finding may be generalized as follows. The solution error in the one-dimensional case for a quasi-uniformly located particles has the form O ( (h λ) η + (Δ x h) ξ) , where ξ is a parameter determined by the shape of kernel (its smoothness, i.e. the number of continuum derivatives), η is a parameter that does not depend on the shape of kernel (for classical non-negative kernels η = 2), λ is the wavelength. Our results indicates that to develop high-order SPH-schemes for hyperbolic equations besides improving the order of approximation with respect to h / λ one need to ensure the order of approximation with respect to Δ x / h. To this end kernels of which smoothness is at least 4 are necessary. • Dispersion relation for SPH allows to find the approximation order on smooth solution • Order of SPH approximation with the number of neighbors depends on the kernel • 4th order of approximation with the number of neighbors is confirmed in simulation [ABSTRACT FROM AUTHOR]

This article presents a comprehensive study of torsional surface wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer bonded to functionally graded (FG) half-space considering electrically short and open boundary conditions. The Strength of Materials (SM) and Rule of Mixtures (ROM) approaches have been adopted to determine the effective properties of the PFRC. The non-ideal mechanical and electrical interfacial boundary has been considered for the problem which appears in various realistic scenarios. For the torsional surface wave propagation through PFRC bonded to FG half-space, the dispersion equation has been derived analytically using Whittaker function. The obtained results are validated and matched with existing results by considering special cases. The variation of phase velocity due to the influence of fiber volume fraction, interfacial imperfection parameters and functionally grading parameters have been analyzed and illustrated by means of graphs. Furthermore, the distribution of the field variables, stress and electric displacements across the composite are presented through surface plots. The model holds potential applications in designing and manufacturing transducers, actuators and sensors. The use of PFRC can be found in a wide range of cutting-edge technology, including vibration-canceling gadgets, energy harvesters, and pressure sensors. • The analytical study of the torsional surface wave propagation in piezo-electric fiber-reinforced composite (PFRC) structure is investigated. • Strength of material (SM) and Rule of mixtures (RoM) are adopted todetermine the effective coefficients of the micro-mechanical modeling ofPFRC structures. • The effect of fibre-matrix volume fraction, functionally grading parameters and imperfect boundary on the propagation of the torsional wave in PFRC structure arediscussed analytically as well as numerically. • The 2D and 3D plots of mode shapes of field variables for torsional wave propagation are presented graphically. [ABSTRACT FROM AUTHOR]

The ability to design materials for wave propagation behaviors has high potential for impact in medical imaging, telecommunications, and signal processing. The dispersion relation is the key mathematical object that describes linear elastic wave propagation behavior in a material. To date, the design of wave propagation behavior in materials has been limited to one or two design objectives, for example, designing for one or two bandgaps or wavespeeds. This is a result of the complicated relationship between a material and its dispersion relation, and the hefty computational cost of traditional dispersion computations. Decreasing the amount of time required to perform dispersion computations will streamline the design process of wave devices, allowing for more thorough design optimization workflows, more highly resolved design features, and multi-functional materials. In this work, we demonstrate a specialized Gaussian Process Regressor as a surrogate model for the computation of dispersion relations to alleviate the immense computational cost of the traditional model. By measuring covariance information from relatively small training sets (10s to 1000s of dispersion relations), our surrogate model efficiently infers the full dispersion relation after solving for the dispersion relation at only a sparse set of wavevector points. Further, we provide a mathematical framework to use this model for material design through gradient-based optimization methods. [Display omitted] [ABSTRACT FROM AUTHOR]

This study investigates the implications of wave–current interaction on the dynamic responses of the W2Power semisubmersible platform for floating offshore wind turbines under operational and extreme conditions. Firstly, two analytical models based on Airy wave theory are developed to analyse the effects of current interaction with regular and irregular waves. Then, these models are integrated with the well-known engineering tool OrcaFlex for the coupled aero-hydro-servo-elastic analysis. The presence of current was found to significantly modify the wave profiles and influence the static equilibrium, mooring system, and motion dynamics of the FOWT. The results reveal that the translational motion responses, such as surge and heave, are affected by wave–current interaction, with mean and maximum values decreasing under a following current and increasing under an opposing current. However, rotational motion responses are minimally affected. Wave–current interaction also notably affects maximum mooring tensions, with variations of up to ± 22 % depending on the current direction and mooring layout. Furthermore, reductions in maximum longitudinal acceleration are observed due to such interaction. Incorporating wave–current interaction in simulations enhances our understanding of FOWT dynamics and allows for more reliable estimations of system behaviour, emphasising the importance of ensuring safe operating conditions, particularly in sites with opposing currents. • Developed two analytical WCI models, revealing current-altered wave characteristics. • Proposed framework to incorporate WCI in the fully coupled analyses of FOWTs. • WCI impacts motion responses, nacelle acceleration and mooring dynamics of FOWTs. [ABSTRACT FROM AUTHOR]