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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]

• 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 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]

• 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]

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]

Ultrasonic guided waves are widely applied in health monitoring of slender structures. Being different from the well-known semi-analytical finite element method (SAFE), the global-discretized semi-analytical formulation (GDSA) exactly satisfies all the continuity and boundary conditions accurately while has improved computational efficiency, but is only applicable to the plate-like problems described in the Cartesian coordinate system currently, which is not applicable to the cylindrical waveguide. In the present work, the polar coordinate system is therefore introduced into the GDSA formulation to improve the computational efficiency of calculating the dispersion relation in a multi-layer cylindrical waveguide without loss of accuracy. The characteristic equations of the unit layer are derived from the principle of virtual work. The involved matrices are explicitly derived in the form of Kronecker product to reduce the dimension of the matrices to be evaluated and a reduced Boolean matrix is introduced to avoid the singularity problem caused by the trivial radial displacement of the central point. The dispersion curves of a steel wire are firstly analyzed and are verified in comparison with the analytical solutions solved from the Pochhammer-Chree equations. Taking the steel wire having a surface corrosion as a two-layer case example, the dispersion curves are obtained based on the quadratic eigenvalue equation. It is found that the cut-off frequency of the F(1,2) mode is sensitive to corrosion, having potential to detect corrosion of hidden cable wires. • Numerical singularity problem is avoided by eliminating trivial basis component. • The total number of DOFs can be significantly reduced without loss of accuracy. • High-order flexural modes are found to be promising for wire corrosion detection. [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]

• 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]

• 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]

• Velocity-profile of Torsional wave in a porous layer over sand-dune deposits have been found. • Single-step and double-step irregularity greatly influence phase velocity. • Heterogeneity varies as sinusoidal function, linear function, and cosine function of depth. • Biot's parameter, Initial stress in the layer, and the half-space affect the velocity marginally. • Higher magnitude velocity has been observed in RT irregularity compared to the RP interface. The current study aims to study the velocity profile of torsional surface waves in a three-layer model consisting of sand-dunes deposit sandwiched between the watery-porous layer and the orthotropic half-space. The top and the middle layers exhibit irregular interfaces employing various geometrical shapes such as parabolic, rectangular, and triangular notch. The main objective is to analyze the effect of these irregular interfaces on torsional wave propagation. Furthermore, the three-layer model involves inhomogeneity through gravity, initial stress, rigidity, and medium density. These inhomogeneity parameters, coupled with irregularity, bears a remarkable impact on the velocity-profile. The generalized dispersion relation has been derived, and one particular case has been deduced to validate the current work. Detailed numerical simulation has been performed to characterize the computations, and graphical illustrations have been exhibited to support the mathematical investigation. [ABSTRACT FROM AUTHOR]

[Display omitted] In a recent measurement LHCb reported pronounced structures in the J / ψ J / ψ spectrum. One of the various possible explanations of those is that they emerge from non-perturbative interactions of vector charmonia. It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons, which hadronise into two pions at the longest distance. In this paper, we demonstrate that, given our current understanding of hadron-hadron interactions, the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di- J / ψ system, and it is possible for two J / ψ mesons to form a bound state. As a side result we find from an analysis of the data for the ψ (2 S) → J / ψ π π transition including both π π and K K ¯ final state interactions an improved value for the ψ (2 S) → J / ψ transition chromo-electric polarisability: | α ψ (2 S) J / ψ | = (1.8 ± 0.1) GeV - 3 , where the uncertainty also includes the one induced by the final state interactions. [ABSTRACT FROM AUTHOR]

Study of the propagation of sound in a single non-ideal fluid originates with Stokes in 1845 and Kirchhoff in 1868. The situation is much more complex in the case of two-fluid flow, both from the physical point of view, as the configuration of the flow matters greatly, and from the analytical point of view. The principle two-fluid models currently in use for CFD are the focus of this article. It is shown that analytical expressions for the speed of sound depend heavily on the chosen model. These sound speed expressions are compared with experimental values. The consequences for CFD models are discussed in the final section of this paper. We outline the fact that any physical model, (on which numerical models could be based through numerical methods) should propagate the pressure-waves in a physically meaningful manner coherent with experimentation. Hence we question the relevance of physical models that imply two sound speeds (e.g.one per fluid). Whatever is the numerical scheme, it is not reasonable to assume that it could correct the physical model. [ABSTRACT FROM AUTHOR]

• 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]

A prospective method to assess thermo-acoustic instabilities based on two reflection coefficients measured from the upstream side of the burner is presented and experimentally validated. In order to compose a model which allows predicting the onset of thermo-acoustic instability of combustion in a practical appliance, one has to characterize the thermo-acoustic properties of the burner including the flame as an acoustically active element and acoustic properties of all other (usually passive) components of the combustion appliance both upstream as well as downstream of the burner. This kind of modeling strategy usually faces serious practical problems related to the need of measurements/modeling at the hot downstream part of the system. In the present work, we propose a measurement and a system modeling approach which relies on two acoustic measurements, namely reflection coefficients, only at the cold (burner upstream) part of the combustion appliance. Both reflection coefficients, termed upstream and input, can be readily measured using standard acoustic techniques. The need to measure the input reflection coefficient of an acoustically active subsystem may impose difficulties related to the acoustic instability of the measurement setup itself. The approach and technical solution to handle this problem via a special modification of the excitation source (loudspeaker box) is proposed. The dispersion relation to search for system eigen frequencies is represented in a form that couples the reflection coefficients of the upstream part of the appliance and input reflection coefficient from the downstream part as observed through the burner with flame. This form of the dispersion relation is commonly used in the theory of radio-frequency circuits and recently introduced for thermo-acoustic problems. The proposed method is applied to burners with premixed burner-stabilized Bunsen-type flames. The observed instability conditions and oscillation frequencies are compared with predictions of the proposed modeling approach and reveal good correspondence. [ABSTRACT FROM AUTHOR]

Remote sensing instruments, especially synthetic aperture radar (SAR), have become valuable tools for monitoring coastal bathymetry in both space and time. In this study, we investigate the viability of using data from spaceborne SAR satellites to detect shallow water depths from swell patterns. Using data from four Sentinel-1A SAR images, we employed numerical simulations to quantify the sensitivity of the bathymetry results to different initial input parameters such as wavelength, swell period, and initial water depth. Our sensitivity experiments indicate that the swell period is most sensitive to the water depth, while the initial water depth has the lowest impact on the shallow water depth estimation. Once we quantified the sensitivity of the estimated water depth to these parameters, we calculated the minimum and maximum detectable shallow water depth ranges of six SAR orbiting satellites (L-band: ALOS-2, C-band: GF-3, RADARSAT-2 and Sentinel-1, X-band: TerraSAR-X and COSMO-SkyMed). Because of its single-polarization SAR data, the TerraSAR-X satellite is ultimately the best source of SAR data for swell-based bathymetry analyses. With an incidence angle of 20° and significant wave height of 0.6 m, the TerraSAR-X satellite has the largest theoretical depth detection range (with a minimum detectable depth of less than 2 m, and a maximum detectable depth of more than 200 m) for swell waves with a period of 15 s. The results of this study demonstrate that for low to moderate wave height, satellites with lower slant range to platform velocity ratios (R RV) can be successfully applied to the task of large-scale bathymetric mapping at shallow depths where there are weak tidal currents or where no recent or accurate ground truth data is available. Based on these results, we can make recommendations that will enable future users to get reliable, robust bathymetry information from their SAR data sets. [ABSTRACT FROM AUTHOR]

The propagation of flexural-gravity waves in a coupled submerged and floating plate system is studied, and the complex flexural gravity wave propagation properties are investigated in the frequency and time domain, The system exhibits two modes of propagation analogous to the surface and internal waves in a two-layer fluid. The effect of the plate properties on the phase velocities of both the faster (floating plate in general) and the slower (submerged plate in general) modes are analysed in detail. Both modes exhibit complex properties, including waves with negative kinetic energy and points of blocking at which no energy can propagate. They also show complex coupling and energy transfer in the time-domain. Furthermore, the dependency of the blocking frequency and the critical opposing current is analysed in both the shallow and deep water limits. The occurrence of blocking in the internal mode under a specific constraint is also demonstrated. As a special case, the influence of the submerged plate's position and compressive force on the dynamics of the free surface flexural-gravity wave blocking is studied. The characteristics of the phase speed in both modes are studied, and the occurrences/non-occurrences of optima are mathematically proved. Some of the analytic results are illustrated by time-domain simulations which illustrate the complex wave propagation phenomena of this system. [ABSTRACT FROM AUTHOR]

The photoelectric conversion efficiency of organic materials is limited by the exciton splitting at the organic interface which is determined by the exciton binding energy (E b). However, E b is controversial and hard to directly measure by current methods. We propose a dispersion relation to establish a model to accurately extract E b from absorption spectrum. We synthesize an organic-inorganic hybrid perovskite crystal (CH 3 NH 3 PbI 3) and use the absorption spectrum to verify the method. The result of E b is 15 meV at room temperature, which is smaller than 26 meV (thermal energy), implying that our model is not affected by the hot carrier effects. Moreover, this model is applicable to various organic materials (18 kinds). Especially, the binding energy of perovskite is 5 meV under 2 K, which is the same as the result estimated experimentally under 50 Tesla condition. Furthermore, this model allows estimating the effective mass, dielectric constant and excition radius. This work will allow a better understanding of the optoelectronic properties at the interface of organic materials. [ABSTRACT FROM AUTHOR]

In this paper, the backward heat conduction problem is solved numerically using a fourth-order compact difference scheme. For the regularization of this ill-posed problem, fourth-order compact filtering which is a spatial filtering technique is proposed. The second derivative approximation in compact difference scheme has been compared with the fourth-order standard finite difference scheme via Fourier analysis. The comparison shows that the resolution ability of the compact difference scheme is better than the standard finite difference scheme. Meanwhile, an error estimate between the exact and regularized solution is derived. Numerical results are provided using the proposed method. The comparison of CPU time shows that the fourth-order compact difference scheme takes lesser CPU time than the fourth-order standard finite difference scheme. [ABSTRACT FROM AUTHOR]

Elastic wave propagation provides a noninvasive way to examine polydisperse, frictional granular materials. The discrete element method (DEM) allows for a micromechanical interpretation of the acoustic response. Using experimentally measured granular microstructures as input, after straining them to various cyclic, oedometric compression states, we numerically perform both static and dynamic probing to deduce elastic moduli/wave velocities from small-strain modulus degradation and time/frequency-domain signals. Static probing allows to understand the path dependency of the elastic moduli, i.e., the stress response to small strain increments, as well as their degradation behavior, for medium-to-large probing strains. Complementarily, dynamic probing provides insights into the acoustic properties (dispersion relations) at different wavelengths, for various probing characteristics. The wave velocities extracted from the space-time evolution of particle motion are sensitive to travel distance and input waveform, but converge to the same long-wavelength velocities far away from the source, where short wavelengths are dispersed and attenuated. Analyzing the same space-time data in the frequency domain leads to the same results, much less dependent on the probing characteristics than in the time domain, and much faster than static probing. Concerning the dependence on the stress history, as expected, the moduli (and wave velocities) increase under initial oedometric compression. First unloading reveals a significant plastic, irreversible decrease of the moduli, whereas reloading along the oedometric path leads to a reduced degradation. The elastic regime, i.e., the probing strain at which the moduli begin to degrade, gradually decays, as the change of the deviatoric to mean stress ratio increases towards its maximum where plasticity/irreversibility is strongest. Interestingly, the moduli from static probing show that the degradation curves immediately before and after a load reversal are almost identical, suggesting that the elastoplastic behavior is symmetric around the turning point for tiny strains, as also confirmed by identical vibrational densities of states at reversal. Remarkably, the moduli, their degradation behavior and the shapes of the dispersion relations (normalized by their large wavelength limits), are all very similar during unloading and reloading, whereas they reflect a strongly different material behavior under initial loading. [ABSTRACT FROM AUTHOR]

The study of wave propagation in the periodic nano-waveguides is of importance to advance the development of energy and wave controlling systems. In this paper, firstly, the element discretization of nano structures is introduced based on the second strain gradient theory. The displacement field is determined through the utilization of six quintic Hermite polynomial interpolating functions. By applying Hamilton's principle, the weak form, which incorporates the element matrices, is determined and the global dynamic stiffness matrix of a unit cell is assembled. Then, the wave finite element method, based on the inverse form, direct form and contour integral solution, is used to analyze the two-dimensional free wave propagation properties of complex nano structures by solving the eigenvalue problems. The interpretation of the frequency spectrum is confined to the irreducible first Brillouin zone, encompassing both the dispersion relation and band structure. Furthermore, the slowness surfaces and energy flow vector fields are discussed via the second strain gradient theory. The novel work, which utilizes the second strain gradient theory equipped with the wave finite element method to investigate two-dimensional complex nano structures, has revealed significant potential in elucidating the two-dimensional wave propagation characteristics of the complex nano-waveguides. [Display omitted] • Second strain gradient theory is used for the modeling of 3D nano-sized structures. • Constitutive relation and weak form are calculated through the Hamilton's principle. • Eigenvalue problems are analyzed within the wave finite element method framework. • Wave propagation properties are illustrated through three complex nano-sized structures. [ABSTRACT FROM AUTHOR]

A comprehensive strategy for computing the dispersion relationship of a nonlinear metamaterial having Duffing-type cubic nonlinearity at the attached oscillator is presented in this paper. Jacobi's elliptic balance method is implemented to obtain the steady-state response of the non-linear metamaterial unit cell. An ingenious approach of defining the force term in equation motion not only reduces the system to a simplified uncoupled form but also facilitates the incorporation of the effect of amplitude dependency. Furthermore, the dispersion relationship can conveniently be obtained by applying Bloch's theorem. Under undamped conditions, the precise response of both the inner and outer mass of the nonlinear metamaterial is determined; whereas, a set of algebraic nonlinear equations is established and numerically solved for the damped system. The attenuation band shifts to the higher frequency range with increasing nonlinearity and excitation amplitude. The effect of excitation amplitude is predominant as compared to the nonlinearity of the spring in altering the dispersion plots. As damping increases, the sharp attenuation drop becomes blunt, and further increment of damping leads to the resonator and outer mass oscillating in nearly perfect harmony and thereby causing the dispersion plots to resemble those of a monoatomic chain. • Damped Duffing type nonlinear mass-in-mass metamaterial. • Jacobi's elliptic balance method for dispersion relation of nonlinear metamaterials. • Stability analysis of nonlinear solutions. • Wider attenuation bandgap in forward frequency sweep. • Shorter attenuation band in backward frequency sweep. [ABSTRACT FROM AUTHOR]

The construction of new structures on existing pile foundations can significantly reduce the overall project costs. The reuse of foundations requires information on the embedded depth of existing piles, which is not always known. In this paper, a novel technique based on the periodic analysis of the phase difference and the 3-dimensional guided wave theory was developed to effectively estimate the embedded depth of unknown foundations. In this method, the guided wave model of a cylindrical pile is built by the spectral element method to determine the dispersion relation. A modified Ridders' algorithm is proposed for root-searching. According to the phase difference of the responses collected by at least two sensors located on top or the lateral side of the pile, and the dispersion relation obtained by the spectral element method, the dispersion analysis diagram can be obtained to show the relationship between the phase difference and the wavenumber. Through the periodic properties of the dispersion analysis diagram, the pile length can be estimated. Furthermore, the periodic analysis of the phase difference for the signals collected on top of the pile is conducted in this paper using the 3-dimensional guided wave model-based dispersion relation. By comparing with synthetic and experimental data, it was shown that the proposed method can achieve an accuracy of greater than 95% in estimating the pile length of unknown foundations. • A novel technique based on the periodic analysis of guided wave theory was developed to estimate unknown pile depth. • The proposed method can be performed either on the lateral side or the top surface of the test pile. • A modified Ridders' algorithm is proposed for root-searching of the dispersion relation determination. [ABSTRACT FROM AUTHOR]

Premixed lean hydrogen-air flames exhibit instabilities due to hydrodynamic instabilities but also thermo-diffusive instabilities. However, in the case of ammonia/hydrogen blends, the effect of ammonia addition on instabilities is still unclear. To investigate intrinsic instabilities in premixed ammonia/hydrogen-air flames, a parametric study of laminar premixed flames is performed for different fuel contents, from pure hydrogen (H 2) to a blend of 40% of H 2 and 60% of ammonia (NH 3) in volume, equivalence ratios (0.4 to 1.0) and pressures (1 and 10 bar) to investigate thermo-diffusive instabilities. Numerical simulations using detailed chemistry are performed where an initial perturbation is set to disturb the planar flame front and to compute its growth rate. During the initial linear phase, the perturbation's amplitude grows or decreases depending on the flame's mixture propensity to be unstable or stable, respectively. At small times, the linear growth rate of the perturbation can be estimated and compared to theory. As expected, the maximum growth rate obtained in the linear phase depends on the mixture's equivalence ratio, fuel ratio, and pressure. Ammonia addition leads to a reduced peak growth rate, likely due to lower reactivity leading to a higher Zel'dovich number. Very lean mixtures (equivalence ratios of 0.4 and 0.5) are thermo-diffusively unstable, regardless of the ammonia content, due to hydrogen's preferential diffusion. [ABSTRACT FROM AUTHOR]

The characterization of geometric and mechanical properties is of great importance for the reuse of unknown foundations. In this paper, we propose a pile characterization method to non-invasively estimate the length and mechanical properties of a pile simultaneously and automatically. The forward model is established based on the guided wave theory for a cylindrical pile and a genetic algorithm-based method is proposed for the inversion process. The guided wave model is built using the spectral element method, which can generate the dispersion relation for the given physical properties. The resonance data (including the resonance frequency and the resonance number) and pile length can be related to the phase velocity, which can be derived by assuming either the displacement control or stress control boundary conditions. The loss function in the inversion method is defined by linking the dispersion relation of the forward model and the resonance analysis for those two boundary conditions. The proposed method is validated against the experimental data. By using the proposed method, pile characterization can be achieved automatically. The average accuracy of the proposed method for characterizing the pile properties (such as pile length, shear wave velocity, and longitudinal wave velocity) and the pile length is within 5 % error for each variable. • An inversion method is proposed to achieve the automatic and simultaneous estimation of the pile mechanical and geometric properties. • Two boundary conditions for the buried pile are analyzed for the design of the loss function for inversion. • A genetic algorithm-based optimization method is proposed to achieve the inversion process. • Based on the experimental analysis, the effectiveness and the accuracy of the proposed method has been validated. [ABSTRACT FROM AUTHOR]

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

Due to the insisted requirement for low cost and a nontoxic buffer layer for the most of optoelectronic applications, optical properties of nickel bis(acetylacetonate), Ni(acac) 2 , are examined for this prospect. This research represents a deep investigation of the linear and nonlinear optical properties of thermally evaporated Ni(acac) 2 thin films accompanied by structural and morphological characterization. The thermogravimetric thermogram revealed the stability of Ni(acac) 2 up to 461 K. The structural properties of the deposited film are investigated using x-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM). The XRD and HRTEM results revealed the polycrystalline nature of as-deposited film with [100] preferred orientation and average crystallite size about 108 nm. Furthermore, both atomic force microscopy, AFM, and field emission scanning electron microscopy, FESEM, are employed to inspect the surface topography of the prepared film. In addition, the spectrophotometric method is utilized for evaluating the linear and nonlinear optical constants of the prepared films. The dispersive parameters of Ni(acac) 2 is determined and analyzed in the point of view of the single oscillator model. The wide band gap (E g ˜ 3.6 eV), high transparency and the small value of Urbach energy (E u ˜ 76 meV) qualify this material to be utilized as a buffer layer. The nonlinear optical parameters of the fabricated film such as nonlinear refractive index and third order optical susceptibility are estimated. Both molecular polarizability and the optical electronegativity of Ni(acac) 2 thin film is calculated and found to be 3.18 Å3 and 1.98, respectively. The obtained results give the opportunity to nickel acetylacetonate for buffering most of the commercial optoelectronic applications. [ABSTRACT FROM AUTHOR]

A comprehensive numerical simulation study on elastic wave propagation for a novel engineered thin plate metamaterial structural system is presented. To enhance the accuracy of model, a mesh convergence study is validated. The wave dispersion spectra with bandgaps for three types of structures are presented. Based on local resonance phenomena, the low frequency pseudo and local resonance bandgaps are reported. Highlights are also included for the Bragg scattering induced directional bandgaps. The effects of material and geometric parameters on bandgaps are discussed. The finite element based frequency response study further validates the reported bandgaps. The conclusions provide a new perspective for designs and applications of thin plate metamaterials for subwavelength wave manipulation including seismic shielding of civil infrastructures. • Elastic thin plate metamaterial with low frequency bandgaps are reported. • Commonly used construction materials based three types of structures are presented. • Bandgap types and generation mechanisms are explained. • Effects of material and geometric parameters on bandgaps are discussed. • The bandgaps are validated by finite unit cell based frequency response study. [ABSTRACT FROM AUTHOR]

Abstract We derive here the dispersion relation for small-amplitude steady two-dimensional periodic water waves that propagate over a flat bed with a specified and fixed mean-depth. The water flow has a discontinuous vorticity distribution reflecting an isolated rotational layer of fluid. We then use the dispersion relation to obtain necessary and sufficient conditions for local bifurcation to occur. Moreover, a stability analysis of the laminar flows is presented. [ABSTRACT FROM AUTHOR]

Abstract We present a technique for measuring the two-dimensional surface water wave elevation both in space and time based on the low-cost Microsoft Kinect sensor. We discuss the capabilities of the system and a method for its calibration. We illustrate the application of the Kinect to an experiment in a small wave tank. A detailed comparison with standard capacitive wave gauges is also performed. Spectral analysis of a random-forced wave field is used to obtain the dispersion relation of water waves, demonstrating the potentialities of the setup for the investigation of the statistical properties of surface waves. [ABSTRACT FROM AUTHOR]

The present paper deals with the propagation of Love waves due to the presence of a point source in the fibre-reinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and half-space, respectively. Three-dimensional Green’s function representation for stresses and displacements are derived in complex-plane line-integral. The frequency equations of Love-type waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model. [ABSTRACT FROM AUTHOR]

Highlights • The elasticity of the external medium has a stabilizing effect on a liquid thread. • If two fluids with equal elasticity the system behaves as if it were Newtonian. • The most unstable combination: inner viscoelastic outer Newtonian fluid. Abstract This paper is concerned with the temporal stability analysis of an infinitely long thread of a viscoelastic fluid surrounded by another immiscible viscoelastic fluid. The study provides an extension of the dispersion relation derived by Tomotika that captures the effects of elasticity on the fastest growing mode. The general case of two Jeffreys fluids is presented first, from which limiting cases, such as the Maxwell model or the Newtonian model, are discussed. We show that the presence of elasticity in the constitutive equation of the external medium decreases the value of the growth rate correspondent to the fastest growing mode. This implies a more stable fluid thread, thus longer breakup lengths. When both fluids have similar elastic properties, the dispersion relation reduces to the Newtonian limit and the interface behaves as if the fluids were purely viscous. [ABSTRACT FROM AUTHOR]

Abstract Calculation of internal gravity-wave ray paths in the atmosphere using a general three-dimensional ray tracing computer program is discussed. To initialize a ray-path calculation, it is necessary to specify the initial values for the components of the wave vector at the source so that the dispersion relation is satisfied. For acoustic waves, or for gravity waves in the absence of wind, there is no ambiguity in determining the magnitude of the wave vector once the frequency and direction of propagation (wave-normal direction) have been specified. For gravity waves with wind, however, it is necessary to solve a quartic equation to specify the magnitude of the wavenumber. Two of the roots of the quartic reduce to the usual solutions in the absence of wind, and we designate these roots as 'ordinary waves.' The two new roots (whose values approach infinity as the wind speed approaches zero), we designate as 'extraordinary waves.' A section contrasts the properties of the different gravity wave types. Comparison with some previously published examples of ray-path calculations of gravity waves shows that those previous examples were actually extraordinary waves, but their significance was not recognized at that time. In the absence of wind, gravity waves are restricted to a fan of propagation directions centered about horizontal propagation, but asymptotic gravity waves (in the Bousinesq approximation) have a fixed propagation direction for a given frequency. In the presence of a horizontal wind, however, the wave-normal direction is restricted to a fan of directions in the upwind direction, but not in the downwind direction. The ray direction for upwind propagation has no restrictions. A short review of gravity wave theory and the gravity wave dispersion relation is included. Highlights • We demonstrate the calculation of atmospheric internal gravity waves using a ray tracing program. • In the presence of wind, there are two types of waves, which we designate as ordinary and extraordinary. • We contrast the properties of four atmospheric gravity wave types outlining their distinguishing characteristics. • We identify the ambiguity in finding atmospheric gravity wave launch ray conditions, which should be of interest to Gravity wave researchers. [ABSTRACT FROM AUTHOR]

The propagation characteristics of the return-stroke current wave along the channel are an important issue in lightning research. The temperature, electrical conductivity and radius of lightning dart‑leader channels were calculated based on spectral diagnosis. Using them as initial parameters the dispersion equation for electric wave propagating along the return-stroke channel in a wide angular frequency range was solved numerically. The dispersion relations for the electric wave with and without considering the corona sheath effect were investigated. The results showed that both the propagation velocity and amplitude of electric wave decay along the channel, and the high frequency components decay faster. The corona sheath hastens the attenuation of the electric wave. The peak current intensity is closely related to the physical characteristics of the leader channel and determines the propagation velocity and amplitude attenuation of electric wave. Inferred from the attenuation characteristics of the wave, the variation of the current intensity along the channel is mainly determined by the different attenuation rate of the harmonic components with different frequencies during the transmission process. • Electric wave propagation of return-stroke was studied by solving its dispersion equation with corona sheath effect. • The influence of the attenuation rate on the variation of return-stroke current intensity along the channel was analyzed. • The corona sheath accelerates the attenuation of the electric wave. [ABSTRACT FROM AUTHOR]

A theoretical model to explain the scattering process of wave attenuation in a marginal ice zone is proposed. Although many numerical methods have been developed to accurately estimate wave attenuation, it is not easy to incorporate this knowledge and results into practical use. Therefore, a simplified estimation method is developed here to explicitly and simply describe its fundamental mechanisms. We consider a periodic array of ice floes, where the floe is modeled by a vertical rigid cylinder. Using a homogenization technique, a homogenized free surface equivalent to the array is obtained. Then, we show that a dispersion relation of the homogenized free surface waves makes all wave numbers complex. As a result, the exponential energy decay in the scattering process is demonstrated. Under the deep water assumption, the wave attenuation coefficient is proportional to the open water's wave number, ice concentration ratio, and imaginary part of the floe's heave motion. To validate the proposed theory, a tank experiment was also conducted using cylindrical synthetic ice plates. Although our model is obtained under many simplifications, the theoretical results show the same tendency and order as the experimental results. [ABSTRACT FROM AUTHOR]

An efficient asymptotic approach, referred to as the Effective Non-Local Asymptotic Model (ENLAM), is developed for the elastodynamic homogenization of periodic composites. In comparison with the relevant two-scale asymptotic method reported in the literature, the effective motion equation obtained by ENLAM has a very compact form which holds for any order of asymptotic approximation. This compact form makes direct use of the effective displacement vector and of its different gradients whose highest order depends on the accuracy degree required. For every wavenumber belonging to the first Brillouin zone, the Floquet-Bloch wave expansion is employed, and compact recursive formulae are derived for determining the effective material parameters of periodic composites. For simplicity, all the results are presented only for a shear wave propagating in a periodic composite. Numerical examples for discussing the effective material parameters, the dispersion relation and the asymptotic approximation error are provided when a periodic composite with inclusions is concerned. [ABSTRACT FROM AUTHOR]

In this study, the effect of thermal annealing under vacuum conditions on structural, morphological and optical properties of thermally evaporated copper (II) acetylacetonate, cu(acac) 2 , thin films were investigated. The copper (II) acetylacetonate thin films were deposited using thermal evaporation technique at vacuum pressure ~1 × 10 −5  mbar. The deposited films were thermally annealed at 323, 373, 423, and 473 K for 2 h in vacuum. The thermogravimetric analysis of cu(acac) 2 powder indicated a thermal stability of cu(acac) 2 up to 423 K. The effects of thermal annealing on the structural properties of cu(acac) 2 were evaluated employing X-ray diffraction method and the analysis showed a polycrystalline nature of the as-deposited and annealed films with a preferred orientation in [ 1 ¯ 01] direction. Fourier transformation infrared (FTIR) technique was used to negate the decomposition of copper (II) acetylacetonate during preparation or/and annealing up to 423 K. The surface morphology of the prepared films was characterized by means of field emission scanning electron microscopy (FESEM). A significant enhancement of the morphological properties of cu(acac) 2 thin films was obtained till the annealing temperature reaches 423 K. The variation of optical constants that estimated from spectrophotometric measurements of the prepared thin films was investigated as a function of annealing temperature. The annealing process presented significantly impacted the nonlinear optical properties such as third-order optical susceptibility χ (3) and nonlinear refractive index n 2 of cu(acac) 2 thin films. [ABSTRACT FROM AUTHOR]

The fundamental equations for Form II of Mindlin's second strain gradient elasticity theory for isotropic materials are first derived. A corresponding simplified formulation is then proposed, with six and two higher-order material parameters for the strain and kinetic energy, respectively. This simplified model is still capable of accounting for free surface effects and surface tension arising in second strain gradient continua. Within the simplified model, at first, surface tension effects appearing in nano-scale solids near free boundaries are analyzed. Next, a thin strip under tension and shear is considered and closed-form solutions are provided for analyzing the free surface effects. Expressions for effective Poisson's ratio and effective shear modulus are proposed and found to be size-dependent. Most importantly, for each model problem a stability analysis is accomplished disallowing non-physical solutions (befallen but not exclusively disputed in a recent Form I article). Finally, a triangular macro-scale lattice structure of trusses is shown, as a mechanical metamaterial, to behave as a second strain gradient continuum. In particular, it is shown that initial stresses prescribed on boundaries can be associated to one of the higher-order material parameters, modulus of cohesion, giving rise to surface tension. For completeness, a numerical free vibration eigenvalue analysis is accomplished for both a fine-scale lattice model and the corresponding second-order continuum via standard and isogeometric finite element simulations, respectively, completing the calibration procedure for the higher-order material parameters. The eigenvalue analysis confirms the necessity of the second velocity gradient terms in the kinetic energy density. [ABSTRACT FROM AUTHOR]

An analytical study for surface gravity wave interaction with submerged flexible porous plate based on small amplitude water wave theory and structural response is presented. The flexible porous plate is modeled based on the thin elastic plate theory and wave past porous plate is using generalized Darcy's law to incorporate both frictional force and inertia force. The dispersion relation is analyzed to determine the wave motion characteristics of two propagating wave modes in the presence of free surface and flexural waves at the submerged horizontal porous plate in specific cases. Further, the linearized long wave equation under shallow water approximation is derived in a direct manner and the limiting cases are compared. The integral forms of Green’s functions are derived using the fundamental solution associated with the two-dimensional Laplace equation. Using Green’s identity, the generalized expansion formulae for the wave-maker problem associated with the surface wave interaction with the submerged flexible porous plate are obtained in both the cases of finite and infinite water depths. The usefulness of the expansion formula is demonstrated by analyzing a physical problem associated with the surface gravity wave interaction with a moored finite submerged horizontal elastic porous plate in finite water depth. In the numerical results, the accuracy of the numerical computations are checked and the combined effect of mooring stiffness and porous-effect parameter are analyzed on the reflection coefficients, wave energy dissipation coefficients, and vertical forces. It is observed that the wave energy dissipation/absorption depends significantly on the mooring stiffness, porous-effect parameter, and suitable positing of the submerged plate. [ABSTRACT FROM AUTHOR]