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We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin's representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the O (G F α) radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and J P = 0 + nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed. [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]

The dispersion and dielectric attenuation characteristics of a double-staggered grating waveguide (DSGW) are two crucial features related to the output characteristics of a sheet-beam traveling-wave amplifier and have been previously studied by using theoretical analysis and simulations. In this work, these two characteristics are both experimentally studied. Two ${H}$ -band (220–325 GHz) DSGW circuit prototypes with and without dielectric attenuators made of the BeO-TiO2 composite ceramic were machined by using nanocomputer numerical control milling. Experimental studies of the dispersion property were performed successfully where the measurement results were in good agreement with those predicted by simulations, exhibiting a wide passband of 70 GHz (230–300 GHz). The measured transmission coefficient has been decreased from −5 to −55 dB after the introduction of dielectric attenuators, experimentally verifying the feasibility of the adopted methodology. The effects of the variations of dispersion relation and transmission loss on the beam-wave interaction stability were also investigated. [ABSTRACT FROM AUTHOR]

The propagation of acoustic waves in a porous medium whose skeleton consists of a gas hydrate with pores filled with water has been studied. A system of equations is written that describes the propagation of acoustic waves in such a porous medium. A dispersion equation is obtained, on the basis of which the phase velocity of sound and the decrement of attenuation of acoustic waves are analyzed. The coefficients of reflection and passage at the "liquid–porous medium" and "porous medium–liquid" interfaces have been derived and investigated. Based on the dispersion equation and corresponding reflection and passage coefficients, the propagation of the finite-duration pulses in the porous medium is investigated. The possibility of estimating the thickness of the gas hydrate bed with the aid of acoustic waves is shown. [ABSTRACT FROM AUTHOR]

In this paper we study electrostatic waves with time‐dependent frequency features in the terrestrial foreshock. These short (0.1–0.3 s) duration waves are characterized by a significant frequency drift where the peak wave power shifts from a few hundred Hz to 2–4,000 Hz in a few hundred milliseconds. Based on the electric field data from the Magnetospheric Multiscale Mission (MMS) we have identified 46 of these wave packets. Using four spacecraft timing approach we find that these waves have a propagation direction pointing upstream. However, their plasma frame velocity is less than the solar wind speed, therefore they are eventually convected downstream toward the bow shock. We use the double‐probes of MMS and present an interferometric analysis, which allows us to obtain the dispersion relation of these waves and directly compare them to theoretical ones. We show that the measured dispersion relations are in good agreement with Doppler shifted ion acoustic waves and discuss potential mechanisms related to impulsive reflected ions that may allow the growth of these waves and cause time‐dependent frequency features. Key Points: We analyze electrostatic waves with time‐dependent frequency features in the foreshock using the double‐probes of Magnetospheric Multiscale MissionThe measured wavenumber‐frequency plots are in excellent agreement with ion acoustic wave dispersion relationsWe discuss potential mechanisms, which may lead to the time‐dependent frequency features of the waves [ABSTRACT FROM AUTHOR]

We study analytic behavior of eigenvalues of the generalized Friedrichs model H μ (p) , with a rank-one perturbation, depending on parameters μ > 0 and p ∈ T 2 . Under certain conditions, the existence of a unique eigenvalue lying below the essential spectrum has been shown in Lakaev (Abstract Appl Anal 2012, 2012). Here, we obtain an absolutely convergent expansion for that eigenvalue at μ (p) , the coupling constant threshold. The expansion is dependent to a large extent on whether the lower bound of the essential spectrum is a threshold resonance, a threshold eigenvalue or neither of them. [ABSTRACT FROM AUTHOR]

Generalized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy. [ABSTRACT FROM AUTHOR]

A new analytical and numerical solution of the electrodynamic waveguide problem for leaky modes of a planar dielectric symmetric waveguide is proposed. The conditions of leaky modes, corresponding to the Gamow-Siegert model, were used as asymptotic boundary conditions. The resulting initial-boundary problem allows the separation of variables. The emerging problem of the eigen-modes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes, the Sturm-Liouville problem is self-adjoint and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the problem for leaky modes is not self-adjoint, so the eigenvalues are complex quantities. The problem of finding eigenvalues and eigenfunctions is associated with finding the complex roots of the nonlinear dispersion equation. To solve this problem, we used the method of minimizing the zero order. An analysis of the calculated distributions of the electric field strength of the first three leaky modes is given, showing the possibilities and advantages of our approach to the study of leaky modes.

The behaviors of bulk magnetoplasmon waves in a magnetized electron gas thin film in the Faraday configuration, as an example of an electric-gyrotropic film, are investigated. General expression for dispersion relation of the waves is obtained by two different approaches. Also, energy distribution and power flow of bulk and surface magnetoplasmon waves are studied. Furthermore, the group velocity and associated group delay time of bulk magnetoplasmon modes are obtained exactly by several different theoretical methods, such as the well-known wave theory method, the zig-zag ray approach based on the stationary-phase method and also the zig-zag ray approach based on the energy concepts. It is shown that the results are in completely consistent with each other.

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

In this manuscript, the anti‐plane shear motion of an asymmetric three‐layered inhomogeneous elastic plate is examined. An asymptotic approach is employed for the present investigation. Both thgeneralized and unified dispersion relations within the long‐wave low‐frequency range have been successfully determined. The obtained unified dispersion relation is investigated taking into account the recently analyzed material contrast for layered plates with mixed stiff‐soft layers of different material properties. The asymptotic formulae for the respective fields in addition to the determination of approximate equations of motions have also been presented. A comparative study with the symmetric plate is made; being a special case of the asymmetric plate under consideration. In the end, we provide some deductions and concluding remarks. [ABSTRACT FROM AUTHOR]

We analyze the chirality of dispersion relations and propagation lengths of two fundamental modes (m=0 and 1) in single silver nanowire coated by chiral TDBC. The systems of both Ag nanowires only coated by left TDBC (ALM) and right TDBC (ARM) are considered, respectively. Finite-difference time-domain method is used to do the mode analysis. The results show that the dispersion relations curves of both ALM and ARM are similar to magnetic hysteresis loops. There is a dip in the propagation length of ALM or ARM versus the incident frequency at the resonant frequency of left TDBC or right TDBC. The propagation length is reduced shapely in chiral TDBC due to the dissipation of TDBC. The difference of the propagation length | Δ L | becomes larger with the incident frequency far away from the resonant frequency of chiral TDBC for these two modes. The maximum difference of the real part of the effective index between ALM and ARM ( Δ n ′ ) is the linear function of m and the radius of Ag nanowire. With the radius decreasing from 100nm to 10nm, the propagation length for m=0 decreases and the propagation length for m=1 increases. Also, the maximum difference of the propagation length for m=1 increases. The maximum normalized difference between Ag nanowires coated by left TDBC and right TDBC in both the dispersion relation for m = 0 (0.024) and the propagation length for m = 1 (0.16) are quite larger than the one of only chiral TDBC (1/3000). According to our analysis, chiral molecules can be distinguished in either the dispersion relation or the propagation length, and our proposed structure has potential applications in chiral molecules detecting. [ABSTRACT FROM AUTHOR]

The propagation of plane sound waves of small amplitude in a mixture of an isothermal carrier gas and solid particles of different sizes is considered based on a multi-fluid macroscopic model of the medium. In the model, the dispersed phase is represented as a set of N fractions of monodisperse particles, and the dynamics of each fraction is described using the equations of a continuous medium without intrinisc pressure. The fractions exchange momenta with the carrier gas, but not with each other. The whole mixture is acted upon by the total pressure determined by the motion of gas molecules, and the dust particles are considered buoyant. An analytical solution of the problem is obtained using the Fourier method and dispersion analysis. In the general case for an arbitrary value of the relaxation time, the solution is found numerically using the developed and published code. In special cases (infinitely small time of velocity relaxation or relaxation equilibrium and infinitely long time of velocity relaxation or frozen equilibrium), the effective speed of sound in the gas-dust mixture is determined and used to obtain simple analytical representations of the solution of the problem. [ABSTRACT FROM AUTHOR]

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

A technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendental-function expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to low-order polynomials exactly, with explicit coefficients which we determine. Hence simple but high-order expansions exist which apply beyond the frequency and wavenumber range of widely used approximations based on kinematic hypotheses. The new expansions are hypothesis-free, in that they are derived rigorously from the governing equations, without approximation. Full details are presented for axisymmetric elastic waves propagating along a tube, for which stretching and bending waves are coupled. New approximate dispersion relations are obtained, and their high accuracy confirmed by comparison with the results of numerical computations. The weak coupling limit is given particular attention, and shown to have a wide range of validity, extending well into the range of strong coupling. [ABSTRACT FROM AUTHOR]

We numerically calculate using the 2-D electromagnetic solver SUPERFISH the dispersion relation for electromagnetic modes supported by finite-length, overmoded, corrugated, cylindrical slow wave structures (SWSs) with azimuthal symmetry by first enforcing electric, and thereafter magnetic boundary conditions on both the left and right boundaries of the SWS. We construct the dispersion relation as a set of dispersion curves related to azimuthally symmetric TM0n modes of the finite-length SWS and compare it with the analytically calculated dispersion relation. It is shown as a result of the numerical calculations that the analytically calculated dispersion curves of higher order TM0n modes of the infinite-length SWS are not the dispersion curves defining each single TM0n mode, but rather are combinations of dispersion curves defining those high-order TM0n modes with some parts of dispersion curves defining lower order TM0n-k) modes, where k = 1 . . . (n−1). [ABSTRACT FROM AUTHOR]

We study the characteristic velocities of the extended thermodynamics of molecular rotational- and vibrational- relaxation processes for a van der Waals gas. The lower and upper bounds of the characteristic velocity are, respectively, estimated by the one of rarefied gases and the one evaluated on the spinodal curve. We also study the dispersion relation of linear waves, in particular, the phase velocity, attenuation factor and attenuation per wavelength in a low frequency region. [ABSTRACT FROM AUTHOR]

Using kinetic theory approach, the dispersion relation ωr and Landau damping rate γ for dust ion acoustic waves are investigated numerically and analytically in an unmagnetized collisionless dusty plasma considering Cairns distribution for electrons and ions in stationary dust particles background. The phase velocity and Landau damping rate are calculated in the limits vtd∥ < vti∥ << ω/k << vte∥. The electrons and ions non‐thermality effects are incorporated via the non‐thermality parameter (0 ≤ α < 1). The real frequency ωr and Landau damping rate γ of the mode in Cairns bi‐Maxwellian distributed plasma are graphically shown to depend on plasma parameters namely non‐thermality index α, ion to electron temperature ratio Ti∥/Te∥ and the dust concentration parameter δ (=1 − ηZd). [ABSTRACT FROM AUTHOR]

Surface waves in layered systems consisting of material media with different frequency dispersions are considered: dielectric–plasma–vacuum, vacuum–plasma–plasma, and dielectric–vacuum–plasma. It is shown that in such systems, one of the surface waves can be radiative into a medium that does not form an interface for the surface wave under consideration, in view of which the wave becomes decaying. In the dielectric–vacuum–plasma system, there is only one surface wave localized at the vacuum–plasma interface, which is radiative into the dielectric in a certain region of wavenumbers with a not too small thickness of the vacuum layer. For all cases, the possibilities of exciting surface waves of a layered structure by an electron beam are analyzed. It is indicated which surface waves will be excited most efficiently. The prospects of using such waves in plasma microwave electronics in the development of sub-terahertz and possibly terahertz frequency ranges are shown. [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 local minimum in the plot of linear reflectance versus angle of incidence, on its own, is insufficient to identify a surface-plasmon-polariton wave (SPPW). Further checks are required in order to confirm the identity of a SPPW. The wavenumber should be compared with that extracted from the dispersion relation for the corresponding canonical boundary-value problem. Also, for prism-coupled configurations such as the Turbadar–Otto configuration which are based on SPPW-excitation via evanescent waves, the angle of incidence should be greater than the critical angle needed for total internal reflection. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is the derivation of properties of edge waves travelling along a submerged horizontal shelf. The problem is formulated within the framework of the linearized theory of water waves and Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the dispersion relation for edge waves in terms of an integral. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for the integral and hence to derive the properties of edge waves over a shelf. The numerical results are illustrated in a table and curves are presented showing the variation of frequency of the edge waves with the width of the shelf.

The plasmonic surface is made of metallic surface with deep sub-wavelength decorations, which are designed to mimic the surface plasmon polaritons at lower frequency. Recently, high-order modes in some special structures are analyzed. In order to analyze the dispersion problem of high-order modes of complex lossless structures faster and simpler, a convenient and simple method using the average input wave impedance obtained by a field-network joint solution is proposed. Meanwhile, based on Forster's reactance theorem, high-order modes of the complex structure always exist. Then, the dispersion curves of the high-order modes calculated using proposed method are in perfect match with the simulated results, which can verify the effectiveness and correctness of the proposed method. Additionally, the simulated and experimentally measured electric field distribution of high-order modes have great agreement. Using the proposed method, one can quickly obtain dispersion curve of a plasmonic structure to verify or estimate structure design. Hence, the proposed method may make a big step forward for obtaining the special dispersion relations.

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

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]

Dispersion of a passive tracer by water waves is of significant importance for many scientific and technological problems including bio-diversity of marine life, ecological impact of anthropogenic incidents, planning of rescue operation and global oceanic transport. Formally, turbulent dispersion of a passive tracer by surface waves is a Brownian motion caused by a prescribed noise, viz., random fluctuations of the wave field. From this perspective, it is similar to the conventional dispersion by tracer particles by turbulent flows initially described in the seminal work of Richardson, Taylor and Obukhov. The additional challenges of this problem are imposed by the complexity of the underlining wave field—different dispersion relations and correlation structure, directionality and its spread, wave breaking—and this complexity necessitates further theoretical and experimental research. The aim of the present study is experimental validation of scaling relations for the mean drift and mean variance of tracer particles predicted by the wave turbulence theory. We report results of a set of targeted experiments in a large three-dimensional wave tank where the positions of the tracer particles—modelled as surface drifters—were tracked down with optical cameras. The experimental data are analysed and discussed in the light of the weak turbulence theory. [ABSTRACT FROM AUTHOR]

The characteristic features of acoustic wave propagation in orthotropic elastic topographic waveguides are investigated for waveguides in the form of extended cylindrical structures with symmetric cross sections of different shapes (rectangular or trapezoidal). A method for an approximate study of problems using variable-rigidity plate models on the basis of the Hamilton–Ostrogradskii principle is proposed. Based on a field structure hypothesis that is similar to the Timoshenko model in the theory of plates, a functional depending on three functions of a single variable has been constructed. The stationary value of the functional is determined by the Ritz method. Its convergence has been investigated depending on the number of coordinate functions. An algebraic system has been formed whose determinant, being set equal to zero, allows one to construct the dispersion equation of the problem. Dispersion dependences were obtained for cross sections of different geometries. A comparison has been carried out between the dispersion curves formed on the basis of the Timoshenko-type model and the previously studied Kirchhoff model. The cut-off frequencies are determined for elastic waveguides with triangular, rectangular, and trapezoidal cross sections, and a comparative analysis has been performed. [ABSTRACT FROM AUTHOR]

A study of the spectral properties of electromagnetic radiation in the ion-cyclotron range from the plasma of the TUMAN-3M tokamak in the NBI heating mode has been carried out. The spectrum of this radiation consists of several (up to four) narrow lines corresponding to different harmonics of the ion-cyclotron resonance frequency of injected fast ions in the center of the plasma. Wave vectors corresponding to individual spectral lines are determined from the signal delays between spatially separated probes. It is shown that under the assumption that all the measured frequencies and wave vectors follow the same dispersion relation, the observed radiation can be explained by the appearance in the plasma of an unstable fast magneto-acoustic wave propagating almost normally to the direction of the magnetic field. [ABSTRACT FROM AUTHOR]

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological contribution given by Lamaître's law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagation time of the photon and the real distance between the source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity. [ABSTRACT FROM AUTHOR]

A simple iterative scheme is proposed for locating the parameter values for which a two-parameter family of real symmetric matrices has a double eigenvalue. The convergence is proved to be quadratic. An extension of the scheme to complex Hermitian matrices (with three parameters) and to the location of triple eigenvalues (five parameters for real symmetric matrices) is also described. Algorithm convergence is illustrated in several examples: a real symmetric family, a complex Hermitian family, a family of matrices with an "avoided crossing" (no convergence), and a five-parameter family of real symmetric matrices with a triple eigenvalue. [ABSTRACT FROM AUTHOR]

In this article, by substituting the dielectric tensor in Maxwell’s equations and using the boundary conditions in a longitudinally magnetized plasma-filled coaxial elliptical waveguide, the dispersion relation in the considered configuration is derived. We study the energy and dynamic of an injected external electron with initial energy using radiation of an electromagnetic source in the considered waveguide having the considered hybrid mode. The trajectory and kinetic energy of an injected electron in the considered waveguide along the propagating axis and hybrid field components are plotted. The obtained differential equations are numerically solved by the fourth-order Runge–Kutta method, and the results are graphically presented. The effects of different parameters on the trajectory and kinetic energy of injected electrons are investigated. [ABSTRACT FROM AUTHOR]

In the present paper, oblique wave scattering by a system of semi-infinite floating and submerged elastic plates of different structural parameters is studied under the assumption of small-amplitude waves and structural response in finite water depth. Matched eigenfunction expansion method is used for the solution of the boundary value problem. Numerical results for wave scattering are computed and analyzed for the reflection and transmission coefficients to reveal the effects of the wave and structural parameters. Assuming infinitely extended floating and submerged plates in the horizontal direction, the amplitude ratio and dispersion relation are derived and the behavior of the roots of the dispersion relation is analyzed through a contour plot. Further, group and phase velocities are demonstrated briefly for various wave and structural parameters. The present model is validated by comparing with known results available in the literature for wave scattering by a semi-infinite floating elastic plate in the absence of the submerged plate. [ABSTRACT FROM AUTHOR]