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Showing papers on "Dispersion relation published in 2018"


Journal ArticleDOI
TL;DR: In this article, it was shown that the information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum.
Abstract: We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon ``diffusion'' can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-${N}_{c}$ holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

170 citations


Journal ArticleDOI
TL;DR: Nonreciprocity in dynamic one-dimensional phononic crystal systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.
Abstract: Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As shown by experimental and numerical results, nonreciprocal mechanical systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.

156 citations


Journal ArticleDOI
TL;DR: In this paper, the decay of gravitational waves into dark energy fluctuations π was studied, through the processes γ → ππ and γ→ γ π, made possible by the spontaneous breaking of Lorentz invariance.
Abstract: We study the decay of gravitational waves into dark energy fluctuations π, through the processes γ → ππ and γ → γ π, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator ½ m42(t) δ g00 ( (3)R + δ Kμν δ Kμν −δ K2 ), so that the recent observations force m4 = 0 (or equivalently 0αH=). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to m42 generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on m42 comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable \hbox{higher-derivative corrections.}

118 citations


Journal ArticleDOI
TL;DR: The authors show that resonators made from granular aluminum, which naturally realizes a network of Josephson junctions, have practically useful impedances and nonlinearities.
Abstract: Granular aluminum (grAl) is a promising high kinetic inductance material for detectors, amplifiers, and qubits. Here we model the grAl structure, consisting of pure aluminum grains separated by thin aluminum oxide barriers, as a network of Josephson junctions, and we calculate the dispersion relation and nonlinearity (self-Kerr and cross-Kerr coefficients). To experimentally study the electrodynamics of grAl thin films, we measure microwave resonators with open-boundary conditions and test the theoretical predictions in two limits. For low frequencies, we use standard microwave reflection measurements in a low-loss environment. The measured low-frequency modes are in agreement with our dispersion relation model, and we observe self-Kerr coefficients within an order of magnitude from our calculation starting from the grAl microstructure. Using a high-frequency setup, we measure the plasma frequency of the film around 70 GHz, in agreement with the analytical prediction.

101 citations


Journal ArticleDOI
TL;DR: In this article, the spontaneous breaking of translational symmetry and the associated Goldstone mode were investigated in a holographic model with Bianchi VII helical symmetry, and the authors observed the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of the setup.
Abstract: We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode — a longitudinal phonon — in a holographic model with Bianchi VII helical symmetry For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature In addition, we extract the optical conductivity as a function of frequency, which reveals a metal-insulator transition as a consequence of the pinning

90 citations


Journal ArticleDOI
TL;DR: In this article, the attenuation-frequency power law dependencies given by three dispersion relation models are obtained under the assumptions of weak attenuation, negligible deviation of the wave number from the open water wave number, and thin ice.
Abstract: Analysis of field measurements of ocean surface wave activity in the marginal ice zone, from campaigns in the Arctic and Antarctic and over a range of different ice conditions, shows the wave attenuation rate with respect to distance has a power law dependence on the frequency with order between two and four. With this backdrop, the attenuation-frequency power law dependencies given by three dispersion relation models are obtained under the assumptions of weak attenuation, negligible deviation of the wave number from the open water wave number, and thin ice. It is found that two of the models (both implemented in WAVEWATCH IIIR ), predict attenuation rates that are far more sensitive to frequency than indicated by the measurements. An alternative method is proposed to derive dispersion relation models, based on energy loss mechanisms. The method is used to generate example models that predict power law dependencies that are comparable with the field measurements.

87 citations


Journal ArticleDOI
TL;DR: In this article, the dispersion relation of the shear-diffusion mode in relativistic hydrodynamics is considered, which is generated to high order as a series in spatial momentum q for a holographic model.
Abstract: We consider the dispersion relation of the shear-diffusion mode in relativistic hydrodynamics, which we generate to high order as a series in spatial momentum q for a holographic model. We demonstrate that the hydrodynamic series can be summed in a way that extends through branch cuts present in the complex q plane, resulting in the accurate description of multiple sheets. Each additional sheet corresponds to the dispersion relation of a different non-hydrodynamic mode. As an example we extract the frequencies of a pair of oscillatory non-hydrodynamic black hole quasinormal modes from the hydrodynamic series. The analytic structure of this model points to the possibility that the complete spectrum of gravitational quasinormal modes may be accessible from the hydrodynamic derivative expansion.

86 citations


Journal ArticleDOI
TL;DR: This Letter proposes and implements a general method for measuring the excitations spectrum in a fluid of light, based on a group velocity measurement and observes a Bogoliubov-like dispersion with a speed of sound scaling as the square root of the fluid density.
Abstract: Quantum fluids of light are a photonic counterpart to atomic Bose gases and are attracting increasing interest for probing many-body physics quantum phenomena such as superfluidity. Two different configurations are commonly used: the confined geometry where a nonlinear material is fixed inside an optical cavity and the propagating geometry where the propagation direction plays the role of an effective time for the system. The observation of the dispersion relation for elementary excitations in a photon fluid has proved to be a difficult task in both configurations with few experimental realizations. Here, we propose and implement a general method for measuring the excitations spectrum in a fluid of light, based on a group velocity measurement. We observe a Bogoliubov-like dispersion with a speed of sound scaling as the square root of the fluid density. This Letter demonstrates that a nonlinear system based on an atomic vapor pumped near resonance is a versatile and highly tunable platform to study quantum fluids of light.

84 citations


Journal ArticleDOI
TL;DR: In this article, a size-dependent model for the hygrothermal wave propagation analysis of an embedded viscoelastic single layer graphene sheet (SLGS) under the influence of in-plane magnetic field was developed.
Abstract: A size-dependent model is developed for the hygrothermal wave propagation analysis of an embedded viscoelastic single layer graphene sheet (SLGS) under the influence of in-plane magnetic field. The bi-Helmholtz nonlocal strain gradient theory involving three small scale parameters is introduced to account for the size-dependent effects. The size-dependent model is deduced based on Hamilton's principle. The closed-form solution of eigenfrequency relation between wave number and phase velocity is achieved. By studying the size-dependent effects on the flexural wave of SLGS, the dispersion relation predicted by the developed size-dependent model can show a good match with experimental data. The influence of in-plane magnetic field, temperature and moisture of environs, structural damping, damped substrate, lower and higher order nonlocal parameters and the material characteristic parameter on the phase velocity of SLGS is explored.

77 citations


Journal ArticleDOI
TL;DR: In this article, the wave propagation behavior and attenuation mechanism of the elastic metamaterial with locally resonant sub-structure was analyzed and it was shown that the band gap always coincides with the frequency range of negative effective properties.

68 citations


Journal ArticleDOI
TL;DR: In this article, an analytically tractable kinetic model of a two-dimensional Fermi liquid of electrons is used to characterize the crossovers among zero sound, first sound, and plasmons.
Abstract: Using an analytically tractable kinetic model of a two-dimensional Fermi liquid of electrons, we characterize the crossovers among zero sound, first sound, and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two-dimensional electron gases.

Journal ArticleDOI
TL;DR: In this paper, the dispersion relation and attenuation zones for surface waves in a periodic pile and layered soil system were derived based on the periodic theory of solid-state physics.

Journal ArticleDOI
TL;DR: In this paper, retrograde-propagating vorticity waves are detected in the shallow subsurface layers of the Sun at azimuthal wavenumbers below 15 with the dispersion relation of textbook sectoral Rossby waves.
Abstract: The Sun’s complex dynamics is controlled by buoyancy and rotation in the convection zone. Large-scale flows are dominated by vortical motions 1 and appear to be weaker than expected in the solar interior 2 . One possibility is that waves of vorticity due to the Coriolis force, known as Rossby waves 3 or r modes 4 , remove energy from convection at the largest scales 5 . However, the presence of these waves in the Sun is still debated. Here, we unambiguously discover and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at azimuthal wavenumbers below 15, with the dispersion relation of textbook sectoral Rossby waves. The waves have lifetimes of several months, well-defined mode frequencies below twice the solar rotational frequency, and eigenfunctions of vorticity that peak at the equator. Rossby waves have nearly as much vorticity as the convection at the same scales, thus they are an essential component of solar dynamics. We observe a transition from turbulence-like to wave-like dynamics around the Rhines scale 6 of angular wavenumber of approximately 20. This transition might provide an explanation for the puzzling deficit of kinetic energy at the largest spatial scales.

Journal ArticleDOI
TL;DR: In this paper, an analytic model of porous nanotubes for the wave propagation analysis is formulated with the help of the nonlocal strain gradient theory, and the dispersion relations between phase velocity and wave number are determined by solving an eigenvalue problem.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the hot plasma effects on the cyclotron-resonant interactions between electromagnetic ioncyclotron (EMIC) waves and radiation belt electrons in a realistic magnetospheric environment, using both cold and hot plasma dispersion relations.
Abstract: To investigate the hot plasma effects on the cyclotron-resonant interactions between electromagnetic ion cyclotron (EMIC) waves and radiation belt electrons in a realistic magnetospheric environment, calculations of the wave-induced bounce-averaged pitch angle diffusion coefficients are performed using both the cold and hot plasma dispersion relations. The results demonstrate that the hot plasma effects have a pronounced influence on the electron pitch angle scattering rates due to all three EMIC emission bands (H+, He+, and O+) when the hot plasma dispersion relation deviates significantly from the cold plasma approximation. For a given wave spectrum, the modification of the dispersion relation by hot anisotropic protons can strongly increase the minimum resonant energy for electrons interacting with O+ band EMIC waves, while the minimum resonant energies for H+ and He+ bands are not greatly affected. For H+ band EMIC waves, inclusion of hot protons tends to weaken the pitch angle scattering efficiency of >5 MeV electrons. The most crucial differences introduced by the hot plasma effects occur for >3 MeV electron scattering rates by He+ band EMIC waves. Mainly due to the changes of resonant frequency and wave group velocity when the hot protons are included, the difference in scattering rates can be up to an order of magnitude, showing a strong dependence on both electron energy and equatorial pitch angle. Our study confirms the importance of including hot plasma effects in modeling the scattering of ultra-relativistic radiation belt electrons by EMIC waves.

Journal ArticleDOI
Gui-Lin She1, Kun-Ming Yan, Yan-Long Zhang1, Hai-Bo Liu1, Yiru Ren1 
TL;DR: In this article, the wave propagation behavior of functionally graded materials (FG) porous nanobeams based on Reddy's higher-order shear deformation beam theory in conjunction with the non-local strain gradient theory is analyzed.
Abstract: In this paper, attention is paid to the prediction of wave propagation behaviors of functionally graded materials (FG) porous nanobeams based on Reddy’s higher-order shear deformation beam theory in conjunction with the non-local strain gradient theory. The governing equations of the porous nanobeams are derived with the help of the Hamilton principle. By solving an eigenvalue problem, the analytic dispersion relation is obtained. The results of Euler-Bernoulli beam and Timoshenko beam models are also presented. The influences of non-local parameter, strain gradient parameter, power law index and porosity volume fraction on the wave propagation are discussed in detail.

Journal ArticleDOI
TL;DR: In this paper, wave propagation in 2D doubled corrugated metasurfaces, including glide-symmetric corrugation, embedded in a thin parallel plate waveguide have been analyzed using the mode matching method.
Abstract: In this letter, wave propagation in 2-D doubled corrugated metasurfaces, including glide-symmetric corrugated metasurfaces, embedded in a thin parallel plate waveguide have been analyzed using the mode matching method. The general dispersion equation for propagation at different directions is derived and dispersion surfaces have been obtained for three different cases. The results are in good agreement with reference results obtained using CST Microwave Studio . Moreover, the method is accurate and computationally much faster than CST Microwave Studio and similar commercial software.

Journal ArticleDOI
TL;DR: In this paper, the wave propagation in magneto-electro-elastic (MEE) nanoshells is investigated via two nonlocal strain gradient shell theories, namely, the Kirchhoff-love shell theory and the first-order shear deformation (FSD) shell theory.

Journal ArticleDOI
TL;DR: In this article, an exact mathematical framework for electromagnetic wave propagation in periodically time-modulated media, in which the permittivity is homogenous and modulated in a step-varying fashion, is presented.
Abstract: We present an exact mathematical framework for electromagnetic wave propagation in periodically time-modulated media, in which the permittivity is homogenous and modulated in a step-varying fashion. By using Hill’s equation theory, we show that this problem has analytical solutions. We connect the dispersion relation, which exhibits $k-$ gaps, with the Hill stability analysis, providing an alternative mathematical description for wave propagation in temporal crystals. Our analysis, which is exact and transposable to other kinds of waves or modulation schemes, provides general useful physical and mathematical insights, complementing the use of numerical techniques such as finite differences in the time domain, or harmonic balance schemes, with a more transparent and practical design tool. The present analytical transient mathematical analysis, in contrast with the existing frequency-domain numerical approaches, can exhibit the parametric properties of electromagnetic waves inside a time periodic medium. For this reason, it can be a useful tool for the design of active microwave and optical devices, which employ time periodic wave medium modulation to filter or parametrically amplify wave signals.

Journal ArticleDOI
TL;DR: The propagation of flexural gravity waves, routinely used to model wave interaction with sea ice, is studied, including the effect of compression and current, and the theory developed is illustrated with simulations of linear waves in the time domain.
Abstract: The propagation of flexural gravity waves, routinely used to model wave interaction with sea ice, is studied, including the effect of compression and current. A number of significant and surprising properties are shown to exist. The occurrence of blocking above a critical value of compression is illustrated. This is analogous to propagation of surface gravity waves in the presence of opposing current and light wave propagation in the curved space-time near a black hole, therefore providing a novel system for studying analogue gravity. Between the blocking and buckling limit of the compressive force, the dispersion relation possesses three positive real roots, contrary to an earlier observation of having a single positive real root. Negative energy waves, in which the phase and group velocity point in opposite directions, are also shown to exist. In the presence of an opposing current and certain critical ranges of compressive force, the second blocking point shifts from the positive to the negative branch of the dispersion relation. Such a shift is known as the Hawking effect from the analogous behaviour in the theory of relativity which leads to Hawking radiation. The theory we develop is illustrated with simulations of linear waves in the time domain.

Journal ArticleDOI
TL;DR: This work derives an original closed-form dispersion relation for the metasurface and reveals the possibility to control the Love waves dispersive properties by varying the resonators mechanical parameters.
Abstract: Metasurfaces of mechanical resonators have been successfully used to control in-plane polarized surface waves for filtering, waveguiding and lensing applications across different length scales. In this work, we extend the concept of metasurfaces to anti-plane surface waves existing in semi-infinite layered media, generally known as Love waves. By means of an effective medium approach, we derive an original closed-form dispersion relation for the metasurface. This relation reveals the possibility to control the Love waves dispersive properties by varying the resonators mechanical parameters. We exploit this capability to manipulate the metasurface refractive index and design two gradient index (GRIN) metalenses, i.e. a Luneburg lens and a Maxwell lens. We confirm the performance of the designed lenses using full 3D finite element simulations. Our work demonstrates the possibility of realizing wave control devices for anti-plane waves.

Journal ArticleDOI
TL;DR: In this article, size-dependent wave dispersion behavior of smart piezoelectric nanotubes conveying viscous fluid is analyzed considering surface stress effects and slip boundary conditions.
Abstract: In this paper, size-dependent wave dispersion behavior of smart piezoelectric nanotubes conveying viscous fluid is analyzed considering surface stress effects and slip boundary conditions The size effects of the nanotube are taken into account by making use of the nonlocal strain gradient theory (NSGT) To take the slip boundary conditions into consideration, the average velocity correction factor is utilized The Newtonian method, in conjunction with the Rayleigh beam theory, is incorporated within the constitutive stress-strain relations of the surface and bulk of a piezoelectric material to derive the governing equations The obtained equations involve size-dependent parameters, surface effects, slip boundary conditions, fluid viscosity and piezoelectric voltage As a consequence, an analytical solution is applied to extract the wave dispersion relation of the nanotube In addition, the influences of different factors, including nonlocal parameter, length scale parameter, surface effects, piezoelectric voltage, surface elastic modulus and surface residual stress on the wave dispersion characteristics of the piezoelectric nanotube, are examined The effects of the piezoelectric voltage on the damping ratio of the nanotube are also studied The obtained results in this paper are expected to be useful for more accurate prediction of the mechanical behaviors as well as of the wave propagation characteristics of viscous-fluid-conveying piezoelectric smart nanotubes Meanwhile, the results will be helpful for efficient applications of piezoelectric nanotubes designing smart mechanical systems on a nanotechnology basis

Journal ArticleDOI
TL;DR: It turns out that the ratio of the thermal conductivity between zigzag and armchair ribbons is almost same as that of the corresponding Young modulus values, providing fundamental insight into the anisotropic thermal transport in low-symmetry crystals.
Abstract: Black phosphorus (BP) has emerged as a promising candidate for next-generation electronics and optoelectronics among the 2D family materials due to its extraordinary electrical/optical/optoelectronic properties. Interestingly, BP shows strong anisotropic transport behavior because of its puckered honeycomb structure. Previous studies have demonstrated the thermal transport anisotropy of BP and theoretically attribute this to the anisotropy in both the phonon dispersion relation and the phonon relaxation time. However, the exact origin of such strong anisotropy lacks clarity and has yet to be proven experimentally. Here, the thermal transport anisotropy of BP nanoribbons is probed by an electron beam technique. Direct evidence is provided that the origin of this anisotropy is dominated by the anisotropic phonon group velocity, verified by Young's modulus measurements along different directions. It turns out that the ratio of the thermal conductivity between zigzag (ZZ) and armchair (AC) ribbons is almost same as that of the corresponding Young modulus values. The results from first-principles calculation are consistent with this experimental observation, where the anisotropic phonon group velocity between ZZ and AC is shown. These results provide fundamental insight into the anisotropic thermal transport in low-symmetry crystals.

Journal ArticleDOI
TL;DR: In this article, a comprehensive mathematical analysis is presented to characterize and fully predict the non-reciprocal wave dispersion in two-dimensional space, in the presence of the spatiotemporal material variations.

Journal ArticleDOI
TL;DR: In this paper, a spin-wave tomography (SWaT) was used to reveal the excitation dynamics of magnetoelastic waves through coherent energy transfer between spin waves and elastic waves via magneto-elastic coupling.
Abstract: Using spin-wave tomography (SWaT), we have investigated the excitation and the propagation dynamics of optically excited magnetoelastic waves, i.e., hybridized modes of spin waves and elastic waves, in a garnet film. By using time-resolved SWaT, we reveal the excitation dynamics of magnetoelastic waves through coherent-energy transfer between optically excited pure-elastic waves and spin waves via magnetoelastic coupling. This process realizes frequency and wavenumber selective excitation of spin waves at the crossing of the dispersion relations of spin waves and elastic waves. Finally, we demonstrate that the excitation mechanism of the optically excited pure-elastic waves, which are the source of the observed magnetoelastic waves, is dissipative in nature.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder, where the cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces.

Journal ArticleDOI
TL;DR: In this paper, a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the dispersive representation is presented.
Abstract: In this work we provide a dispersive analysis of $$\pi \pi \rightarrow K{\bar{K}}$$ scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from $$K{{\bar{K}}}$$ threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.

Journal ArticleDOI
TL;DR: In this article, the possibility of trapped modes and acoustic-induced transparency (AIT) resonances in a simple one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids was investigated.
Abstract: We investigate theoretically and numerically the possibility of existence of Fano and acoustic-induced transparency (AIT) resonances in a simple though realistic one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids. These resonances are obtained by combining appropriately the zeros of transmission (antiresonance) induced by the solid layers and the local resonances induced by the solid or combined solid-fluid layers with surface free boundary conditions. In particular, we show the possibility of trapped modes, also called bound states in continuum, which have recently found a high renewal interest. These modes appear as resonances with zero width in the transmission spectra as well as in the density of states (DOS). We consider three different structures: (i) a single solid layer inserted between two fluids. This simple structure shows the possibility of existence of trapped modes, which are discrete modes of the solid layer that lie in the continuum modes of the surrounding fluids. We give explicit analytical expressions of the dispersion relation of these eigenmodes of the solid layer which are found independent of the nature of the surrounding fluids. By slightly detuning the angle of incidence from that associated to the trapped mode, we get a well-defined Fano resonance characterized by an asymmetric Fano profile in the transmission spectra. (ii) The second structure consists of a solid-fluid-solid triple layer embedded between two fluids. This structure is found more appropriate to show both Fano and acoustic-induced transparency resonances. We provide detailed analytical expressions for the transmission and reflection coefficients that enable us to deduce a closed-form expression of the dispersion relation giving the trapped modes. Two situations can be distinguished in the triple-layer system: in the case of a symmetric structure (i.e., the same solid layers) we show, by detuning the incidence angle $\ensuremath{\theta}$, the possibility of existence of Fano resonances that can be fitted following a Fano-type expression. The variation of the Fano parameter that describes the asymmetry of such resonances as well as their width versus $\ensuremath{\theta}$ is studied in detail. In the case of an asymmetric structure (i.e., different solid layers), we show the existence of an incidence angle that enables to squeeze a resonance between two transmission zeros induced by the two solid layers. This resonance behaves like an AIT resonance, its position and width depend on the nature of the fluid and solid layers as well as on the difference between the thicknesses of the solid layers. (iii) In the case of a periodic structure (phononic crystal), we show that trapped modes and Fano resonances give rise, respectively, to dispersionless flat bands with zero group velocity and nearly flat bands with negative or positive group velocities. The analytical results presented here are obtained by means of the Green's function method which enables to deduce in closed form: dispersion curves, transmission and reflection coefficients, DOS, as well as the displacement fields. The proposed solid-fluid layered structures should have important applications for designing acoustic mirrors and acoustic filters as well as supersonic and subsonic materials.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed flexural-gravity wave characteristics in the presence of a compressive force and a two-layer fluid, under the assumption of linearized water wave theory and small amplitude structural response.
Abstract: Flexural-gravity wave characteristics are analysed, in the presence of a compressive force and a two-layer fluid, under the assumption of linearized water wave theory and small amplitude structural response. The occurrence of blocking for flexural-gravity waves is demonstrated in both the surface and internal modes. Within the threshold of the blocking and the buckling limit, the dispersion relation possesses four positive roots (for fixed wavenumber). It is shown that, under certain conditions, the phase and group velocities coalesce. Moreover, a wavenumber range for certain critical values of compression and depth is provided within which the internal wave energy moves faster than that of the surface wave. It is also demonstrated that, for shallow water, the wave frequencies in the surface and internal modes will never coalesce. It is established that the phase speed in the surface and internal modes attains a minimum and maximum, respectively, when the interface is located approximately in the middle of the water depth. An analogue of the dead water phenomenon, the occurrence of a high amplitude internal wave with a low amplitude at the surface, is established, irrespective of water depth, when the densities of the two fluids are close to each other. When the interface becomes close to the seabed, the dead water effect ceases to exist. The theory developed in the frequency domain is extended to the time domain and examples of negative energy waves and blocking are presented.

Journal ArticleDOI
TL;DR: In this article, a particle-fluid hybrid model is used to model the plasma flow in a configuration similar to a Hall thruster, which shows a coherent rotating structure propagating in the E × B direction with a phase velocity of 2500 m s−1, which agrees with experimental data.
Abstract: Low-frequency rotating spokes are obtained in a cross-field discharge plasma using two-dimensional numerical simulations. A particle-fluid hybrid model is used to model the plasma flow in a configuration similar to a Hall thruster. It has been reported that the drift-diffusion approximation for an electron fluid results in an ill-conditioned matrix when solving for the potential because of the differences in the electron mobilities across the magnetic field and in the direction of the E × B drift. In this paper, we employ a hyperbolic approach that enables stable calculation, namely, better iterative convergence of the electron fluid model. Our simulation results show a coherent rotating structure propagating in the E × B direction with a phase velocity of 2500 m s−1, which agrees with experimental data. The phase velocity obtained from the numerical simulations shows good agreement with that predicted by the dispersion relation of the gradient drift instability.