Showing papers on "Dispersion relation published in 2016"
TL;DR: In this paper, a linear wave theory for the Madden-Julian oscillation (MJO) is extended upon in this study, where column moisture is the only prognostic variable and the horizontal wind is diagnosed as the forced Kelvin and Rossby wave responses to an equatorial heat source/sink.
Abstract: A linear wave theory for the Madden–Julian oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. In this treatment, column moisture is the only prognostic variable and the horizontal wind is diagnosed as the forced Kelvin and Rossby wave responses to an equatorial heat source/sink. Unlike the original framework, the meridional and vertical structure of the basic equations is treated explicitly, and values of several key model parameters are adjusted, based on observations. A dispersion relation is derived that adequately describes the MJO’s signal in the wavenumber–frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of satellite and reanalysis data, it is estimated that the MJO’s group velocity is ~40% as large as its phase speed. This dispersion is the result of the anomalous winds in the wave modulating the mean distribution of moisture such that the moistur...
262 citations
TL;DR: In this paper, the governing equation of wave motion of viscoelastic SWCNTs with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory.
Abstract: The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.
210 citations
TL;DR: In this paper, the dispersion relation between wave frequency and wave number is derived for single-walled carbon nanotubes, based on the formulated equation of wave motion, and the closed-form dispersion relations between the wave frequency (or phase velocity) and the wave number are derived.
159 citations
TL;DR: It is shown using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films.
Abstract: In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates, and good packaging in magnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. It is a purely curvature-induced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. The analytical expression of the dispersion relation has the same mathematical form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore, this curvature-induced effect can be seen as a ``dipole-induced Dzyalonshiinsky-Moriya-like'' effect.
115 citations
TL;DR: This work reports the experimental observation of Snell's law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves and shows that the thickness step modifies the wavelength and the amplitude of the incident waves.
Abstract: We report the experimental observation of Snell's law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves. We use a thickness step as the interface between two media with different dispersion relations. Since the dispersion relation for magnetostatic waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25° with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.
107 citations
TL;DR: In this paper, the dispersion relation of Euler-Bernoulli beam with attached lateral local resonators (LLR) is derived and the existence of the multi-flexural band gaps can be exploited for the design of flexural vibration control of beams.
102 citations
TL;DR: In this article, an efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments, and the results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.
Abstract: An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton\'s principle and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.
80 citations
TL;DR: In this article, spin-wave propagation in an assembly of microfabricated 20 nm thick, 2.5 m wide Yttrium Iron Garnet (YIG) waveguides is studied using propagating spin-Wave spectroscopy (PSWS) and phase resolved micro-focused Brillouin Light Scattering ({\mu}-BLS).
Abstract: Spin-wave propagation in an assembly of microfabricated 20 nm thick, 2.5 {\mu}m wide Yttrium Iron Garnet (YIG) waveguides is studied using propagating spin-wave spectroscopy (PSWS) and phase resolved micro-focused Brillouin Light Scattering ({\mu}-BLS) spectroscopy. We show that spin-wave propagation in 50 parallel waveguides is robust against microfabrication induced imperfections. Spin-wave propagation parameters are studied in a wide range of excitation frequencies for the Damon-Eshbach (DE) configuration. As expected from its low damping, YIG allows the propagation of spin waves over long distances (the attenuation lengths is 25 {\mu}m at \mu$_{0}$H = 45 mT). Direct mapping of spin waves by {\mu}-BLS allows us to reconstruct the spin-wave dispersion relation and to confirm the multi-mode propagation in the waveguides, glimpsed by propagating spin-wave spectroscopy.
75 citations
TL;DR: In this paper, the authors discussed the possibility of the active control action on elastic waves in phononic crystals with the weakly nonlinear monoatomic lattice chain and derived the approximate solution of the dispersion relation.
70 citations
TL;DR: In this article, the impact of wave damping on the dispersion features of 3D viscoelastic periodic structures, which are modeled as Kelvin-Voigt beam-lattices, is analyzed.
69 citations
TL;DR: In this paper, the authors used single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals.
Abstract: The origins and properties of large amplitude whistler wave packets in the solar wind are still unclear. In this Letter we utilise single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarised, travel anti-sunward and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.
TL;DR: It is confirmed that using the ACT/LDV system and implementing simple Snell's law method is highly sensitive and effective in characterizing the dispersion curves of Lamb waves in composite structures as well as its angular dependency.
TL;DR: In this paper, a 1-dimensional phononic crystal (laminate) was shown to exhibit metamaterial wave phenomena which are traditionally associated with 2-and 3-dimensional crystals.
Abstract: In this paper we show that a 1-D phononic crystal (laminate) can exhibit metamaterial wave phenomena which are traditionally associated with 2- and 3-D crystals. Moreover, due to the absence of a length scale in 2 of its dimensions, it can outperform higher dimensional crystals on some measures. This includes allowing only negative refraction over large frequency ranges and serving as a near-omnidirectional high-pass filter up to a large frequency value. First we provide a theoretical discussion on the salient characteristics of the dispersion relation of a laminate and formulate the solution of an interface problem by the application of the normal mode decomposition technique. We present a methodology with which to induce a pure negative refraction in the laminate. As a corollary to our approach of negative refraction, we show how the laminate can be used to steer beams over large angles for small changes in the incident angles (beam steering). Furthermore, we clarify how the transmitted modes in the laminate can be switched on and off by varying the angle of the incident wave by a small amount. Finally, we show that the laminate can be used as a remarkably efficient high-pass frequency filter. An appropriately designed laminate will reflect all plane waves from quasi-static to a large frequency, incident at it from all angles except for a small set of near-normal incidences. This will be true even if the homogeneous medium is impedance matched with the laminate. Due to the similarities between SH waves and electromagnetic (EM) waves it is expected that some or all of these results may also apply to EM waves in a layered periodic dielectric.
TL;DR: In this paper, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission.
Abstract: For the first time, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission. The data are analyzed using the high-resolution adaptive wave telescope technique. Small-scale solar wind turbulence is primarily composed of highly obliquely propagating waves, with dispersion consistent with that of the whistler mode.
TL;DR: The properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE) are studied and it is showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE.
Abstract: In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, $k$. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the $\ensuremath{\beta}$ parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant $k$ and showed that the probability of rogue wave occurrence depends on $k$. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schr\"odinger equation have also been presented.
TL;DR: In this article, the magnetization dynamics in a skyrmion magnonic crystal were investigated theoretically and experimentally for fundamental properties and technological applications in spintronics and magnonics.
Abstract: We investigate theoretically the magnetization dynamics in a skyrmion magnonic crystal. Collective excitations are studied in a chain of touching ferromagnetic nanodots in a skyrmion magnetic configuration. The determined dispersion relation of coupled skyrmions shows a periodic dependence on the wave vector, a characteristic feature of the band structure in magnonic crystals. By spatial analysis of the magnetization amplitude in the magnonic bands we identify the excited modes as breathing and clockwise gyrotropic dynamic skyrmions. Propagating with a negative and positive group velocity, respectively, these high- and low-frequency excitations can be further explored theoretically and experimentally for fundamental properties and technological applications in spintronics and magnonics.
TL;DR: In this article, a low-rank one-step wave extrapolation approach using complex-valued lowrank decomposition is proposed to approximate the mixed-domain space-wavenumber wave extension symbol, which is more flexible than a real-valued phase function of two-step schemes.
Abstract: Reverse time migration (RTM) relies on accurate wave extrapolation engines to image complex subsurface structures. To construct such operators with high efficiency and numerical stability, we have developed a one-step wave extrapolation approach using complex-valued low-rank decomposition to approximate the mixed-domain space-wavenumber wave extrapolation symbol. The low-rank one-step method involves a complex-valued phase function, which is more flexible than a real-valued phase function of two-step schemes, and thus it is capable of modeling a wider variety of dispersion relations. Two novel designs of the phase function leads to the desired properties in wave extrapolation. First, for wave propagation in inhomogeneous media, including a velocity gradient term assures a more accurate phase behavior, particularly when the velocity variations are large. Second, an absorbing boundary condition, which is propagation-direction-dependent, can be incorporated into the phase function as an anisotropic a...
TL;DR: In this article, a dispersion relation for Rayleigh-lamb wave propagation in a plate of thermoelastic material was derived for generalized generalized thermo-elasticity with one relaxation time.
Abstract: In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain the analytical solution for the temperature, displacement components, and stresses using an eigenvalue approach. Finally, we derive a dispersion relation for the plate in closed form taking into account isothermal boundary conditions for wave mode propagation. To obtain the phase velocity and attenuation coefficients of propagating wave mode, we use the function iteration numerical scheme to solve the complex dispersion relation. The phase velocity and attenuation coefficients for the first five modes of waves are represented graphically for Lord–Shulman and classical coupled dynamical theories.
TL;DR: In this article, a wave-based model is developed within the framework of the Kirchhoff theory for a thin plate of locally varying thickness, which is shown to be an efficient vibration damper.
TL;DR: In this article, the authors provide simple and precise parametrizations of the existing πK scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules.
Abstract: In this work we provide simple and precise parametrizations of the existing πK scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.
TL;DR: In this paper, a simplified version of the quasilocalized charge approximations (QLCA) method to calculate the dispersion relations in strongly coupled Yukawa fluids is discussed.
Abstract: A useful simplification of the quasilocalized charge approximations (QLCA) method to calculate the dispersion relations in strongly coupled Yukawa fluids is discussed. In this simplified version, a simplest possible model radial distribution function, properly related to the thermodynamic properties of the system, is used. The approach demonstrates good agreement with the dispersion relations obtained using the molecular dynamics simulations and the original QLCA in the long-wavelength regime.
TL;DR: In this paper, the authors discuss new type of surface anti-plane waves localized near the surface an elastic half-space and in the vicinity of plane interface between two half-spaces, when considering surface strain and kinetic energies.
TL;DR: This paper uses the simplified Hirota’s method to study two integrable members of this new KP hierarchy and shows that these two equations give multiple soliton solutions that possess the same amplitude and the same phase shift, but with distinct dispersion relations.
TL;DR: In this paper, the dispersion relation of spoof surface plasmon polaritons in a metallic Lieb lattice based on the electrical circuit model was derived and three bands were obtained, one of which is independent of the wave vector.
Abstract: We demonstrate a nonradiative flat band for spoof surface plasmon polaritons bounded on a structured surface with Lieb lattice symmetry in the terahertz regime. First, we theoretically derive the dispersion relation of spoof plasmons in a metallic Lieb lattice based on the electrical circuit model. We obtain three bands, one of which is independent of wave vector. To confirm the theoretical result, we numerically and experimentally observe the flat band in transmission and attenuated total reflection configurations. We reveal that the quality factor of the nonradiative flat-band mode decoupled from the propagating wave is higher than that of the radiative flat-band mode. This indicates that the nonradiative flat-band mode is three-dimensionally confined in the lattice.
TL;DR: In this article, the authors studied the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell and showed that they are less common than D modes and that the characteristic rays and shear layers often focus towards a wedge -or point-like attractor.
Abstract: Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelope, with an equatorial acceleration (as in the Sun) or deceleration, which can modify the waves' propagation properties. We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assume that the angular velocity background flow depends on the latitudinal coordinate only, close to what is expected in the external convective envelope of low-mass stars. We use i) an analytical approach in the inviscid case to get the dispersion relation, from which we compute the characteristic trajectories along which energy propagates. This allows us to study the existence of attractor cycles and infer the different families of inertial modes; ii) high-resolution numerical calculations based on a spectral method for the viscous problem. We find that modes that propagate in the whole shell (D modes) behave the same way as with solid-body rotation. However, another family of inertial modes exists (DT modes), which can propagate only in a restricted part of the convective zone. Our study shows that they are less common than D modes and that the characteristic rays and shear layers often focus towards a wedge - or point-like attractor. More importantly, we find that for non-axisymmetric oscillation modes, shear layers may cross a corotation resonance with a local accumulation of kinetic energy. Their damping rate scales very differently from what we obtain for standard D modes and we show an example where it is independent of viscosity (Ekman number) in the astrophysical regime in which it is small.
TL;DR: In this paper, the authors used single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals.
Abstract: The origins and properties of large amplitude whistler wave packets in the solar wind are still unclear. In this Letter we utilise single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarised, travel anti-sunward and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.
TL;DR: In this article, a small angle neutron inelastic scattering measurement has been performed to study the magnon dispersion relation in the field-induced ferromagnetic phase of the noncentrosymmetric binary compound MnSi.
Abstract: A small angle neutron inelastic scattering measurement has been performed to study the magnon dispersion relation in the field-induced ferromagnetic phase of the noncentrosymmetric binary compound MnSi. For the magnons propagating parallel or antiparallel to the external magnetic field, we experimentally confirmed that the dispersion relation is asymmetrically shifted along the magnetic field direction. This magnon dispersion shift is attributed to the relativistic Dzyaloshinskii-Moriya interaction, which is finite in noncentrosymmetric magnets, such as MnSi. The shift direction is found to be switchable by reversing the external magnetic field direction.
01 Dec 2016
TL;DR: In this paper, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission.
Abstract: For the first time, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission. The data are analyzed using the high-resolution adaptive wave telescope technique. Small-scale solar wind turbulence is primarily composed of highly obliquely propagating waves, with dispersion consistent with that of the whistler mode.
TL;DR: In this paper, a general, fast, and effective approach for numerical calculation of kinetic plasma linear dispersion relations is developed for numerical calculating of kinetic plasminar relations. But this approach is not suitable for the case where the dispersion function is approximated by J-pole expansion.
Abstract: A general, fast, and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate; more strongly damped modes are less accurate, but are less likely to be of physical interest. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergence problems. The approach is demonstrated for electrostatic dispersion equations with one-dimensional and two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.
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30 Nov 2016TL;DR: In this article, the influence of different parameters of the zero crossing technique on measurement of the phase velocity of A 0 mode of the Lamb waves is investigated in more details, and the optimal parameters and necessary steps for phase velocity measurement are presented also.
Abstract: The delay time estimation using zero-crossing technique is widely used in ultrasonic measurements. The measurements of the phase velocity of guided waves are more complicated due to the dispersion. Application of zero-crossing technique for the measurements of the phase velocities is more complicated due to changes of the waveform of the signals and limited ranges of the measurements base. The objective of the work presented was to investigate in more details the influence of different parameters of the zero – crossing technique on measurement of the phase velocity of A 0 mode of the Lamb waves. Using the signals obtained from the finite element modelling of Lamb waves in a 2 mm thickness aluminium plate it was demonstrated that an insufficient sampling frequency can lead to the errors in the phase velocity and corresponding frequency estimations. On the other hand it was shown also, that in order to obtain a higher equivalent sampling frequency it is reasonable to exploit interpolation. The optimal parameters of the zero-crossing technique and necessary steps for phase velocity measurement are presented also.