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Showing papers on "Dispersion relation published in 2022"


Journal ArticleDOI
TL;DR: In this paper , the authors characterized transverse oscillations as either Alfvénic or Landau-type in an incompressible non-ideal magnetohydrodynamic (MHD) fluid.
Abstract: ABSTRACT In this paper, we characterize transverse oscillations as either Alfvénic or Landau-type in an incompressible non-ideal magnetohydrodynamic (MHD) fluid. We consider shear viscosity and magnetic diffusivity as dissipation mechanisms to derive a general dispersion relation for the incompressible MHD waves. The solutions of this dispersion relation for k as a function of ω – denoting by the source for any value of θ up to which magnetic tension acts as restoring force and dominates over internal friction forces – result in four roots, as follows. Two roots, which have a high phase velocity $c_{\rm A}\cos\theta $ are identified as almost undamped propagating Alfvén waves. The other two roots, which have a phase velocity $(2c_{\rm A}\cos\theta)/(\sqrt{\eta/ u} + \sqrt{ u/\eta})$, result in Alfvénic-type disturbances of a much shorter decay length than the wavelength. In contrast, when internal frictional forces start dominating over magnetic tension (i.e. for the propagation perpendicular to the background magnetic field, where the tension in the magnetic field becomes zero), the solutions of the dispersion are akin to Landau-type transverse oscillations. Transverse waves of this type were initially reported by Landau in an ordinary viscous fluid. However, our study corresponds to MHD visco-resistive fluid. The prediction for these lateral propagating transverse waves to be of Landau type may be very useful to explain the heating of observed filamentary structures across the magnetic field on a very small spatial scale in the solar coronal plasma, wherein the heating rate is directly proportional to the operating frequency of the driver, while its damping length is inversely proportional to the square root of the frequency.

92 citations


Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the dispersion characteristics of flexural waves in a functionally graded (FG) porous nanobeam and established integro-differential constitutive laws of the stress resultant fields with equivalent differential relations equipped with non-standard boundary conditions.

39 citations


Journal ArticleDOI
TL;DR: In this article , the authors analyzed the dispersion characteristics of flexural waves in a functionally graded (FG) porous nanobeam and established integro-differential constitutive laws of the stress resultant fields with equivalent differential relations equipped with non-standard boundary conditions.

35 citations


Journal ArticleDOI
TL;DR: In this article , the authors directly observed second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation.
Abstract: Abstract Second sound refers to the phenomenon of heat propagation as temperature waves in the phonon hydrodynamic transport regime. We directly observe second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique. The experimentally determined dispersion relation of the thermal-wave velocity increases with decreasing grating period, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation. Through simulation, we reveal this increase as a result of thermal zero sound—the thermal waves due to ballistic phonons. Our experimental findings are well explained with the interplay among three groups of phonons: ballistic, diffusive, and hydrodynamic phonons. Our ab initio calculations further predict a large isotope effect on the properties of thermal waves and the existence of second sound at room temperature in isotopically pure graphite.

30 citations


Journal ArticleDOI
TL;DR: In this article , the authors directly observed second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation.
Abstract: Abstract Second sound refers to the phenomenon of heat propagation as temperature waves in the phonon hydrodynamic transport regime. We directly observe second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique. The experimentally determined dispersion relation of the thermal-wave velocity increases with decreasing grating period, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation. Through simulation, we reveal this increase as a result of thermal zero sound—the thermal waves due to ballistic phonons. Our experimental findings are well explained with the interplay among three groups of phonons: ballistic, diffusive, and hydrodynamic phonons. Our ab initio calculations further predict a large isotope effect on the properties of thermal waves and the existence of second sound at room temperature in isotopically pure graphite.

23 citations


Journal ArticleDOI
TL;DR: In this paper , a generalized dispersive long-wave system was considered and two assemblies of the hetero-Bäcklund transformations and two assembly of the similarity reductions were computed.
Abstract: Swarming with the waves, the oceans are never calm. Concerning certain dispersive long gravity waves on the shallow water of an open ocean, we check into a (2+1)-dimensional generalized dispersive long-wave system. In relation to the wave height above the undisturbed water surface as well as the horizontal velocity, we symbolically compute out two assemblies of the hetero-Bäcklund transformations and two assemblies of the similarity reductions. Each assembly either brings about a known (2+1)-dimensional Broer-Kaup-Kupershmidt system or comes to a known ordinary differential equation. Also, each assembly relies on the coefficients from the original system.

19 citations


Journal ArticleDOI
TL;DR: Berger et al. as discussed by the authors studied the impact of intrinsic combustion instabilities for lean premixed hydrogen flames by means of a series of simulations at different equivalence ratios [0.4-1.0], unburned temperatures [298K-700K], and pressures [1bar-20bar].

15 citations


Journal ArticleDOI
TL;DR: In this article , a mapping between the structural topology and the dispersion relation of elastic metamaterials using deep learning approaches is established, and CNNs enable the inverse design of near-optimal structures based on the target dispersion relations.

12 citations


Journal ArticleDOI
TL;DR: In this paper , the existence and properties of Fast magnetosonic modes in 3D compressible MHD turbulence were studied by carrying out a number of simulations with compressible and incompressible driving conditions.
Abstract: We study the existence and property of Fast magnetosonic modes in 3D compressible MHD turbulence by carrying out a number of simulations with compressible and incompressible driving conditions. We use two approaches to determine the presence of Fast modes: mode decomposition based on spatial variations only and spatio-temporal 4D-FFT analysis of all fluctuations. The latter method enables us to quantify fluctuations that satisfy the dispersion relation of Fast modes with finite frequency. Overall, we find that the fraction of Fast modes identified via spatio-temporal 4D FFT approach in total fluctuation power is either tiny with nearly incompressible driving or ~2% with highly compressible driving. We discuss the implications of our results for understanding the compressible fluctuations in space and astrophysics plasmas.

10 citations


Journal ArticleDOI
TL;DR: In this article, the conditions under which complex-valued dispersion equations are either real- or purely imaginary-valued equations (termed as dichotomy property) are derived for both single and multi-layered composite plates.

10 citations


Journal ArticleDOI
TL;DR: In this paper , the authors exploit non-local effects as a powerful design tool by introducing a versatile effectively two-dimensional metamaterial platform for airborne sound and elastic waves, and analytically show that the lowest band can be engineered by Fourier synthesis.
Abstract: Abstract The interior of the synthetic unit cells and their interactions determine the wave properties of metamaterials composed of periodic lattices of these cells. While local interactions with the nearest neighbors are well appreciated, nonlocal beyond-nearest-neighbor interactions are often considered as a nuisance. Here, by introducing a versatile effectively two-dimensional metamaterial platform for airborne sound and elastic waves, we exploit nonlocal effects as a powerful design tool. Within a simplified discrete model, we analytically show that the lowest band can be engineered by Fourier synthesis, where the $$N$$ N -th order Fourier coefficient is determined by the $$N$$ N -th nearest-neighbor interaction strength. Roton-like dispersion relations are an example. The results of the discrete model agree well with a refined model and with numerical calculations. In addition, we engineer the passage of waves from a local metamaterial into a nonlocal metamaterial by carefully tailoring the transition region between the two.

Journal ArticleDOI
TL;DR: In this paper , the authors derived the plane wave expansion (PWE) and the Extended Plane Wave Expansion (EPWE) formulations in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators.

Journal ArticleDOI
TL;DR: In this paper , the linear wave properties of the low-frequency Alfvén modes (LFAMs) observed in the DIII-D tokamak experiments with reversed magnetic shear are theoretically studied and delineated based on the general fishbone-like dispersion relation.
Abstract: Abstract The linear wave properties of the low-frequency Alfvén modes (LFAMs) observed in the DIII-D tokamak experiments with reversed magnetic shear (Heidbrink et al 2021 Nucl. Fusion 61 016029) are theoretically studied and delineated based on the general fishbone-like dispersion relation. By adopting representative experimental equilibrium parameters, it is found that, in the absence of energetic ions, the LFAM is a reactive-type kinetic ballooning mode instability with a dominant Alfvénic polarization. More specifically, due to diamagnetic and trapped particle effects, the LFAM can be coupled with the beta-induced Alfvén-acoustic mode in the low-frequency region (frequency much less than the thermal-ion transit and/or bounce frequency) or with the beta-induced Alfvén eigenmode in the high-frequency region (frequency higher than or comparable to the thermal-ion transit frequency), resulting in reactive-type instabilities. Moreover, the ‘Christmas light’ and ‘mountain peak’ spectral patterns of LFAMs as well as the dependence of instability drive on the electron temperature observed in the experiments can be theoretically interpreted by varying the relevant physical parameters. Conditions for when dissipative-type instabilities may set in are also discussed.

Journal ArticleDOI
TL;DR: In this article, the authors derived the plane wave expansion (PWE) and the Extended Plane Wave Expansion (EPWE) formulations in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators.

Journal ArticleDOI
TL;DR: In this paper , an angle-resolved coherent probe spectroscopy technique was proposed to study the dispersion of elementary excitation modes in a fluid of polaritons under resonant pumping.
Abstract: Characterising elementary excitations in quantum fluids is essential to study collective effects within. We present an original angle-resolved coherent probe spectroscopy technique to study the dispersion of these excitation modes in a fluid of polaritons under resonant pumping. Thanks to the unprecedented spectral and spatial resolution, we observe directly the low-energy phononic behaviour and detect the negative-energy modes, i.e. the \textit{ghost branch}, of the dispersion relation. In addition, we reveal narrow spectral features precursory of dynamical instabilities due to the intrinsic out-of-equilibrium nature of the system. This technique provides the missing tool for the quantitative study of quantum hydrodynamics in polariton fluids.

Journal ArticleDOI
TL;DR: In this article, the effects of electromagnetic actuation on the dispersion curves as well as wave-filtering capabilities of nonlinear lattice chains are investigated, and the results reveal that successful implementation of the actuation to the studied systems can efficiently manipulate their wave propagation characteristics, providing about 25% tunability in the stop-band frequency range of monoatomic chains and about 15% in mass-in-mass chains.


Journal ArticleDOI
TL;DR: In this paper , a new type of fast particle instability involving axisymmetric modes in magnetic fusion tokamak plasmas is presented, where the resonant interaction with fast ions can drive the oscillatory roots unstable.
Abstract: Abstract A new type of fast particle instability involving axisymmetric modes in magnetic fusion tokamak plasmas is presented. The relevant dispersion relation involves three roots. One corresponds to a vertical plasma displacement that, in the absence of active feedback stabilization, grows on the wall resistivity time scale. The other two, oscillating close to the poloidal Alfvén frequency, are normally damped by wall resistivity. The resonant interaction with fast ions can drive the oscillatory roots unstable. Resonance conditions, stability thresholds and experimental evidence are discussed.

Journal ArticleDOI
13 May 2022-Symmetry
TL;DR: In this paper , the authors examined the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space, where the coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogenous half space layer is considered to be of exponentially varying material properties.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper , the authors report an exhaustive list of sum rules for 4-fermion operators of dimension 6, connecting low-energy Wilson coefficients to cross sections in the UV.
Abstract: A major task in phenomenology today is constraining the parameter space of Standard Model effective field theory and constructing models of fundamental physics from which the Standard Model derives. To this effect, we report an exhaustive list of sum rules for 4-fermion operators of dimension 6, connecting low-energy Wilson coefficients to cross sections in the UV. Unlike their dimension-8 counterparts which are amenable to a positivity bound, the discussion here is more involved due to the weaker convergence and indefinite signs of the dispersion integrals. We illustrate this by providing examples with weakly coupled UV completions leading to opposite signs of the Wilson coefficients for both convergent and nonconvergent dispersion integrals. We further decompose dispersion integrals under weak isospin and color groups, which lead to a tighter relation between IR measurements and UV models. These sum rules can become an effective tool for constructing consistent UV completions for Standard Model effective field theory following the prospective measurement of these Wilson coefficients.

Journal ArticleDOI
TL;DR: In this paper , the dispersion relation of the density and spin collective excitation modes in an elongated two-component superfluid of ultracold bosonic atoms is investigated.
Abstract: We report on the experimental measurement of the dispersion relation of the density and spin collective excitation modes in an elongated two-component superfluid of ultracold bosonic atoms. Our parametric spectroscopic technique is based on the external modulation of the transverse confinement frequency, leading to the formation of density and spin Faraday waves. We show that the application of a coherent coupling between the two components reduces the phase symmetry and gives a finite mass to the spin modes.

Journal ArticleDOI
TL;DR: In this article , a generalized linear elasticity theory with the nonlocal effect in the fundamental stress-strain relation is adopted to address the equation of motion in layered media, and the dispersion of Love-type wave and its limitation in a nonlocal elastic media are analyzed graphically using MATLAB software.

Journal ArticleDOI
TL;DR: In this article , the authors show that a crossing antisymmetric function can be expanded in terms of manifestly crossing antsy objects, which they call the "+ type Polyakov blocks", which are built from AdS$d+1$ Witten diagrams.
Abstract: Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the '+ type Polyakov blocks'. These blocks are built from AdS$_{d+1}$ Witten diagrams. In 1d they encode the '+ type' analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent 'locality constraints' in addition to the usual CFT sum rules given by the 'Polyakov conditions'. We use the Polyakov blocks to simplify more general analytic functionals in $d > 1$ and global symmetry functionals.


Journal ArticleDOI
TL;DR: In this paper , the authors investigated the complex dispersion diagram of a 2-D piezomagnetic phononic structure and derived the improved plane wave expansion ( ω ( k ) and extended plane waveexpansion ( k ( ) ) formulations to obtain the propagating and evanescent modes.

Journal ArticleDOI
TL;DR: In this paper , the authors derived the governing equations for the torsional functionally graded flexoelectric micro/nanotubes with the investigation of the effects of length scale parameters, electromechanical coupling, and micro-inertia on the prediction of actual Torsional wave behavior.
Abstract: In the present study, torsional wave propagation in a functionally graded flexoelectric micro/nano tube was investigated. The governing coupled equations of the torsional flexoelectric micro/nanotube have been developed based on strain gradient and micro-inertia. To derive the governing coupling equations, the variation method has been used and the formulation in general with classical and non-classical boundary conditions for functionally graded flexoelectric micro/nanotube has been extracted in this article. Dispersion phenomenon (asymptotic phase velocity-bounded value) which has not been paid attention in classical elastic theories is observed here for flexoelectric micro/nanotubes. However, the main contribution of this paper is the derivation of governing equations for the torsional functionally graded flexoelectric micro/nanotubes with the investigation of the effects of length scale parameters, electromechanical coupling, and micro-inertia on the prediction of actual torsional wave behavior. The analytical solution for phase velocity in this paper is calculated for harmonic decomposition and the magnitude of the phase velocity and its changes based on the wave velocity are plotted in the results section. The results show that the effect of flexoelectricity, micro inertia as well as the effect of size have a great effect on predicting the actual torsional wave propagation behavior in the micro/nanotubes.


Journal ArticleDOI
TL;DR: In this article , the existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically, and the frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three.
Abstract: The existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically. The frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three. The frozen mode regime is characterized by vanishing group velocity and enhanced field amplitude, which can be very attractive in various applications including dispersion engineering, lasers, and delay lines. Useful and simple design equations that lead to realization of the frozen mode by adjusting a few parameters are derived. The trend in group delay and quality factor with waveguide length that is peculiar of the frozen mode is shown. The symmetry conditions for the existence of exceptional points of degeneracy associated with the frozen mode are also discussed.

Journal ArticleDOI
TL;DR: In this paper , the authors consider the bounds that arise from the requirement of low-energy causality alone, without appealing to any assumptions about UV physics, and show that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints.
Abstract: Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low-energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically-symmetric background. We find that low-energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from $2 \rightarrow 2$ scattering amplitude dispersion relations using full crossing symmetry.

Journal ArticleDOI
TL;DR: In this paper , the Kapitza pendulums and non-local connection stiffness are introduced into the linear mass-spring periodic system to obtain the unusual roton-like behavior.
Abstract: The band gap has been used to control the transmission features of acoustic/elastic waves. Roton-like dispersion relations show that the energy and momentum of acoustic waves are inverse proportional to each other. To modulate the band gap and obtain the unusual roton-like behavior, the Kapitza's pendulums and nonlocal connection stiffness are introduced into the linear mass-spring periodic system. The frequency range with the roton-like behavior is modulated via the parametric excitation. Moreover, the dispersion relations show some fascinating phenomena (i.e. the negative/zero group velocity) under special parameters, which indicate the potential application to control the transmission of acoustic/elastic waves and design a negative/zero-refraction or non-propagating-vibration structure.