Dispersion Relations Of Modes Research Articles

Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone

Context. Several types of global-scale inertial modes of oscillation have been observed on the Sun. These include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. However, the columnar convective modes (predicted by simulations and also known as banana cells or thermal Rossby waves) remain elusive. Aims. We aim to investigate the influence of turbulent diffusivities, non-adiabatic stratification, differential rotation, and a latitudinal entropy gradient on the linear global modes of the rotating solar convection zone. Methods. We numerically solved for the eigenmodes of a rotating compressible fluid inside a spherical shell. The model takes into account the solar stratification, turbulent diffusivities, differential rotation (determined by helioseismology), and the latitudinal entropy gradient. As a starting point, we restricted ourselves to a superadiabaticity and turbulent diffusivities that are uniform in space. We identified modes in the inertial frequency range, including the columnar convective modes as well as modes of a mixed character. The corresponding mode dispersion relations and eigenfunctions are computed for azimuthal orders of m ≤ 16. Results. The three main results are as follows. Firstly, we find that, for m ≳ 5, the radial dependence of the equatorial Rossby modes with no radial node (n = 0) is radically changed from the traditional expectation (rm) for turbulent diffusivities ≳1012 cm2 s−1. Secondly, we find mixed modes, namely, modes that share properties of the equatorial Rossby modes with one radial node (n = 1) and the columnar convective modes, which are not substantially affected by turbulent diffusion. Thirdly, we show that the m = 1 high-latitude mode in the model is consistent with the solar observations when the latitudinal entropy gradient corresponding to a thermal wind balance is included (baroclinically unstable mode). Conclusions. To our knowledge, this work is the first realistic eigenvalue calculation of the global modes of the rotating solar convection zone. This calculation reveals a rich spectrum of modes in the inertial frequency range, which can be directly compared to the observations. In turn, the observed modes can inform us about the solar convection zone.

Scaling law for interchange transport in magnetically confined electron-positron plasmas with ion impurity

Interchange instabilities are a critical issue for confinement and transport in (otherwise exceptionally stable) planned magnetically confined quasi-neutral electron-positron plasma experiments. An additional ion impurity concentration can signifcantly affect the instability. The dispersion relation for interchange modes in perturbed inhomogeneously magnetized electron-positron plasmas in the presence of impurity ions is derived from full-f isothermal gyrofluid equations. The model includes arbitrary ion concentration and Debye screening effects. The resulting interchange growth rate of localized density perturbations is related to the cross-field propagation velocity and associated transport, which is reduced by an additional ion concentration compared to pure electron-positron plasmas. A simplified scaling relation is obtained from the exact analysis and compared with previous pure electron-positron plasma limits and empirical scalings based on simulation data.

Passive odd viscoelasticity.

Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that odd elasticity is not only present in active systems but also in broad classes of passive chiral viscoelastic fluids. In addition, we demonstrate that linear viscoelastic chiral solids require activity in order to manifest odd elastic responses. To model the phenomenon of passive odd viscoelasticity we propose a chiral extension of Jeffreys model. We apply our covariant formalism in order to derive the dispersion relations of hydrodynamic modes and obtain clear imprints of odd viscoelastic behavior.

Investigation of TE and TM modes fields and injected electron dynamic in the plasma waveguide with Piet Hein cross section

In this paper, we consider a metallic waveguide with Piet Hein cross section filled by cold unmagnetized plasma. First by introducing a Piet Hein waveguide and considering a suitable approximation, wave equation as two differential equations are presented. Then electromagnetic fields for TM and TE modes in the Piet Hein waveguide filled plasma are analytically obtained and plotted. Using the boundary conditions in the Piet Hein plasma waveguide the dispersion relations for TM and TE modes are analytically derived and plotted. Electron dynamics in the fields associated with a transverse magnetic and electric wave propagating inside the considered Piet Hein plasma waveguide is investigated. The equations of electron motion in the considered Piet Hein plasma waveguide by fourth-order Runge Kutta method for TM and TE modes are solved. The motion path and kinetic energy of electron injected into the purposed configuration for two modes are graphically investigated.

Recent progress in the interaction between energetic particles and tearing modes.

The dynamics of energetic particles and tearing modes and the interactions between them are of great significance for magnetically confined fusion plasmas. In this review, we focus on these issues in the context of tokamak plasmas. The interaction between energetic particles and tearing modes is considered from two perspectives: (i) the influence of energetic particles on tearing modes and (ii) the transport of energetic particles by tearing modes. The influence of energetic particles on tearing modes is described on the basis of a general dispersion relation for tearing modes. The effects of energetic particles are considered separately in the outer region and the island region of a tearing mode. The physics mainly results from the modification of the perturbed parallel current by energetic particles without wave-particle resonance. In addition, the resonance between energetic particles and tearing modes is also reviewed. For the transport of energetic particles, transport of both circulating and trapped energetic particles by tearing mode is reviewed. Our descriptions of physical phenomena here are based on an analytical approach, while the experiments and simulations are used to illustrate and confirm our results. Finally, a number of open issues are discussed.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part II - variational formulations and applications in plates

A new Mindlin plate model is developed incorporating the couple stress, quadrupole, and curvature-based flexoelectric effects using a non-classical elastic dielectric theory. The general governing equations and complete boundary conditions are derived simultaneously through a variational approach. The new general plate model includes the model for centrosymmetric materials as a special case. As direct applications of the new plate and to illustrate the flexoelectric effect, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the new centrosymmetric model. The numerical results reveal that the flexoelectric effect is present in centrosymmetric materials and is important when the plate thickness is very thin. The dispersion relations for flexure and fundamental shear modes are obtained. We find electrostatic wave also propagates with the flexure or fundamental shear waves by flexoelectric coupling. The present work can be seen as an extension of mechanical analysis of plate structures with couple stress effects and may be useful to the devices design of micro- or nano-sized objects.

Chaos and pole-skipping in rotating black holes

We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency ω∗ = i2πT there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of “pole-skipping” — namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT.

Mode Analyses of Subwavelength Periodic Metallic Structures With Finite Thickness

Deep-subwavelength periodic metallic structures, which are also called as plasmonic metamaterials, have received much attention due to their ability of supporting spoof surface plasmons polariton (SPP) modes. However, it is still difficult to obtain the dispersion relations of different modes for complicated plasmonic metamaterials with finite thickness. To solve the problem, we make further development of a field-network joint dispersion analysis method that was proposed recently, so that the method can be used to analyze the spoof SPP structures with certain thickness. The developed method not only allows us to predict the dispersion relations of complicated spoof SPP structures with finite thickness, but also can be used to find a series of intrinsic high-order modes of the periodic metallic structures. As an ex-ample, we present the theoretical dispersion curves of the fun-damental and high-order modes for a complicated spoof SPP structure, which have good agreements with the simulated re-sults. Meanwhile, the calculated near fields also match to the simulated and measured results well.

Hydrodynamics of ideal fracton fluids

Low-energy dynamics of many-body fracton excitations necessary to describe topological defects should be governed by a novel type of hydrodynamic theory. We use a Poisson bracket approach to systematically derive hydrodynamic equations from conservation laws of scalar theories with fracton excitations. We study three classes of theories. In the first class we introduce a general action for a scalar with a shift symmetry linear in the spatial coordinates, whereas the second one correspond with a complex scalar, while the third class serves as a toy model for disclinations and dislocations propagating along the Burgers vector. We apply our construction to study hydrodynamic fluctuations around equilibrium states and derive the dispersion relations of hydrodynamic modes.

Collective modes in an imbalanced nodal-line semimetal

In this work, we investigate collective modes in a nodal line semimetal with two nodal-lines that have opposite spin polarization in the presence of spin population imbalance. We find the components of polarization operator taking into account the electron-electron exchange interaction and obtain the dispersion relations of collective modes for the bulk and surface states. There exist four modes in the bulk, among which one is gapless and other three are gapped. The gapless surface mode is sensitive to the boundary conditions.

Plasmonic responses with topological transition in semimetallic monolayer WTe2

Recently, semimetallic tungsten ditelluride (WTe2) has been proposed as a natural material that supports hyperbolic plasmonic responses. In this paper, we have theoretically discovered that such hyperbolicity, which is due to strongly anisotropic in-plane interband transition of electrons, exists even in the monolayer and can become elliptic under proper doping. Using density functional theory, the permittivities include both the interband and intraband parts have been calculated, which are then used to derive the in-plane conductivities. Based on two-dimensional conductivity, the dispersion relations of the plasmonic modes in the extended monolayer have been analytically solved. It is surprising that monolayer WTe2 supports both elliptic as well as hyperbolic plasmonic responses in the infrared. Edge-confined modes in the extended monolayer in the elliptic regime and waveguiding modes in nanoribbons in the hyperbolic regime have been numerically investigated. After being doped with electrons, the Fermi level is shifted; it is found that moderate electron doping can change the topology of the plasmonic responses from a hyperbolic to an elliptic one within some frequency range. The effects of band broadening are also discussed and the permittivities are calculated using optimal basis functions to further verify our main conclusions. Then, the states corresponding to large interband transition peaks are marked and the wavefunctions are used to explain the strong in-plane dipole. In the end, the permittivities of bulk WTe2 have been investigated. Our investigations indicate that monolayer WTe2 is a promising platform for plasmonic applications.

Linearized dispersion relations in viscous relativistic hydrodynamics

We compute the dispersion relations for scalar, vector and tensor modes of a viscous relativistic fluid, linearized around an equilibrium solution, for a divergence type theory (which, in the linearized theory, includes Israel-Stewart theory and anisotropic hydrodynamics as particular cases) and contrast them to the corresponding results derived from kinetic theory under the relaxation time approximation, and from causal first order theories. We conclude that all approaches give similar dynamics for the scalar and vector modes, while the particular divergence type theory presented here also contains propagating damped tensor waves, in agreement with kinetic theory. Nonhydrodynamic tensor modes are also a feature of holographic fluids. These results support the application of hydrodynamics in problems involving the interaction between fluids and gravitational waves.

Instability of a viscous liquid sheet under the influence of a tangential electric field

The linear stability analysis has been analyzed for an electrified liquid sheet confined between two symmetric dielectric movable ambient gas. The present study aims to estimate the planer jet systems response when applying a tangential electric field. The dispersion relations for varicose and sinuous modes have been formulated. The electrical Euler number and some flow parameters have been tested for their influence on the electrified liquid sheet instability. In other words, the effects of electric field on the dominant wave number, and instability range (cutoff wave number) are discussed. The results clarify that the tangential electric field has a stabilizing effect for sinuous mode over the whole range of gas velocity ratio. On the other hand, for varicose mode, the electric field slightly improves the system stability to a certain limit, but it has a great role in stability for higher values of gas velocity ratio.

Theory of plasmonic edge states in chiral bilayer systems

We analytically describe the plasmonic edge modes for an interface that involves the twisted bilayer graphene (TBG) or other similar Moire van der Waals heterostructure. For this purpose, we employ a spatially homogeneous, isotropic and frequency-dependent tensor conductivity which in principle accounts for electronic and electrostatic interlayer couplings. We predict that the edge mode dispersion relation explicitly depends on the chiral response even in the nonretarded limit, in contrast to the collective bulk plasmonic excitations in the TBG. We obtain a universal function for the dispersion of the optical edge plasmon in the paramagnetic regime. This implies a correspondence of the chiral-TBG optical plasmon to a magnetoplasmon of a single sheet, and chirality is interpreted as an effective magnetic field. The chirality also opens up the possibility of nearly undamped acoustic modes in the paramagnetic regime. Our results may guide future near-field nanoscopy for van der Waals heterostructures. In our analysis, we retain the long-range electrostatic interaction, and apply the Wiener-Hopf method to a system of integral equations for the scalar potentials of the two layers.

Complex modes in optical fibers and silicon waveguides.

In an open optical waveguide, complex modes that are confined around the waveguide core and have a complex propagation constant may exist, even though the waveguide consists of lossless isotropic dielectric materials. However, the existing studies on complex modes are very limited. In this Letter, we consider circular fibers and silicon waveguides, study the formation mechanism of complex modes, and calculate the dispersion relations for several complex modes in each waveguide. For circular fibers, we also determine the minimum refractive-index ratio for the existence of complex modes. Our study fills a gap in optical waveguide theory and provides a basis for realizing potential applications of complex modes.

Exact dispersion relations for the hybrid plasmon-phonon modes in graphene on dielectric substrates with polar optical phonons.

Intrinsic optical phonons and extrinsic polar optical phonons (POPs) strongly affect the graphene surface plasmons. Specifically, extraneous POPs present on the surface of an underlying substrate change the behavior of the graphene's surface plasmons sharply due to the plasmon-phonon hybridization. Here, we report modeling of exact dispersion relations for graphene's surface plasmons affected by intrinsic optical phonons and extrinsic POPs of the surface of polar dielectric substrates with one or more vibrational frequencies. In doing so, we have employed random phase approximation with modified two-dimensional polarizability (2D-Π0). The adapted Π0 addresses limitations of the previously derived plasmons dispersion, obtained using classical two-dimensional polarizability. We show the new model overcomes the unsatisfying behavior of the plasmonic dispersion relation obtained by the classical 2D-Π0 at high-wavenumbers and its inability to indicate the starting point of the mode damping. Our new simple model eliminates the complexity of the other presented models in describing the surface plasmons' behavior, specifically at high wavenumbers. Besides, we use our dispersion model to learn about the plasmon content of the hybrid modes, which is a vital value to compute output current in plasmonic graphene-based devices. The coupled-mode lifetime due to the hybrid nature depends on both plasmon and phonon lifetimes. We capture this value here. There is an excellent agreement between our theoretical results and the experimental data reported earlier. They pave the way for the exact modeling of graphene plasmons on common polar substrates and bring in the closeness of the theoretical approaches and experimental results.

Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

Context. Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Aims. Rossby waves create small-amplitude, very-low frequency motions, on the order of the rotation rate and lower, which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. Methods. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in the harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. Results. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes, where the azimuthal order is the same as the harmonic degree, s = |t|. Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m s−1. We place an upper bound of 0.2 m s−1 on the sectoral t = 2 mode, which we do not detect in our measurements. Conclusions. This effort adds credence to the mode-coupling methodology in helioseismology.

Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited.

A phenomenological model of anisotropic lattice vibrations is proposed, using a temperature-dependent spectral cutoff and varying Debye temperatures for the vibrational normal components. The internal lattice energy, entropy and Debye-Waller B factors of non-cubic elemental crystals are derived. The formalism developed is non-perturbative, based on temperature-dependent linear dispersion relations for the normal modes. The Debye temperatures of the vibrational normal components differ in anisotropic crystals; their temperature dependence and the varying spectral cutoff can be inferred from the experimental lattice heat capacity and B factors by least-squares regression. The zero-point internal energy of the phonons is related to the low-temperature limits of the mean-squared vibrational amplitudes of the lattice measured by X-ray and γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal close-packed zinc structure, including the temperature evolution of the B factors of zinc. In this case, the lattice vibrations are partitioned into axial and basal normal components, which admit largely differing B factors and Debye temperatures. The second-order B factors defining the non-Gaussian contribution to the Debye-Waller damping factors of zinc are obtained as well. Anharmonicity of the oscillator potential and deviations from the uniform phonon frequency distribution of the Debye theory are modeled effectively by the temperature dependence of the spectral cutoff and Debye temperatures.

Linear propagation of dust acoustic modes in the presence of an electron beam

The physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.

Partially massless theory as a quantum gravity candidate

We study partially massless gravity theory (PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self-interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self-interaction terms necessarily breaks the [Formula: see text] gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, [Formula: see text], where [Formula: see text] is the PM gravity field and [Formula: see text] is the stress-energy tensor of the matter fields. To retain the [Formula: see text] gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be nonlocal in this case. The second type of interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom — 2 of them are traceless tensor modes and they are light-like fields and the other 2 are transverse vector modes and their dispersion relation changes as background space–time (de Sitter) evolutes. In the very early time, they are light-like but in the very late time, their velocities become a half of speed of light. The vector mode dispersion relation shows momentum-dependent behavior. In fact, the higher (lower) frequency modes show the faster (slower) velocity. We call this effect “conformal (or de Sitter) prism”. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators.