Analysis Of Dispersion Relation Research Articles

Parallel propagating electromagnetic waves in magnetized quantum electron plasmas with finite temperature.

We studied parallel propagating electromagnetic waves in a magnetized quantum electron plasma of finite temperature, as an extension of our previous study on a zero temperature plasma. We obtained simple analytic dispersion relations in the long wavelength limit that included the thermal effect as correction terms to the zero temperature results. As in the zero temperature case, the lower branch of the R wave showed significant damping and became ill-defined at short wavelengths. Quantum effects seemed to give qualitative changes, such as the appearance of anomalous dispersion regions, to the classical dispersion relations when v_{F}/v_{th}≤0.2 for a set of exemplary parameters of v_{F}=0.1c and ω_{ce}/ω_{pe}=0.05 was used. We also noted that introduction of the Planck constant in the quantum Vlasov equation changed the shape of the anomalous dispersion region qualitatively, by forming a normal dispersion region in the middle of the original single broad anomalous dispersion region.

Omnidirectional excitation of surface waves and super-Klein tunneling at the interface between two different bi-isotropic media

We study theoretically some unique characteristics of surface electromagnetic waves excited at the interface between two different kinds of general bi-isotropic media, which include Tellegen media and chiral media as special cases. We derive an analytical dispersion relation for those waves, using which we deduce eight different conditions under which they are generated between two Tellegen media and between two chiral media independently of the component of the wave vector along the interface. These make it possible to excite the surface waves for all or a wide range of incident angles in attenuated total reflection experiments on multilayer structures. We generalize the concept of a conjugate matched pair to bi-isotropic media and obtain several conditions under which the omnidirectional total transmission, which we call the super-Klein tunneling, occurs through conjugate matched pairs consisting of Tellegen media and of chiral media. We find that these conditions are closely linked to those for the omnidirectional excitation of surface waves. Using the invariant imbedding method, we perform extensive numerical calculations of the absorptance, the transmittance, and the spatial distribution of the electromagnetic fields for circularly-polarized waves incident on bilayer structures and confirm that the results agree perfectly with the analytical predictions.

A third‐order compact nonlinear scheme for compressible flow simulations

SummaryReynolds‐averaged Navier‐Stokes simulations based on second‐order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin‐friction drag and aerodynamic heating, as well as in simulations of complex flows such as large‐scale separation and transition. A remedy for this is the development of high‐order schemes, by which numerically induced dissipation and dispersion errors of low‐order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high‐resolution nonlinear shock‐capturing methods. A stencil‐selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third‐order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh‐Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.

Horizontal shear instabilities in rotating stellar radiation zones

Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f-plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. While the maximum two-dimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the three-dimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of √f(1 − f) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Péclet number Pe and the Brunt–Väisälä frequency N.

Wave dispersion in nonlocal anisotropic macro/nanoplates made of functionally graded materials

By means of a higher-order shear deformation theory (HSDT) coupled with the nonlocal elasticity theory, this work is attempted to elucidate the size-dependent behavior of functionally graded (FG) Anisotropic macro/nanoplates. In the HSDT, the displacement field is modeled as a combination of an exponential formula and a trigonometric function. This type of theory has only five unknowns but can have precise results in various conditions for thick and thin plates. By employing Hamilton’s principle, the governing equations are derived for FG anisotropic macro/nanoplates. In the case of FG anisotropic materials, all components of elastic stiffness tensor are involved, and the material gradation is considered to be arbitrary in the thickness direction. In order to attain the analytical dispersion relations, an eigenvalue problem is solved. The model’s validation is evaluated by comparing authors’ results with other papers available in the open literature. The influences of nonlocal parameter, exponential factor, geometrical shape, and wave number on the circular frequencies and phase velocities are inspected. From the knowledge of authors, it is the first time that the small-scale influences for FG anisotropic macro/nanoplates based on the present higher-order shear deformation theory are investigated.

Wave dispersion in viscoelastic lipid nanotubes conveying viscous protein solution

This work investigates the wave dispersion characteristics in viscoelastic lipid nanotubes conveying protein solution. The protein solution is assumed to be viscous, incompressible, and irrotational. The theoretical formulation is within the framework of the Rayleigh beam theory and the nonlocal strain gradient theory (NSGT). The analytical wave dispersion relations of protein-conveying lipid nanotubes are obtained. Results show that the nonlocal parameter, the material length-scale parameter, the fluid mass density, and the damping coefficient have important effect on wave dispersion characteristics of viscoelastic lipid nanotubes conveying protein solution. These findings are helpful to understand the wave dispersion characteristics of protein-conveying lipid nanotubes.

Consistency of the standard model effective field theory

We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion relation arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bounds also follow as a consequence of causality of signal propagation in nonvacuum SM backgrounds. These bounds come in two qualitative forms: i) positivity of (various linear combinations of) couplings of CP-even operators and ii) upper bounds on the magnitude of CP-odd operators in terms of (products of) CP-even couplings. We exhibit various classes of example completions, which all satisfy our EFT bounds. These bounds have consequences for current and future particle physics experiments, as part of the observable parameter space is inconsistent with causality and analyticity. To demonstrate the impact of our bounds, we consider applications both to SMEFT constraints derived at colliders and to limits on the neutron electric dipole moment, highlighting the connection between such searches suggested by infrared consistency.

Atomistic simulations of thermal conductivity in GeTe nanowires

The thermal conductivity of GeTe crystalline nanowires has been computed by means of non-equilibrium molecular dynamics simulations employing a machine learning interatomic potential. This material is of interest for application in phase change non-volatile memories. The resulting lattice thermal conductivity of an ultrathin nanowire (7.3 nm diameter) of 1.57 W m−1 K−1 is sizably lower than the corresponding bulk value of 3.15 W m−1 K−1 obtained within the same framework. The analysis of the phonon dispersion relations and lifetimes reveals that the lower thermal conductivity in the nanowire is mostly due to a reduction in the phonon group velocities. We further predict the presence of a minimum in the lattice thermal conductivity for thicker nanowires.

Optical lattice vibrations in monolayer hexagonal boron nitride from macroscopic equations

Using two pairs of macroscopic equations deduced from a dipole lattice model including electronic polarization (EP) of ions and local field effects (LFEs) self-consistently, optical lattice vibrations in monolayer hexagonal boron nitride (BN) are studied theoretically for both in-plane and out-of-plane motions. Longitudinal and transverse optical (LO and TO) modes and out-of-plane (ZO) modes are derived, and explicit expressions are obtained for phonon dispersion, group velocity and density of states. The analytical phonon dispersion relations describe previous numerical results very well; the LO phonon dispersion is identical to the analytical expression of Sohier et al, which shows the degeneracy of the LO and TO modes at and the splitting at finite wavevectors due to the long-range macroscopic field. Whilst relating to microscopic quantities, the linear coefficients of the lattice equations are determined by first-principles calculated quantities (such as macroscopic susceptibilities). Therefore the EP and LFEs on the vibrational properties are studied. With no EP or LFEs, all the phonon frequencies are overestimated significantly. Including EP, the LFEs increase (decrease) the in-plane (out-of-plane) dielectric susceptibility by a factor of 2.5–3.5. Both ionic EP and LFEs should be included to obtain an accurate description of the lattice dynamics.

Analytic Euclidean bootstrap

We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension ∆ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the other channel. Subleading frac{1}{varDelta } tails are systematically captured by including more operators in the Euclidean OPE in the dual channel. We use dispersion relations for conformal partial waves in the complex ∆ plane, the Lorentzian inversion formula and complex tauberian theorems to derive this result. We check our formulas in a few examples (for CFTs and scattering amplitudes) and find perfect agreement. Moreover, in these examples we observe that the large ∆ expansion works very well already for small ∆ ∼ 1. We make predictions for the 3d Ising model. Our analysis of dispersion relations via complex tauberian theorems is very general and could be useful in many other contexts.

Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems

The study of wave propagation in chains of anharmonic periodic systems is of fundamental importance to understand the response of dynamical absorbers of vibrations and acoustic metamaterials working in the nonlinear regime. Here, we derive an analytical nonlinear dispersion relation for periodic chains of anharmonic mass-spring and mass-in-mass systems resulting from considering the hypothesis of factorization for the spatial and temporal parts of the solution and a periodic distribution function as ansatz of a general solution of the temporal part of the nonlinear equations of motion. A comparison with numerical simulations shows the range of validity of this expression. This work provides a tool to design and study nonlinear dynamics for some classes of seismic metamaterials such as composite foundations, perturbative metamaterials, and metasurfaces.

An Accurate Three-Dimensional FDTD(2,4) Method on Face-Centered Cubic Grids With Low Numerical Dispersion

In this letter, a three-dimensional finite-difference time-domain (FDTD) method that is second-order in time and fourth-order in space on a face-centered cubic (FCC) grid, termed as FCC-FDTD(2,4), is proposed to solve the time-domain Maxwell's equations. The proposed method shows a much lower numerical dispersion error compared with the errors of other FDTD schemes, such as the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. This improvement in the numerical dispersion results from the FCC grid and the fourth-order scheme in space used in the proposed FCC-FDTD(2,4) method. Then, the Courant-Friedrichs-Lewy condition is given through spectral analysis, and an analytical numerical dispersion relation is obtained and comprehensively studied through numerical results with the FCC-FDTD(2,2) method, the FDTD(2,2) method, and the FDTD(2,4) method. Compared with the other three FDTD methods, the proposed method has much smaller numerical dispersion errors. Finally, the accuracy of the proposed method is further validated with other numerical examples.

Backfire-to-endfire scanning capability of a balanced metamaterial structure based on slotted ferrite-filled waveguide

In this paper, a new metamaterial structure that consists of a normally magnetized ferrite-filled rectangular waveguide with a long slot on the center of the broad wall is proposed. The analytical dispersion relation for this structure is derived through the transverse resonance method (TRM). The unique dispersion properties, such as the inherent balanced composite right/left-handed (CRLH) response and its magnetically tunable behavior, are studied and validated by some simulated results. As an application of the proposed metamaterial structure, a magnetically backfire-to-endfire scanning leaky-wave antenna (LWA) that is capable of both fixed-bias frequency scanning and fixed-frequency bias scanning is presented. Based on the simulated results, by changing the magnetic DC bias of the ferrite in range of 1192–1336 Oe, the radiation pattern of the proposed LWA can be scanned from about 52 to −54 degrees. The main advantages of the proposed structure in comparison to previous metamaterial LWAs consist of ease of design and fabrication and no use of any mechanical or electrical switches.

Instability of an annular liquid sheet exposed to compressible gas flows

A temporal linear stability analysis was performed for a viscous annular liquid sheet exposed to compressible gas flows. An analytical dispersion relation illustrating the disturbance growth characteristics at the gas–liquid interfaces was formulated and validated, and a parametric study was performed to explore the mechanism that affects the sheet instability. The results reflect that para-sinuous disturbances on the liquid sheet always predominate over para-varicose disturbances under the considered flow conditions. The aerodynamic interaction at the gas–liquid interfaces of the liquid sheet is the decisive factor on sheet instability. As for the main factors affecting the aerodynamic effects, the contribution of the gas–liquid velocity difference to aerodynamic interactions is more significant than that of the gas–liquid density ratio. Neglecting the gas compressibility markedly underestimates the aerodynamic effects at the gas–liquid interfaces for flow conditions of high gas Mach number, which results in decreased disturbance growth rate and dominant wave number. Moreover, both the liquid viscous force and the surface tension force hold back the disturbance growing and stabilize the liquid sheet under the considered conditions. Note that the destabilizing effect of the viscous force is limited for high liquid Reynolds number cases. In general, it is very necessary to consider the compressibility of the gas flows in the instability study of practical twin-fluid atomization.

Interplay between grid resolution and pressure decimation in non-hydrostatic modeling of internal waves

The Pressure Decimation and Interpolation (PDI) method is an effective numerical technique to improve the computational efficiency of a non-hydrostatic model. We carried out an analysis of the wave dispersion relation and quantitative measurements of numerical dissipation and diffusion affected by the PDI scheme in modeling of internal waves. The linear analysis on the wave dispersion relation shows that the accuracy in predicting wave dispersion depends highly on how well the vertical structure of the non-hydrostatic pressure is represented over depth. The accuracy is not only dependent on the resolution of the pressure grid, but also on the interpolation method. The third-order spline interpolation provides a more accurate wave dispersion relation than the lower-order (linear and quadratic) interpolation. Quantitative measurements of wave energy transfer from the basin-scale internal seiche to small-scale internal solitary waves, as well as numerical dissipation and diffusion in the PDI model, were performed in the simulation of internal waves. Results show that the resolution of the pressure grid has a major effect on the wave dispersion but a negligible effect on the numerical dissipation and diffusion. The velocity grid resolution has a significant influence on the numerical diffusion and a minor effect on the numerical dissipation.

Theoretical Prediction of Asymmetric Instability of Drift Kinetic Alfven Waves in Anisotropic Plasmas

AbstractThe asymmetric instability of drift kinetic Alfvén waves (DKAWs) is analyzed to study the interplay between the density inhomogeneity and the temperature anisotropy, including the wave‐particle interaction and finite ion Larmor radius effects. The asymmetric behavior arises due to the opposite diamagnetic drifts of electrons and ions and quantifies the contribution of electron drift waves and ion drift waves in altering the dispersion characteristic of DKAWs. It is shown that the coupling of drift waves with kinetic Alfvén waves leads to the generation of three different frequency (i.e., higher, intermediate, and lower) modes of DKAWs. The comparison of their propagation characteristics and stability mechanisms applicable to a wide range of plasma parameters is provided. The analytical dispersion relation can be used as an improved theoretical tool for identifying the existence of DKAWs and their source region in the multisatellite observations, especially near the reconnection X‐line.

Gyrokinetic simulations of m = 0 mode in sheared flow Z-pinch plasmas

Axisymmetric stability properties of sheared flow Z-pinch plasmas are studied by making use of the gyrokinetic approximation in the long-wavelength limit. Numerical simulations are carried out with the high-order finite-volume code COntinuum Gyrokinetic Edge New Technology (COGENT) and are analyzed for the parameters characteristic of the FuZE experiment. Reduction of the linear growth rate with increasing shear is observed, and the results are elucidated by making use of a local dispersion relation analysis. In addition, COGENT simulations are compared with fully kinetic particle-in-cell simulations, and with an ideal magnetohydrodynamics (MHD) model. Good agreement between the gyrokinetic and fully kinetic results for the linear stability is found, with the gyrokinetic model requiring much less computational time due to its ability to step over particle gyroperiod. The ideal MHD model is found to be consistent with the kinetic models in the long-wavelength part of the spectra (kρi), while failing to adequately predict short-scale (kρi) stability. Here, k is the axial wavelength vector and ρi is the ion gyroradius.

Structural, optical and dielectric studies of Ag nanoparticles decorated by herceptin

Silver nanoparticles (AgNPs) were synthesized (with 17–31 nm sizes) by reduction of AgNO3 by NaBH4 solution and covered by anti-HER2 monoclonal antibody (Herceptin). The morphology, structure, optical and dielectric properties of the prepared AgNPs have been characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD), UV–Vis system and Fourier transform infrared (FTIR) spectroscopy. The complex index of refraction and the dielectric coefficient Herceptin and AgNPs covered by Herceptin were measured over the spectral region of 400–4000 cm−1. The XRD patterns showed the formation of face-centered cubic lattice structure of AgNPs and according to the TEM image AgNPs had spherical shape with an average diameter size of about 25 nm. By using Kramers–Kronig (KK) dispersion relations analysis, these measurements allow the determination of the real and imaginary parts of refractive index and dielectric coefficient over the entire wavelength intervals. By covering AgNPs with antibody, the intensity of n and k peaks were decreased. After decoration with AgNPs, the real and imaginary parts of permittivity in samples were also decreased. In addition, the resonance frequency of decorated samples with AgNPs have red shifts in comparison with the pure samples. These results are applicable in development of methods for detection of airborne pathogenic agent.

Hybridization of epsilon-near-zero modes via resonant tunneling in layered metal-insulator double nanocavities

Abstract The coupling between multiple nanocavities in close vicinity leads to the hybridization of their modes. Stacked metal-insulator-metal (MIM) nanocavities constitute a highly versatile and very interesting model system to study and engineer such mode coupling, as they can be realized by lithography-free fabrication methods with fine control on the optical and geometrical parameters. The resonant modes of such MIM cavities are epsilon-near-zero (ENZ) resonances, which are appealing for nonlinear photophysics and a variety of applications. Here, we study the hybridization of ENZ resonances in MIMIM nanocavities, obtaining a very large mode splitting reaching 0.477 eV, Q-factors of the order of 40 in the visible spectral range, and fine control on the resonance wavelength and mode linewidth by tuning the thickness of the dielectric and metallic layers. A semiclassical approach that analyzes the MIMIM structure as a double quantum well system allows to derive the exact analytical dispersion relation of the ENZ resonances, achieving perfect agreement with numerical simulations and experiments. Interestingly, the asymmetry of the mode splitting in a symmetric MIMIM cavity is not reflected in the classical model of coupled oscillators, which can be directly related to quantum mechanical tunneling for the coupling of the two cavities. Interpreting the cavity resonances as resonant tunneling modes elucidates that they can be excited without momentum matching techniques. The broad tunability of high-quality ENZ resonances together with their strong coupling efficiency makes such MIMIM cavities an ideal platform for exploring light-matter interaction, for example, by the integration of quantum emitters in dielectric layers.

A Framework for Modeling Linear Surface Waves on Shear Currents in Slowly Varying Waters

AbstractWe present a theoretical and numerical framework—which we dub the direct integration method (DIM)—for simple, efficient, and accurate evaluation of surface wave models allowing presence of a current of arbitrary depth dependence and where bathymetry and ambient currents may vary slowly in horizontal directions. On horizontally constant water depth and shear current the DIM numerically evaluates the dispersion relation of linear surface waves to arbitrary accuracy, and we argue that for this purpose it is superior to two existing numerical procedures: the piecewise‐linear approximation and a method due to Dong and Kirby (2012, https://doi.org/10.9753/icce.v33.waves.2). The DIM moreover yields the full linearized flow field at little extra cost. We implement the DIM numerically with iterations of standard numerical methods. The wide applicability of the DIM in an oceanographic setting in four aspects is shown. First, we show how the DIM allows practical implementation of the wave action conservation equation recently derived by Quinn et al. (2017, https://doi.org/10.1016/j.ocemod.2017.03.003). Second, we demonstrate how the DIM handles with ease cases where existing methods struggle, that is, velocity profiles U(z) changing direction with vertical coordinate z and strongly sheared profiles. Third, we use the DIM to calculate and analyze the full linear flow field beneath a 2‐D ring wave upon a near‐surface wind‐driven exponential shear current, revealing striking qualitative differences compared to no shear. Finally we demonstrate that the DIM can be a real competitor to analytical dispersion relation approximations such as that of Kirby and Chen (1989, https://doi.org/10.1029/JC094iC01p01013) even for wave/ocean modeling.