Showing papers on "Dispersion relation published in 2000"

Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability

Abstract: The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Joint inversion of receiver function and surface wave dispersion observations

Abstract: We implement a method to invert jointly teleseismic P-wave receiver functions and surface wave group and phase velocities for a mutually consistent estimate of earth structure. Receiver functions are primarily sensitive to shear wave velocity contrasts and vertical traveltimes, and surface wave dispersion measurements are sensitive to vertical shear wave velocity averages. Their combination may bridge resolution gaps associated with each individual data set. We formulate a linearized shear velocity inversion that is solved using a damped least-squares scheme that incorporates a priori smoothness constraints for velocities in adjacent layers. The data sets are equalized for the number of data points and physical units in the inversion process. The combination of information produces a relatively simple model with a minimal number of sharp velocity contrasts. We illustrate the approach using noise-free and realistic noise simulations and conclude with an inversion of observations from the Saudi Arabian Shield. Inversion results for station SODA, located in the Arabian Shield, include a crust with a sharp gradient near the surface (shear velocity changing from 1.8 to 3.5 km s−1 in 3 km) underlain by a 5-km-thick layer with a shear velocity of 3.5 km s−1 and a 27-km-thick layer with a shear velocity of 3.8 km s−1, and an upper mantle with an average shear velocity of 4.7 km s−1. The crust–mantle transition has a significant gradient, with velocity values varying from 3.8 to 4.7 km s−1 between 35 and 40 km depth. Our results are compatible with independent inversions for crustal structure using refraction data.

Anomalous refractive properties of photonic crystals

Abstract: We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.

Plasma oscillations and nonextensive statistics

Abstract: The dispersion relations for electrostatic plane-wave propagation in a collisionless thermal plasma are discussed in the context of the nonextensive statistics proposed by Tsallis. Analytic formulas both for the undamped (Bohm-Gross) and Landau damped waves are derived and compared with the standard results. In the extensive limiting case $(q=1),$ the classical dispersion relations based on the Maxwellian distribution are recovered. It is shown that the experimental results points to a class of Tsallis's velocity distribution described by a nonextensive q-parameter smaller than unity.

Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

Abstract: The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional (2D) phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.

Scattering-theory analysis of waveguide-resonator coupling

Abstract: Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.

Excitation of zonal flow by drift waves in toroidal plasmas

Abstract: An analytical dispersion relation is derived which shows that, in toroidal plasmas, zonal flows can be spontaneously excited via modulations in the radial envelope of a single-n coherent drift wave, with n the toroidal mode number. Predicted instability features are verified by three-dimensional global gyrokinetic simulations of the ion-temperature-gradient mode. Nonlinear equations for mode amplitudes demonstrate saturation of the linearly unstable pump wave and nonlinear oscillations of the drift-wave intensity and zonal flows, with a parameter-dependent period doubling route to chaos.

The Robustness of Inflation to Changes in Super-Planck-Scale Physics

Abstract: We calculate the spectrum of density fluctuations in models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, and specifically investigate the dependence of the predictions on modifications of the physics on length scales smaller than the Planck length. These modifications are encoded in terms of modified dispersion relations. Whereas for some classes of dispersion relations the predictions are unchanged compared to the usual ones which are based on a linear dispersion relation, for other classes important differences are obtained, involving tilted spectra, spectra with exponential factors and with oscillations. We conclude that the predictions of inflationary cosmology in these models are not robust against changes in the super-Planck-scale physics.

Evidence for an Energy Scale for Quasiparticle Dispersion in Bi 2 Sr 2 CaCu 2 O 8

Abstract: Quasiparticle dispersion in Bi2Sr2CaCu2O8 is investigated with improved angular resolution as a function of temperature and doping. Unlike the linear dispersion predicted by the band calculation, the data show a sharp break in dispersion at 50+/-15 meV binding energy where the velocity changes by a factor of 2 or more. This change provides an energy scale in the quasiparticle self-energy. This break in dispersion is evident at and away from the d-wave node line, but the magnitude of the dispersion change decreases with temperature and with increasing doping.

Refractive indices and absorption coefficients of MgxZn1−xO alloys

Abstract: Indices of refraction for MgxZn1−xO epitaxial films grown by pulsed-laser deposition on sapphire substrates with x up to 0.36 were determined in the range of wavelength 457–968 nm by analysis of optical transmission spectra and prism-coupled waveguide measurements. The dispersion follows the first-order Sellmeier dispersion equation. Absorption coefficients, exciton energy gaps, and binding energies of MgxZn1−xO alloys were determined by transmission spectroscopy. The excitonic absorption features were clearly visible at room temperature despite alloy broadening. These results provide important information for the design and modeling of ZnO/MgZnO heterostructure optoelectronic devices.

Waves on noncommutative space–time and gamma-ray bursts

Abstract: Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski space–time [xi, t]=ιλxi. A natural wave equation is derived and the associated phenomena of in vacuo dispersion are discussed. Assuming the deformation scale λ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigations of astrophysical phenomena such as gamma-ray bursts. We also outline a new approach to the construction of field theories on the noncommutative space–time, with the noncommutativity equivalent under Fourier transform to non-Abelianness of the "addition law" for momentum in Feynman diagrams. We argue that CPT violation effects of the type testable using the sensitive neutral-kaon system are to be expected in such a theory.

Solute transport in variable-aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion

Abstract: Dispersion of solutes in a variable aperture fracture results from a combination of molecular diffusion and velocity variations in both the plane of the fracture (macrodispersion) and across the fracture aperture (Taylor dispersion). We use a combination of physical experiments and computational simulations to test a theoretical model in which the effective longitudinal dispersion coefficient DL is expressed as a sum of the contributions of these three dispersive mechanisms. The combined influence of Taylor dispersion and macrodispersion results in a nonlinear dependence of DL on the Peclet number (Pe 5 V^b&/Dm, where V is the mean solute velocity, ^b& is the mean aperture, and Dm is the molecular diffusion coefficient). Three distinct dispersion regimes become evident: For small Pe (Pe , , 1), molecular diffusion dominates resulting in D L } Pe 0 ; for intermediate Pe, macrodispersion dominates (DL } Pe); and for large Pe, Taylor dispersion dominates (D L } Pe 2 ). The Pe range corresponding to these different regimes is controlled by the statistics of the aperture field. In particular, the upper limit of Pe corresponding to the macrodispersion regime increases as the macrodispersivity increases. Physical experiments in an analog, rough-walled fracture confirm the nonlinear Pe dependence of DL predicted by the theoretical model. However, the theoretical model underestimates the magnitude of DL. Computational simulations, using a particle-tracking algorithm that incorporates all three dispersive mechanisms, agree very closely with the theoretical model predictions. The close agreement between the theoretical model and computational simulations is largely because, in both cases, the Reynolds equation describes the flow field in the fracture. The discrepancy between theoretical model predictions and DL estimated from the physical experiments appears to be largely due to deviations from the local cubic law assumed by the Reynolds equation.

Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals

Abstract: A new type of waveguiding mechanism in three-dimensional photonic band-gap structures is demonstrated. Photons propagate through strongly localized defect cavities due to coupling between adjacent cavity modes. High transmission of the electromagnetic waves, nearly 100%, is observed for various waveguide structures even if the cavities are placed along an arbitrarily shaped path. The dispersion relation of the waveguiding band is obtained from transmission-phase measurements, and this relation is well explained within the tight-binding photon picture. The coupled-cavity waveguides may have practical importance for development of optoelectronic components and circuits.

Transverse waves in a two-dimensional screened-coulomb crystal (Dusty plasma)

Abstract: Transverse shear waves were observed experimentally in a two-dimensional screened Coulomb crystal. They were excited by applying a chopped laser beam to a 2D dusty plasma, i.e., a monolayer of charged microspheres levitated in a plasma. Measurements of the dispersion relation reveal an acoustic, i.e., nondispersive, character over the entire range of wave numbers measured, 0.2

Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide

Abstract: Using both the tight-binding approximation and the finite-difference time domain method, we analyze two types of coupled-resonator optical waveguide (CROW), a coupled-microdisks waveguide and a waveguide composed of coupled defect cavities in a two-dimensional photonic crystal. We find that the dispersion relation of the CROW band can be simply described by a small coupling parameter , and the spatial characteristics of the CROW modes remain the same as those of the single-resonator high Q modes. As applications of these unique properties, we demonstrate that CROWs can be utilized in constructing waveguides without cross talk and enhance the efficiency of second-harmonic generation.

On the applicability of Kramers–Krönig relations for ultrasonic attenuation obeying a frequency power law

Abstract: In the recent literature concern has been raised regarding the validity of Kramers–Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers–Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley–Wiener conditions, forms the conclusion.

Wave dispersion relations in Yukawa fluids.

Abstract: The wave dispersion relations in the fluid phase of Yukawa systems are obtained from molecular dynamics (MD) simulations for a wide range of the parameters. The Yukawa system is a collection of particles interacting through Yukawa (i.e., screened Coulomb) potentials, which can serve as a simple model for dusty plasmas. Our simulations have clearly shown that the transverse wave dispersion has a cutoff at a long wavelength even in the case of weak screening. The MD simulation data are compared with earlier theoretical predictions of the Yukawa dispersion relations and the validity of these theories is clarified.

Asymptotic analysis of Bragg fibers

Abstract: Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis and design of Bragg fibers.

Mechanism of dust-acoustic instability in a direct current glow discharge plasma

Abstract: An observation of low frequency waves spontaneously excited in a dc glow discharge dusty plasma is reported. To analyze possible reasons for the instability observed, a linear dispersion relation which takes into account collisions with neutrals, dust grain charge variations, ion drift, and forces acting on dust particles is derived. Numerical analysis of the dispersion relation shows that the observed instability is the result of dust charge variations in the presence of external charge-dependent forces together with the ion drift effect.

The space filling mode of holey fibers: an analytical vectorial solution

Abstract: We tackle holey fibers in full vectorial terms. From Maxwell's equations, we derive the dispersion relations of the modes guided by an infinitely self-similar air hole lattice. We focus in particular on the fundamental mode (the so-called space filling mode), and show that previous numerical results based on vector methods are accurate, but scalar ones are not. We also find the field flow lines, intensity distribution in the cross section, and linear polarization ratio vs. wavelength.

Electron kinetic firehose instability

Abstract: The linear dispersion equation describing electromagnetic waves propagating in a homogeneous electron-proton plasma along arbitrary directions relative to the direction of the background magnetic field is solved numerically for bi-Maxwellian particle distributions. It is found that in the presence of an electron temperature anisotropy T⊥ 2), several purely growing modes (zero real frequency) and a quasi-parallel electron firehose instability develop. While the quasi-parallel mode is unstable for both parallel and oblique propagation, the zero frequency modes are unstable only for oblique propagation. Comparison of these modes further shows that the propagation angle for maximum growth rate and the maximum growth rate are larger for the purely growing modes than the quasi-parallel electron firehose while the threshold is lower. Potential application of the kinetic electron firehose instability to the slow solar wind is briefly discussed.

In-plane lattice thermal conductivity of a quantum-dot superlattice

Abstract: We have theoretically investigated the in-plane lattice thermal conductivity of a quantum-dot superlattice. The calculations were carried out for a structure that consists of multiple layers of Si with randomly distributed Ge quantum dots separated by wetting layers and spacers. Our model takes into account scattering of acoustic phonons on spherical quantum dots, and corresponding modification of the phonon dispersion relation. The finite acoustic mismatch between Si and Ge is also taken into account. The obtained results are important for the most recently suggested applications of SiGe quantum-dot superlattices for thermoelectric devices.

Linear instability mechanisms for sand wave formation

Abstract: A height- and flow-dependent model for turbulent viscosity is employed to explain the generation of sand waves in tidal seas. This new model resolves the problem of excitation of very long waves in sand wave formation, because it leads to damping of the long waves and gives a finite separation between the most excited mode and the zero mode. For parameters within their physically realistic ranges, a linear analysis of the resulting system yields a first excited mode whose wavelength is similar to the characteristic wavelength of sand waves observed in nature. The physical mechanism of sand wave formation as predicted by the new model is explained in detail. The dispersion relation obtained can be the starting point for a weakly nonlinear analysis of the system.

Spin-waves in cylindrical magnetic dot arrays with in-plane magnetization

Abstract: The discrete spectrum of dipole-exchange spin-wave modes of a tangentially magnetized cylindrical magnetic dot is calculated from the solution of the Landau–Lifshitz equation and the magnetostatic Maxwell equations in a cylindrical geometry. The general surface spin-pinning conditions at the radial dot boundary are considered. The main simplifying assumptions are: (i) the dot radius is much larger than the dot height; (ii) the distribution of the variable magnetization along the dot height is uniform. The approximate dispersion equation for spin-wave modes in a dot is obtained in a simple analytical form similar to the form of the dispersion equation in an infinite film. The quantization effect of the spin-wave frequencies appears due to the finite dot radius and is essential for submicron magnetic dots. The discrete spin-wave frequencies are calculated in a practically important case of the square array of permalloy cylindrical dots. The relative intensities of spin-wave modes, when observed by Brillouin...

Dispersive ionospheric Alfvén resonator

Abstract: A new model of the ionospheric Alfven resonator (IAR) including the effect of wave frequency dispersion is presented. It is shown that the shear Alfven waves in the IAR are coupled to the compressional mode through the boundary conditions at the ionosphere. This coupling results in the appearance of the Hall dispersion and subsequent shift of the IAR frequency spectrum. The excitation mechanism involving the IAR interaction with the magnetospheric convective flow is considered. It is shown that the Hall dispersion of the IAR eigenmode increases the growth rate of the feedback instability. However, for the observed values of ionospheric conductivity this effect is not very high. It is shown that the physical mechanism of the feedback instability is similar to the Cerenkov radiation in collisionless plasmas. The IAR eigenfrequencies and growth rates are evaluated for the case of exponential variation of the Alfven velocity with altitude in the topside ionosphere.

Energy flow in photonic crystal waveguides

Abstract: Theoretical and numerical investigations of energy flow in photonic crystal waveguides made of line defects and branching points are presented It is shown that vortices of energy flow may occur, and the net energy flow along the line defect is described via the effective propagation velocity Single-mode and multimode operations are studied, and dispersion relations are computed for different waveguide widths Both strong positive, strong negative, and zero dispersion are possible It is shown that geometric parameters such as the nature of the lattice, the line defect orientation, the defect width, and the branching-point geometry have a significant influence on the electrodynamics These are important issues for the fabrication of photonic crystal structures

Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity

Abstract: The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco- elastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the

Interferometric coherency determination of wavelength or what are broadband ELF waves

Abstract: To determine the wavelength of waves within a random, isotropic wave field, we introduce the observable of wave coherency measured with plasma wave interferometers. We show generally that within a random direction wave field, wavelengths large compared to the interferometer length produce large coherency (nearly 1), but wavelengths the order of a few times the interferometer length, or smaller, produce small coherency (close to zero). We apply this principle first to examining auroral hiss and lower hybrid waves measured by the Physics of Auroral Zone Electrons (PHAZE) 2 and Topside Probe of the Auroral Zone (TOPAZ) 3 experiments and show that the implied wavelengths are consistent with the expected dispersion relations and with other, different estimates of wavelength for these modes. Next, we apply the principle to broadband extra low frequency (BB-ELF) electric fields observed in both experiments and conclude that the wavelengths are small. In one case we calculate the coherency of BB-ELF electric fields, using an ensemble average of 7889 data samples, and demonstrate that the coherency near the oxygen gyrofrequency is very small (≅0.15), corresponding to wavelengths of 10 m and the order of the ion gyroradius. We conclude that because of the short wavelengths, previous satellite measurements of BB-ELF electric fields may have underestimated the electric field amplitudes, unless ion gyroradii are substantially larger than the case for these rocket measurements. Although the wavelengths and frequencies of BB-ELF electric fields are now known, we are unable to assign the wave to a known, normal mode of homogeneous plasmas. This suggests that inhomogeneities may be essential for describing BB-ELF electric fields.