Showing papers on "Dispersion relation published in 1987"

High-resolution photoemission study of the electronic structure of the noble-metal (111) surfaces.

Abstract: High-resolution angle-resolved photoemission studies of the (111) surfaces of copper, silver, and gold are reported which investigate in detail the properties of the intrinsic surface states located in the projected sp-band gaps at the center of the surface Brillouin zones. Accurate two-dimensional energy dispersion relations are reported for each surface state and are quantified in terms of effective masses at the surface Brillouin-zone center. The masses for the three metals are found to be remarkably similar when normalized to the effective mass of the lower edge of the bulk continuum. The decay length of the surface state wave function into the surface was determined for all three surfaces. These results are expressed in terms of an effective mass of the complex dispersion relation within the projected band gap. In accord with our previous results on the copper state, these effective masses are found to be anomalously large by approximately a factor of 2 relative to expectations based on effective mass theory coupled to first-principles bulk band calculations. An explanation of this anomaly involving the nonorthogonality of effective-mass-theory-derived states is explored. All experimental results are compared to the predictions of recent self-consistent surface electronic structure calculations for these surfaces.

Fully toroidal ion temperature gradient driven drift modes

Abstract: A simple quadratic dispersion relation is derived for electrostatic ion temperature gradient driven modes without expansion in the inverse aspect ratio. It is also shown that these modes experience the local curvature only on the outside of the magnetic surface.

Gap solitons in nonlinear periodic structures.

Abstract: In a medium with a dielectric constant periodic in one spatial direction, there are gaps in the dispersion relation of electromagnetic waves which propagate in the structure. If the index of refraction also contains a term proportional to the local-field intensity, we show that for frequencies within the gap, there exist soliton solutions to the nonlinear wave equation of the medium. This is demonstrated by analytic methods; the results agree with conclusions reached earlier, in numerical studies of power-dependent transmission through a finite superlattice, with a nonlinear element in each unit cell.

Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface.

Abstract: We derive exact dispersion relations for transverse magnetic polarized guided waves at an interface between either a linear dielectric or a metal and a nonlinear dielectric. The nonlinearity is taken to be a Kerr-type nonlinearity. Numerical results are presented for the dielectric–metal case.

Linear plane waves in dissipative relativistic fluids.

Abstract: This paper analyzes the dispersion relations for linear plane waves in the Eckart and the Israel-Stewart theories of dissipative relativistic hydrodynamics. We show that in the long-wavelength (compared to a typical mean-free-path-length) limit the complicated dynamical structure of the Israel-Stewart theory reduces to the familiar dynamics of classical fluids: 9 of the 14 modes of an Israel-Stewart fluid are strongly damped in this limit, two propagate at the adiabatic sound speed (with appropriate viscous and thermal damping), two transverse shear modes decay at the classical viscous damping rate, and the final longitudinal mode is damped at the classical thermal diffusion rate. The short-wavelength limit of these dispersion relations is also examined. We demonstrate that the phase and group velocities of these waves must approach the characteristic velocities in the short-wavelength limit. Finally, we show how some of the perturbations of an Eckart fluid violate causality.

Estimating slowness dispersion from arrays of sonic logging waveforms

Abstract: Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits...

The ion-ion acoustic instability

Abstract: This paper considers the linear theory of ion-acoustic-like instabilities in a homogeneous Vlasov plasma with two ion components, a less dense beam and a more dense core, with a relative drift velocity. Numerical solutions of the full electrostatic dispersion equation are presented, and the properties of the ion-ion acoustic instability are studied in detail. At relatively cold beam temperatures, the instability is fluid-like, but it becomes a beam resonant kinetic instability as the beam temperature becomes of the order of the core temperature; if the mode is unstable, its threshold lies well below the threshold of the electron-ion acoustic instability. An electron temperature anisotropy enhances the instability, and at sufficiently large beam-core relative drift speeds, electron magnetization can either detract from or enhance the instability.

The cusp map in the complex-frequency plane for absolute instabilities

Abstract: It is well known that absolute instabilities can be located by prescribed mappings from the complex‐frequency plane to the wavenumber plane through the dispersion relation D(ω,k)=0. However, in many systems of physical interest the dispersion relation is polynomial in ω while transcendental in k, and the implementation of this mapping procedure is particularly difficult. If one maps consecutive deformations of the Fourier integral path (originally along the real k axis) into the ω plane, points having (∂D/∂k)=0 are readily detected by the distinctive feature of their local maps. It is shown that a simple topological relationship between these points and the image of the real k axis determines the stability characteristics of the system, without mapping from the ω plane back into the k‐plane.

Effects of Doppler shifting on the frequency spectra of atmospheric gravity waves

Abstract: Spectra of atmospheric motions as a function of observed frequency may depart significantly from the spectra as a function of intrinsic frequency due to a nonzero mean wind. In this paper we examine the effects of Doppler shifting on a model spectrum of atmospheric gravity waves. In order to gain insight into the effects of Doppler shifting, we have derived analytic solutions by approximation of the intrinsic frequency spectra and the gravity wave dispersion relation. Our results reveal that Doppler shifting can have major effects on the observed frequency spectrum of both horizontal and vertical gravity wave energy. For levels of Doppler shifting representative of the lower and middle atmosphere, possible effects include a substantial enhancement of horizontal energy density at higher observed frequencies, a corresponding reduction of the vertical energy density at higher frequencies, and a significant transfer of vertical energy to observed frequencies above the buoyancy frequency. The predicted effects are found to be consistent with some of the features of the observed frequency spectra.

Polariton and effective-medium theory of magnetic superlattices.

Abstract: The retarded modes of a superlattice comprising alternating layers of two magnetic media characterized by a gyrotropic permeability tensor are investigated. The transfer matrix and dispersion relation are given in general form; a number of previous results are included as special cases. An effective-medium description, valid for long wavelengths, is derived first by expansion of the general result and second by general continuity arguments. Some numerical illustration of the effective-medium theory is given.

A New Leaky Waveguide for Millimeter Waves Using Nonradiative Dielectric (NRD) Waveguide-Part I: Accurate Theory

Abstract: An almost-rigorous analysis is presented for a new leaky waveguide of simple configuration based on a recent nonradiative modification of H guide suitable for millimeter wavelengths, The analysis employs a transverse equivalent network that yields a dispersion relation in closed form, and contains some interesting and subtle features. Numerical values are presented for the phase and leakage constants in terms of the different geometric parameters and the dielectric constant comparisons with measurements are made in the companion paper, part II.

Surface phonons on GaAs(110) measured by inelastic helium atom scattering

Abstract: Surface phonon dispersion relations have been measured by He-atom inelastic scattering for in situ cleaved GaAs(110). Besides the expected Rayleigh mode and a mode at 13 meV at the Brillouin-zone boundary a third mode with a wave vector independent energy of 10 meV has been observed. This finding is very similar to our recent results for the reconstructed Si(111) (2 × 1) surface. In both cases the observations are unexpected for the presently accepted surface structures.

A separable method for the calculation of dispersion and induction energy damping functions with applications to the dimers arising from He, Ne and HF

Abstract: A separable method for the evaluation of second order non-expanded dispersion and induction energies, and the associated damping functions, is discussed with applications to the dimers arising from ground state He, Ne and HF. The method is based on a partial wave Fourier analysis of the intermolecular Coulomb operator and on Pade approximant techniques, and represents an extension, designed particularly for molecules, of earlier work for atoms. The extension is only partially successful and is particularly useful for non-expanded energies that behave as R-n , with relatively low n = 6, 8, 10, …, as R increases and that are not strongly anisotropic. The examples are used to give a discussion of the usefulness of our method and also provide information relevant for understanding and constructing potential energy functions for the species studied.

Approximate Dispersion Relation for Wave‐Current Interactions

Abstract: An approximate dispersion relation for water waves on a depthdependent current is examined. For infinitely deep water, the approximate dispersion relation provides asymptotic results that are identical to established asymptotic formulas for high and low wave numbers. Further, the approximate dispersion relation provides a highly satisfactory representation to known, exact dispersion relations throughout wave number space. For water of finite depth, the approximate dispersion relation again provides asymptotic results that are identical to established asymptotic results for high wave numbers. For low wave numbers (long waves), the approximate dispersion relation gives results that are in error from established asymptotic formulas by an amount proportional to the standard deviation of the current about its mean value. This error is small for the conditions under which the approximate dispersion relation is derived. The goodness of the approximate dispersion relation allows the extension of the wave kinemati...

Theory and simulation of high-power microwave generation in a magnetically insulated transmission line oscillator

Abstract: The magnetically insulated transmission line (MITE‐LINE) oscillator is an electron beam diode comprised of a field emitting cathode and a corrugated anode. The device is similar to a linear magnetron except that the insulating magnetic field is self‐generated. The self‐insulating property makes this device a robust high‐power microwave tube. Using the thin‐beam approximation we have derived a dispersion relation for a cylindrical MITE‐LINE oscillator. The dispersion relation is used to predict frequency and growth rate of the microwave generating instability. Analytical results are compared with ccube particle simulations.

Finite-element solution of arbitrarily nonlinear, graded-index slab waveguides

Abstract: Dispersion relations for TE modes in arbitrarily nonlinear, graded-index slab waveguides are solved numerically by the finite-element method. In this approach, self-consistent solutions can be obtained by a simple iteration. It is shown that a small deviation from the Kerr-type nonlinear effect gives rise to a drastic change in the power-dependent behaviour of guided waves. The dependence of dispersion relations on the refractive-index profile of the film is also examined.

Acoustic-phonon transmission in quasiperiodic superlattices.

Abstract: Acoustic-phonon transmission through a realistic Fibonacci superlattice is studied theoretically. We find a number of transmission dips corresponding to Bragg-like reflections of phonons. The transmission spectrum is much more complex than in the periodic case; however, the strongest dips in transmission are remarkably correlated with those of the periodic superlattice. We also present the first realistic calculations of the phonon dispersion relations in an actual quasiperiodic superlattice. For oblique angles of incidence, intermode Bragg-like reflections of the phonons are predicted.

Low‐frequency electrostatic noise due to velocity shear instabilities in the regions of magnetospheric flow boundaries

Abstract: The velocity shear of an ion beam interacting with a background plasma is shown to excite low-frequency electrostatic Kelvin-Helmholtz instabilities and ion cyclotron instability propagating nearly transverse to the magnetic field. In the plasma sheet boundary layer region, the noise generated by velocity shear instabilities is broadband with frequencies from 10−4 Hz to 4 Hz and the transverse wavelengths ranging from 30 km to 2400 km. The low-frequency noise can efficiently scatter electrons and the beam ions and is expected to affect significantly the stability of the plasma sheet against ion tearing mode instability. In the polar cusp regions, the velocity shear instabilities can generate a low-frequency broadband electrostatic noise from 2 Hz to 35 Hz provided the temperature of background electrons is ∼100 eV.

Effect of plasma waves on the optical properties of metal-insulator superlattices.

Abstract: We develop a simple transfer-matrix formalism in order to obtain the dispersion relation of the electromagnetic normal modes of an infinite insulator-metal (or highly doped semiconductor) superlattice, taking into account the presence of plasma waves, spatial dispersion, and retardation. We also calculate the p-polarized reflectance and give analytical expressions for the surface impedance, reflection amplitude, and the dispersion relation of the surface modes of a semi-infinite superlattice. We find resonant features corresponding to the propagation of guided plasma waves in the metal layers coupled by transverse fields in the insulating layers. This coupling also yields new bulk modes in regions where propagation would not be allowed without spatial dispersion.

Nonlinear Responsed of Sloshing Based on the Shallow Water Wave Theory : Vibration, Control Engineering, Engineering for Industry

Abstract: Based on the shallow water wave theory, the basic equations to describe the nonlinear responses of sloshing are derived, and a numerical method is presented to simulate sloshing phenomena in a rectangular tank which is oscillated horizontally. As the dispersion relation of the free surface wave plays an important role in the stable calculation of resonant responses, it should thus be taken into consideration. In this study, it is implicitly replaced by the dispersion relation produced by the discretization of the basic equations. Numerical results are in good agreement with those of experiments. In cases of shallow water depths, stable progressive waves are observed both in experiments and in numerical calculations, and the various nonlinear characteristics of sloshing, such as the hardening restoring forces and the jumping phenomena in resonant responses are well-simulated by the basic equations and the calculation method presented in this paper.

Spatial Stability of Jets: The Nonaxisymmetric Fundamental and Reflection Modes

Abstract: A spatial stability analysis of the relativistic dispersion relation governing the growth and propagation of harmonic components comprising a perturbation to the surface of a cylindrical jet is performed. The spatial growth of harmonic components associated with the nonaxisymmetric fundamental solution and reflection solutions of several Fourier modes are analyzed. Approximate analytical expressions describing resonant frequencies and wavelengths, and maximum growth rates at resonance applicable to relativistic jets are found from the dispersion relation, and the nature of the resonances is explored. On transonic jets there is only a fundamental solution for each Fourier mode with no resonance or maximum growth rate. On supersonic jets there is a fundamental solution and reflection solutions for each Fourier mode, and each solution contains a resonance at which the growth rate is a maximum. A numerical analysis of the fundamental and first three reflection solutions of the axisymmetric and first three nonaxisymmetric Fourier modes is performed. The numerical analysis is restricted to nonrelativistic flows but otherwise covers a broad range of Mach numbers and jet densities. The numerical results are used along with the analytical results to obtain accurate expressions for resonant frequencies, wavelengths, and growth rates as a function of Mach numnbermore » and jet density. In all cases the fastest spatial growth rate at a given frequency is of harmonic components associated with the fundamental solution of one of the nonaxisymmetric Fourier modes. The application of these results to jet structure and implication of these results for jet structure in extragalactic radio sources are considered. 23 references.« less

Harmonic waves in a solid with a periodic distribution of spherical cavities

Abstract: A dispersion relation has been obtained for the propagation of harmonic waves in an elastic solid containing a three‐dimensional array of regularly spaced spherical cavities of equal radius. The general pattern of the frequency spectrum is one of passing and stopping bands. Results are presented for the lowest acoustic mode, the transition to the first optical mode, and for a segment of the first optical mode.

Frequency gaps for acoustic phonons in a-Si:H/a-SiN x :H superlattices

Abstract: We investigate the frequency gaps for zone-folded LA and TA phonons propagating perpendicular to the layers in a-Si:H/a-${\mathrm{SiN}}_{\mathrm{x}}$:H superlattices using Raman and phonon transmission spectroscopy. Raman spectra in the forward scattering configuration were used to determine the magnitude of the zone-center gaps and the symmetry of the zone-center modes delimiting these gaps. The zone-boundary gaps were measured in the backscattering geometry by choosing the superlattice period and the excitation wavelength so as to couple the light to the zone-boundary phonons. The phonon transmission spectra show minima corresponding to frequency gaps in the dispersion relation of TA phonons. Other minima appear at those frequencies where the LA and TA zone-folded branches cross. They are associated with additional gaps in the phonon dispersion relation for modes with mixed LA and TA character with wave vectors deviating from the superlattice normal. The phonon blocking within the frequency gaps is degraded as a result of phonon scattering. By comparing the transmission spectra of samples with a different number of layers we conclude that for low phonon energies (l20 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) the scattering takes place mainly at the first superlattice interfaces near the substrate.

On the polarization, compression and nonoscillatory behavior of hydromagnetic waves associated with pickup ions

Abstract: Solution of the kinetic dispersion equation shows that heavy pickup ions with large perpendicular energies excite a new hydromagnetic wave mode with maximum growth, high (magnetic field and mass density) compression ratios, and almost linear polarization coexisting slightly away 6-15 deg from parallel propagation. The mode arises from the coupling of the heavy ion beam to the modified left-hand wave dispersion caused by the multiion nature of the medium. The ion beam can also bring about nonoscillatory, purely growing structures distinct from the mirror wave through the coupling of a counter-streaming left-hand mode to a costreaming right-hand wave. The free energy source parameters are varied to determine their relative influence and define the domain of existence of the instability. Its characteristics may prove helpful in the interpretation of recent cometary (Halley and Giacobini-Zinner) and artificial release (AMPTE) observations.

An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures

Abstract: Despite many attenuation measurements which indicate a linear functional frequency dependence of absorption or constant Q-1 in sediments, several theories predict no such linear dependence. The primary justification for rejecting a first‐power frequency dependence of attenuation is that it implies that seismic waves cannot propagate causally. Seismic waves must also travel with some velocity dispersion to satisfy causality, yet there is a lack of velocity dispersion measurements in sediments. In‐situ attenuation is caused by two distinct mechanisms: anelastic heating, and scattering due to interbed multiples. Apparent, or scattering, attenuation can produce both frequency‐dependent and non‐frequency‐dependent effects. Accurate measurements of attenuation and velocity dispersion are difficult; it is not surprising that a systematic investigation into the frequency dependence of absorption and velocity has not been made. A reinvestigation into two seismic refraction data sets collected over thickly stratifi...

Neutron-scattering studies of phonons in disordered cubic zirconia at elevated temperatures

Abstract: Inelastic-neutron-scattering studies of cubic zirconia at elevated temperatures (300--1700 K) showed well-defined LA and TA phonons but no optical-phonon branches were observed, confirming earlier reported reduced Raman scattering data. The LA and TA phonons were observed to broaden with a q/sup 2/ dependence. The elastic constants C/sub 11/, C/sub 12/, and C/sub 44/ were derived from the dispersion data at room temperature and at elevated temperatures. The frequency distribution of one phonon density of states was generated from the dispersion relation and was found to be in reasonable agreement with the observed Raman spectrum. Also diffuse-elastic-scattering measurements were taken and showed broad intensity peaks in reciprocal space. The scattering and the phonon linewidths showed little temperature dependence; intrinsic defects and anharmonicity dominate the damping mechanism. The unobserved optical branches were obtained by the best fit to the experimentally determined acoustic branches, based upon a rigid-ion-model calculation. Static deformations of the oxygen sublattice due to oxygen vacancies are mainly responsible for the data observed.