Showing papers on "Dispersion relation published in 1976"
TL;DR: In this article, the equations of three-dimensional linear piezoelectricity were applied in the analysis of trapped energy resonators with rectangular electrodes vibrating in coupled thickness shear and thickness twist in the vicinity of the fundmantal and odd overtone thickness-shear frequencies.
Abstract: The equations of three‐dimensional linear piezoelectricity are applied in the analysis of trapped‐energy resonators with rectangular electrodes vibrating in coupled thickness shear and thickness twist in the vicinity of the fundmantal and odd overtone thickness‐shear frequencies. Closed form asymptotic expressions for the frequency wave‐number dispersion relations for the fundamental and odd overtone coupled thickness‐shear and thickness‐twist waves near cutoff are obtained for both the electroded and unelectroded regions of the trapped‐energy resonator. The influence of piezoelectric stiffening, electrode mass loading, and electrical shorting is included in the analysis. Simple approximate boundary conditions at a junction between an electroded and unelectroded region of the plate are obtained in a manner exhibiting the natural limitations inherent in the approximation. In order that these boundary conditions can be satisfied at each such junction, in the adjacent regions the wave numbers in the direction of the junction line are assumed to be the same. The boundary conditions to be satisfied at the junctions between the unelectroded corner region and the unelectroded regions adjacent to the electroded region are obtained from an extended version of the variational principle of linear piezoelectricity. These latter conditions result in the form of the solution in the corner region. One result of the foregoing analysis is the determination of a two‐dimensional condition which is a generalization of Bechmann’s number in one dimension. The above‐mentioned dispersion relations and edge conditions are applied in the analysis of the steady‐state vibrations of a trapped‐energy resonator and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained.Subject Classification: [43]40.24; [43]85.52, [43]85.32.
135 citations
TL;DR: In this article, the effect of isobaric excitations on the weak axial coupling constants in nuclei is studied through P.C.A. and the Klein-Gordon equation for the virtual pion field in the nucleus.
110 citations
TL;DR: In this article, material and mode dispersion in fibers made from glasses in the system GeO2-B2O,3-SiO2 have been calculated using refractive index dispersion results for these glasses.
Abstract: Material and mode dispersion in fibers made from glasses in the system GeO2-B2O,3-SiO2 have been calculated using refractive index dispersion results for these glasses. Refractive indices were measured on bulk glass specimens using the minimum deviation method at wavelengths from 0.4358 to 1.0830 μm. The resultant data were then fitted to a 3-term Sellmeier dispersion relation for each glass composition. The fitted equations and a recent theory on the relation of the optimum index profile in a graded index optical waveguide to pulse dispersion were used to calculate the exponent α, which characterizes the shape of the profile, for several practical fiber models. The most effective profile shape for reducing pulse dispersion is a function of wavelength, composition, and fictive temperature. The present data were used elsewhere to predict accurately the optimum profile for minimization of pulse dispersion in several fiber systems consisting of germanium borosilicate glasses.
107 citations
TL;DR: The dispersion of higher modes of surface waves over a region covered by an array of stations can be measured by applying a frequency-wavenumber transform to segments of the signals in these stations, centered at a number of group-velocities as discussed by the authors.
Abstract: The dispersion of higher modes of surface waves over a region covered by an array of stations can be measured by applying a frequency-wavenumber transform to segments of the signals in these stations, centered at a number of group-velocities. Thus, at a fixed period, modes appear as separate maxima in a display of the power spectrum on a phase-velocity vs. group velocity plane.
100 citations
TL;DR: In this article, the linear dispersion relation for typical solar wind conditions at 1 AU during those times (high-speed streams) when a secondary beam of protons drifting relative to the main proton component is present.
Abstract: The paper sets forth a numerical investigation of the linear dispersion relation for typical solar wind conditions at 1 AU during those times (high-speed streams) when a secondary beam of protons drifting relative to the main proton component is present. Three beam-driven instabilities were found to occur as the beam drift velocity approaches the Alfven speed: (1) a pure, field-aligned magnetosonic wave that is most important at relatively high beta and/or high beam drift speeds; (2) an oblique magnetosonic wave having highest growth rates 15-30 deg from the magnetic field; and (3) an oblique Alfven wave having maximum growth rates at increasing angle to the magnetic field. The linear growth rates for the field-aligned magnetosonic and the Alfven oblique modes are investigated as a function of relative beam density, varying anisotropic pitch angle distributions for the various components, electron temperature, and electron heat flux.
98 citations
TL;DR: In this paper, the phonon dispersion relation of the one-dimensional conductor, deuterated tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ), has been studied by inelastic neutron scattering over a temperature range of 60-300 K.
Abstract: The phonon dispersion relation of the one-dimensional conductor, deuterated tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ), has been studied by inelastic neutron scattering over a temperature range of 60-300 K. Acoustic phonons propagating along the chain direction (the monoclinic ${b}^{*}$ direction) are studied in detail in search for a giant Kohn anomaly. Below 150 K, a sharp anomaly develops near the transverse branch at $2{k}_{F}$ and becomes more pronounced as the Peierls transition at $T=54$ K is approached. Additional room-temperature measurements on our protonated sample showed excellent agreement with the deuterated crystal.
88 citations
TL;DR: In this article, a hydrodynamic model is used to study the effect of the electron density profile at the surface on surface-plasmon modes, and the qualitative features of the model are illustrated by detailed numerical calculations for smooth electron-density profiles.
Abstract: A hydrodynamic model is used to study the effect of the electron-density profile at the surface on surface-plasmon modes. The model consists of an extension of Bloch's original hydrodynamic model to study an inhomogeneous electron gas capable of self-oscillations about a ground state given by the Hohenberg-Kohn-Sham theory of the inhomogeneous electron system. We write down an expression for the conductivity tensor which formally contains all relevant information within the context of our hydrodynamic formulation. The qualitative features of the model are illustrated by detailed numerical calculations for smooth electron-density profiles. The dispersion relation of both regular surface-plasmon and higher-multipole excitations (which occur for sufficiently diffuse profiles) are studied for a wide range of wave vectors from the optical ($\ensuremath{\omega}\ensuremath{\sim}\mathrm{cq}$) to the nonretarded or electrostatic limit.
84 citations
TL;DR: In this paper, approximate and much simplified dispersion relations were obtained for the problem of optical wave propagation within weakly guiding elliptical fibres, where the refractive index difference between the core and its cladding of weakly-guiding optical fibres that are contenders for use as practical optical communication lines is very small.
Abstract: Approximate and much simplified dispersion relations are obtained for the problem of optical wave propagation within weakly guiding elliptical fibres. The refractive index difference between the core and its cladding of weakly guiding optical fibres that are contenders for use as practical optical communication lines is very small; i.e., (n
1/n0−1) ≪1 wheren
1 is the core index andn
0 is the cladding index. These greatly simplified dispersion relations are then used to calculate the propagation constants for several higher order modes on an elliptical optical fibre.
78 citations
73 citations
TL;DR: In this paper, the phonon dispersion relations in NiO have been measured using coherent inelastic neutron diffraction, and the room temperature phonon density of states was calculated and used to determine the temperature dependence of the lattice specific heat and the Debye temperature.
70 citations
TL;DR: In this paper, an analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a 2D thermal Green's functions for electron propagation in a magnetic field developed in closed form.
TL;DR: In this paper, the authors investigated the two-ion hybrid resonance for a warm, collisionless plasma and found an approximate dispersion relation appropriate for a toroidal fusion plasma, where the fast Alfven wave propagates on both sides of the resonance, so the tunneling factor is calculated.
Abstract: I investigate the two-ion hybrid resonance for a warm, collisionless plasma and find an approximate dispersion relation appropriate for a toroidal fusion plasma. The fast Alfven wave propagates on both sides of the resonance, so the tunneling factor is calculated and for fusion plasmas it is found that fast waves incident from the high-magnetic-field side will undergo mode conversion to an ion-Bernstein mode and those incident from the low-field side will be reflected. (AIP)
TL;DR: The measurements of the real parts of the kaon-nucleon amplitudes are shown to impose, via dispersion relations, powerful constraints on the analysis of low energy K−p data as discussed by the authors, which are used in the determination of the S wave K N parameters and in the calculation of coupling constants.
TL;DR: In this article, low frequency instability was used as a source for excitation of traveling waves behind the grid, and the excited waves had the same dispersion relation as ion waves excited by applying external signals to the grid.
Abstract: Low‐frequency instability is excited by passing a dc electron current in a collisionless Q‐machine plasma. The current is driven by applying a positive bias to a grid situated between the hot plate and the cold end plate. The instability shows a standing‐wave pattern between the hot plate and the grid. The frequency can be controlled by varying the hot plate‐grid separation. This instability is used as a source for excitation of traveling waves behind the grid. The excited waves have the same dispersion relation as ion waves excited by applying external signals to the grid.
TL;DR: In this paper, a pump wave with frequency ω0 near the lower-hybrid frequency ϑlh was analyzed with respect to the wavenumber k of the decay waves and the ratio ω 0/ωlh to determine the decay process with the minimum threshold.
Abstract: Resonant decay instabilities of a pump wave with frequency ω0 near the lower‐hybrid frequency ϑlh are analyzed with respect to the wavenumber k of the decay waves and the ratio ω0/ωlh to determine the decay process with the minimum threshold. It was found that the lowest thresholds are for decay into an electron plasma (lower‐hybrid) wave plus either a backward ion‐cyclotron wave, an ion Bernstein wave, or a low‐frequency sound wave. For ω0< (2ωlh)1/2, it was found that these decay processes can occur and have faster growth than ion quasi‐modes provided the drift velocity (cE0/B0) is much less than the sound speed. In many cases of interest, electromagnetic corrections to the lower‐hybrid wave rule out decay into all but short wavelength (kρi ≳1) waves. The experimental results are consistent with the linear theory of parametric instabilities in a homogeneous plasma.
TL;DR: In this article, the dispersion and damping of externally excited lower hybrid waves were measured using a multiple-ring slow-wave antenna, having 2$pi$/k/sub z/ = 23 cm.
Abstract: Experimental measurements of the dispersion and damping of externally excited lower hybrid waves are presented. A multiple-ring slow-wave antenna, having 2$pi$/k/sub z/ = 23 cm, is used to excite these waves in the Princeton L3 or L4 linear devices (B = 0.5 -- 2.8 kG uniform to +- 1 percent for 1.6 m, n approximately 10$sup 10$, T/sub e/ approximately 3-5 eV, T/sub i/ less than or equal to 0.1 eV, He gas, plasma diameter approximately 10 cm). The waves are localized in a spatial wave packet that propagates into the plasma along a conical trajectory which makes a small angle with respect to the confining magnetic field. Measurements of the dependence of wavelength on frequency are in good agreement with the cold plasma dispersion relation. Measured values of the wave damping are in good agreement with Landau damping by the combination of the main body of the electron distribution and a approximately 30 percent high energy (T/sub e/ approximately 15-30 eV) electron tail. (auth)
TL;DR: Caputo et al. as mentioned in this paper studied the vibrations of a plate by obtaining the eigenfrequencies, the amplitude of the displacement, the dispersion relation, the Q−1, the hysteresis cycle, and the yield stress.
Abstract: The dissipation in an elastic medium is represented by a dissipation mechanism which is similar to one used in an earlier paper [M. Caputo, Geophys. J. R. Astron. Soc. 13, 529–539 (1967)], but is simpler and has a frequency‐independent Q−1. The vibrations of a plate are studied by obtaining the eigenfrequencies, the amplitude of the displacement, the dispersion relation, the Q−1, the hysteresis cycle, and the yield stress.Subject Classification: [43]40.24.
TL;DR: In this paper, a fully kinetic, nonlocal, matrix dispersion equation is derived for electrostatic perturbations about a spatially nonuniform cylindrical plasma equilibrium, which is carried out for the class of radially confined rigid-rotor equilibria described by f0j(x,v) = (njmj/2πTj) F (H⊥/Tj− ωjPϑ/tj,vz), where Pϑ is the canonical angular momentum, vz is the axial velocity,
Abstract: A fully kinetic, nonlocal, matrix dispersion equation is derived for electrostatic perturbations about a spatially nonuniform cylindrical plasma equilibrium. The analysis is carried out for the class of radially confined rigid‐rotor equilibria described by f0j(x,v) = (njmj/2πTj) F (H⊥/Tj− ωjPϑ/Tj,vz), where Pϑ is the canonical angular momentum, vz is the axial velocity, H⊥ is the perpendicular energy, and nj, Tj, and ωj are constants. Assuming equilibrium charge neutrality and negligible spatial variation in the axial magnetic field B0ez, it is shown that the particle trajectories (in the equilibrium electric and magnetic fields) and the orbit integrals required in the stability analysis can be evaluated in closed form. Expanding the perturbed electrostatic potential in terms of the vacuum eigenfunctions {Jl(λnr) } for the conducting cylinder leads to a matrix dispersion equation of the form det[δn′,n+ Σjχjn′,n(ω)]=0, where the susceptibility χjn′,n(ω) is expressed as a phase‐space integral over f0j(x,v...
TL;DR: The instability resulting from the interaction of a weak, monoenergetic electron beam with a magnetoplasma (ω≳ω C E ) has been studied experimentally as discussed by the authors.
Abstract: The instability resulting from the interaction of a weak, monoenergetic electron beam with a magnetoplasma (ω≳ω C E ) has been studied experimentally. A calculation, using the dispersion relation appropriate to the experiment, shows that the interaction may take the form of convective or absolute instability, depending on plasma temperature. This is in qualitative and quantitative agreement with the experiment. The convective mode has spatially amplified waves which are steady state in time. Saturation is due to beam trapping, and agrees quantitatively with a trapping calculation which includes cyclotron damping. After saturation the wave damps, which is attributed to untrapping of the beam by relatively low‐level amplified plasma noise. The absolute instability is a feedback oscillation due to the negative group velocity in the plasma. It rises suddenly to large amplitude near the electron gun and has a short over‐all length. There are two nonlinear states: one is steady state in time, and agrees with a beam trapping calculation for absolute instability; the second has temporal quenching, or relaxation oscillations. This is attributed to the interaction of several oscillation modes strongly coupled by the nonlinear beam dynamics. This effect may limit wave amplitudes below the value predicted by trapping theory.
PARC1
TL;DR: In this paper, a theory of the dynamics of coupled crystalline-cage-charged liquid fluctuations in superionic conductors is presented and the dispersion relations of the coupled modes are obtained together with the imaginary parts of their self-energies.
Abstract: We present a theory of the dynamics of the coupled crystalline-cage-charged-liquid fluctuations in superionic conductors. The dispersion relations of the coupled modes are obtained together with the imaginary parts of their self-energies, which determine, among other things, the acoustic attenuation. The light-scattering process due to these fluctuations is studied and we show that it can provide unique information about local site symmetries and hopping times. The nature of the thermal fluctuations is discussed near a critical point.
TL;DR: In this article, the resonant ion-beam-driven electrostatic ion-cyclotron instability is identified and measured dispersion relation and onset versus beam energy and density agree with numerical calculations based on a theory which includes beamacoustic terms.
Abstract: The resonant ion-beam---driven electrostatic ion-cyclotron instability is identified. Measured dispersion relation and onset versus beam energy and density agree with numerical calculations based on a theory which includes beam-acoustic terms. After amplitude saturation, velocity-space diffusion of the beam ions is observed.
TL;DR: In this article, the amplitude dependence in the dispersion relation and in the exponents for the exponential decay away from the shore is corrected by a special perturbation expansion, which results in nonlinear corrections to Stokes's linear edge-wave solution.
Abstract: Nonlinear corrections to Stokes's linear edge-wave solution are obtained by means of perturbation expansions in the amplitude. The shallow-water formulation is considered first, but even for small beach angles β the behaviour in the deep water offshore becomes important and this formulation is limited. In the full formulation, amplitude dependence is required in the dispersion relation and in the exponents for the exponential decay away from the shore. There is a non-uniformity in the results as β → ½ π, which is corrected by a special perturbation expansion.
TL;DR: In this article, a thin rotating relativistic electron beam through a circular waveguide is shown to excite both the transverse electric and transverse magnetic modes of the guide.
Abstract: Propagation of a thin rotating relativistic electron beam through a circular waveguide is shown to excite both the transverse‐electric and transverse‐magnetic modes of the guide. The beam is guided by and rotates symmetrically about a constant uniform external magnetic field. Both the synchronous and cyclotron modes associated with the beam can interact with either waveguide mode to excite electromagnetic radiation. The dispersion relations for the four coupling processes are derived and analyzed. Finally, application of this mechanism to the generation of intense microwave radiation is discussed in the light of recent experiments.
TL;DR: In this article, the effects of surface roughness on the dispersion relation for surface polaritons at the rough interface between vacuum and a semi-infinite dielectric medium, characterized by an isotropic constant, have been determined.
Abstract: The effects of surface roughness on the dispersion relation for surface polaritons at the rough interface between vacuum and a semi-infinite dielectric medium, characterized by an isotropic dielectric constant $\ensuremath{\epsilon}(\ensuremath{\omega})$, have been determined. An integral equation is established for the Green's function for the matrix differential operator in Maxwell's equation for the macroscopic electric field in the presence of a rough interface, in terms of the corresponding Green's function in the presence of a plane interface. On the assumption that the Fourier coefficients of the surface roughness profile function are Gaussianly distributed random variables the integral equation can be solved. The position of the pole in the resulting solution corresponding to the frequency of the surface polariton has been determined through terms of $O({\ensuremath{\delta}}^{2})$, where ${\ensuremath{\delta}}^{2}$ is the mean-square deviation of the surface from flatness. The resulting expressions for the real and imaginary parts of the surface-polariton dispersion relation are evaluated for two different choices of $\ensuremath{\epsilon}(\ensuremath{\omega})$, the first corresponding to a diatomic polar crystal of cubic symmetry, the second corresponding to intraband transitions in a metal or semiconductor with free carriers. The effects of surface roughness are found to be significant only for wavelengths of the surface polariton comparable with or longer than the transverse correlation length characterizing the horizontal distribution of surface roughness.
TL;DR: The πN scattering amplitudes have been determined at 38 momentum transfer values for 0 t −1 GeV 2 and expressed in terms of expansions, which are convergent throughout the energy range and have correct fixed-t analyticity and s − u crossing properties.
TL;DR: In this article, a low-energy beam of sodium ions was injected into a quiescent cesium plasma into which a low energy beam of ion cyclotron was injected, and the instability appeared when the beam velocity was above 12 times the ion thermal velocity.
Abstract: Electrostatic ion cyclotron waves were observed in a quiescent cesium plasma into which a low‐energy beam of sodium ions was injected. The instability appeared when the beam velocity was above 12 times the ion thermal velocity. The waves propagated along the magnetic field with a velocity somewhat smaller than that of the beam. The dispersion relation was in good agreement with theory.
TL;DR: A positive dispersion relation was observed for plasmons propagating along the polymer-chain $b$ axis as discussed by the authors, consistent with the view that the polymer is a poor conductor in the perpendicular direction rather than a quasi-one-dimensional metal.
Abstract: Plasmon dispersion and anisotropy in the metallic polymer ${(\mathrm{SN})}_{x}$ were investigated directly by electron-energy-loss spectroscopy. A positive dispersion relation was observed for plasmons propagating along the polymer-chain $b$ axis. As the plasmon wave vector changes from parallel to perpendicular to the $b$ axis, the plasmon energy decreases from 2.5 to 1.5 eV consistent with the view that ${(\mathrm{SN})}_{x}$ is a poor conductor in the perpendicular direction rather than a quasi-one-dimensional metal.
TL;DR: In this paper, a simple and accurate approximation to the electrostatic hot plasma dispersion relation in the region of the lower hybrid resonance was obtained, using the fact that omega > Omega ci and kperpendicular to nu thi/ Omegaci>>1 in this region.
Abstract: A simple and accurate approximation to the electrostatic hot plasma dispersion relation in the region of the lower hybrid resonance is obtained, using the fact that omega >> Omega ci and kperpendicular to nu thi/ Omega ci>>1 in this region. The approximate dispersion relation is shown to reduce to the warm plasma approximation when also omega /kperpendicular to nu thi>>1, and gives explicit expressions for the damping length. It is particularly appropriate for rapid numerical calculations of the dispersion curves.
TL;DR: In this paper, superconvergence techniques are applied to dispersion relations for the index of refraction in optically active systems to find sum rules applicable to the optical constants for circularly polarized electromagnetic waves.
Abstract: Superconvergence techniques are systematically applied to dispersion relations for the index of refraction in optically active systems to find sum rules applicable to the optical constants for circularly polarized electromagnetic waves. New results include the theorems that (i) the zeroth moment of the circular dichroism and (ii) the first moment of the circular birefringence are zero. The latter theorem yields the simple rule that the rotation of the plane of polarization of linear light caused by an optically active medium averages to zero when integrated over all energies. Generalizations of the $f$ and inertial sum rules to circularly polarized modes are given, as well as a new rule relating the second moment of the circular dichroism to the cyclotron frequency in magneto-optics or to the rotatory strengths in natural optical activity.
TL;DR: In this paper, the authors measured phonon dispersion relations of CuBr having zincblende-type structure with a triple-axis spectrometer and found that the phonon energies at the zone center are in good agreement with the Raman scattering data.
Abstract: Phonon dispersion relations of CuBr having zincblende-type structure were measured by the neutron inelastic scattering technique with a triple-axis spectrometer. The dispersion curves measured at 77 K were well described by the shell model with 14 parameters which has been successfully applied to explain the data for GaAs, GaP and InSb. The elastic constants were obtained both from sound velocities estimated from the initial slopes of acoustic phonon dispersion curves and from the shell-model-fit. The optical phonon energies at the zone center are in good agreement with the Raman scattering data. The temperature dependence of phonon scattering was also measured. It was found that the phonon energies as well as the shape of phonon peaks varied considerably with temperature, suggesting that the effect of anharmonicity is remarkable in CuBr even at room temperature.