Showing papers on "Group velocity published in 1987"

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

Abstract: To provide theoretical basis for the connection between observed radar scattering and wind-generated waves, a model for the response of surface waves in the gravity-capillary equilibrium region of the spectrum is proposed on the basis of a local (in wavenumber) balance between wind input and dissipation. The wind input function was constructed on the basis of laboratory observations of short-wave growth, while the dissipation function was developed from ideas of viscous dissipation and wave breaking in response to local accelerations and modified by kinematic effects of phase and group velocity differences. The model was exercised at L, C, X, and Ka bands to demonstrate the differences in wind speed and water temperature sensitivity.

Modulation instability induced by cross-phase modulation.

Abstract: Modulation instability that leads to breakup of intense cw radiation into a train of ultrashort pulses during propagation in optical fibers occurs only in the presence of anomalous group-velocity dispersion. It is shown that a new kind of modulation instability can occur even in the normal-dispersion regime when two copropagating optical fields interact with each other through cross-phase modulation initiated by the nonlinearity. The quantitative aspects of this cross-phase--modulation--induced modulation instability are discussed and illustrated by use of a realistic experimental example.

Galactic Chaos and the Circular Velocity at the Sun

Abstract: Our galaxy has a substantial nucleus that exhibits itself as a strong rise in the rotation curve inside of 2 kpc, peaking around 500 pc. Stars with very eccentric orbits that pass through the nuclear region generally cannot be confined to a flattened disk distribution; instead, they spend most of their time in the halo. In a local sample of high-velocity-dispersion disk stars, there should be an apparent deficiency of stars with very low angular momenta, because they are scattered to much higher scale heights. The deficiency or gap will be centered on the circular velocity as reflected in the motion of the LSR. Using a new galactic model, we calibrate the predicted depression in the distribution of tangential velocities, finding a half-width of 40 km s -1 with a depth greater than 80%. We present evidence that the expected deficiency of low-angular-momentum stars does exist in the local stars. The strength of the conclusion is limited by the small size of the current sample of appropriate intermediate-population stars: those that are both in a strongly flattened distribution and possess significant numbers of members at low angular momentum. The available data favor a scale and model-free circular velocity at the Sun in the range 225-245 km s with a most probable value of 235 km s. Larger samples that are forthcoming will allow this simple method to be applied with much greater confidence.

Absolute instability of the Gaussian wake profile

Abstract: Linear parallel‐flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution The type of local instability, ie, convective or absolute, is determined by the location of a branch‐point singularity with zero group velocity of the complex dispersion relation for the instability waves The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center‐line velocity defect and the wake half‐width, larger than about 400 Absolute instability occurs only for sufficiently large values of the center‐line wake defect The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38

Synthetic Pn and Sn phases and the frequency dependence of Q of oceanic lithosphere

Abstract: The oceanic lithosphere is an extremely efficient waveguide for high-frequency seismic energy. In particular, the propagation of the regional to teleseismic oceanic Pn and Sn phases is largely controlled by properties of the oceanic plates. The shallow velocity gradient in the sub-Moho lithosphere results in a nearly linear travel time curve for these oceanic phases and an onset velocity near the material velocity of the uppermost mantle. The confinement of Pn/Sn to the lithosphere imposes a constraint on the maximum range that a normally refracted wave can be observed. The rapid disappearance of Sn and the discontinuous drop in Pn/Sn group velocity beyond a critical distance, dependent upon the local thickness of the lithosphere, are interpreted as a shadowing effect of the low Q asthenosphere. Wave number integration was used to compute complete synthetic seismograms for a model of oceanic lithosphere. The results were compared to data collected during the 1983 Ngendei Seismic Experiment in the southwest Pacific. The Pn/Sn coda is successfully modeled as a sum of leaky organ-pipe modes in the sediment layer and oceanic water column. While scattering is present to some degree, it is not required to explain the long duration and complicated nature of the Pn/Sn wave trains. The presence of extremely high frequencies in Pn/Sn phases and the greater efficiency of Sn than Pn propagation are interpreted in terms of an absorption band rheology. A shorter high-frequency relaxation time for P waves than for S waves results in a rheology with the property that Qα > Qβ at low frequency while Qβ > Qα at high frequency, consistent with the teleseismic Pn/Sn observations. The absorption band model is to viewed as only an approximation to the true frequency dependence of Q in the oceanic lithosphere for which analytic expressions for the material dispersion have been developed.

The separation velocity of emerging magnetic flux

Abstract: We measure the separation velocity of opposite poles from 24 new bipoles on the Sun. We find that the measured velocities range from about 0.2 to 1 km s−1. The fluxes of the bipoles range over more than two orders of magnitude, and the mean field strength and the sizes range over one order of magnitude. The measured separation velocity is not correlated with the flux and the mean field strength of the bipole. The separation velocity predicted by the present theory of magnetic buoyancy is between 7.4Ba −1/4 cot θ and 13 cot θ km s−1, where θ is the elevation angle of the flux tube at the photosphere (see Figure 9), B is the mean field strength, and a is the radius of the observed bipole. The rising velocity of the top of flux tubes predicted by the theory of magnetic buoyancy is between 3.7Ba −1/4 and 6.5 km s−1. The predicted separation velocity is about one order of magnitude higher than those measured, or else the flux tubes are almost vertical at the photosphere. There is no correlation between the measured separation velocity and the theoretical value, 7.4Ba −1/4. The predicted rising velocity is also higher than the vertical velocity near the line of inversion in emerging flux regions observed by other authors.

Measurement of Ultrasonic Wavespeeds in Off-Axis Directions of Composite Materials

Abstract: The relationship of NDE with structural analysis is to provide quantitative information about material mechanical properties. For a composite structure (such as a rocket motor case) which is designed to handle in-plane loading, NDE should, ideally, provide information about the in-plane stiffness and strength properties of the structural material [1]. Because acoustic wave propagation depends on material elastic properties as well as being sensitive to material inhomogeneities, ultrasonic NDE has been nominated as a viable means of satisfying the needs of structural analytical modeling [2]. To address the need to detect in-plane properties, leaky Lamb wave [3,4] and non-normal incidence transmission [1] methods are being developed, for example. Development of composite ultrasonic NDE techniques, which are sensitive to material mechanical properties in the plane of a structure, required an understanding of acoustic wave propagation in anisotropic media. If a wave is introduced into the structure wall with an oblique angle of incidence less than critical angle, the refracted wave will travel in a non-principal or off-axis direction of the composite material. As a result, the wave energy will not generally travel in a direction normal to its phase fronts as it would in an isotropic medium. The acoustic wave energy or wave group propagates at a deviation angle, ψ, with respect to the phase front normal [5,6] as shown in Fig. 1. The deviation angle should be considered when measuring acoustic phase velocities from which the stiffnesses are calculated. The following sections discuss the effect of the group velocity propagation direction upon phase velocity measurements of quasi-longitudinal and quasi-shear waves propagating in non-principal directions in principal planes of orthotropic composite materials. Experimental results are shown for unidirectional graphite composite material samples.

Theoretical and experimental studies of combined self-phase modulation and stimulated Raman-scattering in single-mode fibres

Abstract: A theoretical model of pulse propagation through single-mode fibres is presented taking into account the combined action of self-phase modulation, stimulated Raman-scattering and the group velocity mismatch between pump and Stokes pulses. Due to the walk-off of Stokes and laser light an asymmetric pump pulse depletion resulting in considerable reshaping of laser pulses and an asymmetric self-phase modulation spectrum can be calculated and experimentally verified. A maximum laser power is found to be transferable through the fibre.

2-D and 3-D velocity patterns in southeastern Europe, Asia Minor and the eastern Mediterranean from seismological data

Abstract: Summary 2-D group velocity and 3-D P-wave velocity patterns have been obtained from analyses of the group velocity dispersion of Rayleigh waves in south-eastern Europe and Asia Minor and of the P-wave travel-time residuals along ray-paths with a penetration depth of 100–300 km in southeastern Europe, Asia Minor and the eastern Mediterranean. The inversion procedure used is based on Backus–Gilbert formalism for linear inversion of travel-time data extended to 2-D and 3-D inhomogeneous media. Group velocity distributions have been obtained for periods T= 10, 20, 30 s and are in a very good agreement with the well-known characteristics of the crust and upper mantle structure. They can be used for the construction of models of the crust in south-eastern Europe and Asia Minor. The P-wave velocity patterns obtained for the depth interval 50–300 km are discussed in terms of geophysical (regional isostatic anomaly, heat flow) data for the region. It is proposed that the correlation found to exist between the different mapped geophysical parameters can be explained by compositional changes in the low-velocity layer (the increase of the iron content in minerals).

Calculation of the thermal conductivity of alkali halide crystals

Abstract: The thermal conductivities of 17 alkali halides with the sodium chloride structure have been calculated in the medium- and high-temperature ranges. Dispersion relations throughout the whole Brillouin zone have been obtained from a deformation dipole model and low-temperature input data. The linearised Boltzmann equation is solved by a variational method with two different trial functions proportional to the wave-vector and the group velocity, respectively. The results differ significantly and optic branches are found to be very important.

Kinematic properties of the F region ion velocity field inferred from incoherent scatter radar measurements at Arecibo

Abstract: A new multiple-frequency incoherent scatter observing technique has improved the precision of F region ion velocity measurements at Arecibo. This technique makes it possible to analyze velocity data without making the assumption that the horizontal gradients in each component of the velocity vector are zero. By assuming that spatial gradients in ion velocity are constant and that the magnetic field line through the F region is equipotential it is possible to determine completely the variation of the ion velocity vector in the plane of the magnetic meridian. The horizontal divergence of the velocity vector is generally observed to be small. At night the most significant spatial variation in the ion velocity field is usually converging flow parallel to the magnetic field; this reverses to diverging flow in the daytime. Neglect of these horizontal gradients in the vertical ion velocity can result in systematic errors in the evaluation of the meridional ion velocity as large as 30 m s/sup -1/. copyrightAmerican Geophysical Union 1987

Modulating laser intensity in a laser printer proportionately to the velocity of the photoconductive media

Abstract: A photosensitive, photoconductive media moving in a first direction relative to a laser light beam scanning in a second direction, transverse to the first direction, incurs velocity variations. These velocity variations result in variations in the absolute and relative heights of white and black image features. This printed image nonuniformity is especially visually detectable for closely spaced parallel lines in the second direction, and/or gray scale. An optical velocity sensor senses instantaneous media velocity. An analog or digital velocity error processor maintains a running average velocity and determines, by subtraction, an instantaneous velocity error as the difference between currently sensed and running average velocities. The instantaneous velocity error so determined is used to adjust the intensity of the laser light beam to be proportionally brighter (dimmer), exposing a wider (narrower) scan line, on a faster-moving (slower-moving) media region. By this compensating, the ratio of white and black image features is maintained constant during media velocity variations.

Measurement of Bulk and Random Directional Velocity Fields by NMR Imaging

Abstract: A formalism for the multidimensional measurement of velocity fields in liquids by nuclear magnetic resonance (NMR) is introduced. We assume that the velocity at any point within a flow field is given by a superposition of two velocity components. The first one is taken to represent the mean bulk velocity within a voxel and the second component is assumed to be random directional such as one may find in the capillary beds or porous materials. We show that the random directional flow leads to an extra dephasing of the nuclear magnetization in addition to molecular diffusion and spin-spin relaxation (T2) processes. The coherent bulk flow introduces a phase distortion in the NMR images. A procedure for measuring the spin density as well as the two velocity fields is described.

On radiated and scattered waves from a submerged elliptic cylinder in a uniform current

Abstract: The two-dimensional radiation problem and diffraction problem are discussed for submerged elliptic cylinders when a current is present. It is shown that the impact of the current on the wave amplitudes and wave forces is large. The singularity in the problem, corresponding to a wave traveling upstream with a group velocity equal to the speed of the current, is examined. As expected, this singularity influences the motion strongly. It is found, however, that the amplitudes and forces remain finite.

Pulses of oscillatory convection

Abstract: Oscillatory convection in binary fluid mixtures can take the form of traveling waves, in contrast to the stationary flow patterns observed in pure fluids. Using both mechanical and thermal excitation methods, we have been able to create propagating pulses of oscillatory, traveling-wave convection. We report a study of such pulses and measurement of the phase and group velocity, the real and imaginary parts of the dispersion, and the reflection coefficient of the pulses at lateral walls. The collision of two counterpropagating pulses is also described.

Surface-wave ray tracing equations and Fermat's principle in an anisotropic earth

Abstract: Summary. Ray tracing equations for surface waves in an anisotropic earth are derived in two ways: first, from the Hamilton’s canonical equations, and secondly, from Fermat’s principle. Phase velocity, including its azimuthal variation, is required to solve the equations, but group velocity is eliminated from the equations. The difference of direction between the wave vector and the ray path is one of the features of wave propagation in an anisotropic media and the equations explicitly show dependence upon such an angle. By putting that angle to be zero, ray tracing equations in a transversely isotropic (or simply isotropic) medium are obtained. In an isotropic medium, phase traveltime, which is an integration of phase slowness along the ray path, is stationary. In an anisotropic medium, phase travel-times is not stationary. Instead, phase slowness projected onto the ray path and integrated along the ray path is stationary. Ray tracing by the bending method in an anisotropic media should utilize such a stationary quantity. In a weakly anisotropic medium, however, the angle ($a) between the wave vector and the ray path is small and cos $, - 1 up to first order in $a. Thus phase traveltime is approximately stationary in a weakly anisotropic medium.

Measurements of the velocity using a lenticular grating

Abstract: This paper describes a method of eliminating the bi-directional ambiguity in measurements of theflow velocity using a lenticular grating. The deflection characteristics of the light passing through the lenticularis studied theoretically and it is shown that the lenticular grating works as a phase grating. In avelocimeter using the lenticular grating and the four photodetecters, the opposite directions of the flow arediscriminated from the phase relation between the two signals combined appropriately from the output signalsof four photodetectors.The method is used to measure the velocity of a random pattern on the rotating disk. The experimentalresults show the usefulness of this method for eliminating the directional ambiguity.

Waveguide suppression of the free electron laser sideband instability

Abstract: A theoretical analysis is given of an FEL operating in the millimeter range and, hence, operating in a waveguide. For study of the situation in which the average longitudinal velocity of electrons v/sub parallel/ is close to the electromagnetic pulse group velocity v/sub g/, it is shown that the usual paraxial approximation is invalid. The complete analysis is then specialized to a single particle model which, for operation in a steady state, yields a dispersion relation. The resulting dispersion relation is analyzed analytically and numerically. It is shown that when v/sub parallel/ greater than or equal to v/sub g/ there is no sideband instability, and an analytic expression is given for the stability boundary. 10 refs., 7 figs.

Dispersion of acoustic surface waves by velocity gradients

Abstract: The perturbation theory of Auld [Acoustic Fields and Waves in Solids (Wiley, New York, 1973), Vol. II, p. 294], which describes the effect of a subsurface gradient on the velocity dispersion of surface waves, has been modified to a simpler form by an approximation using a newly defined velocity gradient for the case of isotropic materials. The modified theory is applied to nitrogen implantation in AISI 4140 steel with a velocity gradient of Gaussian profile, and compared with dispersion data obtained by the ultrasonic right‐angle technique in the frequency range from 2.4 to 14.8 MHz. The good agreement between experiments and our theory suggests that the compound layer in the subsurface region plays a dominant role in causing the dispersion of acoustic surface waves.

Wavelength dependence of electrostatic plasma wave propagation in the auroral E region

Abstract: The propagation of electrostatic plasma wave packets in the auroral E region has been studied using kinetic theory and is found to confirm previous results obtained using fluid theory, which showed that the wave packet travels at high speed nearly parallel to the magnetic field, except possibly for a small height interval in which it is reflected upward. The principal effect of decreasing the plasma wavelength is to increase the group velocity and to sharpen any reversal in propagation. Effects on the propagation of enhanced electron collision frequencies are also examined. it is shown that under some circumstances it might be possible to observe these wave packet motions experimentally. By comparing propagation speeds with estimates of wave packet lifetimes, it is found that linear growth rates can probably not be used to estimate amplitudes of meter scale waves.