Variation Of Phase Velocity Research Articles

A Wide-Bandwidth Ultrasonic Study of Suspensions: The Variation of Velocity and Attenuation with Particle Size

Wide-bandwidth measurements of ultrasonic velocity and attenuation have been made in a series of monodisperse suspensions of polystyrene in water and silica in water. Suspensions with three different particle sizes at fixed volume fractions were used in each case. The results enable comparison between theory and experiment of the variation in phase velocity and attenuation with frequency and with particle size. It is shown that there is good agreement between the attenuation results and the Allegra and Hawley theoretical model for both types of suspension investigated. However, in the case of the polystyrene suspensions, measured phase velocity as a function of frequency does not follow the expected R f dependence, although the form of the measured dispersion curve is close to theoretical. Reasons for the discrepancies between the model and the experimental data are suggested, and it is concluded that the Allegra and Hawley formulation could form the basis of a particle sizing technique, provided that attenuation and velocity measurements were made over a broad, and continuous, frequency band.

Prevention of alcohol-impaired driving : R. Hingson. Alcohol Health & Research World, 17(1), 28–34.

Thermal damage in concrete usually induces contact-type defects, which result in degradation of the concrete's performance. This paper attempts to visualize the thermal damage in a multiscale, and characterizes the thermally damaged concrete using a nonlinear ultrasonic method. An impact-modulation method is used to obtain nonlinearity parameters, as a quantitative measure of contact-type defects, and shows better sensitivity than phase velocity variation as a linear ultrasonic method for thermally damaged concrete. The measured nonlinearity parameter is compared with the permeable pores, which reflect the occurrence of opening and pores in thermally damaged concrete. Degradation of concrete strength due to thermal damage is also assessed via the measurement.

Surface Waves in Vertically Heterogeneous and Transversely Isotropic Layer Overlying a Homogeneous Isotropic Half-Space and under a Uniform Layer of Liquid.

The effect of heterogeneity and anisotropy on the dispersion of Rayleigh-type surface waves in a heterogeneous anisotropic layer of elastic medium overlying a homogeneous elastic solid half-space and lying under a homogeneous liquid layer of uniform depth is discussed. The variation of phase velocity with the wavenumber is obtained numerically for the fundamental mode. The results are compared with the homogeneous case. The results show that the heterogeneity of the layer decreases the phase velocity for small values of wavenumber. The problem of Gogna (1979) has been reduced as a special case.

Variation of type I plasma wave phase velocity with electron drift velocity in the equatorial electrojet

Using a 54.95‐MHz coherent backscatter radar at Thumba (8.5°N, 77°E; 0.5°N dip angle), the phase velocity variations of type I plasma waves generated by the modified two‐stream instability process in the equatorial electrojet have been measured on several occasions of large and rapid electric field fluctuations associated with geomagnetic substorms and storms. The measurements show a clear linear variation of type I wave phase velocity (VpI) over a considerable range with the simultaneously measured phase velocity (VpII) of gradient drift instability‐generated type II plasma waves. Since VpII is proportional to the drift velocity of electrons, the observed variations of VpI with VpII mean that VpI varies in step with the variations of the electron drift velocity Vey. The observed variation of VpI with Vey is consistent with the current theoretical understanding that the plasma wave‐associated electric fields cause anomalous electron diffusion and heating which result in the stabilization of the type I wave phase velocity near the increased value of the ion‐acoustic velocity. The enhanced electron temperatures estimated from the largest values of the observed VpI are found to be 2.0‐2.4 times the ambient value in the absence of waves.

Twisting magnetic field and multiple resonance mechanism in the solar neutrino problem

The magnetic moment solution to the solar neutrino problem is investigated in the context of a solar magnetic field with varying phase velocity on the transverse plane. This phase velocity is assumed to successively take values which are approximately proportional to the solar density, giving rise to the appearance of many resonances along the neutrino trajectory. We obtain a magnetic moment necessary for a neutrino reduction compatible with the experimental situation in the range (6–7)×10 −13μ B, an improvement by a factor of 4–6 relative to the one resonance case under the same field conditions.

Aspect angle variations in intensity, phase velocity, and altitude for high‐latitude 34‐cm E region irregularities

The sensitivity of the Millstone 440‐MHz radar system is such that coherent echoes from E region irregularities can be observed over a 90‐dB dynamic range above the incoherent scatter background. At antenna elevation angles between 4° and 20°, aspect angles between 0° and 10° (from perpendicularity with the magnetic field) are viewed at E region heights at invariant latitudes between 61°Λ and 57°Λ. During disturbed conditions, when convection electric fields in excess of 15 mV/m and E region irregularities span this range of latitudes, antenna scanning experiments have been performed to determine the aspect angle sensitivity with high precision. Our measurements are unique in that they provide a clear high‐frequency description of the variation in both power and Doppler shift as functions of aspect angle, all the way from a region where the waves are known to be linearly unstable, in a direction perpendicular to the geomagnetic field, to as much as 10° away from perpendicularity. We find that the 440‐MHz aspect sensitivity is about −15 dB deg−1 for aspect angles between 0° and 3°, −10 dB deg−1 for aspect angles between 3° and 6°, and −7 dB deg−1 for aspect angles between 6° and 9°. The magnitude of the phase velocity is at an approximate ion acoustic level (350 m/s) for aspect angles <2° and decreases to <200 m/s as the aspect angle increases to >3°. For highly disturbed conditions the magnitude of the velocity can increase to >700 m/s for aspect angles <2°. The tendency for the altitude of the most intense return to decrease by ∼5 km as the aspect angle increases beyond 2° can be explained as a consequence of the variation of aspect angle with height.

Excitation of solitons by an external resonant wave with a slowly varying phase velocity

A novel mechanism is proposed for the excitation of solitons in nonlinear dispersive media. The mechanism employs an external pumping wave with a varying phase velocity, which provides a continuous resonant excitation of a nonlinear wave in the medium. Two different schemes of a continuous resonant growth (continuous phase-locking) of the induced nonlinear wave are suggested. The first of them requires a definite time dependence of the pumping wave phase velocity and is relatively sensitive to the initial wave phase. The second employs the dynamic autoresonance effect and is insensitive to the exact time dependence of the pumping wave phase velocity. It is demonstrated analytically and numerically, for a particular example of a driven Korteweg-de Vries (KdV) equation with periodic boundary conditions, that as the nonlinear wave grows, it transforms into a soliton, which continues growing and accelerating adiabatically. A fully nonlinear perturbation theory is developed for the driven KdV equation to follow the growing wave into the strongly nonlinear regime and describe the soliton formation.

Guiding-centre orbits for particles in cross-field devices

The motion of a particle driven by a slow RF wave inside crossed electrostatic and magnetostatic fields is examined. A time-scale separation exists in the synchronous frame, moving at the slow-wave phase velocity, where all fields appear static in time and the cyclotron motion is much faster than the guidingcentre drift. The averaging of the periodic gyromotion is performed systematically with canonical transformations up to second order in the smallwave amplitude. The first-order guiding-centre drift follows the equipotential surfaces of the transformed electric field. The second-order effects, due to the field-line curvature, and/or the nonlinear variation in the wave phase velocity, cause departures from the parapotential flow. The topology of the trajectories depends on the departure of the drift velocity from synchronism with the wave. Various flow topologies corresponding to different values of the control parameters are examined.

P- andSV-wave transversely isotropic phase velocities analysis from VSP data

SUMMARY The purpose of this paper is to obtain some measurements of the seismic anisotropy from VSP data independently of the complexity of the medium between source and receiver locations. The anisotropy at receiver locations is studied by analysing Pand SV-wave phase velocities as well as polarization directions under the hypothesis of a transversely isotropic (TI) medium with a vertical axis of symmetry. Multiple-source offset VSPs provide generally direct P- and SV-waves for different incident angles. In this study, the data pairs used are the interval apparent vertical velocities and the polarization directions related to both P- and SV-waves. These directions are given, in the vertical plane, by the angle y from the vertical axis. Apparent vertical velocities are computed from the delays for a constant phase which travels in the interval between two receivers. This interval has to be smaller than the seismic wavelength in order to consider these velocities as P- and SV-wave phase velocities. The forward problem is defined by the exact equations of P- and SV-wave velocities as a function of four parameters (a, p, 11, z) and of the polarization angle y. Parameters a and /3 are tied to the P- and SV-wave vertical velocities, and parameters 11 and t explain phase velocity variations with incidence. With this model, these four parameters can be inverted by a least-squares method. This method has been applied to the Pierre Shale data (White, MartineauNicoletis & Monash 1983). Inverted parameters have been compared with results obtained by White et al. (1983). The parameter 11 (which explains velocity variations for small incidences) is accurately recovered because data (in particular phase velocities) are reliable at incident angles lower than 45. The parameter z (which explains velocity variations for high incidence) is less accurately recovered because there are not enough reliable data for incident angles higher than 45. The lack of data (only 8 P shots and 8 S shots) and uncertainties in data provide a large a posteriori error in inverted parameters. However, it is hoped that this method can provide accurate recovery of anisotropy parameters if there is a large number of shot locations (case of a walkaway).

Elastic wave reflection from liquid-anisotropic substrate interfaces

We derive analytical expressions for the reflection and transmission coefficients from the interfaces of liquid-anisotropic half-spaces possessing up to as low as monoclinic symmetry. Also we present expressions for the distributions of stresses and displacements throughout the fluid-solid system. Solutions are obtained for an acoustic wave impinging the interface at an arbitrary angle θ from the normal as well as at any azimuthal angle ø. By examining the behavior of the reflection coefficient we are able to identify all of the propagation characteristics that influence the distribution of the reflected field. These include the possible existence of secondary (pseudo-surface) modes besides those associated with the normal surface ones. We also deduce the variations of phase velocity and beam shifting parameters with azimuthal angles. Material systems of higher symmetry, such as orthotropic, transversely isotropic, cubic and isotropic are contained implicitly in our analysis. We present numerical results drawn from several examples of materials belonging to these symmetry groups.

Global Love wave phase velocity variation and its significance to plate tectonics

Global Love wave phase velocity variation was constructed for periods between 80 and 200 s by using approximately 9000 paths from 971 earthquakes (with M ≥ 5.5). The data set was from GDSN and GEOSCOPE networks between 1980 and 1987. We examined both the spherical harmonic expansion method and the block parameterization method. With a simple, constant damping parameter approach, synthetic tests showed that more accurate results were obtained by the block parameterization method than by the spherical harmonic expansion method. We adopted the block inversion method with a (nearly) equal area block (5° × 5° near the equator) discretization. The general pattern of the resulting maps were consistent with previous global and local studies. With a discretization of 5° by 5°, the maps were detailed enough to test some plate tectonic models. For the Pacific, Atlantic and Indian Oceans, surface-wave velocities increased smoothly to plate ages older than 100 Ma. Simple forward modeling showed that seismic phase velocity variation with a continuous thickening of lithosphere up to about 150 Ma fits the present observation, disagreeing with the model deduced from the heat flow and ocean depth data, which change variations at about 60–80 Ma. The seismic phase velocity variations in different oceans showed systematic differences at younger ages, and convergence beyond 100 Ma. The difference at younger ages implies a failure of scaling derived from a simple thermal boundary layer model for oceanic plates. Age-seismic phase velocity relationships on each side of ridges were also examined and asymmetric velocity variations were found, which suggests differences in thermal states from one side of the ridge to the other. In order to further examine the thermal state of the lithosphere, average age-phase velocity relations were established for each ocean, and subtracted from phase velocity variation maps. The results indicated broad, low-velocity regions in the south Pacific (super-swell region), the south and west Indian Ocean, and high-velocity regions east of the East Pacific Rise and in the north to northeast Indian Ocean. The results reflect the asymmetry of phase velocity variation about ridges. There is some correlation between hot-spot locations and low-velocity anomalies, but additional, large-scale thermal anomalies exist under old oceanic plate.

“Unlimited” particle acceleration by an intense plasma wave with a varying phase velocity

Abstract An “unlimited” electron and ion acceleration is shown to occur in the field of an intense “tapered” plasma wave. This acceleration scheme does not require high injection energies and pre-bunching of the accelerated particles and could operate at moderate plasma wave amplitudes. A possible way of the phase velocity “tapering” is suggested.

Smoothness criteria in surface wave tomography

We discuss and develop further the methods of surface wave tomography in the frame of the geometric say approximation. The general approach for determining the lateral phase or group velocity distribution, which is a standard 2-D tomography problem, involves linearization, representation of the unknown function as series in some basis functions, and evaluation of the coefficients by the methods of linear algebra. If the wave paths cover the area under investigation non-uniformly, the basis functions should not be chosen a priori, but constructed proceeding from the pattern of paths. Different criteria for constructing the basis functions are compared, and a relation between them is considered. A more preferable approach is joint interpretation of phase and group velocity data for different periods, because it allows the information about phase velocity variations to be enlarged due to the use of the group velocity data. Both the phase and group traveltimes are represented as linear functionals of the unknown phase slowness corrections. A specific form of the data kernels allows the basis functions to be represented as a product of two functions, one depending on the horizontal coordinates, and the other on frequency.

Wave splitting in the time domain for a radially symmetric geometry

A decomposition of the field of the wave equation in three dimensions is suggested. This wave splitting decomposes the field into two components such that in free space simple propagation properties are obtained. The inhomogeneous region is assumed to have a phase velocity variation that varies only in the radial coordinate r from the origin. The suggested wave splitting is a generalization of the wave splitting concept in one spatial dimension. Specifically, the propagation properties in free space in the three-dimensional wave splitting are very analogous to the corresponding properties in free space in one dimension. The three-dimensional decomposition is illustrated in an example of scattering by a sound-soft sphere of radius a.

Amplitude spectrum method for the measurement of phase velocity

An amplitude spectrum technique for the measurement of the phase velocities of waves in media, which can be dispersive and attenuating is presented. In this method the variation of phase velocity with frequency is calculated from the longitudinal resonant frequencies, the corresponding mode numbers and the distance between the boundaries of the tested material. The amplitude spectrum method has been found to be superior to the existing phase spectrum technique when testing thin specimens, where the different reflections from the two boundaries cannot be separated in the time domain. Comparison between the phase spectrum technique and the amplitude spectrum method has been carried out on a 3.2 mm thick aluminium plate (non-dispersive medium) and a 3.15 mm thick epoxy resin (dispersive medium), excellent agreement being shown between the two methods.

Three-dimensional modelling of upper mantle structure under the Pacific Ocean and surrounding area

SUMMARY Long-period (75-250 s) fundamental-mode Love and Rayleigh waves are inverted for the seismic velocity variations in the upper mantle under the Pacific Ocean and surrounding area. The data are inverted to map the regional variation of phase velocity, and then the velocity structure of the upper mantle. No a priori regionalization is used in this study, and the lateral heterogeneity is expanded horizontally into blocks (lo' X 10'). To estimate the reliability of the velocity distribution, we have calculated the resolving kernels. In the central, NW, NE and SW regions, the resolving kernels have fairly sharp peaks. In the SE region, however, resolution is not so good. The results show good correlation with surface tectonics. In the velocity map, shields and ridges are the major features in the depth interval 50-100km. Anomalies associated with the East Pacific Rise and the shields persist to 300 km. At 400 and 500 km, high-velocity anomalies appear under the eastern and southern Pacific ridges, and a low-velocity anomaly appears beneath Australia. The present study provides better resolution than previous studies because of the better path coverage. For example, a large low-velocity anomaly emerges under Hawaii down to the depth of 200 km for SH velocity. The horizontal extent of this anomaly is comparable to the sue of the Hawaiian swell. This feature supports that the Hawaii hotspot is an isolated, truly anomalous feature in the Pacific Ocean.

Design of variable phase velocity kinetic inductance delay lines and their measured characteristics when fabricated by a simple Nb based process

A simple design for superconducting kinetic inductance delay lines is presented. Delay lines were fabricated with a thin-film process involving only DC magnetron deposition and anodization of Nb. Phase-velocity measurements demonstrated wave slowing to less than 1/150 of the velocity of light in free space with associated impedances in the ohm range. Phase velocity changes on lines which were in physical proximity to long Josephson junctions and normal conducting lines were investigated. Variations larger than 10% of the equilibrium value were observed with junction-coupled lines under bias application. Locally heated lines exhibited changes exceeding a factor of two. Loss and phase velocity were determined as a function of bias conditions in both cases. Measured line loss was within expectations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

NONLINEAR THEORY OF DISTORTION OF BOUNDED ULTRA- SONIC BEAM IN RELAXATING MEDIA

In this article, a nonlinear wave equation of bounded acoustic beam in relaxating media is presented and a general solution of higher harmonics resulting from the nonlinear distortion of propagation is found by using the pertubation approach. Investigation shows that for the Gaussian ultrasonic field, the solution of higher harmonics can be given analytically, moreover their corresponding radical distributions of amplitude always maintain the Gaussian profiles. Although the dispersion may affect the amplitude of various harmonics, the variation of phase velocity of those keep the same law as the small amplitude waves of corresponding frequencies do.We also show that by means of Blackstock' operator the obtained results can be applied te the case of media with arbitrary dissipation and dispersion, including some biomedia in which the relationship between the absorption and frequency may be obtained only empirically.

Effects of anisotropy in southwest Germany on the propagation of surface waves

This paper discusses the effects of anisotropy in southwest Germany on the propagation of surface waves. A model for the anisotropy has been compiled previously by Fuchs from the combined information of petrological and seismological data. Seismic evidence for the anisotropy has been derived from the observations of azimuthal variation of Pn velocity and from a P-velocity depth function for a refraction seismic profile. The purpose of this paper is to present the effects of this model of the seismic anisotropy in southern Germany and similar ones on the dispersion and polarization of surface waves. For quasi-Rayleigh and quasi-Love waves the phase velocity variations with azimuth amount to about 2%. The period of maximum variation is 20 s for Rayleigh waves and about 30 s for Love waves. Anisotropy causes the particle motion for both generalized surface waves to be elliptical, where the plane of the ellipse is inclined with respect to the direction of particle motion in isotropic media. For Love waves the angular variation of the polarization plane is about 6° maximum, whereas for Rayleigh waves it amounts to 16°. The sign of the azimuthal effect of dispersion is independent of the period for both wave types. This means for all periods the same directions are fast or slow. In contrast, there is a change in sign for the polarization effect, which causes the plane of polarization to be inclined in the opposite direction for long-period waves as compared to rather short periods. For rather simple models it is shown that the period of the polarization node depends linearly on the depth of the anisotropic layer and that independent of the layer thickness, the change in the polarization direction occurs where the wavelength is about five times as large as the mean depth of the anisotropic layer. Observed dispersion data for surface waves in the area of southern Germany do not yet allow us to derive a detailed model of anisotropy as it has been compiled from body-wave data. This is due to the lack in azimuthal coverage, reduced resolution for analog data, the lack in overlapping period ranges for the observations and the travel-time differences caused by heterogeneities crossed by the ray paths.

Generation of Annual Rossby Waves in the North Pacific by the Wind Stress Curl

Abstract The Rossby wave field generated by the annual cycle of the observed wind stress curl over the North Pacific Ocean (15°N–53°, 100°W–175°E) has been obtained through numerical integration of the linearized, reduced-gravity vorticity equation in spherical coordinates. The dominant source region of Rossby waves is adjacent to the eastern boundary between 20°–44°N. More specifically this source is shown to be made up essentially of two distinct parts: a southern region off California-Baja California, which was first identified by White and Saur, and a northern region corresponding to a generation area first proposed by Mysak. In addition, a second, midocean generation region has been identified over the central North Pacific from 35° to 45°N, 150° to 160°W. The behavior of the model is strongly affected by wave refraction due to the variation of phase velocity with latitude as described in Schopf et al. As waves emanate from the eastern boundary they are refracted such that the wavenumber vector, init...