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Showing papers on "Group velocity published in 1994"


Journal ArticleDOI
TL;DR: In this article, the pathintegrated linear growth of electromagnetic ion cyclotron waves in the outer (L is greater than or equal to 7) magnetosphere was investigated using a realistic thermal plasma distribution with an additional anisotropic energetic ring current H(+) to provide free energy for instability.
Abstract: The path-integrated linear growth of electromagnetic ion cyclotron waves in the outer (L is greater than or equal to 7) magnetosphere is investigated using a realistic thermal plasma distribution with an additional anisotropic energetic ring current H(+) to provide free energy for instability. The results provide a realistic simulation of the recent Active Magneto- spheric Particle Tracer Explorers (AMPTE) observations. For conditions typical of the dayside magnetosphere, high plasma beta effects reduce the group velocity and significantly increase the spatial growth rates for left-handed polarized instabilities just below the helium gyrofrequency Omega(sub He(+)), and on the guided mode above Omega(sub He(+)) but below the cross over frequency omega(sub cr). Relatively high densities, typical of the afternoon local time sector, favor these low group velocity effects for predominantly field-aligned waves. Lower densities, typical of those found in the early morning local time sector, increase the group velocity but allow strong convective instabilities at high normalized frequencies well above Omega(sub He(+)). These waves are reflected in the magnetosphere and can exist for several equatorial transits without significant damping. They are left-handed polarized only on the first equatorial crossing and become linearly polarized for the remainder of the ray path. Consequently, these waves should be observed with basically linear polarization at all frequencies and all latitudes in the early morning local time sector. Wave growth below Omega(sub He(+)) is severely limited owing to the narrow bandwidth for instability and the small resonant path lengths. In the afternoon sector, where plasma densities can exceed 10(exp 7)/cu m, intense convective amplification is possible both above and below Omega(sub He(+)). Waves below Omega(sub He(+)) are not subject to reflection when the O(+) concentration is small and therefore should be observed with left-handed polarization near the equator and essentially linear polarization at higher latitudes. Since the He(+) concentration is usually large in the afternoon sector, guided mode waves above Omega(sub He(+)) reflect to form a background distribution with basically linear polarization. We suggest that the strong left-handed polarized emissions observed by AMPTE in the afternoon sector near the equator are probably due to strongly growing low group velocity waves at frequencies just below Omega(sub He(+)), and on the guided mode above Omega(sub He(+)).

138 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed radiation boundary conditions for the numerical modeling of dispersive waves, which can be interpreted in terms of phase velocities of waves that are absorbed exactly at the computational boundary.
Abstract: The author develops radiation boundary conditions for the numerical modeling of dispersive waves. During the construction of such boundary conditions, the goal is to simulate the outward radiation of waves near an artificial computational boundary. The velocities of the outgoing waves are typically involved in processes of this nature. A central problem in the dispersive case is that two different types of velocities are present, phase velocity and group velocity, and each can vary with wavenumber and frequency. With the boundary conditions developed in this paper, the user needs to specify some parameters; in the cases that are emphasized here, the parameters can be interpreted in terms of phase velocities of waves that are absorbed exactly at the computational boundary. The amount of reflected error is a continuous function of the parameters, and the performance of the boundary conditions is not sensitive to the choice of parameters. Good performance is obtained in numerical tests involving data that ha...

138 citations


Journal ArticleDOI
TL;DR: In this article, the elastic properties of layered rocks are measured using the pulse through-transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal.
Abstract: The elastic properties of layered rocks are often measured using the pulse through-transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first-break traveltimes of P, SV, and SH-waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near-field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

132 citations


Journal ArticleDOI
TL;DR: It is shown that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape.
Abstract: For a pulse with carrier frequency detuned less than an atomic plasma frequency but outside a narrow Lorentzian gain line, the group velocity will be negative. Unlike propagation at the center of an absorption line, the energy velocity is approximately equal to the group velocity, and is also negative. We show that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape. The peak of the transmitted pulse leaves the gain medium before the peak of the incident pulse enters, i.e., the pulse is transmitted superluminally. For a sufficiently long medium the exit pulse is well resolved from a comparison pulse traveling through an equal distance of vacuum. There is no conflict with causality, as numerical simulations with a switched-on Gaussian demonstrate. We propose an experiment to observe this kind of propagation by sending a pulsed probe beam through a Xe gas cell pumped to achieve inversion.

116 citations


Journal ArticleDOI
TL;DR: In this paper, the receptivity theory of Goldstein and Ruban is extended within the quasi-parallel framework of Zavol'skii et al. to predict the roughness-induced generation of stationary and nonstationary instability waves in three-dimensional, incompressible boundary layers.
Abstract: The receptivity theory of Goldstein and Ruban is extended within the nonasymptotic (quasi-parallel) framework of Zavol'skii et al to predict the roughness-induced generation of stationary and nonstationary instability waves in three-dimensional, incompressible boundary layers. The influence of acoustic-wave orientation, as well as that of different types of roughness geometries, including isolated roughness elements, periodic arrays, and two-dimensional lattices of compact roughness shapes, as well as random, but spatially homogeneous roughness distributions, is examined. The parametric study for the Falkner-Skan-Cooke family of boundary layers supports our earlier conjecture that the initial amplitudes of roughness-induced stationary vortices are likely to be significantly larger than the amplitudes of similarly induced nonstationary vortices in the presence of acoustic disturbances in the free stream. Maximum unsteady receptivity occurs when the acoustic velocity fluctuation is aligned with the wavenumber vector of the unsteady vortex mode. On the other hand, roughness arrays that are oriented somewhere close to the group velocity direction are likely to produce higher instability amplitudes. Limitations of the nonasymptotic theory are discussed, and future work is suggested.

94 citations


Journal ArticleDOI
TL;DR: In this paper, the basic properties of SAW propagating in a ZnO/diamond/Si structure were studied utilizing thin film poly-crystalline diamond, and it was confirmed that this structure provides high phase velocity up to 10000 m/s, high K2 up to 4.8% and pratical TCF value of -28 ppm/° C.
Abstract: Diamond films grown by chemical vapor deposition (CVD) method is receiving much attention as surface acoustic wave (SAW) substrate material, due to its remarkable characteristics of large SAW velocity to offer much attraction in fabrication of high frequency SAW devices. The basic properties of SAW propagating in a ZnO/diamond/Si structure were studied utilizing thin film poly-crystalline diamond. Phase velocity, group velocity, electro-mechanical coupling coefficient (K2), and temperature coefficient of frequency ( TCF) were examined by experiments and theoretical calculations. And it was confirmed that this structure provides high phase velocity up to 10000 m/s, high K2 up to 4.8% and pratical TCF value of -28 ppm/° C. An 1.3 GHz SAW filter of a ZnO/diamond/Si structure was fabricated for the first time.

84 citations


Journal ArticleDOI
TL;DR: In this article, the impulsive Green's function is applied to the generation of internal gravity waves by a moving point mass source, and the steady analysis based on the monochromatic Green's functions is shown to reveal the presence of two insignificant contributions overlooked by the unsteady analysis.
Abstract: The Green's function method is applied to the generation of internal gravity waves by a moving point mass source. Arbitrary motion of a source of arbitrary time dependence is treated using the impulsive Green's function, while ‘classical’ approaches of uniform motion of a steady or oscillatory source are recovered using the monochromatic Green's function. Waves have locally the structure of impulsive waves, emitted at the retarded time tr, and having propagated with the group velocity; at each position and time an implicit equation defines tr, in terms of which the waves are written. A source both oscillating and moving generates two systems of waves, with respectively positive and negative frequencies, and when oscillations vanish these systems merge into one.Three particular cases are considered: the uniform horizontal and vertical motions of a steady source, and the uniform horizontal motion of an oscillatory source. Waves spread downstream of the steady source. For the oscillatory source they can extend both upstream and downstream, depending on the ratio of the source frequency to the buoyancy frequency, and are contained inside conical wavefronts, parts of which are caustics. For horizontal motion, moreover, the steady analysis (based on the monochromatic Green's function) reveals the presence of two insignificant contributions overlooked by the unsteady analysis (based on the impulsive Green's function), but which for an extended source may become of the same order as the main contribution. Among those is an upstream columnar disturbance associated with blocking.

70 citations


Journal ArticleDOI
TL;DR: In this article, a wave-packet analysis about this wavenumber is presented, which leads in the first instance to a higher-order nonlinear Schrodinger equation, from which the steady solitary wave solution is obtained.

69 citations


Journal ArticleDOI
TL;DR: The coherent synchrotron radiation process in a waveguide is theoretically investigated and a single, short bunch propagating through a wiggler is considered.
Abstract: The coherent synchrotron radiation process in a waveguide is theoretically investigated. A single, short bunch propagating through a wiggler is considered. In a waveguide, two very distinct regimes are possible. At grazing, where the beam velocity matches the wave group velocity, the bunch emits a single, ultrashort chirped pulse whose duration is determined by the interaction bandwidth and the waveguide dispersion. Away from grazing, where slippage dominates, two distinct pulses are radiated at the Doppler upshifted and downshifted frequencies. Both the time and frequency domain expressions for the radiation characteristics are derived.

66 citations


Journal ArticleDOI
TL;DR: In this article, a technique for estimating the total velocity vector, using only two transducers, is described, making use of the fact that the bandwidth of a Doppler spectrum has been shown to be proportional to the velocity component normal to the sound beam.
Abstract: Current ultrasonic blood flow measurement systems estimate only that component of flow which is parallel to the incident ultrasound beam. This is done by relating the mean backscattered frequency shift to the axial velocity component through the classical Doppler equation. A number of ultrasonic techniques for estimating the two-dimensional (2D) blood velocity vector have been published, both Doppler and non-Doppler. Several three-dimensional (3D) blood velocity vector techniques have also been proposed, all of which require a multiplicity of transducers or lines of sight. Here a technique is described for estimating the total velocity vector, using only two transducers. This is achieved by measuring not only the frequency shifts but also the bandwidths of the backscattered spectra, making use of the fact that the bandwidth of a Doppler spectrum has been shown to be proportional to the velocity component normal to the sound beam. Partial experimental verification of the proposed vector flow estimation scheme is demonstrated by using a constant velocity thread phantom. >

66 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the displacement polarization factors to define the degree of material anisotropy and represent solutions of the Christoffel equation, and then derived simple expressions for coefficients describing the sensitivity of ultrasonic waves to different elastic constants.
Abstract: The determination of elastic constants from ultrasonic bulk wave velocity data taken in a plane of symmetry is studied. It is shown that the problem is well‐posed, i.e., the solution is unique and stable. The displacement polarization factors are used to define the degree of material anisotropy and represent solutions of the Christoffel equation. Such a representation in a rotated coordinate system helps to derive simple expressions for coefficients describing the sensitivity of ultrasonic waves to different elastic constants. Thus the optimal refraction angles for velocity measurement can be determined simply. The analysis performed shows that the elastic constants reconstructed from velocity data are not affected by the selection of initial guesses used in a nonlinear least‐square optimization (the solution is unique). The solution stability is validated by performing reconstruction with different levels of random scatter in the velocity data. The effect of the angle range used for velocity measurements...

Journal ArticleDOI
TL;DR: In this paper, it was shown that the time autocorrelation function C 1 ( t ) = E (0) E ∗ (t )>/E(0)¦ 2 > of the scattered light field E( t ) is not sensitive to the mean velocity flow but rather to the root mean square of velocity gradient.
Abstract: We report dynamic light scattering experiments on turbid colloidal suspension under stationary and laminar flow, as well as in the regime of flow instabilities. It is shown that the time autocorrelation function C 1 ( t ) = E (0) E ∗ ( t )>/ E (0)¦ 2 > of the scattered light field E ( t ) is not sensitive to the mean velocity flow but rather to the root mean square of velocity gradient. C 1 ( t ) is characterised on the level of each scattering event by the correlation time required by a pair of scatterers initially separated by a transport mean free path to move a relative distance of optical wavelength due to the velocity gradient. We verified this theoretical analysis using planar Couette flow as an example for homogenous velocity gradients, and planar Poiseuille flow for inhomogeneous velocity gradients. Agreement between expirement and theory is excellent. Finally, this technique is applied to spatially varying velocity gradient fields for measuring the threshold and wave number of the Taylor-Coutte instability. This illustrates the possibility of studying hydrodynamic instabilities and quasi-local velocity gradients even under conditions of strong multiple scattering.

Journal ArticleDOI
TL;DR: In this article, the modal density of one-and two-dimensional periodic structures is derived in terms of the phase constants associated with propagating wave motion, and it is formally proved that the energy velocity is always equal to the group velocity for an undamped system.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the distribution of peculiar velocities of rich clusters and of groups of galaxies for different cosmological models and are compared with observations, and they found that rich clusters of galaxies exhibit a Maxwellian distribution of particular velocity, as expected from a Gaussian initial density field.
Abstract: The distributions of peculiar velocities of rich clusters and of groups of galaxies are investigated for different cosmological models and are compared with observations. Four cosmological models are studied: standard cold dark matter (CDM) (omega = 1); low-density CDM (omega = 0.3); hot dark matter (HDM) (omega = 1); and primeval baryonic isocurvature (PBI) (omega = 0.3). All models are normalized to the microwave background fluctuations observed by Cosmic Background Explorer (COBE). We find that rich clusters of galaxies exhibit a Maxwellian distribution of peculiar velocities in all models, as expected from a Gaussian initial density field. The clusters appear to be fundamental and efficient tracers of the large-scale velocity field. The cluster three-dimensional velocity distribution typically peaks at v approximately 600 km/s and extends to high cluster velocities of v approximately 2000 km/s. The low-density CDM model exhibits somewhat lower velocities: it peaks at approximately 400 km/s and extends to approximately 1200 km/s. Approximately 10% (approximately 1% for low-density CDM) of all model rich clusters move with high peculiar velocities of V greater than or = 10(exp 3) km/s. The highest velocity clusters frequently originate in dense superclusters. The model velocity distributions of rich clusters are compared with the model velocity distributions of small groups of galaxies, and of the total matter. The group velocity distribution is, in general, similar to the velocity distribution of the rich clusters. The matter velocity distribution is similar to that of the rich clusters for the omega = 0.3 models; these models exhibit Maxwellian velocity distributions for clusters, for groups, and for matter that are all similar to one another. The mass distribution in the omega = 1 models, however, exhibits a longer tail of high velocities than do the clusters. This high-velocity tail originates mostly from the high velocities that exist within rich clusters. The model velocity distributions of groups and clusters of galaxies are compared with observations. The data exhibit a larger high-velocity tail, to v(sub r) greater than or = 2000 km/s, than is seen in the model simulations (except for HDM). Because of the large observational uncertainties, however, the data are consistent at a approximately 1-3 sigma level with the model predictions and with a Gaussian initial density field. Accurate observations of cluster peculiar velocities, especially at the high-velocity tail, shoud provide powerful constraints on the cosmological models.

Journal ArticleDOI
TL;DR: It is found that the leading edge of a pulse moves at the linear group velocity and that the phase velocity of the excited wake is found to be less than the group Velocity of the pulse.
Abstract: The nonlinear group velocity of a short intense laser pulse propagating in a cold underdense unmagnetized plasma is examined. Analytical expressions for the group velocity are derived. These expressions reduce to the usual \ensuremath{\partial}\ensuremath{\omega}/\ensuremath{\partial}k form for small amplitude and are verified for arbitrary amplitude using particle in cell simualations on a cyclic mesh. We find that the leading edge of a pulse moves at the linear group velocity and that the phase velocity of the excited wake is found to be less than the group velocity of the pulse. The techniques used can be applied to other waves in a plasma.

Journal ArticleDOI
01 Jun 1994-Chaos
TL;DR: A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions, finding that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can exist.
Abstract: A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center-of-mass velocity of localized structures must be found. The existence condition is that this velocity should be outside the region of linear phase velocities. After a presentation of the method, previous work on the plasma drift wave model and the shallow-water equations is reviewed. In both cases it is found that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can therefore exist. New results are then obtained for a number of two-field models. For the coupled ion acoustic-drift modes in plasmas, it is found that the center-of-mass velocity depends on the ratio between the parallel ion velocity component and the electrostatic potential in the vortex. If this ratio is large enough, the vortex can be steady. For the drift-Alfven mode the "center-of-charge" velocity is proportional to the ratio between the parallel current and the total charge in the vortex. It can therefore be steady if this ratio satisfies the appropriate conditions. For the quasigeostrophic two-layer equations, describing stratified flow on a rotating planet, it is found that the center-of-mass velocity is determined by the ratio between the baroclinic and the barotropic components in the vortex. If a baroclinic component with an appropriate sign is added to a barotropic vortex, it propagates faster than the barotropic Rossby waves, and can be steady. Finally, the existence conditions for a vortex in an external zonal flow are examined. It is found that the center-of-mass velocity acquires an additional westward contribution in an anticyclonic shear zone in the framework of the shallow-water equations, and also that an easterly jet south of this shear zone partly shields a vortex situated in the shear zone from the dispersive influence of the fast Rossby waves on the equatorward side.

Journal ArticleDOI
TL;DR: Experimental intracavity compression of generated pulses (down to one quarter of the pumppulse duration) in a widely tunable synchronously pumped picosecond optical parametric oscillator is reported.
Abstract: We report on experimental intracavity compression of generated pulses (down to one quarter of the pump-pulse duration) in a widely tunable synchronously pumped picosecond optical parametric oscillator. This pulse compression takes place when the optical parametric oscillator is well above threshold and is due to the pronounced group-velocity mismatch of the pump and oscillating waves in the nonlinear crystal.

Journal ArticleDOI
TL;DR: In this paper, the conditional mean transverse velocity across a turbulent scalar mixing layer is conditioned on mixture fraction, and it is found that the distribution of the conditional transversal velocity is closely related to the local mean mixture fraction in physical space.
Abstract: This paper presents the experimental results on conditional mean transverse velocity across a turbulent scalar mixing layer. The velocity is conditioned on mixture fraction. It is found that the distribution of the conditional mean transverse velocity is closely related to the local mean‐mixture fraction in physical space. Near the local mean‐mixture fraction a linear relationship exists between the conditional mean transverse velocity and the mixture‐fraction fluctuations. Departure from the linear relationship at large mixture‐fraction fluctuations is mainly due to the nonlinear distribution of the mean mixture‐fraction profile and it is not, as has been suggested by others, due to the limiting velocity of the large eddies in the flow.

Journal ArticleDOI
28 Jan 1994-Science
TL;DR: The time-dependent velocity field in a rotating Couette system has been decomposed and it is shown that the so-called broadband component corresponds to a global motion of the wave propagating from roll to roll.
Abstract: The time-dependent velocity field in a rotating Couette system has been decomposed. Successive instantaneous velocity profiles were obtained by an ultrasonic Doppler velocity profile method, and the spatiotemporal velocity field had been analyzed by two-dimensional Fourier transform. The Fourier spectrum is depicted by intrinsic peaks, and the velocity field cpan be reconstructed with these peak components only, indicating a successful decomposition of the velocity field. This method shows that the so-called broadband component, which is purely spatiotemporal and attributed to chaos, corresponds to a global motion of the wave propagating from roll to roll.


Journal ArticleDOI
TL;DR: In this article, the authors proposed a method for measuring the group velocity dispersion, including the polarity, of optical fiber by using a single wavelength light source based on the interplay between phase modulation-amplitude modulation (PM-AM) conversion and self-phase modulation (SPM).
Abstract: The authors propose a method for measuring the group velocity dispersion, including the polarity, of optical fibre by using a single wavelength light source. The method is based on the interplay between phase modulation-amplitude modulation (PM-AM) conversion and self-phase modulation (SPM).

Journal ArticleDOI
TL;DR: In this article, a modified energy flux is defined by adding a nondivergent term that involves β to the traditional energy flux, and the resultant flux, when normalized by the total eddy energy, is exactly equal to the group velocity of Rossby waves on a β plane with constant zonal flow.
Abstract: A modified energy flux is defined by adding a nondivergent term that involves β to the traditional energy flux. The resultant flux, when normalized by the total eddy energy, is exactly equal to the group velocity of Rossby waves on a β plane with constant zonal flow. In this study, we computed the normalized energy flux for linear wave packets in baroclinic basic states with different vertical profiles. The results show that the normalized energy flux is a good approximation to the group velocity of all parts of the wave packet for the basic states examined. The extension to the nonlinear case is briefly discussed. The magnitude of the fluxes of a downstream developing wave group over the wintertime northern Pacific storm track defined by a regression analysis is computed, and the group velocity defined by the energy fluxes is found to be comparable to the group velocity of propagation of the observed wave packet. The results indicate a very strong component of downstream energy radiation, sugges...

Journal ArticleDOI
TL;DR: In this article, femtosecond Ti: sapphire laser pulses were used for harmonic generation in barium metaborate (BBO) by femto-cond Ti-sparve laser pulses.

Journal ArticleDOI
TL;DR: In this article, the analysis of acoustic wave propagation in fluid-filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low-velocity layered media.
Abstract: The analysis of acoustic wave propagation in fluid‐filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low‐velocity layered media. Constitutive relations, the balance equation, and the generalized Darcy law of the modified Biot theory yield a coupled system of differential equations which governs the wave motion in each layer. The displacement and stress fields satisfy the boundary conditions of continuity of displacements and tractions across each interface, and the radiation condition at infinity. To avoid precision problems caused by the growing exponential in individual matrices for large wave numbers, the global matrix method was implemented as an alternative to the traditional propagation approach to determine the periodic equations. The complex wave numbers of the guided wave modes were determined using a combination of two‐dimensional bracketing and minimization techniques. The results of this work indica...

Patent
Kenneth W. Winkler1
30 Mar 1994
TL;DR: In this paper, the velocity variation around a borehole at a particular depth of the borehole is taken as an indication of susceptibility to failure, with higher velocity variations indicative of a more poorly consolidated formation or a formation with a large uniaxial stress.
Abstract: Borehole tools are provided with at least one transmitter which generates acoustic waves at a plurality of azimuthal locations about the borehole, and at least one receiver which receives and measures a characteristic (e.g., velocity) of the acoustic waves at related azimuthal locations. The direction of minimum velocity around the borehole is considered the direction of maximum uniaxial stress in the formation. From the velocity as a function of azimuth information, determinations of formation properties, and logs of the same can be made. The azimuthal direction of minimum velocity around the borehole predicts the propagation direction of artifically induced hydrofractures. The velocity variation around the borehole at a particular depth of the borehole is taken as an indication of susceptibility to failure, with higher velocity variations indicative of a more poorly consolidated formation or a formation with a large uniaxial stress. The curvature of the velocity versus stress curve in the formation is also indicated by how poorly a sine wave fits to the velocity data. Other parameters of the formation are obtained by fitting a best fit curve to the azimuth versus velocity data, where adjustable parameters of the best fit curve constitute the formation parameters.

Journal ArticleDOI
TL;DR: In this paper, the authors draw attention to several differences between wave propagation in dissipative anisotropic media and purely elastic anisometric media and show that the wavefront is defined as the envelope of the family of planes that makes the phase of the plane waves zero.
Abstract: The purpose of this work is to draw attention to several differences between wave propagation in dissipative anisotropic media and purely elastic anisotropic media. In an elastic medium, the wavefront is defined as the envelope of the family of planes that makes the phase of the plane waves zero. It turns out that this definition coincides with the wavefronts obtained from the group and energy velocities, i.e., the three concepts are equivalent. However, for plane waves traveling in dissipative anisotropic media these concepts are different. Despite these differences, the velocity of the envelope of plane waves closely approximates the energy velocity, and therefore can represent the wavefront from a practical point of view. On the other hand, the group velocity describes the wavefront only when the attenuation is relatively low, i.e., for Q values higher than 100. The values of the different velocities and the shape of the wavefront are considerably influenced by the relative values of the attenuation along the principal axes of the anisotropic medium. This means that the anisotropic coefficients in attenuating anisotropic media may differ substantially from the corresponding elastic coefficients. Moreover, it is shown that the usual orthogonality properties between the slowness surface and energy velocity vector and the wavefront and wavenumber vector does not hold for dissipative anisotropic media.

Journal ArticleDOI
TL;DR: In this article, the authors observed the oscillation of a waveguide mode free-electron laser using the coherent synchrotron radiation emitted from electron bunches and found that the oscillating radiation had the same group velocity as the velocity of the electrons passing through the wiggler field.
Abstract: We have observed the oscillation of a waveguide mode free‐electron laser using the coherent synchrotron radiation emitted from electron bunches. The oscillation was observed at 2.73 mm with a linewidth of 0.4%. This spectral selection was attributed to the dispersion of the radiation in the waveguide. We found that the oscillating radiation had to have the same group velocity as the velocity of the electrons passing through the wiggler field.

Journal ArticleDOI
TL;DR: In this paper, the vibrational energy flow associated with helical wave motion in a thin cylindrical shell is considered, and a detailed analysis is presented in which the governing differential equations are solved exactly and the energy flows are calculated from the elastic forces in the shell.

Journal ArticleDOI
TL;DR: In this article, the velocities of two Devonian-mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation.
Abstract: The velocities of two Devonian-Mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation. Both samples were found to be transversely isotropic at elevated pressures with the main symmetry axis perpendicular to bedding. The elastic constants of the shales were used to calculate phase and group velocity surfaces as a function of angle to the bedding normal. Multiple velocity measurements in non-symmetry directions, not undertaken in previously published studies of shales, have been used to confirm features observed on calculated velocity surfaces. It is demonstrated that velocities measured in non-symmetry directions are phase velocities. Group velocities were found to be significantly lower than the corresponding phase velocities of the shales due to their high anisotropies. Shear wave splitting was found to be negligible for propagation directions within approximately 30° of the bedding normals.

Journal ArticleDOI
TL;DR: In this article, a linear array of receivers is used to obtain data simultaneously at a number of different ranges, which correspond to propagation over a short portion (typically 5 m) of the total path at many different ranges.
Abstract: Dispersion analysis of interface waves (Scholte/Stoneley/Rayleigh) has been used extensively to determine geoacoustic models of near‐bottom ocean sediments. In the traditional approach, a single seismic trace is analyzed to obtain group velocity dispersion using the multiple filter technique. A dispersion curve obtained in this manner reflects the averaged influence of the sediment acoustic properties over the entire path from source to receiver. Thus a geoacoustic model derived from this dispersion curve is not a true vertical section in the vicinity of the receiver unless the sediment properties do not change over the entire propagation path. However, when a linear array of receivers is used to obtain data simultaneously at a number of different ranges, it is possible to derive both group and phase velocity dispersion curves that correspond to propagation over a short portion (typically 5 m) of the total path at many different ranges. With this kind of data, the range‐dependent variation of geoacoustic properties in the sediment may be assessed. Results are presented based on data obtained with a 24‐receiver array and an explosive source, both deployed on the seafloor. Analysis of data from a number of shallow water sites suggests that there is a considerable amount of lateral inhomogeneity even over very short ranges.