Showing papers on "Group velocity published in 1998"

Eurasian surface wave tomography: Group velocities

Abstract: This paper presents the results of a study of the dispersion characteristics of broadband fundamental surface waves propagating across Eurasia. The study is broader band, displays denser and more uniform data coverage, and demonstrates higher resolution than previous studies of Eurasia performed on this scale. In addition, the estimated group velocity maps reveal the signatures of geological and tectonic features never before displayed in similar surface wave studies. We present group velocity maps from 20 s to 200 s period for Rayleigh waves and from 20 s to 125 s for Love waves. Broadband waveform data from about 600 events from 1988 through 1995 recorded at 83 individual stations across Eurasia have produced about 9000 paths for which individual dispersion curves have been estimated. Dispersion curves from similar paths are clustered to reduce redundancy, to identify outliers for rejection, and to assign uncertainty estimates. On average, measurement uncertainty is about 0.030–0.040 km/s and is not a strong function of frequency. Resolution is estimated from “checker-board” tests, and we show that average resolutions across Eurasia range from 5° to 7.5° but degrade at periods above about 100 s and near the periphery of the maps. The estimated maps produce a variance reduction relative to the Preliminary Reference Earth Model (PREM) of more than 90% for Rayleigh waves below 60 s period but reduce to about 70% between 80 and 200 s period. For Love waves, variance reductions are similar, being above 90% for most periods below 100 s and falling to 70% at 150 s. Synthetic experiments are presented to estimate the biases that theoretical approximations should impart to the group velocity maps, in particular source group time shifts, azimuthal anisotropy, and systematic event mislocations near subducting slabs. The most significant problems are probably caused by azimuthal anisotropy, but above 100 s the effect of source group time shifts may also be appreciable. These effects are probably below the signal levels that we interpret here, however. Many known geological and tectonic structures are observed in the group velocity maps. Of particular note are the signatures of sedimentary basins, continental flood basalts, variations in crustal thickness, backarc spreading, downgoing slabs, and continental roots. Comparison of the estimated group velocity maps with those predicted by CRUST5.1/S16B30 is qualitatively good, but there are significant differences in detail which provide new information that should help to calibrate future crustal and upper mantle models of Eurasia.

Higher–order Boussinesq–type equations for surface gravity waves: derivation and analysis

Abstract: Boussinesq–type equations of higher order in dispersion as well as in nonlinearity are derived for waves (and wave–current interaction) over an uneven bottom. Formulations are given in terms of various velocity variables such as the depth–averaged velocity and the particle velocity at the still water level, and at an arbitrary vertical location. The equations are enhanced and analysed with emphasis on linear dispersion, shoaling and nonlinear properties for large wave numbers. As a starting point the velocity potential is expanded as a power series in the vertical coordinate measured from the still water level (SWL). Substituting this expansion into the Laplace equation leads to a velocity field expressed in terms of spatial derivatives of the vertical velocity ŵ and the horizontal velocity vector u at the SWL. The series expressions are given to infinite order in the dispersion parameter, μ. Satisfying the kinematic bottom boundary condition defines an implicit relation between ŵ and u, which is recast as an explicit recursive expression for ŵ in terms of u under the assumption that μ ≪ 1. Boussinesq equations are then derived from the dynamic and kinematic boundary conditions at the free surface. In this process the infinite series solutions are truncated at O (μ6), while all orders of the nonlinearity parameter, ϵ are included to that order in dispersion. This leads to a set of higher–order Boussinesq equations in terms of the surface elevation η and the horizontal velocity vector u at the SWL. The equations are recast in terms of the depth–averaged velocity, U leaving out O (ϵ2μ4, which corresponds to assuming ϵ =O(μ). This formulation turns out to include singularities in linear dispersion as well as in nonlinearity. Next, the technique introduced by Madsen and others in 1991and Schaffer & Madsen in 1995 is invoked, and this results in aset of enhanced equations formulated in U and including O (μ4,ϵμ4)terms. These equations contain no singularities and the embedded linear and nonlinear properties are shown to be significantly improved. To quantify the accuracy, Stokes's third–order theory is used as reference and Fourier analyses of the new equations are carried out to third order (in nonlinearity) for regular waves on a constant depth and to first order for shoaling characteristics. Furthermore, analyses are carried out to second order for bichromatic waves and to first order for waves in ambient currents. These analyses are not restricted to small values of the linear dispersion parameter, μ. In conclusion, the new equations are shown to have linear dispersion characteristics corresponding to a Pade [4,4] expansion in k′h′ (wave number times depth) of the squared celerity according to Stokes's linear theory. This corresponds to a quite high accuracy in linear dispersion up to approximately k′h′ = 6. The high quality of dispersion is also achieved for the Doppler shift in connection with wave–current interaction and it allows for a study of wave blocking due to opposing currents. Also, the linear shoaling characteristics are shown to be excellent, and the accuracy of nonlinear transfer of energy to sub– and super–harmonics is found to be superior to previous formulations. The equations are then recast in terms of the particle velocity, ũ, at an arbitrary vertical location including O μ4,ϵ5μ4)terms. This formulation includes, as special subsets, Boussinesq equations in terms of the bottom velocity or the surface velocity. Furthermore, the arbitrary location of the velocity variable can be used to optimize the embedded linear and nonlinear characteristics. A Fourier analysis is again carried out to third order (in ϵ) for regular waves. It turns out that Pade [4,4] linear dispersion characteristics can not be achieved for any choice of the location of the velocity variable. However, for an optimized location we achieve fairly good linear characteristics and very good nonlinear characteristics. Finally, the formulation in terms of ũ is modified by introducing the technique of dispersion enhancement while retaining only O (μ4,ϵ5μ4) terms. Now the resulting set of equations do show Pade [4,4] dispersion characteristics in the case of pure waves as well as in connection with ambient currents, and again the nonlinear properties (such as second– and third–order transfer functions and amplitude dispersion) are shown to be superior to those of existing formulations of Boussinesq–type equations.

Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site Characterization

Abstract: Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site

Gyro-TWT with a helical operating waveguide: new possibilities to enhance efficiency and frequency bandwidth

Abstract: A helical corrugation of the inner surface of an oversized cylindrical waveguide provides, for certain parameters, an almost constant value of group velocity and close to zero longitudinal wavenumber of an eigenwave for a very broad frequency band. The use of such a helical waveguide as an operating section of a gyrotron traveling wave tube (gyro-TWT) allows significant widening of its bandwidth and an increase in the efficiency at very large particle velocity spreads. In this paper, the new concept is confirmed by theoretical analysis and "cold" measurements of the helical waveguide dispersion. Results of a linear and nonlinear theory of the helical gyro-TWT as well as two designs for subrelativistic (80 keV, 20 A) and relativistic (300 keV, 80 A) electron beams are also presented. For both designs, parameters providing a very broad frequency band (about 20%) and high efficiency (above 30%) have been found. When the transverse velocity spread is increased from zero up to a very high value of 40%, simulations showed only a 20%-30% narrowing in the frequency band and a 20% decrease in electron efficiency. The theoretical analysis demonstrates important advantages of the helical gyro-TWT over the "smooth" one in frequency bandwidth, sensitivity to electron velocity spread, and stability to parasitic self-excitation.

On a technique for measurement of turbulent shear stress in the presence of surface waves

Abstract: Surface waves can produce large biases in estimates of turbulent shear stress obtained from single-sensor measurements of velocity if there is even a small uncertainty in the orientation of either the velocity sensor or the principal axes of the wave-induced velocity field. The wave-induced bias can be diminished substantially by differencing measurements obtained from two velocity sensors separated by a distance larger than the correlation scale of the turbulence but small in comparison to the inverse wavenumber of the surface waves. If the scale separation is sufficiently large, then minus the density times half of the covariance between horizontal and vertical velocity differences is a nearly wave-free estimate of the average of the turbulent shear stresses at the two sensors. A theoretical analysis determines the bias associated with this technique under simplified conditions, in which waves and turbulence are uncorrelated and the waves are weakly nonlinear and narrow-banded in both frequency...

Velocity, acceleration and vorticity under a breaking wave

Abstract: The fluid particle velocities in the overturning jet of a breaking wave have been measured by the Particle Image Velocimetry (PIV) technique. Monochromatic waves with wave height of 14.5 cm and wavelength of 121 cm were generated in the water depth of 20 cm. The measured fluid particle velocity at the tip of the overturning jet reached 1.68 times of the phase velocity calculated from the linear wave theory. Fluid particle accelerations were estimated from the velocity data with the following results: The overturning jet enters the horizontal water surface with an acceleration of 1.1 g at an angle of 88° downward. The PIV technique was also used to measure the instantaneous vertical vorticities generated by breaking waves. The number and locations of the vortices on the horizontal plane appear to be random. The maximum instantaneous vorticity was in the order of magnitude of 20–30 s−1, whereas the ensemble-averaged vorticity was quite small.

Accurate measurement of laser-driven shock trajectories with velocity interferometry

Abstract: We describe a velocity interferometer used to measure the velocity and trajectory of laser driven shocks in liquid deuterium accurately and continuously. This demonstration of velocity interferometry to measure shock velocity and shock trajectory in condensed matter shows strong potential for future studies of laser-driven shocks in transparent media. Accuracy of this technique can be better than 1% in velocity and ±0.2 μm in position during a 10 ns interval.

Incoherent scatter radar observations of AGW/TID events generated by the moving solar terminator

Abstract: . Observations of traveling ionospheric disturbances (TIDs) associated with atmospheric gravity waves (AGWs) generated by the moving solar terminator have been made with the Millstone Hill incoherent scatter radar. Three experiments near 1995 fall equinox measured the AGW/TID velocity and direction of motion. Spectral and cross-correlation analysis of the ionospheric density observations indicates that ST-generated AGWs/TIDs were observed during each experiment, with the more-pronounced effect occurring at sunrise. The strongest oscillations in the ionospheric parameters have periods of 1.5 to 2 hours. The group and phase velocities have been determined and show that the disturbances propagate in the horizontal plane perpendicular to the terminator with the group velocity of 300-400 m s-1 that corresponds to the ST speed at ionospheric heights. The high horizontal group velocity seems to contradict the accepted theory of AGW/TID propagation and indicates a need for additional investigation. Key words. Ionosphere (wave propagation) · Meteorology and atmospheric dynamics (waves and tides)

Structure of the crust in the Black Sea and adjoining regions from surface wave data

Abstract: Group velocities of Rayleigh and Love waves along the paths across the Black Sea and partly Asia Minor and the Balkan Peninsula are used to estimate lateral variations of the crustal structure in the region. As a first step, lateral variations of group velocities for periods in the range 10–20 s are determined using a 2D tomography method. Since the paths are oriented predominantly in NE–SW or N–S direction, the resolution is estimated as a function of azimuth. The ‘local’ dispersion curves are actually averaged over the extended areas stretched in the predominant direction of the paths. The size of the averaging area in the direction of the best resolution is approximately 200 km. As a second step, the local averaged dispersion curves are inverted to vertical sections of S-wave velocities. Since the dispersion curves in the 10–20 s period range are mostly affected by the upper crustal structure, the velocities are estimated to a depth of approximately 25 km. Velocity sections along 43° N latitude are determined separately from Rayleigh and Love wave data. It is shown that the crust under the sea contains a low-velocity sedimentary layer of 2–3 km thickness, localized in the eastern and western deeps, as found earlier from DSS data. Beneath the sedimentary layer, two layers are present with velocity values lying between those of granite and consolidated sediments. Velocities in these layers are slightly lower in the deeps, and the boundaries of the layers are lowered. S-wave velocities obtained from Love wave data are found to be larger than those from Rayleigh wave data, the difference being most pronounced in the basaltic layer. If this difference is attributed to anisotropy, the anisotropy coefficient χ = (SH - SV)/Smean is reasonable (2–3%) in the upper layers, and exceeds 9% in the basaltic layer.

Group velocity of acoustic waves in strongly scattering media: Dependence on the volume fraction of scatterers

Abstract: We study, both experimentally and theoretically, the ballistic propagation of ultrasonic wave pulses through a random strongly scattering medium as a function of the volume fraction of the scatterers. The scattering medium consists of a liquid suspension of monodisperse glass beads, whose concentration is varied by controlling the upward flow of the liquid in a fluidized bed. At intermediate frequencies, where the acoustic wavelength \ensuremath{\lambda} is comparable to the size of the glass bead scatterers, very strong scattering is observed, with the scattering mean free path reaching values as low as \ensuremath{\lambda}/2. At high volume fractions of scatterers, the scattering results in pronounced dispersion, as demonstrated experimentally by the strong frequency dependence found in both the phase and group velocities. However, as the volume fraction is lowered, the dispersion is substantially reduced, in marked contrast to recent predictions for electromagnetic waves. Our experimental results are explained quantitatively by a theoretical model, based on a spectral function approach, that accounts for the renormalization of the scattering within the medium, an effect that is greatest when the concentration of scatterers is largest. The mechanisms underlying the frequency dependence of the velocities and their dependence on volume fraction are further elucidated by examining the ultrasonic energy density, both inside the scatterers and in the surrounding fluid. This allows us to show that the velocities are substantially slowed down both by (i) resonant scattering from the glass spheres, where energy is trapped within the solid scatterers, and by (ii) tortuosity effects, where the wave energy is largely confined to the tortuous fluid pathways. These results demonstrate convincingly why the phase and group velocities of acoustic waves vary strongly with frequency at high volume fractions of scatterers, but only show weak dispersive effects at low volume fractions. Furthermore, our microscopic picture of the dispersion gives a simple physical explanation of why its volume fraction dependence is opposite to that expected for light and other electromagnetic waves, where the velocity inside the scatterers is normally less than in the surrounding medium.

The thermal self-focusing instability near the critical surface in the high-latitude ionosphere

Abstract: A fully nonlinear development of the thermal self-focusing instability of high power radio waves in the ionosphere in the region near the critical surface is the subject of the present study. In the simulation model studied, a high-powered radio wave in the frequency range 5 - 10 MHz, with a 1% amplitude modulation, is launched vertically. In the high latitude geometry this represents a direction antiparallel to the magnetic field which is almost vertically downwards. The modulated wave undergoes strong self-focusing at the critical surface, where the group velocity of the wave goes to zero. The scale size of the structures transverse to the magnetic field is controlled by the wave intensity and the diffraction effects. The large parallel thermal conduction leads to the diffusion of these irregularities into the underdense and overdense plasma in narrow filaments. The depletion in the density in the overdense plasma allows propagation of the wave to higher altitude above the original critical surface and hence into the overdense plasma.

Linear theory of a wide-band gyro-TWT amplifier using spiral waveguide

Abstract: A novel electrodynamic system to realize high efficiency and a broad frequency band in a gyro-TWT amplifier at millimeter and microwave frequencies is described. A cylindrical waveguide having a helically grooved wall selectively couples an electromagnetic waveguide mode at a frequency close to cutoff to the forward travelling wave of a lower mode, resulting in an eigenwave with a constant positive group velocity and approximately zero axial wavenumber over a wide frequency band. For a travelling-wave gyroamplifier, such a dispersion characteristic permits operation with significantly increased bandwidth and reduced sensitivity to electron-beam axial velocity spread. Numerical calculations will be presented to show the beam-coupled dispersion characteristics, stability, and gain profiles of a simple amplifier, based upon a linearized coupled-wave theory.

A new mean velocity scaling for turbulent boundary layers

Abstract: A new scaling, originally developed for the mean velocity profile of turbulent pipe flow, was extended to the case of zero pressure gradient turbulent boundary layers. At low Reynolds numbers, the new scaling leads to a power law for the overlap region of the mean velocity profile. At high Reynolds numbers, the conventional overlap region given by a log law is also obtained. Comparisons were made between the power law and 17 velocity profiles covering a large range of Reynolds numbers. This comparison showed that a power law with empirical constants determined from pipe flow data was in good agreement with boundary layer data. A new outer velocity scale was also proposed. The new outer velocity scale was used to normalize the 17 velocity profiles and the collapse of these profiles was significantly better than for profiles normalized by the friction velocity or the freestream velocity.

Enhancement of optical gain in two-dimensional photonic crystals with active lattice points

Abstract: Photonic crystals with active lattice points (two-dimensional gain photonic crystals) are proposed, in which all lattice points are made of the same gain material embedded in other dissipative medium. The optical gain spectrum is found to exhibit a pronounced gain enhancement in the vicinity of the band edge of the photonic band. This gain value also shows a spatial anisotropy reflecting the symmetry of the photonic band. These gain values have a strong correlation with the variation of the group velocity of light, indicating that the marked reduction in the group velocity near the photonic band edge causes the optical gain enhancement.

Electromagnetic mode density for finite quasi-periodic structures

Abstract: The transmission properties of quasi-periodic Cantor-like and Fibonacci photonic bandgap structures that have the same optical paths are studied and compared with one-dimensional, finite, N-period stacks. The electromagnetic mode densities and group velocities are also discussed. We show that the density of modes at the edge of the bandgap is greater for Cantor-like multilayers, so at the band edge a sharp decrease in the group velocity is found.

The velocities of light in modified QED vacua

Abstract: QED vacua under the influence of external conditions (background fields, finite temperature, boundary conditions) can be considered as dispersive media whose complex behaviour can no longer be described in terms of a single universal vacuum velocity of light c. Beginning in the early 1950's (J.S. Toll), quantum field theoretic investigations have led to considerable insight into the relation between the vacuum structure and the propagation of light. Recent years have witnessed a significant growth of activity in this field of research. After a short overview, two characteristic situations are discussed: the propagation of light in a constant homogeneous magnetic field and in a Casimir vacuum. The latter appears to be particularly interesting because the Casimir vacuum has been found to exhibit modes of the propagation of light with phase and group velocities larger than c in the low frequency domain ω ≪ m where m is the electron mass. The impact of this result on the front velocity of light in a Casimir vacuum is discussed by means of the Kramers-Kronig relations.

Implication of DC-space-charge-induced velocity spread on gyrotron gun performance

Abstract: The confinement of mirror-trapped electrons under the influence of dc space charge and their effect on the velocity distribution in a magnetron injection gun is investigated theoretically and computationally. Most trapped electrons are found to escape from the gun due to pitch angle scattering by the spatially periodic electrostatic potential created by the forward propagating beam. However, a small portion scatters into orbits which are more deeply trapped and can escape only by striking the modulation anode. As electrons diffuse in velocity, the velocity distribution in the gun region extends toward increasing perpendicular velocity. On the other hand, the accumulation of trapped particles near the cathode induces an additional velocity spread in the main beam. Consequently, the main beam exhibits an increased velocity spread and a reduced transverse momentum when it enters the cavity.

Method and apparatus for ultrasonic doppler velocimetry using speed of sound and reflection mode pulsed wideband doppler

Abstract: According to the present invention, a method and apparatus rely upon tomographic measurement of the speed of sound and fluid velocity in a pipe. The invention provides a more accurate profile of velocity within flow fields where the speed of sound varies within the cross-section of the pipe. This profile is obtained by reconstruction of the velocity profile from the local speed of sound measurement simultaneously with the flow velocity. The method of the present invention is real-time tomographic ultrasonic Doppler velocimetry utilizing a to plurality of ultrasonic transmission and reflection measurements along two orthogonal sets of parallel acoustic lines-of-sight. The fluid velocity profile and the acoustic velocity profile are determined by iteration between determining a fluid velocity profile and measuring local acoustic velocity until convergence is reached.

Effect of birefringence in a bulk semiconductor optical amplifier on four-wave mixing

Abstract: We present experimental results on birefringence effects in an InGaAsP bulk semiconductor optical amplifier (SOA). Although the gain of the device is polarization insensitive, we observed a strong variation of the four-wave mixing (FWM) efficiency if the parallel input polarization of pump and signal wave was changed with respect to the device structure. This variation, which is attributed to birefringence in the SOA, can be as high as 10 dB for frequency detunings of about 6 THz. Thus, it might strongly affect the various applications of FWM for optical signal processing and parameter extraction. In addition, we performed polarization resolved measurements of the amplified spontaneous emission demonstrating different group velocity indices for TE and TM polarized light.

Experimental technique to determine the band structure of two-dimensional photonic lattices

Abstract: An experimental technique to probe the energy against wavevector dispersion curves of two-dimensional photonic bandgap structures is demonstrated from the study of 360 nm period air hole honeycomb lattices etched in AlGaAs waveguides. The technique relies on the coupling of external radiation incident on the lattices to the zone-folded bands of the photonic structures, This coupling is detected owing to observation of resonance features in the reflectivity spectra. Good agreement between experiment and theory is found for the second, third and fourth photonic bands, The technique allows external photons to be coupled into regions of the photonic dispersion curves close to the Brillouin zone boundaries, where the photon group velocity tends to zero, and thus has the potential to allow novel effects related to 'heavy photons' to be investigated.

Experimental technique to determine the band structure of two-dimensional photonic lattices : Photonic crystals and microstructures

Abstract: An experimental technique to probe the energy against wavevector dispersion curves of two-dimensional photonic bandgap structures is demonstrated from the study of 360nm period air hole honeycomb lattices etched in AlGaAs waveguides. The technique relies on the coupling of external radiation incident on the lattices to the zone-folded bands of the photonic structures. This coupling is detected owing to observation of resonance features in the reflectivity spectra. Good agreement between experiment and theory is found for the second, third and fourth photonic bands. The technique allows external photons to be coupled into regions of the photonic dispersion curves close to the Brillouin zone boundaries, where the photon group velocity tends to zero, and thus has the potential to allow novel effects related to 'heavy photons' to be investigated.

Velocity selection for ultracold atoms using a micromaser

Abstract: The velocity distribution of ultracold atoms passing through a resonant microwave cavity can narrow by more than an order of magnitude. This velocity selection is due to resonances in the transmission through dressed-state potentials. The proposed device is an atom-optical analog of a Fabry-Perot resonator and allows for macroscopic coherence lengths.

Nonlinear Reflection of Internal Waves at a Density Discontinuityat the Base of the Mixed Layer

Abstract: Internal waves propagating with an upward component of group velocity toward the ocean surface are reflected at the base of the mixed layer. A simple model is constructed to examine nonlinear aspects of the reflection. It consists of a uniform layer of depth h, representing the mixed layer, bounded above by a rigid surface and below by an interface, across which there is a density discontinuity Δρ and beneath which fluid is stably stratified with buoyancy frequency, N = const. Attention is given to the case in which an internal wave in the stratified layer, incident from below on the density interface, has frequency σ < N/2. In addition to a first-order wave of frequency σ that is reflected downward from the density discontinuity, a second-order wave is then generated with frequency 2σ and with horizontal wavenumber twice that of the incident wave, which also propagates downward away from the interface. The shape of the waves generated at the interface is investigated and a measure of their nonli...

Mode locking by cascading of second-order nonlinearities

Abstract: We present a comprehensive theoretical and experimental study on a new passive mode-locking technique, called cascaded second-order nonlinearity mode locking (CSM), which exploits cascaded second-order nonlinearities to obtain large third-order susceptibilities from an intracavity second harmonic crystal. The nonlinear phase shift that originates in the nonlinear crystal is converted into a nonlinear amplitude modulation by a suitable intracavity aperture. A numerical model, based on a perturbative approach, allows the nonlinear loss modulation of resonators used for CSM to be calculated as a function of the resonator parameters and of the phase mismatch. The predictions of the model are confirmed by experiments performed on a CW Nd:YAG laser. The effects of group velocity mismatch and the limitations which it poses on the minimum achievable pulsewidth are analyzed both experimentally and theoretically.

Leaky waves and the elastic wave resonance reflection on a crystal-thin solid layer interface. II. Leaky waves given rise to by exceptional bulk waves

Abstract: A study is made of the elastic wave resonance reflection in a crystal-thin solid layer structure near the velocity of a leaky wave which originates from an exceptional bulk wave. The latter is a homogeneous mode with group velocity parallel to the boundary of a medium which satisfies the condition of the mechanically free surface. On the surface coated with a thin layer, the exceptional bulk wave can transform into the leaky wave and then there arises a narrow interval of incident angles where the coefficients of mode conversion suffer abrupt and strong variations in phase and magnitude. A criterion of occurence of the leaky wave is found. Approximate expressions describing the behavior of the coefficients of mode conversion within the resonance interval of incident angles are derived and analyzed.

Wave packets, rays, and the role of real group velocity in absorbing media

Abstract: In an absorbing medium, where the vector W5]v/]k usually is complex for real values of the wave vector k, the group velocity W may become real for some complex values of k. The role of real group velocity in the propagation of one-dimensional wave packets in homogeneous absorbing media is examined. Applying the saddle point method to an analysis of the asymptotic behavior of the Gaussian wave packets shows that for absorbing media, at large times and distances, the real group velocity appears as a local characteristic of any small section of a wave packet. For each section we can find the complex values of the local wave number and the local frequency defining a real group velocity. Thus, the real group velocity concepts in absorbing media do not have to be based on the signals having real wave vectors or real frequencies. The analysis of the exact solution for a Gaussian wave packet in a medium with a complex law of dispersion describing whistler waves in a collisional plasma is performed. It is shown that at all times the initial carrier wave number exists as a real part of the local complex wave number at some point of the Gaussian envelope and this point moves with a constant real group velocity. For large times the local wave group with the initial carrier wave number can be found far away from the envelope center. @S1063-651X~98!05601-3# The concepts of wave packet~s !~ WP!, group velocity, and ray tracing come up in many areas of physics—quantum mechanics, optics, plasma physics, fluid mechanics, solid state physics, geophysics, and astrophysics. The group velocity concept seems to have been first introduced by Rayleigh @1# for the transverse sound waves propagating in thin elastic rods. Since then this concept was applied to studying WP and signals based on various kinds of waves in dispersive, nonabsorbing media. The theory of WP in dispersive media without absorption of the wave energy has been amply discussed in the literature @2,3#. As is well known, any WP in a homogeneous medium is constructed by the continuous superposition ~integration! of the elementary plane waves, sinusoidal in both space and time, with neighboring values of the wave vector k and the frequency v. Usually such a superposition is presented in the form of the integral of the function A(k)exp@i(kix2vt)# in the k space. The dispersion equation D(v,k)50 characterizes the properties of the medium with respect to wave propagation. The spatial Fourier transform of the WP at t50 is the function A(k) concentrated in some vicinity of the carrier wave vector kc . The spatial maximum of the WP envelope propagates with the group velocity W5]v/]k calculated at k5kc . The concept of rays in the theory of WP propagation in nonabsorbing media appears in studies of the asymptotic behavior of the WP for large values of t and uxu. A powerful tool that leads to the asymptotic formulas for the WP solutions is the saddle point ~SP! method for the Fourier integrals. Whitham @3# shows that for large times each small section of the WP can be characterized by the instantaneous values of the local wave vector k (x,t) and the local frequency v (x,t)5v@k (x,t)#, where the dependence v 5v(k) is determined by the dispersion equation D(v,k) 50. These local characteristics of the WP remain constant along the straight-line trajectories x5X(t) termed the rays. The value of the local wave vector k at the point x5xm(t) corresponding to the spatial maximum of the WP envelope equals kc . The description of the rays associated with the WP propagation admits the Hamiltonian formalism: the vectors X(t) and k determine the position of the dynamic system in the configuration ~coordinate! space and in representation ~momentum! space, respectively, while the frequency

Index of refraction and mechanical behavior of soda lime glass under shock and release wave propagations

Abstract: This article reports a set of experiments designed to measure change in the refractive index of transparent material under both planar shock and release wave propagations. Information about both mechanical and optical properties of transparent material were obtained simultaneously through the measurement of particle velocity at or near the impact surface and the free surface velocity. Data thus obtained is used to determine shock and release wave velocities and the Hugoniot elastic limit (HEL) of the material. Shock wave velocity in soda lime glass remains unchanged at 5.83±0.04 km/s, i.e., equal to the measured ultrasonic longitudinal wave velocity, when it is shock compressed to less than or equal to 4.3 GPa. The value of shock wave velocity begins to decline when the impact stress in the glass exceeds this value. The release wave velocity, however, remains equal to the measured ultrasonic longitudinal wave velocity to only 3 GPa, it begins to decline at higher stresses. The variation in the refractive ...

Three-dimensional shear wave velocity structure in the upper mantle beneath the Philippine Sea region

Abstract: The three-dimensional shear wave velocity structure in the upper mantle beneath the Philippine Sea was investigated with Rayleigh wave phase velocities in the periods 30–100 s More than 900 Rayleigh wave phase velocity curves were obtained for this region with good path coverage The phase velocity data were inverted for the phase velocity distribution maps in the Philippine Sea with 2-D tomographic technique without any a priori regionalization The resolutions of the tomographic analysis were quite good in almost of the target region The phase velocity maps were inverted for the 3-D shear wave velocity structure in the upper mantle down to 220 km In the shallow depths lateral heterogeneities with short wavelength were seen in the shear wave velocity maps This might be related with complicated surface structures In the middle depths the shear wave velocity was well correlated to the main tectonic features seen at the surface and well explained by the evolution history of the Philippine Sea The older western Philippine Sea had higher shear wave velocities than the younger eastern Philippine Sea In the western Philippine Sea the central basin ridge, which is the youngest in this area, showed the low velocity anomaly This is supported by the fact that the West Philippine Basin was formed in this area In the depths 150–200 km the low velocity anomaly was dominant inside the Philippine Sea, which might suggest the existence of the mantle return flows The thickness of the lithosphere in the south of the West Philippine Basin reached about 100 km, which is much thicker than the results of previous studies for this region