Showing papers on "Wave propagation published in 1992"

On undamped heat waves in an elastic solid

Abstract: This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.

Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations

Abstract: The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J/sub 0/ Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed. >

Wide-angle beam propagation using Pade approximant operators.

Abstract: A new beam-propagation method is presented whereby the exact scalar Helmholtz propagation operator is replaced by any one of a sequence of higher-order (n, n) Pade approximant operators. The resulting differential equation may then be discretized to obtain (in two dimensions) a matrix equation of bandwidth 2n + 1 that is solvable by using Standard implicit solution techniques. The final algorithm allows (for n = 2) accurate propagation at angles of greater than 55 deg from the propagation axis as well as propagation through materials with widely differing indices of refraction.

Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow

Abstract: For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor’s hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor’s hypothesis, space‐time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space‐time correlation of dilatation fluctuations is explained via a wave propagation model.

Numerical simulations of convectively generated stratospheric gravity waves

Abstract: A 2D model of a mesoscale convective flow is used to simulate the excitation and vertical propagation of gravity waves. Data obtained show that, in the absence of storm-relative mean winds in the stratosphere, the primary mode of excitation of gravity waves is by mechanical forcing owing to oscillatory updrafts. The stratospheric response consists of waves whose periods match the primary periods of the forcing. Due to the tendency of the oscillating updrafts to propagate toward the rear of the storm, gravity wave propagation is limited primarily to the rearward direction. Results suggest that squall-line-generated gravity waves arise from mechanical forcing rather than thermal effects.

Measurement of photonic band structure in a two-dimensional periodic dielectric array.

Abstract: The photonic band structure in a two-dimensional dielectric array is investigated using the coherent microwave transient spectroscopy (COMITS) technique. The array consists of alumina-ceramic rods arranged in a regular square lattice. The dispersion relation for electromagnetic waves in this photonic crystal is determined directly using the phase sensitivity of COMITS. The experimental results are compared to theoretical predictions obtained using the plane-wave expansion technique. Configurations with the electric field parallel and perpendicular to the axis of the rods are investigated.

Effects of Multiple Modes on Rayleigh Wave Dispersion Characteristics

Abstract: The effects of multiple modes on Rayleigh wave dispersion are discussed to reduce the ambiguity of uniqueness of shear wave velocity (Vs) profiles estimated by the surface wave method. Based on a review of previous studies, dispersion curves of multiple‐mode Rayleigh waves induced by harmonic vertical point loading are derived for both vertical and horizontal particle motions. Also presented is the variation with frequency of the amplitude ratio between horizontal and vertical particle motions. Numerical studies indicate that a stiff soil layer overlying a softer soil layer induces a higher mode or multiple modes, leading to an inversely dispersive characteristic. Consideration of the effects of higher modes is strongly recommended in the inverse process when the observed data show an inversely dispersive trend. The ambiguity of uniqueness of the inverted soil profiles may be reduced by using either the dispersion data of horizontal motion or the amplitude ratio of particle motions in addition to the disp...

Dispersive perturbations of solitons of the nonlinear Schrödinger equation

Abstract: A useful analysis of dispersive (radiative) perturbations of solitons of the nonlinear Schrodinger equation is developed. With reference to the propagation of optical solitons in glass fibers, the analysis is used to treat the collision of a low-intensity wave packet with a soliton, the radiation field created by the local perturbation of a soliton, and finally that created by a spatially periodic perturbation of the parameters of the fiber, or equivalently by a periodic variation in gain and loss that averages to zero. Perturbations whose wavelength is short compared with the soliton period produce exponentially small radiation fields as a result of the need for phase matching.

A statistical study of Pc 1–2 magnetic pulsations in the equatorial magnetosphere: 2. Wave properties

Abstract: A statistical study of narrowband transverse 0.1- to 4.0-Hz magnetic pulsations, essentially Pc 1–2 (0.1–5.0 Hz), occurring from L=3.5 to L=9, |MLAT| 7 have not previously been discussed and are found to exhibit remarkable polarization behavior. The A.M. events have the highest X observed in the data base, with X averaging 0.4 to 0.5, but most remarkably, they are linearly polarized at all magnetic latitudes sampled. Given the high normalized frequency, the equatorial linear polarization of the A.M. events cannot be explained in terms of a crossover from left- to right-hand polarization occurring during propagation from low to high magnetic field strengths. Oblique propagation or the effects of multiple reflection through the wave growth region might lead to linear polarizations. The results suggest that a new examination of EMIC wave generation specifically addressing the properties of this A.M. population may be needed.

Experimental verification of nondiffracting X waves

Abstract: The propagation of acoustic waves in isotropic/homogeneous media and electromagnetic waves in free space is governed by the isotropic/homogeneous (or free space) scalar wave equation. A zeroth-order acoustic X wave (axially symmetric) was experimentally produced with an acoustic annular array transducer. The generalized expression includes a term for the frequency response of the system and parameters for varying depth of field versus beam width of the resulting family of beams. Excellent agreement between theoretical predictions and experiment was obtained. An X wave of finite aperture driven with realizable (causal, finite energy) pulses is found to travel with a large depth of field (nondiffracting length). >

Internal solitary wave breaking and run-up on a uniform slope

Abstract: Laboratory experiments have been conducted to study the shoaling of internal solitary waves of depression in a two-layer system on a uniform slope. The shoaling of a single solitary wave results in wave breaking and the production of multiple turbulent surges, or boluses, which propagate up the slope. Significant vertical mixing occurs everywhere inshore of the breaking location. The kinematics of the breaking and bolus runup are described and a breaking criterion is found. The energetics of the breaking are investigated. Over the range of parameters examined, 15 (±5) % of the energy lost from first-mode wave motion inshore of the break point goes into vertical mixing.

Dispersion cancellation in a measurement of the single-photon propagation velocity in glass.

Abstract: We have demonstrated for the first time that single photons in glass travel at the group velocity, and have observed a novel, nonlocal dispersion-cancellation effect. We used a two-photon interferometer in which a conjugate pair of photons produced in parametric fluorescence travel separate paths and are detected in coincidence after being recombined at a beam splitter. A piece of glass was placed in the path of one of the photons, and a variable delay was adjusted to precisely compensate for it. The single-photon propagation time was thus measured to within approximately 4 fsec.

Interaction of energetic alpha particles with intense lower hybrid waves.

Abstract: Lower hybrid waves are a demonstrated, continuous means of driving toroidal current in a tokamak. When these waves propagate in a tokamak fusion reactor, in which there are energetic {alpha}- particles, there are conditions under which the {alpha}-particles do not appreciably damp, and may even amplify, the wave, thereby enhancing the current-drive effect. Waves traveling in one poloidal direction, in addition to being directed in one toroidal direction, are shown to be the most efficient drivers of current in the presence of the energetic {alpha}-particles.

Refraction of diffuse photon density waves.

Abstract: Experiments are performed which illustrate the properties of damped traveling waves in diffusive media. Our observations demonstrate the manipulation of these waves by adjustment of the photon diffusion coefficients of adjacent turbid media. The waves are imaged, and are shown to obey simple relations such as Snell's law. The extent to which analogies from physical optics may be used to understand these waves is further explored, and the implications for medical imaging are briefly discussed.

Multilayer waveguides: efficient numerical analysis of general structures

Abstract: An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically. >

Laser generation and detection of surface acoustic waves: Elastic properties of surface layers

Abstract: A noncontact all‐optical method for surface photoacoustics is described. The surface acoustic waves (SAWs) were excited employing a KrF laser and detected with a Michelson interferometer using a 633‐nm HeNe laser. Due to an active stabilization scheme developed for the interferometer a surface displacement of 0.2 A could be detected. The materials investigated included pure materials such as polycrystalline aluminum, and crystalline silicon; films of gold, silver, aluminum, iron, and nickel on fused silica; and a‐Si:H on Si(100). In the case of pure materials the shape of the acoustic pulse and the phase velocity were determined. The dispersion of the SAW phase velocity observed for the film systems was used to extract information on the film thickness, density, and transverse and longitudinal sound velocity. Models for the theoretical treatment of film systems and the calculation of dispersion curves are presented.

Iterative asymptotic inversion in the acoustic approximation

Abstract: We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays,...

Relativistic, perpendicular shocks in electron-positron plasmas

Abstract: One-dimensional particle-in-cell plasma simulations are used to examine the mechanical structure and thermalization properties of collisionless relativistic shock waves in electron-positron plasmas. Shocks propagating perpendicularly to the magnetic field direction are considered. It is shown that these shock waves exist, and that they are completely parameterized by the ratio of the upstream Poynting flux to the upstream kinetic energy flux. The way in which the Rankine-Hugoniot shock jump conditions are modified by the presence of wave fluctuations is shown, and they are used to provide a macroscopic description of these collisionless shock flows. The results of a 2D simulation that demonstrates the generality of these results beyond the assumption of the 1D case are discussed. It is suggested that the thermalization mechanism is the formation of a synchrotron maser by the coherently reflected particles in the shock front. Because the downstream medium is thermalized, it is argued that perpendicular shocks in pure electron-positron plasmas are not candidates as nonthermal particle accelerators.

Surface electromagnetic waves in optics

Abstract: The basic concepts of surface electromagnetic waves (SEWs) in the optical band, the unique features of their excitation by light at the boundary of condensed media, and the participation of SEWs in the formation of periodic structures and other photophysical processes that occur on surfaces due to the influence of high-intensity laser radiation are presented. The use of middle infrared SEW for measuring optical characteristics of materials is considered. A method, developed by the authors, for measuring the real part of the SEW wave vector to obtain metal plasma frequency directly, is presented.

Solitons in a nonlinear model medium

Abstract: The periodic stationary solutions of a model nonlinear evolution equation simulating the propagation of short-wave perturbations in a relaxing medium are studied. Solutions expressed by a multiple-valued function are shown to exist. A method for determining the nonlinear interaction between solitary waves is suggested. An example of a collision of solitons is given.

Direct Time Integration of Maxwell's Equations in Nonlinear Dispersive Media for Propagation and Scattering of Femtosecond Electromagnetic Solitons

Abstract: The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.

Time delay of evanescent electromagnetic waves and the analogy to particle tunneling.

Abstract: The analogy between quantum tunneling of particles and evanescent electromagnetic waves can be used to study particle tunneling. Possibilities for the measurement of the time delay resulting from the transmission of waves through an evanescent region, say with lower dielectric constant, are discussed. In contrast to particle tunneling, an electromagnetic pulse can consist of many photons and can be probed in a noninvasive way. We emphasize the delay of the centroid of an electromagnetic pulse transmitted below cutoff through a portion of a waveguide with the same cross section as the adjacent propagating guides. The boundary conditions at the interface between the propagating and the evanescent region lead to the same transmission and reflection coefficients as for a square-barrier tunneling problem. For a pulse restricted to a narrow frequency range, the time delay depends only on the frequency derivative of the phase shift associated with transmission. The delay of a centroid is just that; there is no deeper physical sense which links the incoming centroid to the outgoing centroid. For sufficiently long evanescent regions, the delay is independent of thickness.

Effects of Numerics on the Physics in a Third-Generation Wind-Wave Model

Abstract: Numerical errors in third-generation ocean wave models can result in a misinterpretation of the physics in the model. Using idealized situations, it is shown that numerical errors significantly influence the initial growth, the response of wave fields to turning winds, the scaling behavior of model results with wind speed, and the propagation of swell. Furthermore, the numerics may influence the dynamic interaction between wind sea and swell. Surprisingly, fetch-limited model behavior is hardly influenced by numerical errors in wave propagation. Simple modifications of the numerics are presented to reduce or eliminate such errors. The impact of numerical improvements for realistic conditions is illustrated by performing hindcasts for the Atlantic basin and for a smaller region off the east coast of the United States.

Electromagnetic waves in Faraday chiral media

Abstract: Plane wave propagation in two kinds of Faraday chiral media, where Faraday rotation is combined with optical activity, is studied to examine methods of controlling chirality. The two types of media studied are magnetically biased chiroplasmas and chiroferrites. For propagation along the biasing magnetic field, four wavenumbers and two wave impedances are found which are dependent on the strength of the biasing field. Dispersion diagrams for the chiroplasma case are plotted. Propagation at the plasma frequency of the chiroplasma is also investigated. >

Funnel-shaped, low-frequency equatorial waves

Abstract: Funnel-shaped, low-frequency radiation, as observed in frequency time spectrograms, is frequently found at the earth's magnetic equator which extends from the proton-cyclotron frequency up to the lower hybrid frequency. Ray-tracing calculations can qualitatively reproduce the observed frequency-time characteristics of these emissions if the waves are propagating in the fast magnetosonic mode starting with wave normal angles of about 88 deg at the magnetic equator. The funnel-shaped emissions are consistent with generation by protons with a ring-type velocity space distribution. A ring-shaped region of positive slope in the velocity space density distribution of protons is observed near the Alfven velocity, indicating that the ring protons strongly interact with the waves. Ray-tracing calculations show that for similar equatorial wave normal angles lower-frequency fast magnetosonic waves are more closely confined to the magnetic equator than higher-frequency fast magnetosonic waves. For waves refracted back toward the equator at similar magnetic latitudes, the lower-frequency waves experience stronger damping in the vicinity of the equator than higher-frequency waves. Also, wave growth is restricted to higher frequencies at larger magnetic latitudes. Wave damping at the equator and wave growth off the equator favors equatorial wave normal angle distributions which lead to the funnel-shaped frequency time characteristic.

Elastic wave propagation simulation in the presence of surface topography

Abstract: SUMMARY We present a 2-D numerical modelling algorithm based on a pseudo-spectral method which accounts for surface topography. The modelling scheme uses Fourier derivative operators for spatial differencing in the horizontal direction, whereas a Chebyshev operator is used for vertical derivatives. The incorporation of surface topography is achieved by mapping a rectangular grid onto a curved grid. Modelling of surface topography is important to study near-surface effects of wave propagation in field seismic situations, since diffraction and scattering at rough surfaces are non-ray effects and can only be understood as wave phenomena. Static corrections cannot always account for these effects and some care has to be taken in their interpretation. The presented modelling algorithm can serve as a powerful tool for the study of wave propagation phenomena in the vicinity of non-planar surfaces or interfaces.