Showing papers on "Wave propagation published in 1996"

Electromagnetic Waves in Stratified Media

Abstract: This book [1] was written at an important point in the development of applications of electromagnetic (radio) waves to communications, navigation, and remote sensing. Such applications require accurate propagation predictions for a variety of path conditions, and this book provides the theoretical basis for such predictions. The book is based on fundamental research in electromagnetic wave propagation that James R. Wait performed in the Central Radio Propagation Laboratory (CRPL) of NBS from 1956 to 1962. The mathematical theory in the book is very general, and the “stratified media” models are applicable to the earth crust, the troposphere, and the ionosphere. The frequencies of the communication, navigation, and remote sensing applications treated in this book range all the way from extremely low frequencies (ELF) to microwaves. The mathematical theory of electromagnetic wave propagation is based on Maxwell’s equations [2], formulated by James Clerk Maxwell in the 1860s. Experimental propagation studies in free space [3] and over the earth [4] also go back over 100 years. Research in radio science, standards, and measurements began in NBS in the early 1900s, and the long history of radio in NBS has been thoroughly covered by Snyder and Bragaw [5]. CRPL was moved to Boulder in 1954, and Wait joined the organization in 1955. The mathematics of electromagnetic wave propagation in stratified (layered) media is very complicated, and progress in propagation theory in the early 1900s was fairly slow. Wait’s book [1] included the most useful theory (much of which he developed) and practical applications that were available in 1962. A hallmark

Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena

Abstract: The processes involving the basic phenomena of relaxation, diffusion, oscillations and wave propagation are of great relevance in physics; from a mathematical point of view they are known to be governed by simple differential equations of order 1 and 2 in time. The introduction of fractional derivatives of order α in time, with 0

Fully nonlinear internal waves in a two-fluid system

Abstract: We derive general evolution equations for two-dimensional weakly nonlinear waves at the free surface in a system of two fluids of different densities. The thickness of the upper fluid layer is assumed to be small compared with the characteristic wavelength, but no restrictions are imposed on the thickness of the lower layer. We consider the case of a free upper boundary for its relevance in applications to ocean dynamics problems and the case of a non-uniform rigid upper boundary for applications to atmospheric problems. For the special case of shallow water, the new set of equations reduces to the Boussinesq equations for two-dimensional internal waves, whilst, for great and infinite lower-layer depth, we can recover the well-known Intermediate Long Wave and Benjamin-Ono models, respectively, for one-dimensional uni-directional wave propagation. Some numerical solutions of the model for one-dimensional waves in deep water are presented and compared with the known solutions of the uni-directional model. Finally, the effects of finite-amplitude slowly varying bottom topography are included in a model appropriate to the situation when the dependence on one of the horizontal coordinates is weak.

Dispersion of Plasma Dust Acoustic Waves in the Strong-Coupling Regime

Abstract: Low-frequency compressional waves were observed in a suspension of strongly coupled $9.4\ensuremath{\mu}\mathrm{m}$ spheres in an rf Kr plasma. Both parts of the complex wave number were measured to determine the dispersion relation, which agreed with a theoretical model of damped dust acoustic waves, ignoring strong coupling, but not with a strongly coupled dust-lattice wave model. The results yield experimental values for the dust plasma frequency, charge, Debye length, and damping rate, and support the applicability of fluid-based dispersion relations to strongly coupled dusty plasmas, which has been a controversy.

Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation

Abstract: Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ansatze. By a Cole-Hopf transformation, this Kolmogorov-Petrov-skii-Piskunov equation is also written as a bilinear equation and two solutions to describe nonlinear interaction of traveling waves are further generated. Backlund transformations of the linear form and some special cases are considered.

Lattice waves in dust plasma crystals

Abstract: Techniques previously known from solid state physics are used to look at linear and weak non‐linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one‐dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi‐particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non‐linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λD. This is a condition which very often applies to dust crystal in...

On the kinetic dispersion relation for shear Alfvén waves

Abstract: Kinetic Alfven waves have been invoked is association with auroral currents and particle acceleration since the pioneering work of Hasegawa. However, to date, no work has considered the dispersion relation including the full kinetic effects for both electrons and ions. Results from such a calculation are presented, with emphasis on the role of Landua damping in dissipating Alfven waves which propogate from the warm plasma of the outer magnetosphere to the cold plasma present in the ionosphere. It is found that the Landua damping is not important when the perpendicular wavelength is larger than the ion acoustic gyroradius and the electron inertial length. In addition, ion gyroradius effects lead to a reduction in the Landua damping by raising the parallel phase velocity of the wave above the electron thermal speed in the short perpendicular wavelength regime. These results indicate that low-frequency Alfven waves with perpendicular wavelengths greater than the order of 10 km when mapped to the ionosphere will not be significantly affected by Landau damping. While these results based on the local dispersion relation, are strictly valid only for short parallel wavelength Alfven waves, they do give an indication of the importance of Landua damping for longer parallel wavelengthmore » waves such as field line resonances. 26 refs., 5 fig.« less

Global mantle shear velocity model developed using nonlinear asymptotic coupling theory

Abstract: We present a three-dimensional shear velocity model of the whole mantle developed using S H waveform data. The model is expressed horizontally in terms of spherical harmonics up to degree 12, and vertically in terms of Legendre polynomials up to degrees 5 and 7 in the upper and lower mantle, respectively. What distinguishes this model from other tomographic models published to date is (1) the theoretical normal mode-based wave propagation approach, where we include across branch mode coupling terms in order to model the body wave sensitivity to structure along the path more accurately; (2) the wave-packet weighting scheme which allows to balance contributions from high-amplitude and low-amplitude phases, increasing the resolution in some parts of the mantle. We also relax the constraints on the Moho depth, which is allowed to vary in the inversion, thus absorbing some uncertainties in crustal structure. The resulting model is generally in good agreement with other recent global mantle S velocity models and with some regional models. The rms profile with depth has more power than other models in the upper mantle/lower mantle transition region and the zone of increased power and low degree structure near the base of the mantle is confined to the last 500 km in depth. This model provides a particularly good fit to the non-hydrostatic geoid through harmonic degree 12 (79% variance reduction), as well as good fits to observed splitting functions of S velocity sensitive mantle modes, indicating that both large-scale and small-scale features are really well constrained.

Electromagnetic transmission line elements having a boundary between materials of high and low dielectric constants

Abstract: An electromagnetic wave propagation structure, suitable for the transmission of an electromagnetic wave and the formation of resonators within filters, is constructed of both high and low dielectric-constant materials wherein the high dielectric-constant is in excess of approximately 80 and the low dielectric-constant is less than approximately 2. A boundary between the high and the low dielectric-constant materials serves as an electric wall to waves propagating in the low dielectric-constant material and as a magnetic wall to waves propagating in the high dielectric-constant material. This permits substitution of the high dielectric-constant material for metal elements, such as resonators and feed structures in filters. Furthermore, the use of a cladding of dielectric material of one of the foregoing dielectric ranges about a core of material of the other of the foregoing dielectric ranges enables construction of waveguides having rectangular and circular cross-sections. Microstrip and stripline structures with substitution of the high dielectric-constant material for the harmonic elements may also be constructed.

Electroseismic wave properties

Abstract: In a porous material saturated by a fluid electrolyte, mechanical and electromagnetic disturbances are coupled. The coupling is due to an excess of electrolyte ions that exist in a fluid layer near the grain surfaces within the material; i.e., the coupling is electrokinetic in nature. The governing equations controlling the coupled electromagnetic‐seismic (or ‘‘electroseismic’’) wave propagation are presented for a general anisotropic and heterogeneous porous material. Uniqueness is derived as well as the statements of energy conservation and reciprocity. Representation integrals for the various wave fields are derived that require, in general, nine different Green’s tensors. For the special case of an isotropic and homogeneous wholespace, both the plane‐wave and the point‐source responses are obtained. Finally, the boundary conditions that hold at interfaces in the porous material are derived.

A Laboratory Study of Nonlinear Surface Waves on Water

Abstract: This paper describes an experimental investigation in which a large number of water waves were focused at one point in space and time to produce a large transient wave group. Measurements of the water surface elevation and the underlying kinematics are compared with both a linear wave theory and a second-order solution based on the sum of the wave-wave interactions identified by Longuet-Higgins & Stewart (1960). The data shows that the focusing of wave components produces a highly nonlinear wave group in which the nonlinearity increases with the wave amplitude and reduces with increasing bandwidth. When compared with the first- and second-order solutions, the wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacent wave troughs are broader and less deep. The water particle kinematics are also strongly nonlinear. The accumulated experimental data suggest that the formation of a focused wave group involves a significant transfer of energy into both the higher and lower harmonics. This is consistent with an increase in the local energy density, and the development of large velocity gradients near the water surface. Furthermore, the nonlinear wave-wave interactions are shown to be fully reversible. However, when compared to a linear solution there is a permanent change in the relative phase of the free waves. This explains the downstream shifting of the focus point (Longuet-Higgins 1974), and appears to be similar to the phase changes which result from the nonlinear interaction of solitons travelling at different velocities (Yuen & Lake 1982).

P-wave signatures and notation for transversely isotropic media: An overview

Abstract: Progress in seismic inversion and processing in anisotropic media depends on our ability to relate different seismic signatures to the anisotropic parameters. While the conventional notation (stiffness coefficients) is suitable for forward modeling, it is inconvenient in developing analytic insight into the influence of anisotropy on wave propagation. Here, a consistent description of P -wave signatures in transversely isotropic (TI) media with arbitrary strength of the anisotropy is given in terms of Thomsen notation. The influence of transverse isotropy on P -wave propagation is shown to be practically independent of the vertical S -wave velocity VS0 , even in models with strong velocity variations. Therefore, the contribution of transverse isotropy to P-wave kinematic and dynamic signatures is controlled by just two anisotropic parameters, e and δ, with the vertical velocity VP0 being a scaling coefficient in homogeneous models. The distortions of reflection moveouts and amplitudes are not necessarily correlated with the magnitude of velocity anisotropy. The influence of transverse isotropy on P -wave normal-moveout (NMO) velocity in a horizontally layered medium, on small-angle reflection coefficient, and on point-force radiation in the symmetry direction is entirely determined by the parameter δ. Another group of signatures of interest in reflection seisimology–the dip-dependence of NMO velocity, magnitude of nonhyperbolic moveout, time-migration impulse response, and the radiation pattern near vertical–is dependent on both anisotropic parameters (e and δ) and is primarily governed by the difference between e and δ. Since P -wave signatures are so sensitive to the value of e − δ, application of the elliptical-anisotropy approximation (e = δ) in P -wave processing may lead to significant errors. Many analytic expressions given in the paper remain valid in transversely isotropic media with a tilted symmetry axis. Moreover, the equation for NMO velocity from dipping reflectors, as well as the nonhyperbolic moveout equation, can be used in symmetry planes of any anisotropic media (e.g., orthorhombic).

A boundary element solution for a mode conversion study on the edge reflection of Lamb waves

Abstract: The boundary element method, well known for bulk wave scattering, is extended to study the mode conversion phenomena of Lamb waves from a free edge. The elastodynamic interior boundary value problem is formulated as a hybrid boundary integral equation in conjunction with the normal mode expansion technique based on the Lamb wave dispersion equation. The present approach has the potential of easily handling the geometrical complexity of general guided wave scattering with improved computational efficiency due to the advantage of the boundary‐type integral method. To check the accuracy of the boundary element program, vertical shear wave diffraction, due to a circular hole, is solved and compared with previous analytical solutions. Edge reflection factors for the multibackscattered modes in a steel plate are satisfied quite well with the principle of energy conservation. In the cases of A0, A1, and S0 incidence, the variations of the multireflection factors show similar tendencies to the existing results fo...

A normal mode model for acousto‐elastic ocean environments

Abstract: A normal mode method for propagation modeling in acousto‐elastic ocean waveguides is described. The compressional (p‐) and shear (s‐) wave propagation speeds in the multilayer environment may be constant or have a gradient (1/c2 linear) in each layer. Mode eigenvalues are found by analytically computing the downward‐ and upward‐looking plane wave reflection coefficients R1 and R2 at a reference depth in the fluid and searching the complex k plane for points where the product R1R2=1. The complex k‐plane search is greatly simplified by following the path along which |R1R2|=1. Modes are found as points on the path where the phase of R1R2 is a multiple of 2π. The direction of the path is found by computing the derivatives d(R1R2)/dk analytically. Leaky modes are found, allowing the mode solution to be accurate at short ranges. Seismic interface modes such as the Scholte and Stonely modes are also found. Multiple ducts in the sound speed profile are handled by employing multiple reference depths. Use of Airy function solutions to the wave equation in each layer when computing R1 and R2 results in computation times that increase only linearly with frequency.

Derivation of the pulse front tilt caused by angular dispersion

Abstract: A simple and device-independent derivation of the relation between the angular dispersion and the pulse front tilt of short pulses is given. The obtained relation is also applicable when material dispersion is present.

Some observations on localisation in non-local and gradient damage models

Abstract: Classical continuum descriptions of material degradation may cease to be mathematically meaningful in case of softening-induced localisation of deformation. Several enhancements of conventional models have been proposed to remove this deficiency. The properties of two of these so-called regularisation methods, the non-local and the gradient approach, are examined and compared in a continuum damage context. It is shown that the enhanced models allow for the propagation of waves in the softening zone, in contrast to conventional damage models. For both types of enhancement wave propagation becomes dispersive. The behaviour under quasi-static loading conditions is studied numerically. Finite element simulations of a one-dimensional problem yield quite similar results.

Volume and surface rf power absorption in a helicon plasma source

Abstract: We consider the excitation and absorption of waves in a plasma cavity with parameters typical for helicon sources. rf power is shown to be transferred into the plasma via two channels. The first is realized by weakly damping helicon waves which are excited directly by the azimuthal parts of the antenna and penetrate into the bulk plasma. Electrostatic waves arising at a plasma edge owing to the linear mode conversion form the second channel. Strongly damped electrostatic waves can reach a plasma core at low magnetic fields only, while at high fields they deposit energy at the periphery of the plasma column. A principal fraction of the rf power is transferred into the plasma via the electrostatic channel, and so the power input turns out to be volume at low magnetic fields and surface at high fields. An enhanced volume input is possible at high fields in special anti-resonance regimes when the excitation of the electrostatic wave is suppressed. The effective collision frequency is introduced to describe effective damping of helicon waves arising due to their conversion into electrostatic waves. The results obtained permit explanation of both measured field profiles and the high absorption efficiency in helicon sources.

Wave propagation in anisotropic, saturated porous media: Plane-wave theory and numerical simulation

Abstract: Porous media are anisotropic due to bedding, compaction, and the presence of aligned microcracks and fractures. Here, it is assumed that the skeleton (and not the solid itself) is anisotropic. The rheological model also includes anisotropic tortuosity and permeability. The poroelastic equations are based on a transversely isotropic extension of Biot’s theory, and the problem is of plane strain type, i.e., two dimensional, describing qP−qS propagation. In the high‐frequency case, the (two) viscodynamic operators are approximated by Zener relaxation functions that allow a closed differential formulation of Biot’s equation of motion. A plane‐wave analysis derives expressions for the slowness, attenuation, and energy velocity vectors, and quality factor for homogeneous viscoelastic waves. The slow wave shows an anomalous polarization behavior. In particular, when the medium is strongly anisotropic the polarization is quasishear and the wave presents cuspidal triangles. Anisotropic tortuosity affects mainly th...

Some Applications of the Homogenization Theory

Abstract: Publisher Summary This chapter describes some applications of the homogenization theory. The basic idea of the theory of homogenization has been employed for a long time. In the theory of wave propagation over slowly varying media, the familiar ray theory (geometrical optics approximation) is one such example. There, the method of multiple scales is employed to average over the locally periodic waves and find the slow variation of the wave envelope. Seepage through a porous media is one of the first examples to which the method of homogenization was applied. It is a good example to explain the role of physical scales and the mathematical procedure for three-dimensional problems. Furthermore, it can be used to illustrate the derivation of many properties of the constitutive coefficients. Examples of applications are particularly rich in the mechanics of composite media. The obvious example is to determine the relations between stresses and strains in a fiber-reinforced material. The problem of sound propagation through a liquid populated sparsely by bubbles is another interesting application of homogenization theory. The main objective is to find an effective equation for the propagation of sound whose wavelength is much greater than the bubble spacing, which is, in turn, much greater than the bubble radius.

Nonstationary Analysis of the Directional Properties of Propagating Waves

Abstract: It is proposed that the sea surface be studied in a way that takes into account the observed groupiness of wind-generated waves A new method of analysis to study the directional properties of the surface is developed It is demonstrated that this method, based on wavelet transforms, allows the instantaneous wave propagation directions at various frequencies to be estimated Furthermore, the approach is shown to yield wavenumber spectra directly–-a result of particular importance to such pursuits as remote sensing, gas transfer, and air-sea coupling

Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity

Abstract: This study presents computations and analysis of the dynamics of reentrant spiral waves in a realistic model of cardiac electrical activity, incorporating the Beeler–Reuter equations into a two‐dimensional cable model. In this medium, spiral waves spontaneously break up, but may be stabilized by shortening the excitation pulse duration through an acceleration of the dynamics of the calcium current. We describe the breakup of reentrant waves based on the presence of slow recovery fronts within the medium. This concept is introduced using examples from pulse circulation around a ring and extended to two‐dimensional propagation. We define properties of the restitution and dispersion relations that are associated with slow recovery fronts and promote spiral breakup. The role of slow recovery fronts is illustrated with concrete examples from numerical simulations.

Acoustic touch position sensor using higher order horizontally polarized shear wave propagation

Abstract: An acoustic wave touch position sensor in which a transducer (14) coupled to a substrate (10) imparts a surface acoustic wave, into the substrate (10) for propagation along a first axis. A reflecive array (28, 34, 30, 36) having selective reflection characteristics for various wave propagation modes is disposed along the first axis to create a higher order horizontally polarized shear wave having an order greater than zero perpendicular to the axis, so that a touch surface (40) of the substrate (10) is imparted with shear wave energy. This energy may be partially absorbed, attenuated or perturbed by an object touching the substrate (10), to create a modified waveform having a characteristic indicative of the axial displacement and/or contact condition of the object with the substrate (10).

SBR image approach for radio wave propagation in tunnels with and without traffic

Abstract: We propose a deterministic approach to model the radio propagation channels in tunnels with and without traffic. This technique applies the modified shooting and bouncing ray (SBR) method to find equivalent sources (images) in each launched ray tube and sums the receiving complex amplitude contributed by all images coherently. In addition, the vector effective antenna height (VEH) is introduced to consider the polarization-coupling effect resulting from the shape of the tunnels. We verify this approach by comparing the numerical results in two canonical examples where closed-form solutions exist. The good agreement indicates that our method can provide a good approximation of high-frequency radio propagation inside tunnels where reflection is dominant. We show that the propagation loss in tunnels can vary considerably according to the tunnel shapes and the traffic inside them. From the results we also find a "focusing" effect, which makes the power received in an arched tunnel higher than that in a rectangular tunnel. Besides, the deep fading that appears in a rectangular tunnel is absent in an arched tunnel. The major effect of the traffic is observed to be the fast fading due to the reflection/obstruction of vehicles. Additional considerations, such as time delay, wall roughness, and wedge diffraction of radio wave propagation in tunnels are left for future studies.

Electron acceleration by inertial Alfvén waves

Abstract: Alfven waves reflected by the ionosphere and by inhomogeneities in the Alfven speed can develop an oscillating parallel electric field when electron inertial effects are included. These waves, which have wavelengths of the order of an Earth radius, can develop a coherent structure spanning distances of several Earth radii along geomagnetic field lines. This system has characteristic frequencies in the range of 1 Hz and can exhibit electric fields capable of accelerating electrons in several senses: via Landua resonance, bounce or transit time resonance as discussed by Andre and Eliasson or through the effective potential drop which appears when the transit time of the electrons is much smaller than the wave period, so that the electric fields appear effectively static. A time-dependent model of wave propagation is developed which represents inertial Alfven wave propagation along auroral field lines. The disturbance is modeled as it travels earthward, experiences partial reflections in regions of rapid variation, and finally reflects off a conducting ionosphere to continue propagating antiearthward. The wave experiences partial trapping by the ionospheric and the Alfven speed peaks discussed earlier by Polyakov and Rapoport and Trakhtengerts and Feldstein and later by Lysak. Results of the wave simulation and an accompanyingmore » test particle simulation are presented, which indicate that inertial Alfven waves are a possible mechanism for generating electron conic distributions and field-aligned particle precipitation. The model incorporates conservation of energy by allowing electrons to affect the wave via Landau damping, which appears to enhance the effect of the interactions which heat electron populations. 22 refs., 14 figs.« less

Numerical Modeling of Wave Breaking Induced by Fixed or Moving Boundaries

Abstract: 374 Abstract In this paper, several numerical aspects of an existing model for fully nonlinear waves are improved and validated to study ware breaking due to shoaling over a gentle plane slope and wave breaking induced by a moving lateral boundary. The model is based on fully nonlinear potential flow theory and combines a higher-order Boundary Element Method (BEM) for solving Laplace's equation at a given time and Lagrangian Taylor expansions for the time updating of the free surface position and potential. An improved numerical treatment of the boundary conditions at the intersection between moving lateral boundaries and the free surface (corner) is implemented and tested in the model, and the free surface interpolation method is also improved to better model highly curved regions of the free surface that occur in breaking waves. Finally, a node regridding technique is introduced to improve the resolution of the solution dose to moving boundaries and in breaker jets. Examples are presented for solitary wave propagation, shoaling, and breaking over a 1:35 slope and for wave breaking induced by a moving vertical boundary. Using the new methods, both resolution and extent of computations are significantly improved compared to the earlier model, for similar computational efforts. In all cases computations can be carried out up to impact of the breaker jets on the free surface.

Stationary magnetic shear reversal experiments in Tore Supra

Abstract: Stable and stationary states with hollow current density profiles have been achieved in Tore Supra with lower hybrid current drive (LHCD) during reduced toroidal magnetic field operation and in weak LH absorption regimes. For these plasma conditions, off-axis LH power deposition profiles are obtained in a reproducible manner when the internal LH caustics prevent central absorption of the waves. In the multipass LH wave propagation regime, the validity of the statistical treatment of stochastic wave diffusion is shown both theoretically and experimentally. When a large fraction of the plasma current (above 50%) is non-inductively sustained by the LH waves, the magnetic shear is reversed in the plasma core, i.e. inside a normalized plasma radius of the order of 0.4. The resulting hollow current density profiles have led to an enhancement of the total electron thermal energy content, up to a factor of 1.6 compared with L-mode discharges. The confinement improvement is attributed to a strong reduction of the electron thermal diffusivity in the central reversed shear region, nearly down to its neoclassical level.