Showing papers on "Wave propagation published in 1994"

Electromagnetic Waves in Chiral and Bi-Isotropic Media

Abstract: For scientists, research engineers, physicists and postgraduate students, this work introduces the essential aspects of electromagnetic waves in chiral and bi-isotropic media, to give the practical working knowledge necessary for new application development. It includes sections on effective methods of measurement, how chiral and BI media affect electromagnetic fields and wave propagation, and how to apply the theory to basic problems in waveguide, antenna and scattering analysis.

Traveling wave solutions of parabolic systems

Abstract: Part I. Stationary waves: Scalar equation Leray-Schauder degree Existence of waves Structure of the spectrum Stability and approach to a wave Part II. Bifurcation of waves: Bifurcation of nonstationary modes of wave propagation Mathematical proofs Part III. Waves in chemical kinetics and combustion: Waves in chemical kinetics Combustion waves with complex kinetics Estimates and asymptotics of the speed of combustion waves Asymptotic and approximate analytical methods in combustion problems (supplement) Bibliography.

Numerical methods for shallow-water flow

Abstract: Preface. 1. Shallow-water flows. 2. Equations. 3. Some properties. 4. Behaviour of solutions. 5. Boundary conditions. 6. Discretization in space. 7. Effect of space discretization on wave propagation. 8. Time integration methods. 9. Effects of time discretization on wave propagation. 10. Numerical treatment of boundary conditions. 11. Three-dimensional shallow-water flow. List of notations. References. Index.

On the Wave Theory in Heat Conduction

Abstract: This work contains three major components: a thorough review on the research emphasizing engineering applications of the thermal wave theory, special features in thermal wave propagation, and the thermal wave model in relation to the microscopic two-step model. For the sake of convenience, the research works are classified according to their individual emphases. Special features in thermal wave propagation include the sharp wavefront and rate effects, the thermal shock phenomenon, the thermal resonance phenomenon, and reflections and refractions of thermal waves across a material interface. By employing the dual-phase-lag concept, we show that the energy equation may be reduced to that governing the heat transport through the metal lattice in the microscopic two-step model

Electrical alternans and spiral wave breakup in cardiac tissue.

Abstract: This paper reports the results of a theoretical investigation of spiral wave breakup in model equations of action potential propagation in cardiac tissue. A general formulation of these equations is described in which arbitrary experimentally determined restitution and dispersion curves can in principle be fitted. Spiral wave behavior is studied in two-dimension as a function of a parameter Re which controls the steepness of the restitution curve at short diastolic intervals. Spiral breakup is found to occur when the minimum period T(min), below which a periodically stimulated tissue exhibits alternans in action potential duration, exceeds by a finite amount the spiral rotation period T(S). At this point, oscillations in action potential duration are of sufficiently large amplitude to cause a spontaneous conduction block to form along the wavefront. The latter occurs closer to the initiation point of reentry (spiral tip) with increasing steepness and, hence, in smaller tissue sizes. Spiral breakup leads to a spatially disorganized wave activity which is always transient, except for tissues larger than some minimum size and within a very narrow range of Re which increases with dispersion.

Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function.

Abstract: Motivated by problems in scanning near-field optical microscopy, we discuss light propagation in circular dielectric waveguides with finite aluminum cladding. In order to understand the origin of the different solutions, optical modes are first investigated for the dielectric waveguide with infinite aluminum cladding and for the aluminum cylinder. For aluminum a plasma dispersion law is assumed, leading to complex dielectric constants with negative real parts and to generally complex propagation constants. The dependence of the dispersion on the geometry and on the frequency is discussed for the various kinds of modes. We find that the existence of most of the modes is limited to certain frequencies and geometries, i.e., the solutions have a cutoff in the complex propagation constant plane. Contrary to dielectric waveguide theory, where cutoff describes the abrupt transition from propagating to evanescent modes, no other solution is generated when cutoff of a mode is reached. Surface modes and other kinds of modes, such as guided or bulk modes, can either couple between each other or transform into each other.

Dynamics and Response of Polymer-Coated Surface Acoustic Wave Devices: Effect of Viscoelastic Properties and Film Resonance

Abstract: The response of polymer-coated surface acoustic wave (SAW) devices to temperature changes and polymer vapor absorption is examined. A perturbational approach is used to relate velocity and attenuation responses to film translational and strain modes generated by the SAW. Two distinct regimes of film behavior arise, causing different SAW responses. For glassy films, displacement is nearly uniform across the film thickness, varying only in the direction of propagation. A model developed to predict velocity and attenuation in this regime (model 1), reduces to the familiar Tiersten (Wohltjen) equation for purely elastic films. For elastomeric (rubbery) films, inertial effects cause a phase lag to occur across the film for shear displacements. A model to account for these cross-film displacement gradients (model 2) predicts a characteristic resonant response when the film phase shift reaches n[pi]/2, where n is an odd integer. These model predictions are compared with measured responses from polyisobutylene-coated SAW devices as temperature is varied and during exposure to high vapor concentrations. 48 refs., 15 figs., 6 tabs.

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract: The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering. The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific s...

Tidal propagation in strongly convergent channels

Abstract: Simple first- and second-order analytic solutions, which diverge markedly from classical views of cooscillating tides, are derived for tidal propagation in strongly convergent channels. Theoretical predictions compare well with observations from typical examples of shallow, “funnel-shaped” tidal estuaries. A scaling of the governing equations appropriate to these channels indicates that at first order, gradients in cross-sectional area dominate velocity gradients in the continuity equation and the friction term dominates acceleration in the momentum equation. Finite amplitude effects, velocity gradients due to wave propagation, and local acceleration enter the equations at second order. Applying this scaling, the first-order governing equation becomes a first-order wave equation, which is inconsistent with the presence of a reflected wave. The solution is of constant amplitude and has a phase speed near the frictionless wave speed, like a classical progressive wave, yet velocity leads elevation by 90°, like a classical standing wave. The second-order solution at the dominant frequency is also a unidirectional wave; however, its amplitude is exponentially modulated. If inertia is finite and convergence is strong, amplitude increases along channel, whereas if inertia is weak and convergence is limited, amplitude decays. Compact solutions for second-order tidal harmonics quantify the partially canceling effects of (1) time variations in channel depth, which slow the propagation of low water, and (2) time variations in channel width, which slow the propagation of high water. Finally, it is suggested that phase speed, along-channel amplitude growth, and tidal harmonics in strongly convergent channels are all linked by morphodynamic feedback.

Active and nonlinear wave propagation devices in ultrafast electronics and optoelectronics

Abstract: We describe active and nonlinear wave propagation devices for generation and detection of (sub)millimeter wave and (sub)picosecond signals. Shock-wave nonlinear transmission lines (NLTL's) generate /spl sim/4-V step functions with less than 0.7-ps fall times. NLTL-gated sampling circuits for signal measurement have attained over 700-GHz bandwidth. Soliton propagation on NLTL's is used for picosecond impulse generation and broadband millimeter-wave frequency multiplication. Picosecond pulses can also be generated on traveling-wave structures loaded by resonant tunneling diodes. Applications include integration of photodetectors with sampling circuits for picosecond optical waveform measurements and instrumentation for millimeter-wave waveform and network (circuit) measurements both on-wafer and in free space. General properties of linear and nonlinear distributed devices and circuits are reviewed, including gain-bandwidth limits, dispersive and nondispersive propagation, shock-wave formation, and soliton propagation. >

Foundations of Anisotropy for Exploration Seismics

Abstract: Fundamentals tools for the description of wave propagation under piecewise homogeneous anisotropic conditions elasticity elastic waves - the dispersion relation and some generalities about slowness and wave surfaces stability constraints one-parameter expressions for the slowness surfaces of transversely isotropic media and the slowness curves in the planes of symmetry of orthorhombic media one-parameter expressions for the wave curves in the symmetry planes of orthorhombic media squared slowness surfaces and squared slowness curves causes of anisotropy - periodic fine layering anisotropy and seismic exploration eigentensors of the elastic tensor and their relationship with material symmetry.

Solitary wave dynamics of film flows

Abstract: The development and interaction of solitary wave pulses is critical to understanding wavy film flows on an inclined (or vertical) surface. Sufficiently far downstream, the wave structure consists of a generally irregular sequence of solitary waves independent of the conditions at the inlet. The velocity of periodic solitary waves is found to depend on their frequency and amplitude. Larger pulses travel faster; this property, plus a strong inelasticity, causes larger pulses to absorb others during interactions, leaving a nearly flat interface behind. These wave interactions lead to the production of solitary wave trains from periodic small amplitude waves. The spacings between solitary waves can be irregular for several different reasons, including the amplification of ambient noise, and the interaction process itself. On the other hand, this irregularity is suppressed by the addition of periodic forcing.

Nonlinear Water Waves

Abstract: Basic Equations of Motion of Inviscid and Viscous Fluids. The Theory of Surface Waves on Water. Transient Wave Motions in an Inviscid Fluid. Nonlinear Shallow Water Waves and Solitons. Ship Waves and Wave Resistance. NonlinearDiffraction of Water Waves. The Theory of Nonlinear Dispersive Waves. Nonlinear Instability of Dispersive Waves with Applications to Water Waves. Bibliography. Index.

The photonic band edge optical diode

Abstract: Using numerical methods, we study pulse propagation near the band edge of a one‐dimensional photonic band gap material with a spatial gradiation in the linear refractive index, together with a nonlinear medium response. We find that such a structure can result in unidirectional pulse propagation. That is, the field will be transmitted for, say, a left‐to‐right direction of propagation, while for right‐to‐left nearly complete reflection occurs. This behavior constitutes the operational mechanism for a passive optical diode.

Equation of state and wave propagation in hysteretic nonlinear elastic materials

Abstract: Heterogeneous materials, such as rock, have extreme nonlinear elastic behavior (the coefficient characterizing cubic anharmonicity is orders of magnitude greater than that of homogeneous materials) and striking hysteretic behavior (the stress-strain equation of state has discrete memory). A model of these materials, taking their macroscopic elastic properties to result from many mesoscopic hysteretic elastic units, is developed. The Preisach-Mayergoyz description of hysteretic systems and effective medium theory are combined to find the quasistatic stress-strain equation of state, the quasistatic modulus-stress relationship, and the dynamic modulus-stress relationship. Hysteresis with discrete memory is inherent in all three relationships. The dynamic modulus-stress relationship is characterized and used as input to the equation of motion for nonlinear elastic wave propagation. This equation of motion is examined for one-dimensional propagation using a Green function method. The out-of-phase component of the dynamic modulus due to hysteresis is found to be responsible for the generation of odd harmonics and to determine the amplitude of the nonlinear attenuation.

Solitary waves due to χ (2) :χ (2) cascading

Abstract: Solitary waves in materials with a cascaded χ(2):χ(2) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the χ(2):χ(2) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrodinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrodinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrodinger-equation solitons, which are a two-parameter family of solutions. Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.

Fundamentals of Acoustic Field Theory and Space-Time Signal Processing

Abstract: Part I ACOUSTIC FIELD THEORY: The Linear Wave Equation and Fundamental Acoustical Quantities: Equations of Motion. Equation of Continuity. Equation of State and the Speed of Sound. Derivation of the Linear Wave Equation. Time-Average Intensity Vector and Time-Average Power. Sound-Pressure Level, Source Level, Transmission Loss, and Sound-Intensity Level. Problems. Appendices. Bibliography. Wave Propagation in the Rectangular Coordinate System: Solution of the Linear Three-Dimensional Homogeneous Wave Equation. Free-Space Propagation. Reflection and Transmission Coefficients. The Rectangular Cavity. Waveguide with Rectangular Cross-Sectional Area. The Time-Independent Free-Space Green's Function. Solution of the Linear Three-Dimensional Inhomogeneous Wave Equation with Arbitrary Source Distribution. Integral Representations of the Time-Independent Free-Space Green's Function in Rectangular Coordinates. Problems. Appendices. Bibliography. Wave Propagation in the Cylindrical Coordinate System: Solution of the Linear Three-Dimensional Homogeneous Wave Equation. Free-Space Propagation. The Cylindrical Cavity. Waveguide with Circular Cross-Sectional Area. Scattering by a Cylinder. Integral Representations of the Time-Independent Free-Space Green's Function in Cylindrical Coordinates. Reflection and Transmission of Spherical Waves at Planar Boundaries. Waveguide Models of the Ocean: Normal Modes. Waveguide Model of the Ocean: Full-Wave Solution. Problems. Appendices. Bibliography. Wave Propagation in the Spherical Coordinate System: Solution of the Linear Three-Dimensional Homogeneous Wave Equation. Free-Space Propagation. The Spherical Cavity. Scattering by a Sphere. Problems. Bibliography. Wave Propagation in Inhomogeneous Media: The WKB Approximation. Ray Acoustics. The Parabolic Equation Approximation. Problems. Appendices. Bibliography. Part II SPACE-TIME SIGNAL PROCESSING: Complex Aperture Theory: Coupling Transmitted and Received Electrical Signals to the Fluid Medium. Near-Field and Far-Field Directivity Functions of Volume Apertures. Linear Apertures and Far-Field Directivity Functions. Linear Apertures and Near-Field Directivity Functions. Planar Apertures and Far-Field Directivity Functions. Planar Apertures and Near-Field Directivity Functions. Directivity Index. Problems. Appendix. Bibliography. Array Theory: Linear Arrays and Far-Field Directivity Functions. Linear Arrays and Near-Field Directivity Functions. Array Gain. Planar Arrays and Far-Field Directivity Functions. Planar Arrays and Near-Field Directivity Functions. Volume Arrays and Far-Field Directivity Functions. Problems. Bibliography. Signal Processing: FFT Beamforming for Planar Arrays. Complex Envelopes. The Auto-Ambiguity Function. Time Compression/Stretch Factor, Time Delay, and Doppler Shift Expressions. Problems. Appendix. Bibliography. Fundamentals of Linear, Time-Variant, Space-Variant Filters and the Propagation of Small-Amplitude Acoustic Signals: Impulse Response and Transfer Function. Bifrequency Function. Output Frequency and Angular Spectrum. Coupling Equations and Pulse Propagation. Bibliography. SYMBOLS AND ABBREVIATIONS. INDEX.

Small amplitude theory of Richtmyer–Meshkov instability

Abstract: This paper presents a new analysis of small amplitude Richtmyer–Meshkov instability. The linear theory for the case of reflected rarefaction waves, a problem not treated in previous work, is formulated and numerically solved. This paper also carries out a systematic comparison of Richtmyer’s impulsive model to the small amplitude theory, which has identified domains of agreement as well as disagreement between the two. This comparison includes both the reflected shock and reflected rarefaction cases. Additional key results include the formulation of criteria determining the reflected wave type in terms of preshocked quantities, identification of parameter regimes corresponding to total transmission of the incident wave, discussion of an instability associated with a rarefaction wave, investigation of phase inversions and the related phenomenon of freeze‐out, and study of the sensitivity of the numerical solutions to initial conditions.

Relativistic self-focusing and channel formation in laser-plasma interactions.

Abstract: Nonparaxial wave propagation theory is used to study relativistic self-focusing and channel formation in the propagation of an intense, short-pulse laser through an underdense plasma. The stable on-axis channel predicted by paraxial theory is found to break up into on-axis channel remnants and off-axis rings.

Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method

Abstract: In this paper a system of equations for wide-angle one-way elastic wave propagation in arbitrarily heterogeneous media is formulated in both the space and wavenumber domains using elastic Rayleigh integrals and local elastic Born scattering theory. The wavenumber domain formulation leads to compact solutions to one-way propagation and scattering problems. It is shown that wide-angle scattering in heterogeneous elastic media cannot be formulated as passage through regular phase-screens, since the interaction between the incident wavefield and the heterogeneities is not local in both the space domain and the wavenumber domain. Our more generally valid formulation is called the “thin-slab” formulation. After applying the small-angle approximation, the thin-slab effect degenerates to that of an elastic complex-screen (or “generalized phase-screen”). Compared with scalar phase-screen, the elastic complex-screen has the following features. (1) For P-P scattering and S-S in-plane scattering, the elastic complex-screen acts as two separate scalar phase-screens for P and S waves respectively. The phase distortions are determined by the P and S wave velocity perturbations respectively. (2) For P-S and S-P conversions, the screen is no longer a pure phase-screen and becomes complex (with both phase and amplitude terms); both conversions are determined by the shear wave velocity perturbation and the shear modulus perturbation. For Poisson solids the S wave velocity perturbation plays a major role. In the special case of α0 = 2β0, S wave velocity perturbation becomes the only factor for both conversions. (3) For the cross-coupling between in-plane S waves and off-plane S waves, only the shear modulus perturbation δμ has influence in the thin-slab formulation. For the complex-screen method the cross-coupling term is neglected because it is a higher order small quantity for small-angle scattering. Relative to prior derivations of vector phase-screen method, our method can correctly treat the conversion between P and S waves and the cross-coupling between differently polarized S waves. A comparison with solutions from three-dimensional finite difference and exact solutions using eigenfunction expansion is made for two special cases. One is for a solid sphere with only P velocity perturbation; the other is with only S velocity perturbation. The Elastic complex-screen method generally agrees well with the three-dimensional finite difference method and the exact solutions. In the limiting case of scalar waves, the derivation in this paper leads to a more generally valid new method, namely, a scalar thin-slab method. When making the small-angle approximation to the interaction term while keeping the propagation term unchanged, the thin-slab method approaches the currently available scalar wide-angle phase-screen method.

Introduction to elastic wave propagation

Abstract: Earthquakes are detected and studied by measuring the waves they create. Waves are transmitted through the Earth to detect oil and gas deposits and to study the Earth's geological structure. Properties of materials are determined by measuring the behaviour of waves transmitted through them. In recent years, elastic waves transmitted through the human body have been used for medical diagnosis and therapy. Many students and professionals in various branches of engineering encounter problems requiring an understanding of elastic waves. In this book, they will find the basic concepts and methods of the theory of wave propagation in elastic materials. One-dimensional waves, transient waves and harmonic waves including reflections of plane waves at interfaces. Rayleigh waves, waves in elastic layers and in layered materials are discussed. Analytical methods in nonlinear wave propagation are presented. This book includes exercises with solutions and many explanatory figures.

A Spectral Wave Model for the Coastal Zone

Abstract: Spectral wave models that represent the evolution of the waves on a grid superior in several respects to conventional wave ray models. Spectral models on a grid have been developed for applications in the deep ocean and for shelf seas. However, they are not economically feasible in coastal waters due to numerical limitations. We present the first step in implementation of a version that does not have these limitations. we remove time as an independent variable (reducing the computations to stationery or quasi-stationery computations, which is proper considering the residence time of the waves in the area) and we use an unconditionally stable propagation scheme. The propagation scheme is successfully tested in academic cases, including a case with complete reversal of wave direction. As a preliminary test of propagation in an observed field case, computations are carried out for waves travelling across and around an extended (5 km) shoal. With a limited representation of the bottom induced processes (bottom friction and surf dissipation), realistic results are obtained for the significant wave height. This test also shows the relevance of the planned implementation of the wave-wave interactions (in particular grid interactions) and wind generation. The model is planned to be optionally second-or-third-generation (with or without predefined spectral constraints).

Shoaling of Solitary Waves on Plane Beaches

Abstract: Shoaling of solitary waves on both gentle (1:35) and steeper slopes ( 1:6.50) is analyzed up to breaking using both a fully nonlinear wave model and high-accuracy laboratory experiments. For the mildest slope, close agreement is obtained between both approaches up to breaking, where waves become very asymmetric and breaking indices reach almost twice the value for the largest stable symmetric wave. Bottom friction does not seem to affect the results at all. Wave celerity decreases during shoaling and slightly increases before breaking. At breaking, the crest particle velocity is almost horizontal and reaches 90% of the crest celerity, which is two to three times larger than the bottom velocity. The nonlinear shallow water equations and the Boussinesq approximation both fail to predict these results. Finally, shoaling rates for various wave heights and bottom slopes differ from the predictions of Green's or Boussinesq shoaling laws. On the mildest slope, shoaling rates roughly follow a "two-zone" model proposed earlier but on steeper slopes reflection becomes significant and wave heights change little during shoaling.

Dispersion and wave coupling in inhomogeneous MHD waveguides

Abstract: The propagation of the fast mode is considered in nonuniform waveguides. We show how the natural dispersion inherent in a waveguide will select waveguide modes with a small wavenumber (ky) along the guide to remain near a localized source region of fast mode energy. It is these modes that are shown to have a coherent periodic time dependence over many cycles that are suitable for driving observable Alfven resonances (magnetic pulsations). We expect the frequencies of Alfven resonances to be very close to the eigenfrequencies of waveguide modes with ky = 0.

Geometrical Theory of Diffraction

Abstract: Details the ideas underlying geometrical theory of diffraction (GTD) along with its relationships with other EM theories.

Low-Frequency Oscillations in Radiative-Convective Systems

Abstract: Although eastward propagation has long been considered one of the essential features of the Madden-Julian waves, recent observations have revealed a stationary or quasi-stationary component in the oscillations, particularly in measures of the diabatic heating rate. Wave-CISK theories of the low-frequency oscillations have struggled to explain the observed period and vertical structure of the waves. On the other hand, theoretical and numerical studies have shown that low-frequency waves strongly resembling the observed oscillations can be excited by specified low-frequency oscillations of the convective heating. A problem with the latter set of theories is that the cause of the oscillatory heating has not been satisfactorily explained. It is proposed here that the observed low-frequency wave motions are the response to forcing by an essentially stationary, self-excited oscillating heat source that is produced by nonlinear interactions among radiation, cumulus convection, and the surface fluxes of sensible heat and moisture. Feedback of the large-scale motions on the latent heating is not required. Results from two very different one-dimensional models are presented to support this hypothesis. The physical processes included in the models are essentially the same, that is, radiation, cumulus convection, and the surface fluxes of sensible heat and moisture; the first model is highly simplified, however, while the second includes relatively sophisticated parameterizations of all the relevant physical processes. Results from both models show low-frequency oscillations of the latent heating, temperature, and moisture. Experiments show that the oscillations are favored by a warm sea surface and weak surface wind speeds, consistent with the observed conditions over the Indian Ocean and the tropical western Pacific Ocean.

Elastic waves in plates with periodically placed inclusions

Abstract: We calculated the frequency ω versus the wave vector K for elastic waves propagating in both thick and thin plates consisting of solid inclusions placed periodically in the host material. We were particularly interested in the possible creation of spectral gaps (stop bands) in all directions of propagation for bending waves. We found that Mo, Fe, steel, or Pb inclusions forming a two dimensional hexagonal lattice in a Lucite host give rise to spectral gaps.