Showing papers on "Wave propagation published in 2000"

Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces

Abstract: Some materials may naturally form discontinuities such as cracks as a result of deformation. As an aid to the modeling of such materials, a new framework for the basic equations of continuum mechanics, called the "peridynamic" formulation, is proposed. The propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived. Material stability and its connection with wave propagation is investigated. It is demonstrated by an example that the reformulated approach permits the solution of fracture problems using the same equations either on or off the crack surface or crack tip. This is an advantage for modeling problems in which the location of a crack is not known in advance.

Gain-assisted superluminal light propagation

Abstract: Einstein's theory of special relativity and the principle of causality imply that the speed of any moving object cannot exceed that of light in a vacuum (c) Nevertheless, there exist various proposals for observing faster-than-c propagation of light pulses, using anomalous dispersion near an absorption line, nonlinear and linear gain lines, or tunnelling barriers However, in all previous experimental demonstrations, the light pulses experienced either very large absorption or severe reshaping, resulting in controversies over the interpretation Here we use gain-assisted linear anomalous dispersion to demonstrate superluminal light propagation in atomic caesium gas The group velocity of a laser pulse in this region exceeds c and can even become negative, while the shape of the pulse is preserved We measure a group-velocity index of n(g) = -310(+/- 5); in practice, this means that a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region

Fundamentals of Physical Acoustics

Abstract: Detailed Development of the Acoustical Wave Equation. Reflection and Transmission of Normally Incident Plane Waves of Arbitrary Waveform. Normal Incidence Continued: Steady-State Analysis. Transmission Phenomena: Oblique Incidence. Normal Modes in Cartesian Coordinates: Strings, Membranes, Rooms, and Rectangular Waveguides. Horns. Propagation in Stratified Media. Propagation in Dissipative Fluids: Absorption and Dispersion. Spherical Waves. Cylindrical Waves. Waveguides. Radiation from a Baffled Piston. Diffraction. Arrays. Appendices. Index.

Parabolic Equation Methods for Electromagnetic Wave Propagation

Abstract: This book is the first to present the application of parabolic equation methods in electromagnetic wave propagation. These powerful numerical techniques have become the dominant tool for assessing clear-air and terrain effects on radiowave propagation and are growing increasingly popular for solving scattering problems. The book gives the mathematical background to parabolic equation modelling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar cross section computation. This book will prove useful to scientists and engineers who require accurate assessment of diffraction and ducting on radio and radar systems. Its self-contained approach should also make it particularly suitable for graduate students and other researchers interested in radiowave propagation scattering.

Boussinesq modeling of wave transformation, breaking, and runup. ii: 2d

Abstract: In this paper, we focus on the implementation and verification of an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions The time-domain numerical model is based on the fully nonlinear Boussinesq equations As described in Part I of this two-part paper, the energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves Wave runup on the beach is simulated using a permeable-seabed technique We apply the model to simulate two laboratory experiments in large wave basins They are wave transformation and breaking over a submerged circular shoal and solitary wave runup on a conical island Satisfactory agreement is found between the numerical results and the laboratory measurements

An acoustic wave equation for anisotropic media

Abstract: A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Abstract: A number of physical phenomena are described by nonlinear hyperbolic equations Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of hyperbolic systems Construction of such methods for systems more complicated than the Euler gas dynamic equations requires the investigation of existence and uniqueness of the self-similar solutions to be used in the development of discontinuity-capturing high-resolution numerical methods This frequently necessitates the study of the behavior of discontinuities under vanishing viscosity and dispersion We discuss these problems in the application to the magnetohydrodynamic equations, nonlinear waves in elastic media, and electromagnetic wave propagation in magnetics

Characterization of intertidal flat hydrodynamics

Abstract: The paper reviews the different physical forcings that control tidal flat hydrodynamics. Tidal propagation and cross-shore or long-shore currents, tidal asymmetry, wind-induced circulation, wave propagation and drainage processes are successively considered. Some simple methods are described for estimating cross-shore currents and wave-induced bottom shear stresses, and the results obtained are compared to field measurements on three contrasted sites in Europe. In particular the cross-shore current is shown uniform in the lower part of the flat, and decreasing towards the shore. Bottom friction-induced wave attenuation is simply formulated on gently sloping beds, leading to a maximum wave height that a flat can experience; it is proportional to the water height according to the ratio between the slope and the wave friction factor. The maximum related shear stress occurs at high water and is also proportional to the water depth. Maximum tidal velocities are very similar in the three sites where bottom sediment is muddy, suggesting a relationship between physical stresses and sediment characteristics. The consequences of physical forcings on sediment transport are listed. The bottom shear stress is suggested as the relevant parameter for comparing tidal and wave effects. In general, tide induces onshore sediment transport, whereas waves and drainage favour offshore transport. The processes leading to a possible tidal equilibrium profile are analysed: they involve the intrinsic asymmetry that favours net deposition at high water, and an ebb dominance generated by the resulting bottom profile convexity. Eroding waves are likely to upset such a balance; this equilibrium then reduces to a trend for the system.

Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment

Abstract: We extend the multiple-scattering theory for elastic waves by taking into account the full vector character. The formalism for both the band structure calculation and the reflection and transmission calculations for finite slabs is presented. The latter is based on a double-layer scheme which obtains the reflection and transmission matrix elements for the multilayer slab from those of a single layer. As a demonstration of applications of the formalism, we calculate the band structures of elastic waves propagating in a three-dimensional periodic arrangement of spherical particles and voids, as well as the transmission coefficients through finite slabs. In contrast with the plane-wave method, the multiple-scattering approach exhibits advantages in handling specialized geometries (spherical geometry in the present case). We also present a comparison between theory and ultrasound experiment for a hexagonal-close-packed array of steel balls immersed in water. Excellent agreement is obtained.

A model for longitudinal and shear wave propagation in viscoelastic media

Abstract: Relaxation models fail to predict and explain loss characteristics of many viscoelastic materials which follow a frequency power law. A model based on a time-domain statement of causality is presented that describes observed power-law behavior of many viscoelastic materials. A Hooke’s law is derived from power-law loss characteristics; it reduces to the Hooke’s law for the Voigt model for the specific case of quadratic frequency loss. Broadband loss and velocity data for both longitudinal and shear elastic types of waves agree well with predictions. These acoustic loss models are compared to theories for loss mechanisms in dielectrics based on isolated polar molecules and cooperative interactions.

Observation of superluminal behaviors in wave propagation

Abstract: The possibility of observing superluminal behavior in the propagation of localized microwaves over distances of tens of wavelengths is experimentally demonstrated. These types of waves, better than the evanescent modes of tunneling, can contribute to answering the question on the luminal limit of the signal velocity.

Communication through a diffusive medium: coherence and capacity

Abstract: Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.

Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials.

Abstract: It is shown, for the first time, that the transmittivity of wave guides created as rectilinear defects in periodic elastic band-gap materials oscillates as a function of frequency. The results are obtained using the finite difference time domain method for elastic waves propagating in two-dimensional inhomogeneous media. The oscillations of the transmittivity are due to the richness of modes in the elastic systems and, mainly, due to the periodicity of the potential in the direction of the wave propagation. Results are presented for a periodic array of Pb and Ag cylinders inserted in an epoxy host, as well as for Hg cylinders in an Al host.

Simulation of anisotropic wave propagation based upon a spectral element method

Abstract: We introduce a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method. The technique solves a weak formulation of the wave equation, which is discretized using a high-order polynomial representation on a finite element mesh. For isotropic media, the spectral element method is known for its high degree of accuracy, its ability to handle complex model geometries, and its low computational cost. We show that the method can be extended to fully anisotropic media. The mass matrix obtained is diagonal by construction, which leads to a very efficient fully explicit solver. We demonstrate the accuracy of the method by comparing it against a known analytical solution for a 2-D transversely isotropic test case, and by comparing its predictions against those based upon a finite difference method for a 2-D heterogeneous, anisotropic medium. We show its generality and its flexibility by modeling wave propagation in a 3-D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.

Wave propagation near a fluid-solid interface : A spectral-element approach

Abstract: We introduce a spectral-element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments. The problem is formulated in terms of displacement in elastic regions and a velocity potential in acoustic regions. Matching between domains is implemented based upon an interface integral in the framework of an explicit prediction-multicorrection staggered time scheme. The formulation results in a mass matrix that is diagonal by construction. The scheme exhibits high accuracy for a 2-D test case with known analytical solution. The method is robust in the case of strong topography at the fluid-solid interface and is a good alternative to classical techniques, such as finite differencing.

Time-domain beam propagation method and its application to photonic crystal circuits

Abstract: A time-domain beam propagation method (BPM) based on the finite-element scheme is described for the analysis of reflections of both transverse electric and transverse magnetic polarized pulses in waveguiding structures containing arbitrarily shaped discontinuities. In order to avoid nonphysical reflections from the computational window edges, the perfectly matched layer boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first time-domain beam propagation method which can treat wide-band optical pulses. After validating this method for an optical grating with modulated refractive indexes, various photonic crystal circuit components are simulated.

Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method

Abstract: This work presents results on finite-difference time-domain (FDTD) integration of the full three dimensional elastic wave equation in nonhomogenous periodic media, for understanding the propagation and gap existence in these media. Extensive calculations are compared with plane wave expansion (PWE) data for different three dimensional systems consisting of Pb spheres in epoxy matrix forming an fcc lattice. The method of solving the wave equation provides good convergence and the agreement with the PWE method is excellent. The FDTD method, however, can handle cases such as fluids in solids which cannot be treated with the PWE method. Transmission results are presented for the case of Hg spheres in Al with fcc lattice, in order to prove the general use of the FDTD method.

A model for generating relativistic electrons in the Earth's inner magnetosphere based on gyroresonant wave-particle interactions

Abstract: During the recovery phase of a magnetic storm, fluxes of relativistic (> 1 MeV) electrons in the inner magnetosphere (3 ≤ L ≤ 6) increase to beyond prestorm levels, reaching a peak ∼4 days after the initiation of the storm. In order to account for the generation of these "killer electrons" a model is presented primarily on the basis of the stochastic acceleration of electrons by enhanced whistler mode chorus. In terms of a quasi-linear formulation a kinetic (Fokker-Planck) equation for the electron energy distribution is derived comprising an energy diffusion coefficient based on gyroresonant electron-whistler mode wave interaction and parallel wave propagation, a source term representing substorm-produced (lower-energy) seed electrons, and a loss term representing electron precipitation due to pitch angle scattering by whistler mode waves and electromagnetic ion cyclotron (EMIC) waves. Steady state solutions for the electron energy distribution are constructed and fitted to an empirically derived relativistic Maxwellian distribution for the high-energy "hard" electron population at geosynchronous orbit. If the average whistler amplitude is sufficiently large, for instance, 75-400 pT, dependent on the values of the other model parameters, and assuming a background plasma density of N 0 = 10 cm -3 outside the plasmasphere, then a good fit to the empirical distribution is obtained and corresponds to a timescale for the formation of the high-energy steady state distribution of 3-5 days. For a lower representative value of the background plasma density, N 0 = 1 cm -3, smaller whistler amplitudes, in the range 13-72 pT, can produce the high-energy distribution in the required time frame of several days. It is concluded from the model calculations that the process of stochastic acceleration by gyroresonant electron-whistler mode wave interaction in conjunction with pitch angle scattering by EMIC waves constitutes a viable mechanism for generating killer electrons during geomagnetic storms. The mechanism is expected to be particularly effective for the class of small and moderate storms possessing a long-lasting recovery phase during which many substorms occur.

Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments

Abstract: A linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed in this article. Since the grains are unbonded, it is assumed that the shear rigidity modulus of the medium is zero, implying the absence of a skeletal elastic frame. The analysis is based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave. These shearing processes act as stress-relaxation mechanisms, which tend to return the material to equilibrium after the application of a dynamic strain. The stress arising from shearing is represented as a random stick-slip process, consisting of a random succession of deterministic stress pulses. Each pulse is produced when micro-asperities on opposite surfaces of a contact slide against each other. The quantity relevant to wave propagation is the average stress from all the micro-sliding events, which is shown to be a temporal convolution between the deterministic stress, h(t), from a single event and the probability, q(t), of an event occurring between times t and t+dt. This probability is proportional to the velocity gradient normal to the tangent plane of contact between grains. The pulse shape function, h(t), is derived by treating the micro-sliding as a strain-hardening process, which yields an inverse-fractional-power-law dependence on time. Based on two convolutions, one for the stress relaxation from translational and the other from radial shearing, the Navier–Stokes equation for the granular medium is derived. In a standard way, it is split into two equations representing compressional and shear wave propagation. From these wave equations, algebraic expressions are derived for the wave speeds and attenuations as functions of the porosity and frequency. Both wave speeds exhibit weak, near-logarithmic dispersion, and the attenuations scale essentially as the first power of frequency. A test of the theory shows that it is consistent with wave speed and attenuation data acquired recently from a sandy sediment in the Gulf of Mexico during the SAX99 experiment. If dispersion is neglected, the predicted expressions for the wave speeds reduce to forms which are exactly the same as those in the empirical elastic model of a sediment proposed by Hamilton. On this basis, the concept of a “skeletal elastic frame” is interpreted as an approximate, but not equivalent, representation of the rigidity introduced by grain-to-grain interactions.

Tsunami features of solid block underwater landslides

Abstract: Near-field and far-field wave features generated by solid block underwater landslides are described qualitatively and quantitatively. The characteristic time of landslide motion and maximum near-field wave amplitude suffice to scale many of these water wave features. Criteria are provided to determine if water waves generated by underwater landslides propagate as deepwater or shallow water waves. Estimates of the dominant far-field wavelength are provided for both cases. A precise location is given for the beginning of far-field wave propagation for deepwater waves. Weakly nonlinear and dispersive effects of shallow water wave propagation are examined. Around 5% of solid block maximum kinetic energy is converted into wave energy.

Simulation of laser propagation in a turbulent atmosphere

Abstract: The split-step Fourier-transform algorithm for numerical simulation of wave propagation in a turbulent atmosphere is refined to correctly include the effects of large-scale phase fluctuations that are important for imaging problems and many beam-wave problems such as focused laser beams and beam spreading. The results of the improved algorithm are similar to the results of the traditional algorithm for the performance of coherent Doppler lidar and for plane-wave intensity statistics because the effects of large-scale turbulence are less important. The series solution for coherent Doppler lidar performance converges slowly to the results from simulation.

Solitary shock waves and other travelling waves in a general compressible hyperelastic rod

Abstract: In the literature, it has been conjectured that solitary shock waves can arise in incompressible hyperelastic rods. Recently, it has been shown that this conjecture is true. One might guess that when compressibility is taken into account, such a wave, which is both a solitary wave and a shock wave, can still arise. One of the aims of this paper is to show the existence of this interesting type of wave in general compressible hyperelastic rods and provide an analytical description. It is difficult to directly tackle the fully nonlinear rod equations. Here, by using a non–dimensionalization process and the reductive perturbation technique, we derive a new type of nonlinear dispersive equation as the model equation. We then focus on the travelling–wave solutions of this new equation. As a result, we obtain a system of ordinary differential equations. An important feature of this system is that there is a vertical singular line in the phase plane, which leads to the appearance of shock waves. By considering the equilibrium points and their relative positions to the singular line, we are able to determine all qualitatively different phase planes. Those paths in phase planes which represent physically acceptable solutions are discussed one by one. It turns out that there is a variety of travelling waves, including solitary shock waves, solitary waves, periodic shock waves, etc. Analytical expressions for all these waves are obtained. A new phenomenon is also found: a solitary wave can suddenly change into a periodic wave (with finite period). In dynamical systems, this represents a homoclinic orbit suddenly changing into a closed orbit. To the authors9 knowledge, such a bifurcation has not been found in any other dynamical systems.

Proton and electron heating by radially propagating fast magnetosonic waves

Abstract: We investigate the propagation, growth, and decay of fast magnetosonic waves in the Earth's magnetosphere which are believed to contribute to proton heating up to energies of a few hundred eV near the magnetic equator. We construct a model of the proton and electron distribution functions from spacecraft data and use the HOTRAY code to calculate the path-integrated growth and decay of the waves over a range of L shells from L = 2 to L = 7. Instability calculations show that the waves are excited at very large angles of propagation with respect to the magnetic field, ψ ≈ 89°, at the harmonics of the proton gyrofrequency ΩH+ up to the lower hybrid resonance frequency ωLHR by a proton ring distribution at energies of the order of 10 keV. As a “rule of thumb”, we find that growth is possible for ω > 30ΩH+ when the ring velocity exceeds the Alfven speed vR > vA, and for ω 2vA. For propagation in the meridian plane, waves generated just outside the plasmapause grow with large amplification as they propagate away from the Earth but eventually lose energy to plasma sheet electrons at energies of a few keV by Landau damping. The waves grow to large amplification at frequencies just below ωLHR. For inward propagation we find that waves generated just outside the plasmapause can propagate to L ≈ 2 with very little attenuation, suggesting that waves observed well inside the plasmasphere could originate from a source region just outside the plasmapause. Strong wave growth only occurs for large angles of propagation, and thus the waves are confined to within a few degrees of the magnetic equator. Waves generated near geostationary orbit and which propagate toward the Earth are absorbed by Doppler-shifted cyclotron resonance when they propagate into a region where vR < vA. Cyclotron resonant absorption causes pitch angle scattering and heating transverse to the ambient magnetic field. The amount of absorption, and hence transverse proton heating, increases significantly as the thermal proton temperature is increased up to 100 eV, suggesting a feedback process. Ray tracing shows that transverse heating of the thermal proton distribution is most likely to occur just outside the plasmapause where vA is large. Since proton ring distributions are formed during magnetic storms at ring current energies, we suggest that fast magnetosonic waves provide an additional energy loss process for ring current decay.

Transverse waves in a two-dimensional screened-coulomb crystal (Dusty plasma)

Abstract: Transverse shear waves were observed experimentally in a two-dimensional screened Coulomb crystal. They were excited by applying a chopped laser beam to a 2D dusty plasma, i.e., a monolayer of charged microspheres levitated in a plasma. Measurements of the dispersion relation reveal an acoustic, i.e., nondispersive, character over the entire range of wave numbers measured, 0.2

Breaking and broadening of internal solitary waves

Abstract: Solitary waves propagating horizontally in a stratified fluid are investigated. The fluid has a shallow layer with linear stratification and a deep layer with constant density. The investigation is both experimental and theoretical. Detailed measurements of the velocities induced by the waves are facilitated by particle tracking velocimetry (PTV) and particle image velocimetry (PIV). Particular attention is paid to the role of wave breaking which is observed in the experiments. Incipient breaking is found to take place for moderately large waves in the form of the generation of vortices in the leading part of the waves. The maximal induced fluid velocity close to the free surface is then about 80% of the wave speed, and the wave amplitude is about half of the depth of the stratified layer. Wave amplitude is defined as the maximal excursion of the stratified layer. The breaking increases in power with increasing wave amplitude. The magnitude of the induced fluid velocity in the large waves is found to be approximately bounded by the wave speed. The breaking introduces a broadening of the waves. In the experiments a maximal amplitude and speed of the waves are obtained. A theoretical fully nonlinear two-layer model is developed in parallel with the experiments. In this model the fluid motion is assumed to be steady in a frame of reference moving with the wave. The Brunt-Vaisala frequency is constant in the layer with linear stratification and zero in the other. A mathematical solution is obtained by means of integral equations. Experiments and theory show good agreement up to breaking. An approximately linear relationship between the wave speed and amplitude is found both in the theory and the experiments and also when wave breaking is observed in the latter. The upper bound of the fluid velocity and the broadening of the waves, observed in the experiments, are not predicted by the theory, however. There was always found to be excursion of the solitary waves into the layer with constant density, irrespective of the ratio between the depths of the layers.

Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation

Abstract: This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics The time-marching methods include Runge--Kutta methods, Adams--Bashforth methods, and the leapfrog method In addition, the following fully-discrete finite-difference methods are studied: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil For each method, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented The results provide a clear understanding of the relative merits of the methods compared, especially the trade-offs associated with the use of optimized methods A numerical example is given which shows that the benefits of an optimized scheme can be small if the waveform has broad spectral content