Showing papers on "Wave propagation published in 2002"

Ocean waves and oscillating systems : linear interactions including wave-energy extraction

Abstract: 1. Introduction 2. Mathematical description of oscillations 3. Interaction between oscillations and waves 4. Gravity waves on water 5. Wave-body interactions 6. Wave-energy absorption by oscillating bodies 7. Wave interactions with oscillating water columns Bibliography Index.

Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers

Abstract: A full-vectorial imaginary-distance beam propagation method based on a finite element scheme is newly formulated and is effectively applied to investigating the problem of leakage due to a finite number of arrays of air holes in photonic-crystal holey fibers (HFs). In order to treat arbitrarily shaped air holes and to avoid spurious solutions, a curvilinear edge/nodal hybrid element is introduced. Furthermore, in order to evaluate propagation characteristics of not only bound modes but leaky modes in HFs, an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. It is confirmed from numerical results that the propagation loss increases rapidly with increasing wavelength, especially for HFs with one ring of smaller air holes, and that the propagation loss is drastically reduced by adding one more ring of air holes to the cladding region.

Left-Handed-Media Simulation and Transmission of EM Waves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides

Abstract: At microwave frequencies, hollow metallic waveguides behave in certain aspects as a ``one-dimensional plasma.'' This feature will be advantageously used for simulating the propagation of electromagnetic (EM) waves in left-handed metamaterials provided the hollow waveguide is periodically loaded with split ring resonators. It will be shown that EM transmission in this structure is feasible within a certain frequency band even if the transverse dimensions of the waveguide are much smaller than the associated free-space wavelength. This effect can be qualitatively and quantitatively explained by the left-handed metamaterial theory, thus providing a new experimental validation for such a theory.

Electromagnetic and absorption properties of some microwave absorbers

Abstract: Electromagnetic properties of a thermoplastic natural rubber (TPNR), a lithium–nickel–zinc (Li–Ni–Zn) ferrite and a TPNR–ferrite composite subjected to transverse electromagnetic (TEM) wave propagation were investigated. The incorporation of the ferrite into the matrix of the TPNR was found to reduce the dielectric loss but the magnetic loss increased. The absorption characteristics of all the samples subjected to a normal incidence of TEM wave were investigated based on a model of a single-layered plane wave absorber backed by a perfect conductor. It is evident from a computer simulation that the ferrite is a narrowband absorber, whereas the polymeric samples show broadband absorption characteristics. Minimal reflection of the microwave power or matching condition occurs when the thickness of the absorbers approximates an odd number multiple of a quarter of the propagating wavelength. This is discussed as due to cancellation of the incident and reflected waves at the surface of the absorbers. The Li–Ni–Z...

Magnetoinductive waves in one, two, and three dimensions

Abstract: The propagation of waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops. Since the coupling is due to induced voltages the waves are referred to as magnetoinductive (MI) waves. The mathematical formulations are mostly analytical thanks to long standing previous work on the magnetic and electric fields generated by currents flowing in loops. Retardation is neglected, i.e., dimensions of the structure are assumed to be small relative to the free space wavelength. The dispersion relations, derived in the most general case for a tetragonal three-dimensional structure, exhibit both forward and backward waves within a pass band. It is shown that for reproducing the salient features of the waves it is sufficient to take nearest neighbor coupling into account but coupling between loops further away must also be considered if higher accuracy is required. The investigations include that of resonances, conditions for the existence of traveling waves, tolerances, and streamlines of the Poynting vector. Waveguide components, like bends, power dividers and couplers are considered due to the potential applications of the MI waves as magnetic guides. Generality of the results, their possible implications for transverse electromagnetic wave propagation, previous work on similar waves, including the possibility of phase conjugation, are discussed in a separate section.

Reflection Coefficients and Azimuthal Avo Analysis in Anisotropic Media

Abstract: Reflection and transmission of plane waves at a plane boundary between two isotropic media are two of the most fundamental subjects in wave propagation. Zoeppritz (1919) w as among the first to investigate and publish their analytic solutions. Given the medium properties on both sides of a reflector and invoking continuity of stress and displacement across the interface, he came up with a set of equations to describe the amplitudes of the scattered (i.e., reflected and transmitted) waves. Chapter [2][1] provides an overview of the reflection and transmission problem in isotropic media. It also introduces the notation that is used throughout the text and contains a review of the basic physical principles that lead to the boundary conditions for media in welded contact. Because of the algebraic complexity of the Zoeppritz equations, the inverse problem of esti-mating medium properties from the reflection signature is based mostly on approximate analytic expressions for reflection coefficients. Several approximations for isotropic models have been described in the literature (Richards and Frasier, 1976; Aki and Richards, 1980; Shuey, 1985; Thomsen, 1990). As described in Chapter [2][1], they differ in their assumptions, as well as in the choice of medium parameters. [1]: /gswbk/9781560801764/9781560801764/SEC2.atom

Riemann wave description of erosional dam-break flows

Abstract: This work examines the sudden erosional flow initiated by the release of a dam-break wave over a loose sediment bed. Extended shallow-water equations are formulated to describe the development of the surge. Accounting for bed material inertia, a transport layer of finite thickness is introduced, and a sharp interface view of the morphodynamic boundary is adopted. Approximations are sought for an intermediate range of wave evolution, in which equilibration of the sediment load can be assumed instantaneous but momentum loss due to bed friction has not yet been felt. The resulting homogeneous hyperbolic equations are mathematically tractable using the Riemann techniques of gas dynamics. Dam-break initial conditions give rise to self-similar flow profiles. The wave structure features piecewise constant states, two smoothly varied simple waves, and a special type of shock: an erosional bore forming at the forefront of the wave. Profiles are constructed through a semi-analytical procedure, yielding a geomorphic generalization of the Stoker solution for dam-break waves over rigid bed. For most flow properties, the predictions of the theoretical treatment compare favourably with experimental tests visualized using particle imaging techniques.

Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings

Abstract: In this paper, it is pointed out that the light transmission anomalies observed for thin-film metallic gratings can be explained entirely in terms of dynamical diffraction theory. Surface plasmons are an intrinsic component of the diffracted wave field and, as such, play no independent causal role in the anomalies, as has been implied by others. The dynamical scattering matrix for the Bloch-wave modes of the diffracted photon wave field (E, H) is derived for a three-dimensionally periodic medium with arbitrary dielectric constant. A new theoretical treatment and numerical results are presented for a one-dimensional array of slits. In model metallic slit arrays, with negative dielectric constant, 100% and 0% transmission is possible at different wavelengths in the zero-order beam. In slit arrays, both propagating and evanescent modes (traditional surface plasmons) are strongly excited at both the peak and the minimum transmission conditions.

A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions

Abstract: We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where the flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function fi(q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences fi(Qi)-f-1(Qi-1) into eigenvectors of an approximate Jacobian matrix. This method is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities. Balance laws $q_t+f(q,x)_x=\psi(q,x)$ are also considered, in which case the source term is used to modify the flux difference before performing the wave decomposition, and an additional term is derived that must also be included to obtain full accuracy. This method is particularly useful for quasi-steady problems close to steady state.

Complex Wave Dynamics on Thin Films

Abstract: Formulation and Linear Orr-Sommerfeld Theory: Navier-Stokes Equation with interfacial conditions Linear stability of the trivial solution to two- and three-dimensional perturbations Longwave expansion for surface waves Unusual case of zero surface tension Surface waves - Numerical solution of the Orr-Sommerfeld equations. Hierarchy of Model Equations: Kuramoto-Sivashinsky (KS), KdV and related weakly nonlinear equations Lubrication theory to derive Benney's longwave equation Depth-averaged integral equations Combination of Galerkin-Petrov method with weighted residuals Validity of the equations Spatial and temporal primary instability of the Shkadov model. Experiments and Numerical Simulation: Experiments on falling-film wave dynamics Numerical formulation Numerical simulation of noise-driven wave transitions Pulse formation and coarsening. Periodic and Solitary Wave Families: Main properties of weakly nonlinear waves in an active/dissipative medium Phase space of stationary KS equation Solitary waves and Shilnikov theorem Bifurcations of spatially periodic travelling waves and their stability Normal Form analysis for the Kawahara equation Nonlinear waves far from criticality - the Shkadov model Stationary waves of the boundary layer equation and Shkadov model Navier-Stokes equation of motion - the effects of surface tension. Floquet Theory and Selection of periodic Waves: Stability and selection of stationary waves Stable intervals from a Coherent Structure Theory Evolution towards solitary waves. Spectral Theory for gKS Solitary Pulses: Pulse spectra Some numerical recipes to construct eigenfunctions and obtain spectra Stability of gKS pulses Attenuation of radiation wave packet by stable pulses Resonance pole-a discrete culmination of the continuous spectrum Resonance pole description of mass drainage Suppression of wave packets by a periodic train of pulses. (Part contents).

Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method.

Abstract: An efficient recursive algorithm, the stiffness matrix method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer matrix method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.

Elastic waves in bodies with initial (residual) stresses

Abstract: An analysis is made of the results obtained in the three-dimensional linearized theory of elastic waves propagating in initially stressed solids. Consideration is given to surface waves along planar and curvilinear boundaries and interfaces, waves in layers and cylinders, waves in composite materials, waves in hydroelastic systems, and dynamic problems for moving loads. The results were obtained in exact formulations.

Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution

Abstract: A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys Plasmas 2, 2098 (1995)] In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique

Control and Plasticity of Intercellular Calcium Waves in Astrocytes: A Modeling Approach

Abstract: Intercellular Ca2+ waves in astrocytes are thought to serve as a pathway of long-range signaling. The waves can propagate by the diffusion of molecules through gap junctions and across the extracellular space. In rat striatal astrocytes, the gap-junctional route was shown to be dominant. To analyze the interplay of the processes involved in wave propagation, a mathematical model of this system has been developed. The kinetic description of Ca2+ signaling within a single cell accounts for inositol 1,4,5-trisphosphate (IP3) generation, including its activation by cytoplasmic Ca2+, IP3-induced Ca2+ liberation from intracellular stores and various other Ca2+ transports, and cytoplasmic diffusion of IP3 and Ca2+. When cells are coupled by gap junction channels in a two-dimensional array, IP3 generation in one cell triggers Ca2+ waves propagating across some tens of cells. The spatial range of wave propagation is limited, yet depends sensitively on the Ca2+-mediated regeneration of the IP3 signal. Accordingly, the term "limited regenerative signaling" is proposed. The gap-junctional permeability for IP3 is the crucial permissive factor for wave propagation, and heterogeneity of gap-junctional coupling yields preferential pathways of wave propagation. Processes involved in both signal initiation (activation of IP3 production caused by receptor agonist) and regeneration (activation of IP3 production by Ca2+, loading of the Ca2+ stores) are found to exert the main control on the wave range. The refractory period of signaling strongly depends on the refilling kinetics of the Ca2+ stores. Thus the model identifies multiple steps that may be involved in the regulation of this intercellular signaling pathway.

A numerical study of submarine-landslide-generated waves and run-up

Abstract: A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth–integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency–dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep–water limit for the depth–integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave–generation region and on the shoreline movement is discussed.

The Interaction of High-Power Lasers with Plasmas

Abstract: This book deals with the fundamental physics of numerous plasma processes that occur during laser plasma interactions. The subject matter is related to both basic plasma physics and applied physics. The author starts with the essentials of high power lasers whose duration ranges from nanoseconds to femtoseconds, and then builds up an introduction to plasma physics by describing ionization, well known transport coefficients (electrical and thermal conductivities, diffusion, viscosity, energy transport etc), Debye length, plasma oscillations and the properties of the laser induced plasma medium. The book contains plasma dynamical equations for describing the hydrodynamic and kinetic phenomena, and treating particle dynamics by computer simulation. The ponderomotive force is discussed for small amplitude electromagnetic fields in an unmagnetized plasma. However, for intense laser beams one should obtain new expressions for the relativistic ponderomotive force, which are totally absent from this book. Furthermore, in laser plasma interactions strong magnetic fields are produced which will drastically modify the relativistic ponderomotive force expressions. The physics of collisional absorption of electromagnetic waves and their propagation in a nonuniform unmagnetized plasma has been elegantly described. The phenomena of the resonance absorption of laser light is also discussed. Simple models for the parametric processes are developed, while there are no discussions of cavitons/envelope solitons. The latter are usually regarded as possible nonlinear states of the modulational/filamentational instabilities. Rather, the author presents a description of a K-dV equation for nonlinear ion-acoustic waves without the laser field. The description of a non-envelope ion-acoustic soliton has already appeared in many plasma physics textbooks. The book contains a short chapter on the self-similar plasma expansion in vacuum, double layers, and charged particle acceleration. However, the author has not touched on the plasma based high energy charged particle accelerators, which involve short intense laser pulses and which are at the frontier of modern plasma physics. There is a nice chapter dealing with laser induced magnetic fields and waves in magnetized plasmas. The physics and mathematical details of the electron energy transport and heat waves, which are of significant interest in inertial confinement fusion, are described in depth. Comprehensive studies of shock waves and rarefaction waves are presented, and their relevance to high power pulsed laser drivers is discussed. Finally, the author has given a lucid description of hydrodynamic instabilities (i.e. the Rayleigh-Taylor, the Richtmyer-Meshkov, the Kelvin-Helmholtz), which are of great importance in laser-plasma interactions and in astrophysics. It would have been nice if the author would have also included a more physical description of the nonlinear evolution of those instabilities which play a significant role in the formation of fingers, bubbles and vortices in laboratories and in astrophysical settings. The book is well written and will serve as a valuable asset for graduate students and physicists working in the area of laser plasma interactions and high energy astrophysics. It should also be useful for teaching masters level courses on laser plasma interactions. The reviewer highly recommends the book to the interested reader. P K Shukla

The negative index of refraction demystified

Abstract: We study electromagnetic wave propagation in media in which the effective relative permittivity and the effective relative permeability are allowed to take any value in the upper half of the complex plane. A general condition is derived for the phase velocity to be oppositely directed to the power flow. That extends the recently studied case of propagation in media for which the relative permittivity and relative permeability are both simultaneously negative, to include dissipation as well. An illustrative case study demonstrates that in general the spectrum divides into five distinct regions.

A k-space method for coupled first-order acoustic propagation equations.

Abstract: A k-space method for large-scale simulation of ultrasonic pulse propagation is presented. The present method, which solves the coupled first-order differential equations for wave propagation in inhomogeneous media, is derived in a simple form analogous to previous finite-difference methods with staggered spatial and temporal grids. Like k-space methods based on second-order wave equations, the present method is exact for homogeneous media, unconditionally stable for "slow" [c(r) < or = c0] media, and highly accurate for general weakly scattering media. In addition, unlike previous k-space methods, the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer (PML) nonreflecting boundary conditions. Numerical examples illustrate the capabilities of the present k-space method. For weakly inhomogeneous media, accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite-difference and pseudospectral methods. The low dispersion of the k-space method allows accurate representation of frequency-dependent attenuation and phase velocity associated with relaxation absorption. A technique for reduction of Gibbs phenomenon artifacts, in which compressibility and exponentially scaled density functions are smoothed by half-band filtering, is introduced. When employed together with this smoothing technique, the k-space method provides high accuracy for media including discontinuities, high-contrast inhomogeneities, and scattering structures smaller than the spatial grid resolution.

Design and Control of Wave Propagation Patterns in Excitable Media

Abstract: Intricate patterns of wave propagation are exhibited in a chemical reaction-diffusion system with spatiotemporal feedback. Wave behavior is controlled by feedback-regulated excitability gradients that guide propagation in specified directions. Waves interacting with boundaries and with other waves are observed when interaction terms are incorporated into the control algorithm. Spatiotemporal feedback offers wide flexibility for designing and controlling wave behavior in excitable media.

Guided ultrasonic waves in long bones: modelling, experiment and in vivo application

Abstract: Existing ultrasound devices for assessing the human tibia are based on detecting the first arriving signal, corresponding to a wave propagating at, or close to, the bulk longitudinal velocity in bone. However, human long bones are effectively irregular hollow tubes and should theoretically support the propagation of more complex guided modes similar to Lamb waves in plates. Guided waves are attractive because they propagate throughout the bone thickness and can potentially yield more information on bone material properties and architecture. In this study, Lamb wave theory and numerical simulations of wave propagation were used to gain insights into the expected behaviour of guided waves in bone. Experimental measurements in acrylic plates, using a prototype low-frequency axial pulse transmission device, confirmed the presence of two distinct propagating waves: the first arriving wave propagating at, or close to, the longitudinal velocity, and a slower second wave whose behaviour was consistent with the lowest order Lamb antisymmetrical (A0) mode. In a pilot study of healthy and osteoporotic subjects, the velocity of the second wave differed significantly between the two groups, whereas the first arriving wave velocity did not, suggesting the former to be a more sensitive indicator of osteoporosis. We conclude that guided wave measurements may offer an enhanced approach to the ultrasonic characterization of long bones.

Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials

Abstract: We investigate the characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed media. We discuss mainly under what conditions anomalous reflection or refraction shall occur at the interface when propagating waves pass from one isotropic regular medium into another uniaxially anistotropic left-handed medium and under what conditions anomalous transmission shall occur when an evanescent wave is transmitted through a slab of uniaxially anisotropic left-handed medium. We show that the characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.

Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid‐saturated stratified porous media

Abstract: [1] We present a full-waveform modeling technique of the coupled seismoelectromagnetic wave propagation in fluid-saturated stratified porous media. Our simulation code uses the macroscopic governing equations derived by Pride [1994], which couple Biot's theory and Maxwell equations via flux/force transport equations. In this theory the coupling mechanism is explained by electrokinetic effects taking place at the pore level. The synthetic seismoelectrograms and seismomagnetrograms are computed by extending the generalized reflection and transmission matrix method and by using a discrete wave number integration of the global reflectivity obtained in the frequency wave number domain. Synthetic time sections and snapshots of the wave propagation are used to study the seismic, electromagnetic, and seismoelectromagnetic waves properties in fluid-saturated layered porous media. Two wave phenomena are investigated: (1) the electric and magnetic fields induced by the propagation of a seismic perturbation in a homogeneous porous medium and (2) the electromagnetic waves generated at depth when seismic waves propagate through a vertically heterogeneous porous medium. Concentrating on the second effect, we show that the zone which effectively contributes to the generation of EM disturbances along a plane interface coincides with the first Fresnel zone associated with a seismic-to-electromagnetic wave conversion. A numerical sensitivity study shows that the EM waves generated at depth by the passage of seismic waves through an interface are particularly sensitive to contrasts in porosity, permeability, fluid salinity, and fluid viscosity. Our numerical simulations highlight the potential of artificially generated seismoelectromagnetic converted waves for the characterization of the subsurface and its fluid content.

A σ-coordinate three-dimensional numerical model for surface wave propagation

Abstract: A three-dimensional numerical model based on the full Navier–Stokes equations (NSE) in σ-coordinate is developed in this study. The σ-coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the σ-coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485–501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd.

A numerical investigation of solitary internal waves with trapped cores formed via shoaling

Abstract: The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

Canonical transform method for processing radio occultation data in the lower troposphere

Abstract: [1] The methods of processing radio occultation data in multipath zones which were used up to now have very strong restrictions of the applicability. In this paper, we introduce a new approach to the problem of deciphering the ray structure of wave fields in multipath zones using the short-wave asymptotic solution of the wave problem. In geometric optics a canonical transform resolves multipath by introducing new coordinate and momentum in such a way that different rays are distinguished by their coordinates. The wave field is processed by a Fourier integral operator associated with the canonical transform. The transformed wave function can then be written in the single-ray approximation, which allows for the determination of refraction angles from the derivative of the eikonal. The new method retains all the advantages of the back propagation such as the removal of effects of diffraction in free space and the enhancement of the vertical resolution in retrieved profiles, but it has much wider applicability limits. The method is convenient for operational applications. We discuss a fast numerical implementation of the method and present the results of numerical simulations confirming the applicability of the method.

Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation

Abstract: An investigation to deepen the connection between the family of nonlinear Schrodinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schrodinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schrodinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x-u0 s (s being a time-like variable). This novel method in solving the nonlinear Schrodinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented.

Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case

Abstract: Non-local dispersive model for wave propagation in heterogeneous media is derived from the higher-order mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space–time co-ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long-term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth-order differential equation, also known as a ‘bad’ Boussinesq problem. Regularization procedures are then introduced to construct the so-called ‘good’ Boussinesq problem, where the need for C1 continuity is eliminated. Numerical examples are presented to validate the present formulation. Copyright © 2002 John Wiley & Sons, Ltd.