Showing papers on "Plane wave published in 1991"

The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross- sectional shape

Abstract: The general Kirchhoff theory of sound propagation in a circular tube is shown to take a considerably simpler form in a regime that includes both narrow and wide tubes. For tube radii greater than rw=10−3 cm and sound frequencies f such that rwf3/2<106 cm s−3/2, the Kirchhoff solution reduces to the approximate solution suggested by Zwikker and Kosten. In this regime, viscosity and thermal conductivity effects are treated separately, within complex density and complex compressibility functions. The sound pressure is essentially constant through each cross section, and the excess density and sound pressure (when scaled by the equilibrium density and pressure of air, respectively) are comparable in magnitude. These last two observations are assumed to apply to uniform tubes having arbitrary cross‐sectional shape, and a generalized theory of sound propagation in narrow and wide tubes is derived. The two‐dimensional wave equation that results can be used to describe the variation of either particle velocity or...

Transient scattering by conducting surfaces of arbitrary shape

Abstract: The time-domain electric field integral equation (EFIE) is used along with the method of moments to develop a simple and efficient numerical procedure for treating problems of transient scattering by arbitrary shaped conducting objects. The conducting surface is modeled by planar triangular patches for numerical purposes. Because the EFIE is used in the solution procedure, the method is applicable to both open and closed bodies. the EFIE approach is applied to the scattering problems of Gaussian plane wave illumination of a flat square plate and sphere. Comparisons of surface current densities and far-scattered fields are made with previous computations and good agreement is obtained in each case. >

Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena

Abstract: A rigorous analysis of the numerical error associated with the use of stair-stepped (saw-toothed) approximation of a conducting boundary for finite-difference time-domain (FDTD) simulations is presented. First, a dispersion analysis in two dimensions is performed to obtain the numerical reflection coefficient for a plane wave scattered by a perfectly conducting wall, tilted with respect to the axes of the finite-difference grid, under both transverse electric and transverse magnetic polarizations. The characteristic equation for surface waves that can be supported by such saw-tooth conducting surfaces is derived. This equation leads to expressions that show the dependence of the propagation constant along the boundary and the attenuation constant perpendicular to it on cell size and wavelength. Numerical simulations that demonstrate the effects predicted by the dispersion analysis are presented. >

Spatial dark-soliton stripes and grids in self-defocusing materials.

Abstract: Spatial dark-soliton (SDS) stripes are experimentally found in the transverse plane of a laser beam that passes through a rectilinear diffraction screen before propagating in a self-defocusing nonlinear material. Materials with different mechanisms of nonlinearity manifest the same qualitative results. The SDS nature of the observed phenomenon is verified by numerical simulations of the (2+1)-D nonlinear Schr\"odinger equation, analytical solutions for the (1+1)-D case, and their comparison with experimental data.

Photonic bound states in periodic dielectric materials

Abstract: It is demonstrated that lattice imperfections in a periodic array of dielectric material can give rise to fully localized electromagnetic states. Calculations are performed by using a plane-wave expansion to solve Maxwell's equations. The frequency of these localized states is tunable by varying the size of the defect. Potential device applications in the microwave and millimeter wave regime are proposed.

Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite element method: Application to Alberich anechoic coatings

Abstract: The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single periodic structures, such as compliant tube gratings [A. C. Hennion et al., J. Acoust. Soc. Am. 87, 1861-1870 (1990) ]. In this paper, the same approach is extended to doubly periodic structures, such as Alberich anechoic coatings. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, due to the use of classical Bloch type relations. Then, the effects of the remaining fluid domain are accounted for by matching the pressure field in the finite element mesh with simple plane-wave expansion• of the ingoing and outgoing waves. After an outline of the method, the paper describes the results obtained for the scattering of a plane wave by different periodic structures. Internal losses are taken into account and the incident plane wave impinges at normal or oblique incidence. Numerical results obtained for Alberieh aneehoie coatings are first analyzed to check the convergence and then compared to previous numerical results or to experimental results, demonstrating that the finite element approach is accurate and well suited to predict the behavior of these gratings. Moreover, careful attention is devoted to the analysis of the inclusion vibrations, to identify the origin of the resonance mechanisms.

On the direct calculation of a transient plane wave reflected from a finitely conducting half space

Abstract: An approach to the computation of the electromagnetic field reflected from a lossy half-space directly in the time domain is discussed. This approach requires first evaluating the impulse response of the half-space and then convolving it with the specified incident field waveform. To obtain the impulsive reflected field, either for vertical or horizontal polarization, approximations to the Fresnel reflection coefficients are made, thereby permitting an analytical expression in the time domain. Several different numerical examples using this technique are presented to illustrate the use of the method and the error contained in the solution. >

Reflection and refraction by uniaxial crystals

Abstract: Explicit formulae are found for the electric field vectors of the ordinary and extraordinary modes produced when plane waves of p or s polarization are incident on an arbitrary face of a uniaxial crystal. The angle of incidence is unrestricted, and the anisotropic medium may be absorbing. The reflection amplitudes rpp, rps, rss, rsp, the transmission amplitudes tpo, tpe,tso,tse, and the wavevector and ray directions are then determined in terms of the direction cosines of the optic axis relative to the laboratory axes.

Scattering by a multilayer chiral cylinder

Abstract: An efficient recursive eigenfunction solution for the problem of scattering by a multilayer chiral circular cylinder, with or without a surface impedance center cylinder, is presented. For an M layer cylinder, the solution requires the multiplication of M4*4 matrices, versus the solution of a 4M*4M matrix equation in a standard approach. The problem of a transverse electric (TE) incident plane wave differs from that of a transverse magnetic (TM) wave only by a plus/minus sign at one step in the solution. The addition of the surface impedance center cylinder requires only one additional matrix multiplication. Numerical results, including echo width and internal fields, are presented for several sample cylinders. >

Patterns and waves : the theory and applications of reaction-diffusion equations

Abstract: Basic considerations Pattern formation Plane waves A geometrical theory for waves Nonlinear dispersal mechanisms.

Effects of focusing on the nonlinear interaction between two collinear finite amplitude sound beams

Abstract: A study of the propagation and interaction of two collinear finite amplitude sound beams, presented in a previous paper [Naze Tjo/tta et al., “Propagation and interaction of two collinear finite amplitude sound beams,” J. Acoust. Soc. Am. 88, 2859–2870 (1990)] is extended to include the effects of focusing. The validity of the parabolic equation when applied to strongly focused sound beams is discussed. Equations and algorithms based on a transformed parabolic equation are presented and used to compute the interaction between two collinear, focused sound beams, and between one plane wave and a focused sound beam. Numerical results are shown, with special emphasis on parametric generation and parametric reception of sound.

Analysis of Lagrangian gauge measurements of simple and nonsimple plane waves

Abstract: Analysis of multiple, embedded gauge measurements of large‐amplitude plane waves is addressed. Although many of the developments are general, the emphasis is on the determination of stress and density fields from particle velocity measurements. Practical considerations for embedded particle velocity and stress gauge measurements are discussed. Difficulties with existing analysis methods are described. The use of wave similarity as a criterion for determining the preferred analytic approach is emphasized. Simple waves are easily analyzed using the approaches suggested by Fowles, Cowperthwaite, and Williams J. Appl. Phys. 41, 360 (1970); 42, 456 (1971)]. Nonsimple waves, of broader interest, are best analyzed using surfaces explicitly fit to measured histories and directly integrating the conservation equations. Analytic and numerical examples of the surface‐fitting procedure are presented. Uniqueness and verification of calculated results in past and present work are discussed.

Electromagnetic radiation and scattering from finite conducting and dielectric structures: surface/surface formulation

Abstract: An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made. >

Microwave reflectometry for the study of density fluctuations in tokamak plasmas

Abstract: The effect of small scale density fluctuations on the propagation of electromagnetic waves in an inhomogeneous magnetized plasma in the presence of a cut-off is investigated. It is shown that, provided the fluctuation scale length is greater than the free space wavelength of an incident plane wave, the scattered field is strongly enhanced from fluctuations near the turning point. Numerical results for wave propagation in a Tokamak plasma demonstrate the feasibility of reflectometry for the localized measurement of density fluctuations in the range k perpendicular to rho i<<1.

Nonlinear waveform inversion of plane-wave seismograms in stratified elastic media

Abstract: We present a method for determining the elastic parameters of a horizontally stratified medium from its plane-wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least-squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency-wave slowness domain and can be readily adapted to various source-receiver configurations.The behavior of the algorithm conforms to the predictions of generalized least-squares inverse the-ory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P-wave velocity (or P-wave impedance) by considering plane waves in the low slowness region (near-normal angles of incidence), then in optimizing for the S-wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise-free synthetic data prove that the proposed inversion method satisfactorally reconstructs the elastic properties of a stratified medium from a limited set of plane-wave components, at a reasonable computing cost.

Reflection and transmission of acoustic plane waves on an immersed orthotropic and viscoelastic solid layer

Abstract: This paper presents a method of characterizing orthotropic and viscoelastic behavior of some composite materials. The purpose is to measure the nine coefficients of the complex stiffness matrix, by using ultrasonic waves transmitted through a plate-shaped sample immersed in water. From a study or propagation in principal planes that has been reported in a previous publication [B. Hosten et al., J. Acoust. Soc. Am. 82, 1763–1770 (1987)], this paper emphasizes heterogeneous mode conversion and propagation through a nonprincipal plane, inside the composite. A numerical method is proposed for computing reflection and transmission coefficients of plane waves for any incidence plane through an orthotropic, lossy solid layer. Numerical calculations of reflection and transmission are compared to experimental data: Amplitudes, wave vectors, and damping vectors are given for a unidirectional graphite/epoxy composite.

A free-space bistatic calibration technique for the measurement of parallel and perpendicular reflection coefficients of planar samples

Abstract: A free-space bistatic measurement system suitable for operation in the frequency range of 5.85-40 GHz is calibrated to measure the parallel and perpendicular reflection coefficients of metal-backed planar samples for obliquely incident waves. The measurement system consists of transmit and receive antennas in the bistatic configuration, mode transitions, precision coaxial cables, and the network analyzer. Diffraction effects of the edges of the sample are minimized by using spot-focusing horn lens antennas, which focus most of the energy on a one-wavelength-diameter circular section of the sample. A new free-space bistatic calibration technique is developed to eliminate errors due to multiple reflections between transmit and receive antennas via the surface of the sample. The effect of defocusing due to the obliquely incident plane wave with focused antennas is minimized by introducing correction factors which modify measured reflection coefficients. Details of the calibration procedure and a discussion of the experimental results obtained for planar samples of Teflon and Eccogel 1365-90 in the frequency range 12.4-18 GHz are presented. >

Propagation of transients in dispersive dielectric media

Abstract: The propagation of transient electromagnetic fields in dispersive dielectric media is studied. The dielectric medium is assumed to be linear, isotropic, and homogeneous, and is described by the Debye model. Incident fields are assumed to be transverse electromagnetic plane wave pulses. The dielectric body can assume the form of infinite half space or an infinite circular cylinder, either of which may be homogeneous or stratified. The electric fields induced in the dielectric are calculated from time-domain Maxwell's equations using the finite-difference time-domain method. >

Dual-series solution to scattering from a semicircular channel in a ground plane

Abstract: Exact dual-series eigenfunction solutions, and simple closed-form low-frequency asymptotic approximations are determined for the problems of TM and TE scattering from a semicircular channel in a perfectly conducting ground plane. The eigenfunction solutions provide benchmarks for channel scattering, and the low-frequency solutions can be used to determine directly incremental length diffraction coefficients for narrow channels. >

Stokes drift in two-dimensional wave flumes

Abstract: A complete second-order solution is presented for the two-dimensional wave motion forced by a generic planar wavemaker. The wavemaker is doubly articulated and includes both piston and hinged wavemakers of variable draught. It is shown that the first-order evanescent eigenseries cannot be neglected when computing the amplitude of the second-order free wave. A previously neglected, time-independent solution that is required to satisfy an inhomogeneous kinematic boundary condition on the wavemaker as well as an inhomogeneous Neumann boundary condition on the free surface is examined in detail for the first time. The time-independent solution is found to accurately estimate the mean return flow in a closed wave flume computed by the Eulerian method. This mean return current due to Stokes drift is usually estimated using the principle of kinematic conservation of mass flux. Even though the first-order eigenseries will converge for any geometry of a generic planar wavemaker, the second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries.

Nonlinear Methods in Offshore Engineering

Abstract: 1. Introduction. Definition of nonlinear systems. Consistent methodology. Probability distributions. 2. Environments. Wave theories. Nonlinear waves. Random waves. Wave simulation. Waves plus current. Breaking waves. Wind spectra. 3. Wave Loading on Structures. Wave force formulations. Morison equation. Modified Morison equation. Four-term Morison equation. Transverse force. Random wave force. Wave breaking force. Steady drift force. 4. Offshore Structure Response. Nonlinear motion response. Response analysis of jacket structure. Single-degree of freedom system. Moorling line analysis. Time domain solution of moored systems. Low frequency oscillation. High frequency oscillation. Damping at low and high frequency responses. Riser deflection analysis. 5. Distribution of Short-Term Wave Parameters. Wave elevation distribution. Nonlinearity of sea waves. Wave height distribution. Distribution of wide-banded wave amplitudes. Nonlinear Gaussian waves. Nonlinear non-Gaussian waves. Wave group statistics. Wave period distribution. Non-stationary wave height distribution. Wave height-period distribution. Extreme wave height-steepness distribution. Review of nonlinear wave statistics. 6. Short Term Loading Distribution. Linear systems. Linearized systems. Loading spectra. Statistics of narrow-band Morison force. Statistics of wide-band Morison force. Statistics of wave-current force. Statistics of free surface structural response. Review of nonlinear excitation statistics. 7. Short Term Response Distribution. Structural response spectrum. Statistics of nonlinearly dampled system. Statistics of drift force. Statistics of low frequency motion. Discussion of nonlinear response statistics. 8. Long-Term Response Prediction. Long-term wave height distribution. Joint distribution of H s and T z . Extrapolation of wave scatter diagram to longer duration. Long-term wave load distribution. Prediction of extreme wave loads. Return periods of extreme events and non-encounter probabilities. Bivariate short- and long-term prediction. Time and frequency domain long-term predictions. Short and long-term response prediction for nonlinear systems. Review of extreme value prediction for linear and nonlinear systems. References at the end of each chapter. Author index. Subject index.

Full resolution focusing of Seasat SAR images in the frequency-wave number domain

Abstract: Synthetic aperture radar (SAR) data focusing has been traditionally performed using matched filter techniques. However, downward continuation techniques can produce, with a great computational efficiency, results that only the most sophisticated conventional techniques can achieve. The basic idea is to decompose the measured field into monochromatic plane waves of appropriate amplitudes, wave lengths and propagation directions. The backpropagation of these plane waves, and their recombination at the time when the sounding pulse was emitted, can produce a map of the backscattered electromagnetic field. In order to obtain correct focusing of synthetic aperture radar raw data, both the geometrical and the transmission parameters of the system should be known as precisely as possible. The transmission parameters are generally known very precisely, whereas the geometrical ones (i.e. sensor-target relative position, satellite velocity and attitude, etc.) can be derived from the ephemerides of the satel...

Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution

Abstract: The problem of diffraction by a thick, conducting grating situated in an inhomogeneous dielectric slab is investigated using the generalized network formulation. This formulation combines the method of moments and the finite-element method, permitting the treatment of periodic elements of arbitrary cross section and inhomogeneous profiles. Solutions are presented for both transverse electric (TE) and transverse magnetic (TM) polarizations. Transmission gratings composed of rectangular conductors filled with dielectric materials of arbitrary profiles are studied. >

Diffraction by an arbitrary-angled dielectric wedge. I. Physical optics approximation

Abstract: A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45 degrees , relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150 degrees are plotted in figures, revealing abrupt discontinuities at dielectric interfaces. >

The behaviour of elastic surface waves polarized in a plane of material symmetry. I, Addendum

Abstract: This addition to a recent paper by Chadwick (Proc. R. Soc. Lond. A 430, 213 (1990); hereafter referred to as part I) has been prompted mainly by the discovery of secluded supersonic surface waves propagating in configurations of transversely isotropic elastic media in which the reference plane is not a plane of material symmetry and coexisting with a subsonic surface wave. The occurrence of a supersonic surface wave travelling in a direction e$\_{1}$ with speed v$\_{\text{s}}$ implies that there are two homogeneous plane waves, with slowness vectors s$\_{\text{i}}$ and s$\_{\text{r}}$ such that s$\_{\text{i}}\ \cdot $ e$\_{1}$ = s$\_{\text{r}}\ \cdot $ e$\_{1}$ = v$_{\text{s}}^{-1}$, which comprise the incident and reflected waves in a case of simple reflection at the traction-free boundary. Supersonic surface waves may therefore be found by searching within a suitably defined space of simple reflection, $\boldsymbol{\scr{R}}$. This is the approach which has led to the new results mentioned above and the principal conclusions of part I are re-examined here from the same point of view. It is found that, whereas the secluded supersonic surface waves in transversely isotropic media correspond to isolated points on a curvilinear projection of $\boldsymbol{\scr{R}}$ which does not intersect the curve representing subsonic surface waves, the symmetric surface waves studied in part I define a curve which may lie partly inside and partly outside a projection of $\boldsymbol{\scr{R}}$ in the form of a region, the interior points representing supersonic and the exterior points subsonic surface waves. This discussion is preceded by a simplification of the existence-uniqueness theorem proved in part I and followed by a reconsideration of the possibility that an inhomogeneous plane elastic wave can qualify as a surface wave. Such one-component surface waves do exist, but a symmetric surface wave necessarily contains two inhomogeneous plane waves.

Plane-wave reflection properties of two artificially hard surfaces

Abstract: The concepts of artificially hard and soft surfaces are interpreted in terms of the plane-wave reflection properties of the surfaces, in particular the reflection phase angles for two orthogonal polarizations. Numerical results are presented for two types of nearly hard surfaces. The first is a surface with longitudinally oriented and dielectrically filled corrugations. The second is a surface with longitudinally oriented strips on a grounded dielectric substrate. Neither of the two realizations is ideally hard in the strictest sense of the concept, but a good approximation can be achieved over a limited bandwidth. The numerical results demonstrate how various geometrical parameters affect the behavior of the surfaces. One important result is that the strip-loaded surface is the most favorable with respect to bandwidth. Another is that the strip-loaded surface can be made arbitrarily thin, though at the expense of bandwidth. >