Showing papers on "Wave propagation published in 1991"

Correlation model for shadow fading in mobile radio systems

Abstract: A simple autocorrelation model for shadow fading in mobile radio channels is proposed. The model is fitted to both large cells and microcells. Results show that the model fit is good for large to m ...

Photonic band structure of two-dimensional systems: The triangular lattice

Abstract: By the use of a position-dependent dielectric constant and the plane-wave method, we have calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane form a triangular lattice. The rods are embedded in a background medium with a different dielectric constant. The electromagnetic waves are assumed to propagate in a plane perpendicular to the rods, and two polarizations of the waves are considered. Absolute gaps in the resulting band structures are found for waves of both polarizations, and the dependence of the widths of these gaps on the ratio of the dielectric constants of the rods and of the background, and on the fraction of the total volume occupied by the rods, is investigated.

Nonlinear nature of gravitation and gravitational-wave experiments.

Abstract: It is shown that gravitational waves from astronomical sources have a nonlinear effect on laser interferometer detectors on Earth, an effect which has hitherto been neglected, but which is of the same order of magnitude as the linear effects. The signature of the nonlinear effect is a permanent displacement of test mases after the passage of a wave train.

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...

A model for the propagation and scattering of ultrasound in tissue

Abstract: An inhomogeneous wave equation is derived describing propagation and scattering of ultrasound in an inhomogeneous medium. The scattering term is a function of density and propagation velocity perturbations. The integral solution to the wave equation is combined with a general description of the field from typical transducers used in clinical ultrasound to yield a model for the received pulse-echo pressure field. Analytic expressions are found in the literature for a number of transducers, and any transducer excitation can be incorporated into the model. An example is given for a concave, nonapodized transducer in which the predicted pressure field is compared to a measured field.

Feedback instability of the ionospheric resonant cavity

Abstract: A model is developed that provides a theoretical basis for previous numerical results showing a feedback instability with frequencies characteristic of Alfven travel times within the region of the large increase of Alfven speed above the ionosphere. These results have been extended to arbitrary ionospheric conductivity by developing a numerical solution of the cavity dispersion relation that involves Bessel functions of complex order and argument. It is concluded that the large contrast between the magnetospheric and ionospheric Alfven speed leads to the formation of resonant cavity modes with frequencies ranging from 0.1 to 1 Hz. The presence of the cavity leads to a modification of the reflection characteristics of Alfven waves with frequencies that compare to the cavity's normal modes.

Electromagnetic Bloch waves at the surface of a photonic crystal

Abstract: We find that electromagnetic modes are localized at the interface between air and a photonic crystal. General arguments that surface modes must always exist for some termination of any surface of a photonic crystal are presented, and the importance of the surface band structure for semiconducting laser systems is discussed.

Colliding plane waves in general relativity

Abstract: Elements of general relativity colliding impulsive gravitational waves plane waves geometrical considerations the field equations boundary conditions singularity structure the Szekeres class of vacuum solutions other vacuum solutions with aligned polarization Ernst's equation for colliding gravitational waves solution generating techniques vacuum solutions with non-aligned polarization the initial value problem colliding electromagnetic waves: the Bell-Szekeres solution Ernst's equations for colliding electromagnetic waves colliding electromagnetic waves - exact solutions colliding electromagnetic waves - diagonal solutions electromagnetic waves colliding with gravitational waves other sources related results conclusions and prospects. Appendix: Co-ordinate systems.

On tidal variability induced by nonlinear interaction with planetary waves

Abstract: Short-time variability of the atmospheric tides is frequently observed in the meteor region but is not yet fully explained in terms of production mechanisms. This is probably due to the existence of several such mechanisms acting together or separately. In this paper we show that many observations can be explained by nonlinear interactions between tides and planetary waves having periods corresponding to those of the observed tidal amplitude modulations. These nonlinear interactions generate two secondary waves whose frequencies are the sum and difference of frequencies of the primary waves. These two waves beat with the tide, modulating its amplitude with the planetary wave period. A numerical model is used to demonstrate that with primary waves of reasonable amplitudes the nonlinear interactions can be quite large. This is because the importance of nonlinearity depends essentially on the amplitude of the induced fluid velocity in the direction of wave propagation compared to the wave propagation velocity. When two waves propagate simultaneously, the fluid velocity can have a large component in the direction of propagation of one of the waves, and advective (nonlinear) terms can be large. This point is further illustrated in the case of two gravity waves interacting together. Finally, some observational campaigns carried out above Garchy (45°N) are analyzed using a nonparametric method. The results indicate that nonlinear interactions between tides and planetary waves really take place in the upper mesosphere and lower thermosphere.

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. >

Phase speed spectra of transient eddy fluxes and critical layer absorption

Abstract: Tropospheric zonal mean eddy fluxes of heat and momentum, and the divergence of the Eliassen-Palm flux, are decomposed into contributions from different zonal phase speeds Data analyzed are the European Center for Medium Range Weather Forecasts operational global analyses covering 1980-1987 Eastward moving medium-scale waves (zonal waves 4-7) dominate the spectra of lower tropospheric heat fluxes in both hemispheres and all seasons Upper tropospheric wave flux spectra are similar to the low level spectra in midlatitudes, but shift to slower zonal phase speeds as low latitudes are approached The cause of this shift is the selective absorption of faster moving components in midlatitudes as the waves propagate meridionally Latitude-phase speed distributions of eddy fluxes are constructed and compared to the zonal mean wind structure These results demonstrate that upper tropospheric eddies break and decelerate the zonal mean flow approximately 10-20 deg in latitude away from their critical line (where phase speed equals zonal wind speed) Comparisons are also made with results from the middle stratosphere

Plate wave acoustic emission

Abstract: Plate theory is more easily applied to the analysis of composite laminates than exact three‐dimensional elasticity theory. Under conditions such that plate theory is applicable, it is suggested that plate waves are useful for understanding acoustic emission (AE) phenomena. To test this idea, pencil leads were broken on aluminum plates and composite plates, and the resulting waves were detected with a broadband ultrasonic transducer. Both the fundamental extensional and flexural modes were observed. Their characteristics are described and the implications for AE source location are discussed as well. Several transducers, commonly used for acoustic emission measurements, are compared with regard to their ability to reproduce the characteristic shapes of plate waves. Their different responses show why similar test specimens and test conditions can yield disparate results.

Speed of propagation of classical waves in strongly scattering media.

Abstract: We present results of optical experiments which demonstrate that in a strongly scattering medium containing resonant scatterers the velocity for electromagnetic energy may differ by an order of magnitude from the phase velocity. We derive a microscopic theory that yields an expression for this velocity. Discrepancies are removed, and excellent agreement is found between experiment and theory.

Scattering wave energy propagation in a random isotropic scattering medium: 1. Theory

Abstract: In this paper we provide a complete formulation of scattered wave energy propagation in a random isotropic scattering medium. First, we formulate the scattered wave energy equation by extending the stationary energy transport theory studied by Wu (1985) to the time dependent case. The iterative solution of this equation gives us a general expression of temporal variation of scattered energy density at arbitrary source and receiver locations as a Neumann series expansion characterized by powers of the scattering coefficient. The first term of this series leads to the first-order scattering formula obtained by Sato (1977). For the source and receiver coincident case, our solution gives the corrected version of high-order formulas obtained by Gao et al. (1983b). Solving the scattered wave energy equation using a Fourier transform technique, we obtain a compact integral solution for the temporal decay of scattered wave energy which includes all multiple scattering contributions and can be easily computed numerically. Examples of this solution are presented and compared with that of the single scattering, energy flux, and diffusion models. We then discuss the energy conservation for our system by starting with our fundamental scattered wave energy equation and then demonstrating that our formulas satisfy the energy conservation when the contributions from all orders of scattering are summed up. We also generalize our scattered wave energy equations to the case of nonuniformly distributed isotropic scattering and absorption coefficients. To solve these equations, feasible numerical procedures, such as a Monte Carlo simulation scheme, are suggested. Our Monte Carlo approach to solve the wave energy equation is different from previous works (Gusev and Abubakirov, 1987; Hoshiba, 1990) based on the ray theoretical approach.

Microwave propagation in two-dimensional dielectric lattices.

Abstract: We have calculated and measured the properties of X-band microwaves propagating in a 2D array of low-loss high-dielectric-constant cylinders. Transmission bands and photonic band gaps are conclusively identified in excellent agreement with the theoretical predictions. Detailed data on the properties of isolated defect states are also presented. We conclude that studies of this model scattering system allow the quantitative evaluation and testing of ideas regarding wave propagation and localization in strongly scattering media.

The Saturation of Gravity Waves in the Middle Atmosphere. Part II: Development Of Doppler-Spread Theory

Abstract: The irregular winds of the middle atmosphere are commonly attributed to an upwardly propagating system of atmospheric gravity waves. Their one-dimensional (in vertical wavenumber m) power spectrum has been reported to exhibit a nearly universal behavior in its “tail” region of large m: both the form (∼m−3) and the intensity of the tail are approximately invariant with meteorological conditions, time, place and height. This universality is often described as resulting from “saturation” of the system, with the physical cause of saturation being left for separate identification and analysis. Here the cause is attributed to nonlinear interaction between the waves of the full spectrum, most specifically to the advective nonlinearity of the Eulerian fluid-dynamic equations. This nonlinearity has the effect of Doppler shifting the local intrinsic frequency of any given wave in the wind field imposed by all waves. Only an approximation to its effects is sought here, the wind field of the full spectrum be...

Localisation in a Cosserat continuum under static and dynamic loading conditions

Abstract: Localisation studies have been carried out for an unconstrained, elasto-plastic, strain-softening Cosserat continuum. Because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions. Because of the existence of rotational degrees-of-freedom in a Cosserat continuum additional wave types arise and wave propagation becomes dispersive. This has been investigated analytically and numerically for an elastic Cosserat continuum and an excellent agreement has been found between both solutions.

Linear and nonlinear dust drift waves

Abstract: The linear and nonlinear properties of low-frequency motion in inhomogeneous, magnetized, dusty plasmas are investigated. The dynamics of the dust grains are taken into account by means of a fluid model. A new type of low-frequency waves, the dust-drift waves, is shown to exist. The nonlinear mode coupling equations are derived, and the possibility of propagating vortex structures is discussed. The dust-drift waves may be relevant in astrophysical and cometary plasmas.

Green's law revisited: tidal long-wave propagation in channels with strong topography

Abstract: Green's Law states that tidal long-wave elevation ζ and tidal transport Q vary with width b and depth h according to ζ ≌ b−1/2h−1/4 and Q ≌ b+1/2h+/4. This solution is of limited utility because it is restricted to inviscid, infinitesimal waves in channels with no mean flow and weak topography (those with topographic scale L ≫ wavelength λ). An analytical perturbation model including finite-amplitude effects, river flow, and tidal flats has been used to show that (1) wave behavior to lowest order is a function of only two nondimensional parameters representing, respectively, the strength of friction at the bed and the rate of topographic convergence/divergence; (2) two different wave equations with nearly constant coefficients can be derived that together cover most physically relevant values of these parameters, even very strong topography; (3) a single, incident wave in a strongly convergent or divergent geometry may mimic a standing wave by having a ≡ 90° phase difference between Q and ζ and a very large phase speed, without the presence of a reflected wave; (4) channels with strong friction and/or strong topography (L ≪ λ) show very large deviations from Green/s Law; and (5) these deviations arise because both frictional damping and the direct dependence of |Q| and |ζ| on topography (topographic funnelling) must be considered.

A dispersive effective medium for wave propagation in periodic composites

Abstract: The problem of wave propagation through a periodic medium is considered. It is assumed that the ratio between the cell size and the shortest wavelength of the initial disturbance is small. Within this regime, an effective medium model of the propagation phenomena is obtained using the Bloch expansion. The effective medium obtained is shown to be dispersive. It is known that a dominant feature of the transient wave train in a periodic medium is that of dispersion. It is shown that our model recovers homogenization formally when the cell size approaches zero. Explicit formula for the constants appearing in the effective medium equation is derived for the case of one dimension. The accuracy of the resulting approximation is assessed in numerical simulations.

Variational approach to collapse of optical pulses

Abstract: Optical pulses, which propagate under the combined effects of nonlinearity, dispersion, and diffraction, may collapse in space and time. The standard method for analyzing these collapses is the aberrationless paraxial ray approximation. This method is known to give a quantitatively correct, although not particularly accurate, picture of most properties of the pulse dynamics. However, it is found that the predictions for some of the important pulse parameters are qualitatively wrong and could lead to incorrect conclusions. An alternative variational approach is suggested that remedies these deficiencies and gives results in good agreement with numerical results.

Source location in thin plates using cross-correlation

Abstract: In this paper an alternative method to first threshold crossing for acoustic emission (AE) source location is presented. For wave propagation in dispersive media, the accuracy of source location can be improved by locating corresponding phase points on the transducer outputs to determine the difference in arrival times. The phase point location was done by cross‐correlating the transducer outputs with a single frequency cosine wave modulated by a Gaussian pulse. Experiments were performed using a lead break as the AE source on the surface of an aluminum plate. Due to the plate geometry and source orientation, the wave produced was highly dispersive. Although this wave was unsuitable for first threshold crossing techniques, the time differences needed for triangulation could be determined using the cross‐correlation technique.

Heating solar coronal holes

Abstract: It has been shown that the coronal hole, and the associated high-speed stream in the solar wind, are powered by a heat input of the order of 500,000 ergs/sq cm s, with most of the heat injected in the first 1-2 solar radii, and perhaps 100,000 ergs/sq cm s introduced at distances of several solar radii to provide the high speed of the issuing solar wind. The traditional view has been that this energy is obtained from Alfven waves generated in the subphotospheric convection, which dissipate as they propagate outward, converting the wave energy into heat. This paper reviews the generation of waves and the known wave dissipation mechanisms, to show that the necessary Alfven waves are not produced under the conditions presently understood to exist in the sun, nor would such waves dissipate significantly in the first 1-2 solar radii if they existed. Wave dissipation occurs only over distances of the order of 5 solar radii or more.

New approaches to nonlinear diffractive field propagation

Abstract: In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the fields of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effects of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform tec...

Oscillations and Waves : In Strong Gravitational and Electromagnetic Fields

Abstract: This book emerged from a course given at Moscow State University and provides an introduction to current research in general relativity, relativistic gas dynamics, and cosmology, touching on the different methods used in wave theory. Each chapter begins with an elementary introduction and then proceeds to a more sophisticated discussion including a presentation of the current state of the art. Topics covered include: original results of and approaches to the mathematical theory of strong gravitational and electromagnetic fields in general relativity which reduce the problem to a single linear integral equation; the theory of black holes; wave propagation in the vicinity of black holes; the effect of strong external electromagnetic fields on gravitational and electromagnetic waves of short length; the theory of integrable nonlinear two-dimensional systems in theoretical physics; methods of relativistic and magneto-gas dynamics in cosmology including shock and acoustic waves; hydrodynamical effects due to the rotation of a pulsar in a closed binary system.

Resonant interaction of sound wave with internal solitons in the coastal zone

Abstract: Naturally occurring internal solitary wave trains (solitons) have often been observed in the coastal zone, but no reported measurements of such solitary waves include low‐frequency long‐range sound propagation data. In this paper, the possibility that internal waves are responsible for the anomalous frequency response of shallow‐water sound propagation observed in the summer is investigated. The observed transmission loss is strongly time dependent, anisotropic and sometimes exhibits an abnormally large attenuation over some frequency range. The parabolic equation (PE) model is used to numerically simulate the effect of internal wave packets on low‐frequency sound propagation in shallow water when there is a strong thermocline. It is found that acoustic transmission loss is sensitive to the signal frequency and is a ‘‘resonancelike’’ function of the soliton wavelength and packet length. The strong interaction between acoustic waves and internal waves, together with the known characteristics of internal waves in the coastal zone, provides a plausible explanation for the observed anomalous sound propagation in the summer. By decomposing the acoustic field obtained from the PE code into normal modes, it is shown that the abnormally large transmission attenuation is caused by ‘‘acoustic mode‐coupling’’ loss due to the interaction with the internal waves. It is also shown that the ‘‘resonancelike’’ behavior of transmission loss predicted by the PE analysis is consistent with mode coupling theory. As an inverse problem, low‐frequency acoustic measurements could be a potential tool for remote‐sensing of internal wave activity in the coastal zone.

Gravity waves in the middle atmosphere observed by Rayleigh lidar: 2. Climatology

Abstract: A large data set obtained by Rayleigh lidars during 4 years has been analyzed in order to describe the gravity wave climatology in the 30- to 75-km altitude range at mid-latitude. The lidar data were collected in two sites different with respect to orography, both located in the south of France (44°N). The seasonal variability of the wave activity, the vertical growth of potential energy density per unit mass, and the power spectral density versus vertical wave number are shown. The seasonal variability of the wave activity is found to be mainly annual, the maximum of activity occurring during winter. A semiannual component, with a secondary maximum in summer, is superposed to the annual cycle above 60-km altitude. The power spectral density increases from the stratosphere to the mesosphere in the entire spectral range. A significant positive correlation is found between the wave activity and the wind intensity in the stratosphere. Finally, some simple hypotheses, in terms of wave sources and wave transmission, are advanced in order to get an insight into the causes of the observed seasonal and geographical variability of the wave activity.

Instability of Taylor-Sedov blast waves propagating through a uniform gas.

Abstract: We present the first measurements of an instability in Taylor-Sedov blast waves propagating through a uniform gas. The instability occurred in a gas whose adiabatic index was low. Amplitude perturbations grew as a power of time. Our observations are compared to theory.