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Straightforward relationships between Weinstock's (1969) propagator, U sub A, the Vlasov propagator, U, and the ensemble average Vlasov propagator, U (in carets) are derived. It is shown that U and U (in carets) are related to the characteristic trajectories of the Vlasov equation, and that U (in carets) can be related to various statistical correlations of the turbulent fields.
Measurement of the characteristics of the propagating waves on an array of identical wires. Experimental data showed that propagating waves could be supported on the structure without significant attenuation for two frequency bands. The central frequency of the higher passband was about three times higher tha n that of the lower passband. All propagating waves were slow waves. Phase velocities were varied from 0.99 to 0.25 of the free-space velocity. The k-beta diagrams of the waves were obtained and were found to be in good agreement with theory.
Propagation of waves in curved ducts and pipes belong to the class of motion which is characterized by wave patterns totally different from those known in straight ducts or in unlimited space. The curvilinear boundaries are responsible for the appearance of a continuous standing radial wave which in turn affects the transmitted tangential waves. The purpose of this paper is to solve the problem of propagation of long acoustic waves in slightly and sharply bent ducts. This problem has been only partially analyzed by various authors. In this study two acoustic systems are considered which allow determination of the basic modes of motion and describe the transition and distortion of plane waves as they propagate down the curved channel. A detailed study of the behavior of waves in junctions between straight and curved ducts is also given. Solutions and expressions for principal modes of the wave are obtained by using the linearized equation of motion solved for its characteristic values. This original approach required a novel use of Bessel functions to determine the characteristic values of the steady and the decaying fields of motion.
The mid-latitude ionospheric and neutral atmospheric models are coupled with an advanced three dimensional ray tracing program to see what success would be obtained in predicting the wave propagation conditions and to study to what extent the use of theoretical ionospheric models is practical. The Penn State MK 1 ionospheric model, the Mitra-Rowe D region model, and the Groves' neutral atmospheric model are used throughout this work to represent the real electron densities and collision frequencies. The Faraday rotation and differential Doppler velocities from satellites, the propagation modes for long distance high frequency propagation, the group delays for each mode, the ionospheric absorption, and the spatial loss are all predicted.
One of the key parameters in estimation of the probability of contamintion of the outer planets (Jupiter, Saturn, Uranus, etc.) is the probability of growth (Pg) of terrestrial microorganisms on or near these planets. For example, Jupiter appears to have an atmosphere in which some microbial species could metabolize and propagate. This study includes investigation of the likelihood of metabolism and propagation of microbes suspended in dynamic atmospheres. It is directed toward providing experimental information needed to aid in rational estimation of Pg for these outer planets. Current work is directed at demonstration of aerial metabolism under near optimal conditions and tests of propagation in simulated Jovian atmospheres.
A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described.
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
A ten year summary was given of university research on the nature and characteristics of space related plasma resonance phenomena, whistler propagation in laboratory plasmas, and theoretical and experimental studies of plasma wave propagation. Data are also given on long delayed echoes, low frequency instabilities, ionospheric heating, and backscatter, and pulse propagation. A list is included of all conference papers, publications, and reports resulting from the study.
Analytical methods developed for consolidation of fatigue and fatigue-crack-propagation data for use in design of metallic aerospace structural components are evaluated. A comprehensive file of data on 2024 and 7075 aluminums, Ti-6Al-4V alloy, and 300M steel was established by obtaining information from both published literature and reports furnished by aerospace companies. Analyses are restricted to information obtained from constant-amplitude load or strain cycling of specimens in air at room temperature. Both fatigue and fatigue-crack-propagation data are analyzed on a statistical basis using a least-squares regression approach. For fatigue, an equivalent strain parameter is used to account for mean stress or stress ratio effects and is treated as the independent variable; cyclic fatigue life is considered to be the dependent variable. An effective stress-intensity factor is used to account for the effect of load ratio on fatigue-crack-propagation and treated as the independent variable. In this latter case, crack-growth rate is considered to be the dependent variable. A two term power function is used to relate equivalent strain to fatigue life, and an arc-hyperbolic-tangent function is used to relate effective stress intensity to crack-growth rate.
Recent studies have used the superposition principle (extended Huygens-Fresnel principle) to characterize completely the statistics of a field that has propagated through a thick slab of turbulent air in terms of the statistics for spherical-wave sources. In this paper, we consider the normal-mode decomposition associated with this linear system propagation model. In particular, we use the statistics of the atmospheric impulse response (Green's function) to show that the atmospheric mode decomposition exhibits far-field and near-field regimes very similar to those of free-space propagation. The significance of these results for optical communication through the atmosphere is briefly discussed.
Radio wave propagation predictions are described in which modern comprehensive theoretical ionospheric models are coupled with ray-tracing programs. In the computer code described, a network of electron density and collision frequency parameters along a band about the great circle path is calculated by specifying the transmitter and receiver geographic coordinates, time, the day number, and the 2800-MHz solar flux. The ray paths are calculated on specifying the frequency, mode, range of elevation angles, and range of azimuth angles from the great circle direction. The current program uses a combination of the Penn State MKI E and F region models and the Mitra-Rowe D and E region model. Application of the technique to the prediction of satellite to ground propagation and calculation of oblique incidence propagation paths and absorption are described. The implications of the study to the development of the next generation of ionospheric models are discussed.
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Next, computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
This study is concerned with the problem of electromagnetic wave propagation in a magneto-plasma filled coaxial structure. The problem is formulated using the classical boundary value problem approach. A numerical investigation shows the existence of propagating slow modes, backward modes, a quasi-TEM mode, and waveguide-type modes in a magneto-plasma filled coaxial structure. Dispersion curves for these different modes are presented. Measurements have been made of electromagnetic propagation in a coaxial electrode structure filled with longitudinally magnetized plasma. The annular plasma region had a 9.55 cm outer diameter, a 3.82 cm inner diameter and was approximately 60 cm long. A magnetic field of 300 gauss was employed. Electromagnetic wave frequencies were in the range .5 to 2.4 GHz. The plasma was generated by a continuous glow discharge. The resulting dispersion curves closely follow the predicted curves for the quasi-TEM mode.
Continuum theory is unsatisfactory for describing wave propagation in the transitional ionosphere, since the mean free path is of the same order as the characteristic length (i.e., Knudsen number in this region is of the order of unity). Therefore a transition model in which isotropic electrons behave as a fluid while the ions are governed by the kinetic equation modified by ion-electron collision effects is proposed to study acoustic wave propagation in the upper atmosphere in the altitude region from 500 to 2000 km. The results show that the dissipation of acoustic waves by electrons is through the viscous and thermal conduction effects, and the dissipation of acoustic waves by ions is through Landau damping. Comparisons of the characteristics of acoustic mode propagation and wave dissipation mechanisms in the collision-dominated, transitional from collisional to collisionless, and collisionless media are also discussed.
The continuity equation for cosmic ray propagation is used to derive a set of linear equations interrelating the fluxes of multiply charged nuclei as observed at any particular part of the galaxy. The derivation leads to model independent definitions for cosmic ray storage time, mean density of target nuclei and effective mass traversed. The set of equations form a common framework for comparisons of theories and observations. As an illustration, it is shown that there exists a large class of propagation models which give the same result as the exponential path length model. The formalism is shown to accommodate dynamic as well as equilibrium models of production and propagation.
A statistical study on the propagation characteristics of about 80 solar particle events is carried out using the data from Goddard cosmic-ray experiments. It is found that for particles near onset as well as maximum particle intensity at 1 AU, a linear relation exists between the velocity and the traveled distance. This holds for both relativistic electrons (0.5-1.1 MeV) and nonrelativistic protons (4-80 MeV). The relation indicates that particle propagation is independent of both rigidity and energy. It is shown that in general interplanetary diffusion plays a minor role in particle propagation during the initial phase of a flare effect. A study of the onset characteristics indicates that the speed of particle transport in the corona may be as high as 40 deg/hr. This behavior can not be accounted for by either magnetic-field or curvature drift.