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A high-degree spherical harmonic series is used to compute the radial deformation of the Earth by oceanic tidal loading. By exploiting fast numerical transforms, this approach is found to be much more efficient, but no less accurate, than the traditional Green's function approach. The method is used to derive an atlas of load tide maps for 10 constitutents of the NSWC ocean tide model.
The antiplane strain problem of an edge cracked elastic plate subjected to a surface displacement load is solved, and the surface line loads are obtained using conformal mapping techniques. Results are presented for the yield, stress, strain and displacement distributions, and stress intensity factors in the plate. A superposition technique and Green's functions are used to determine the strain field on the upper plate surface due to arbitrarily applied tensile stress on the lower plate surface.
Using the two-layer anisotropic random medium, a mathematically rigorous, fully polarimetric model is developed to compute the Mueller and covariance matrices in the backscattering direction for various kinds of earth terrain. The electric field is first written in the form of an integral equation involving the unperturbed dyadic Green's function in the absence of the permittivity fluctuations. The integral equation is then solved by an iterative series known as the Born series. With only the first term of the series, which physically describes a single scattering process, the fully polarimetric backscattering coefficients are derived. Four different kinds of upgoing and downgoing waves exist due to the excitation of both ordinary and extraordinary waves in the anisotropic random medium. An averaging scheme over the azimuthal direction is used to simulate the effects on the radar backscattering due to the azimuthal randomness in the growth direction of leaves in tree and grass fields.
Transient sound propagation in an inhomogeneous moving medium is considered. For circumstances in which the medium is slowly varying over distances of a wavelength but possibly varying substantially over the propagation distance, a derivation is given of a new wave equation, which implicitly allows for diffraction and scattering and which also is consistent with earlier geometrical acoustics formulations. This wave equation is used as a starting point to derive a version of the Helmholtz-Kirchhoff integral relation that applies to inhomogeneous moving medium. It is suggested that a good approximation to the Green's function that appears in this relation is that derived from geometrical acoustics, the approximation becoming progressively better the shorter the distance between surfaces in the computation. It should also be at least as good as conventional ray acoustics, but can account for diffraction effects, such as at caustics.
A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.
Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.
A method is developed to compute frequency response and acoustic radiation of a complex shell. The axisymmetric geometry of the shell includes cylindrical, conical, and spherical segments stiffened by discrete rings and bulkheads. The shell is coupled to internal masses and elastic frames. Shell segments are treated by transfer matrices. Rings, bulkheads, frames, and concentrated masses are treated by impedances at junctions of segments. The shell is coupled to an external acoustic fluid treated by Green's function and curved surface elements. A major issue facing the method's treatment of the fluid would be lack of existence or uniqueness encountered in the uncoupled, external acoustic problem at characteristic wavenumbers. By using a simple spherical shell, without internal structures, this potential hindrance is shown not to arise. A fuller application of the method awaits subsequent results.
Ab initio potential energy curves for He2(+) are computed using full CI wavefunctions in conjuction with large Gaussian and Slater basis sets. The computed curves yield rotational-vibrational transitions with errors of less than 1/cm. They also yield quasi-bound levels with energies and lifetimes in reasonable agreement with translational spectroscopy measurements. The best D(e) is estimated to be 2.470 eV. Green's function Monte Carlo calculations yield a very similar value, 2.466 + or - 0.005.
A method is presented for analyzing a finite planar array of circular microstrip patches fed by coaxial probes. The self- and mutual impedances between array elements are calculated using the method of moments with the dyadic Green's function for a dielectric layer on a ground plane. The patch circuits are determined by using the reaction integral equation. The active input impedance as well as the active element pattern of the array are computed from a knowledge of the resultant patch currents. The calculated results for two-element and eight-element linear arrays are in good agreement with experimental data. The active reflection coefficient and element pattern for the center and edge elements of a two-dimensional array as a function of scan angle are also presented.
An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.
Pressure fluctuations in a turbulent channel and a homogeneous shear flows are investigated by analyzing databases obtained from direct numerical simulations. Detailed statistics associated with the pressure fluctuations in both flows are discussed. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are examined. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them.
High- and low-frequency methods to analyze various radiation elements located on aerospace vehicles with combinations of conducting, nonconducting, and energy absorbing surfaces and interfaces. The focus was on developing fundamental concepts, techniques, and algorithms which would remove some of the present limitations in predicting radiation characteristics of antennas on complex aerospace vehicles. In order to accomplish this, the following subjects were examined: (1) the development of techniques for rigorous analysis of surface discontinuities of metallic and nonmetallic surfaces using the equivalent surface impedance concept and Green's function; (2) the effects of anisotropic material on antenna radiation patterns through the use of an equivalent surface impedance concept which is incorporated into the existing numerical electromagnetics computer codes; and (3) the fundamental concepts of precipitation static (P-Static), such as formulations and analytical models. A computer code was used to model the P-Static process on a simple structure. Measurement techniques were also developed to characterized the electrical properties at microwave frequencies. Samples of typical materials used in airframes were tested and the results are included.
A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.
A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is used to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require a knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.
The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.
The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.
The surface displacements of elastic waves scattered from a surface-breaking crack are measured with a capacitive transducer on a 2D plate, and comparisons with theoretical predictions are reported. The noncontacting detector has a wide and flat frequency response which measures the response of a glass plate to the propagation of Rayleigh-Lamb waves. A theoretical simulation of the surface displacements is generated by multiplying experimental traces with a cosine window, and Green's function is used to compute the source function. Power spectra are also recorded from the experiment to compare the results with a finite-element model of the crack, and good agreement is reported for results in both the time and frequency domains. The crack can be detected in the far field when the spacing of the receiver locations is small, and the transducer/probe appears to be a practical flaw-detection instrument.
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.