Numerical methods for mixed boundary value problems of shells of revolution
Numerical methods for mixed boundary value problem of axisymmetric shells of revolution, using truncated series expansion and finite difference expressions
Kalnins, A.↗
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Influence of bandwidth restriction on the signal-to-noise performance of a modulated PCM/NRZ signal, part 2
Analyzing effects of bandlimiting on performance of digital transmission corrupted by additive white Gaussian noise by averaging and series expansion
Shehaden, N. M.↗
Transformation of a potential function under coordinate rotations
Potential function transformation under coordinate rotations, deriving coefficients for Laplace equation series expansion
Levie, S. L., Jr.↗
A note on laminar shear flow over impulsively started bodies.
Prediction of the shear flow around bodies impulsively set into motion at a uniform velocity. Information is presented on the local wall shear stress, velocity distribution, steady flow times, and thermal response for wedge flows where local flow acceleration occurs. The essential features of the flow field are found to be describable by the approximate series expansion method of Goldstein and Rosenhead (1936). This method would appear to be useful in rapidly calculating the viscous drag on the forward face of various shaped bodies where local flow acceleration occurs.
Back, L. H.↗
An initial value method for the Ambarzumian integral equation.
It is shown that a general class of nonlinear integral equations may be transformed into a Cauchy system. That this leads to an effective numerical scheme is demonstrated by solving the Ambarzumian integral equation. The new method does not involve successive approximations or series expansions.
Buell, J.↗
Noniterative estimation of a nonlinear parameter
An algorithm is described which solves the parameters X = (x1,x2,...,xm) and p in an approximation problem Ax nearly equal to y(p), where the parameter p occurs nonlinearly in y. Instead of linearization methods, which require an approximate value of p to be supplied as a priori information, and which may lead to the finding of local minima, the proposed algorithm finds the global minimum by permitting the use of series expansions of arbitrary order, exploiting an a priori knowledge that the addition of a particular function, corresponding to a new column in A, will not improve the goodness of the approximation.
Bergstroem, A.↗
On propagation of long waves in curved ducts.
A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.
Rostafinski, W.↗
Some approximation concepts for structural synthesis.
An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss example problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.
Schmit, L. A., Jr.↗
Auroral ion velocity distributions using a relaxation model.
Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.
St-Maurice, J.-P.↗
Quantitative magnetospheric models derived from spacecraft magnetometer data
Quantitative models of the external magnetospheric field were derived by making least-squares fits to magnetic field measurements from four IMP satellites. The data were fit to a power series expansion in the solar magnetic coordinates and the solar wind-dipole tilt angle, and thus the models contain the effects of seasonal north-south asymmetries. The expansions are divergence-free, but unlike the usual scalar potential expansions, the models contain a nonzero curl representing currents distributed within the magnetosphere. Characteristics of four models are presented, representing different degrees of magnetic disturbance as determined by the range of Kp values. The latitude at the earth separating open polar cap field lines from field lines closing on the dayside is about 5 deg lower than that determined by previous theoretically-derived models. At times of high Kp, additional high latitude field lines are drawn back into the tail.
Mead, G. D.↗
X-alpha calculation of transition energies in multiply ionized atoms
It is shown that the accuracy of calculations can be improved if appropriate (different) values of alpha are used for each configuration. Alternatively, the Slater Transition state can be used, wherein a total energy difference is related to a difference in single electron eigenvalues. By a series expansion, the value of alpha for an excited configuration can be related to its value for the ground state configuration. The terms Delta alpha (delta Epsilon/delta alpha) exhibit a similar dependence on atomic number as the ground state values of alpha. Results of sample calculations are reported and compared with experiment.
Ringers, D. A.↗
Theoretical study of H2/+/ spectroscopic properties. II, III
Description of the theoretical spectroscopic properties of the 2p pi/sub u/ and 3d sigma/sub g/ excited states of the H2/+/ hydrogen molecular ion. Numerical integration of the Schrodinger equation is used to determine vibration-rotation eigenvalues. Dunham power series expansions are used to determine the equilibrium separation, potential coefficients, and spectroscopic constants. The eigenvalues are used to determine delta-G, Bv, Dv, and Hv.
Beckel, C. L.↗
An implicit sampling theorem for bounded bandlimited functions
A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.
Bar-David, I.↗
Digital approximation of continuous-data control systems by point-by-point state comparison
This paper presents a point-by-point state comparison method of approximating a continuous-data system by a sampled-data system. The problem is to attempt the matching of the states of the two systems at the sampling instants. A partial matching has to be conducted if the systems have more states than controls. A weighting matrix is used to regulate the partial matching and weights placed on each state. The digital approximation is affected by use of forward gain E(T) and feedback gain G(T) in the sampled-data system. It is shown that, in general, these gains can be approximated by truncated Taylor series expansions. An illustrative example is given using the one-axis dynamics of the Skylab satellite.
Kuo, B. C.↗
Electrocardiogram signal analyzer
Algorithm based on Taylor series expansion of Fourier transform has been developed and used for detection of cardiac arrhythmias in real-time electrocardiogram signal.
Portnoy, W. M.↗
Some approximation concepts for structural synthesis
An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.
Schmit, L. A., Jr.↗
Proton tissue dose for the blood forming organ in human geometry: Isotropic radiation
A computer program is described which calculates doses averaged within five major segments of the blood forming organ in the human body taking into account selfshielding of the detailed body geometry and nuclear star effects for proton radiation of arbitrary energy spectrum (energy less than 1 GeV) and isotropic angular distribution. The dose calculation includes the first term of an asymptotic series expansion of transport theory which is known to converge rapidly for most points in the human body. The result is always a conservative estimate of dose and is given as physical dose (rad) and dose equivalent (rem).
Khandelwal, G. S.↗
Analysis of three-component aeromagnetic data
The numerical method of obtaining three field components from total field measurements, using double Fourier series expansion, is presented. The expressions for moments of the anomalous field components over a finite area are given. The magnitude and direction of the magnetization vector indicate that the vertical component of the magnetic field calculated from total field observations is more accurate at higher geomagnetic latitudes than at lower latitudes. The opposite is true for the horizontal components. The error in determining the magnetization vector directions are significantly large over most of the range of variation of declination and inclination of the vector, demonstrating the practical limitations of computing field components from total field data even under the best of conditions.
Bhattacharyya, B. K.↗