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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Nonsimilar solution to complex laminar boundary layer problems, applying matrix concept to integral relations via Taylor series expansion of parameters
Multispecies quantum fluids ground state energy, using variational method and series expansion
Series expansion to evaluate periodic solvents ejection paths
Radiating collinear open ended waveguides and near field coupling analyzed using simultaneous integral equations and Fourier series expansion of aperture field
Taylor series expansion used in correcting quantized digital coefficient errors in hybrid feedback control system
Differential approximation for radiant energy loss in nonequilibrium plasma generated from truncated Taylor series expansion of radiation source function
Boundary layer flow in thin shock layer about axisymmetric blunt bodies studied by Blasius type series expansion technique
Series expansion for least squares optimization of random signal systems
Calculating exponential integral using Chebyshev series expansion of associated functions
Planar restricted three body problem in Thiele coordinates, developing recurrence formulas for coefficients in Taylor series expansions of solution
Numerical methods for mixed boundary value problem of axisymmetric shells of revolution, using truncated series expansion and finite difference expressions
Analyzing effects of bandlimiting on performance of digital transmission corrupted by additive white Gaussian noise by averaging and series expansion
Potential function transformation under coordinate rotations, deriving coefficients for Laplace equation series expansion
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.
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.
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.
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.
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.