An approximate method for predicting annulus inlet turbulent flow development characteristics
Newtonian fluid turbulent flow development characteristics in inlet region of smooth concentric annulus from momentum integral equations
Bathie, W. W.↗
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Results for “integral equations”
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Non-symmetrical two dimensional scattering program
Computer program, 2DSCAT, solves integral equation for currents induced by electric or magnetic plane wave incident upon one or more conducting cylinders. Subroutine, FIELD, assumes that an incident wave is perpendicular to the cylindrical surface. Restrictions on this program are given.
Hatfield, J.↗
Symmetrical two dimensional scattering program
Computer program solves integral equation for currents induced by electric or magnetic plane wave incident upon one or more conducting cylinders with a midplane of symmetry. Program utilizes symmetry of the geometry. Restrictions on the program are given.
Hatfield, J.↗
Numerical methods of integration applied in the nonlinear dynamic analysis of shells of revolution
Evaluating methods of numerically integrating equations of motion for nonlinear dynamic analyses of shells of revolution by matrix displacement method
Stricklin, J. A.↗
FORTRAN 4 program for studying ion polar molecule collisions
Computer programs for integrating equations of motion of ion-polar-molecule collisions
Canright, R. B., Jr.↗
A computer program to determine radiating, nonadiabatic, inviscid flow over a blunt body by the method of integral relations
Computer program for determining radiating nonadiabatic inviscid flow over blunt body by integral equations
Taylor, F. W.↗
Self-consistent Green's-function approach to the electron-gas problem
Electron gas problem in metal physics by self consistent Green function formalism, presenting momentum-space Feynman rules and integral equations derivation
Zmuidzinas, J. S.↗
Almost-periodic behavior of solutions of a nonlinear Volterra system
Almost periodic solutions of two nonlinear Volterra integral equations
Miller, R. K.↗
Studies in spectral line formation. IV - Singly ionized calcium
Integral equations for source functions of Ca II H, K and IR triplet lines for transfer through homogeneous stellar atmosphere
Finn, G. D.↗
Analysis of elastic cover plates
Stress intensity factors of periodically spaced elastic cover plates bonded to elastic half plane, solving contact problem by Fredholm integral equation
Erdogan, F.↗
Asymptotically almost periodic solutions of a nonlinear Volterra system
Nonlinear Volterra integral equation system solution using almost periodic forced oscillations
Miller, R. K.↗
Elastic cracks and screw dislocation pile-ups crossing a bimaterial interface
Elastic cracks and screw dislocation pile-ups crossing bimaterial interface, deriving dual singular integral equations
Chou, T.-W.↗
Lifting-surface theory for calculating the loading induced on a wing by a flap
A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.
Johnson, W. A.↗
Prediction of unsteady aerodynamic loadings caused by trailing edge control surface motions in subsonic compressible flow: Analysis and results
A theoretical analysis and a computer program have been developed for the prediction of unsteady lifting surface loadings caused by motions of trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation has been formulated by isolating the singularities from the non-singular terms and establishing a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to four control surfaces on each half span can be accommodated.
Rowe, W. S.↗
A selective review of ground based passive microwave radiometric probing of the atmosphere
The absorption of the various atmospheric constituents with significant microwave spectra is reviewed. Based on the available data, an estimate is made of the uncertainty in the microwave absorption coefficients of the major constituents, water vapor and oxygen. Then there is an examination of the integral equations which describe the three basic types of observations: measurement of the spectrum of absorption of the sun's radiation by an atmospheric constituent, measurement of the emission spectrum of a constituent, and measurement at one frequency of the zenith angle dependence of the absorption or emission of the atmosphere.
Welch, W. J.↗
Two-dimensional finite-element temperature variance analysis
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Heuser, J. S.↗
A theoretical study of radar return and radiometric emission from the sea
The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.
Peake, W. H.↗
On backscatter from spatially varying surfaces
The theory of radar backscatter from rough (spatially varying) surfaces is discussed. An integral equation developed to describe the radar backscatter from a perfectly conducting surface is applied to nonsmooth surfaces. The results are compared with those obtained by Beckmann as well as those obtained by Wright. Differences between the three solutions are discussed.
Grody, N. C.↗