Application of a supersonic kernel-function procedure to flutter analysis of thin lifting surfaces
Flutter analysis for thin lifting surfaces by application of supersonic kernel function procedure
Cunningham, H. J.↗
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Nuclear rocket shielding methods, modification, updating, and input data preparation. Volume 6 - Point kernel techniques Final progress report
Point kernel techniques for use with nuclear rocket shielding methods, modification, updating, and input data preparation - Vol. 6
Disney, R. K.↗
Experimental determination of some kernel functions in the multiple integral method for nonlinear creep of polyvinyl chloride
Polyvinyl chloride nonlinear viscoelastic behavior by multiple integral representation, determining kernel functions for mixed time parameters from tension/torsion creep experiments
Findley, W. N.↗
Smoothness of solutions of Volterra integral equations with weakly singular kernels
Differentiability of nonlinear Volterra integral equations of second kind with convolutional weakly singular kernels
Feldstein, A.↗
Kernel function for nonplanar oscillating surfaces in supersonic flow
Kernel function for nonplanar oscillating surfaces in supersonic flow, using finite element method for interfering configurations
Harder, R. L.↗
Application of the matrix exponential kernel
A point matrix kernel for radiation transport, developed by the transmission matrix method, has been used to develop buildup factors and energy spectra through slab layers of different materials for a point isotropic source. Combinations of lead-water slabs were chosen for examples because of the extreme differences in shielding properties of these two materials.
Rohach, A. F.↗
Derivation of aerodynamic kernel functions
The method of Fourier transforms is used to determine the kernel function which relates the pressure on a lifting surface to the prescribed downwash within the framework of Dowell's (1971) shear flow model. This model is intended to improve upon the potential flow aerodynamic model by allowing for the aerodynamic boundary layer effects neglected in the potential flow model. For simplicity, incompressible, steady flow is considered. The proposed method is illustrated by deriving known results from potential flow theory.
Dowell, E. H.↗
On the Kernel function for the unsteady supersonic cascade with subsonic leading edge locus
A function integral equation governing the unsteady motion of a supersonic cascade is derived. Various representations of the Kernel function are derived and discussed.
Goldstein, M. E.↗
A steady and oscillatory kernel function method for interfering surfaces in subsonic, transonic and supersonic flow
The theory, results and user instructions for an aerodynamic computer program are presented. The theory is based on linear lifting surface theory, and the method is the kernel function. The program is applicable to multiple interfering surfaces which may be coplanar or noncoplanar. Local linearization was used to treat nonuniform flow problems without shocks. For cases with imbedded shocks, the appropriate boundary conditions were added to account for the flow discontinuities. The data describing nonuniform flow fields must be input from some other source such as an experiment or a finite difference solution. The results are in the form of small linear perturbations about nonlinear flow fields. The method was applied to a wide variety of problems for which it is demonstrated to be significantly superior to the uniform flow method. Program user instructions are given for easy access.
Cunningham, A. M., Jr.↗
A computer program to find the kernel of a polynomial operator
This paper presents a FORTRAN program written to solve for the kernel of a matrix of polynomials with real coefficients. It is an implementation of Sain's free modular algorithm for solving the minimal design problem of linear multivariable systems. The structure of the program is discussed, together with some features as they relate to questions of implementing the above method. An example of the use of the program to solve a design problem is included.
Gejji, R. R.↗
On the logarithmic-singularity correction in the kernel function method of subsonic lifting-surface theory
A logarithmic-singularity correction factor is derived for use in kernel function methods associated with Multhopp's subsonic lifting-surface theory. Because of the form of the factor, a relation was formulated between the numbers of chordwise and spanwise control points needed for good accuracy. This formulation is developed and discussed. Numerical results are given to show the improvement of the computation with the new correction factor.
Lan, C. E.↗
The Stokes problem for the ellipsoid using ellipsoidal kernels
A brief review of Stokes' problem for the ellipsoid as a reference surface is given. Another solution of the problem using an ellipsoidal kernel, which represents an iterative form of Stokes' integral, is suggested with a relative error of the order of the flattening. On studying of Rapp's method in detail the procedures of improving its convergence are discussed.
Zhu, Z.↗
An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow
The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
Desmarais, R. N.↗
Characterization of a maximum-likelihood nonparametric density estimator of kernel type
Kernel type density estimators calculated by the method of sieves. Proofs are presented for the characterization theorem: Let x(1), x(2),...x(n) be a random sample from a population with density f(0). Let sigma 0 and consider estimators f of f(0) defined by (1).
Geman, S.↗
The NAS kernel benchmark program
A collection of benchmark test kernels that measure supercomputer performance has been developed for the use of the NAS (Numerical Aerodynamic Simulation) program at the NASA Ames Research Center. This benchmark program is described in detail and the specific ground rules are given for running the program as a performance test.
Bailey, D. H.↗
On the solution of integral equations with strong ly singular kernels
In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.
Kaya, A. C.↗
On the solution of integral equations with strongly singular kernels
Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.
Kaya, A. C.↗
A simple method for computing the relativistic Compton scattering kernel for radiative transfer
Correct computation of the Compton scattering kernel (CSK), defined to be the Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution, is reported. The CSK is analytically reduced to a single integral, which can then be rapidly evaluated using a power series expansion, asymptotic series, and rational approximation for sigma(s). The CSK calculation has application to production codes that aim at understanding certain astrophysical, laser fusion, and nuclear weapons effects phenomena.
Prasad, M. K.↗