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Uranium burnout values

Description: Attached is the interpolated uranium burnout values for .570% through 3.000% U-235. Due to increasing interest in higher U-235 values, this document was issued to replace HW-77929 which contained values to 1.519% U-235. The source data was based on the Reactor Cost Studies burnout schedule obtained from Washington -- AEC.
Date: January 30, 1964
Creator: Smith, W. G.
Partner: UNT Libraries Government Documents Department

Flexible cubic spline interpolation

Description: This report describes a simple, efficient, and flexible program for cubic spline interpolation in one dimension, suitable for inclusion in the ANL Subroutine Library and in an interactive timesharing system. Most of the cubic spline programs already available either restrict the boundary conditions to knowledge of the first derivative at both end points, or require the second derivatives to vanish at these points. The program described here removes these restrictions and enables the user to adopt boundary conditions appropriate for his own problem. The advantage is demonstrated for the extreme case of interpolating the function x log (1/x), which has singularities in all its derivatives at x = 0.
Date: March 1, 1972
Creator: Abu-Shumays, I. K.
Partner: UNT Libraries Government Documents Department

Flexible cubic spline interpolation

Description: This report describes a simple, efficient, and flexible program for cubic spline interpolation in one dimension, suitable for inclusion in the ANL Subroutine Library and in an interactive timesharing system. Most of the cubic spline programs already available either restrict the boundary conditions to knowledge of the first derivative at both end points, or require the second derivatives to vanish at these points. The program described here removes these restrictions and enables the user to adopt boundary conditions appropriate for his own problem. The advantage is demonstrated for the extreme case of interpolating the function x log (1/x), which has singularities in all its derivatives at x = 0.
Date: March 1, 1972
Creator: Abu-Shumays, I.K.
Partner: UNT Libraries Government Documents Department

Computer simulation studies of parabolic interpolation circuitry

Description: A computer-simulation study of parabolic interpolation circuitry for machine tool controllers was completed. Results showed that a tool center can be moved along any parabolic arc to within any realistic tolerance. Circuit design requirements were determined and input data required by the parabolic interpolators were defined. Simulation results showed that tool motion along a pronounced parabolic path would stay within a 1/2-microinch tolerance. An application of the parabolic interpolation toward reducing the large input data volumes required by conventional numerical controllers was achieved. (auth)
Date: December 28, 1973
Creator: Davenport, C.M.
Partner: UNT Libraries Government Documents Department

Piecewise polynomial functions

Description: This report contains a series of talks presented during the summer of 1975 at LLL on the general topic of piecewise polynomial functions. Such functions offer simple, accurate, economical, and flexible procedures for solving a wide variety of problems. The emphasis is on curve fitting, surface fitting, and applications to finite element approximations. This discussion is not intended as an all-inclusive, general presentation of piecewise polynomials. Rather, attention is directed to the basic of cubic (and bicubic) interpolation and approximation, since they represent a good first choice for many problems when increased accuracy over linear (or bilinear) approximations is desired. The text is divided into sections on univariate functions, cubic splines, bivariate functions, blending functions, and nonrectangular domains. 10 figures, 1 table. (RWR)
Date: January 1, 1976
Creator: Carlson, R. E.
Partner: UNT Libraries Government Documents Department

Iterative solution of the diffusion and P$sub 1$ finite element equations

Description: A method for obtaining solutions to the time-independent Boltzmann neutron transport equation on triangular grids with nonorthogonal boundaries and anisotropic scattering is developed. A functional is obtained from the canonical form of the multigroup transport equation. The angular variable is then removed by expanding the functional in spherical harmonics, retaining only the first two moments and limiting the anisotropic scattering to be linear. The finite element method is then implemented by using quadratic Lagrange-type interpolating polynomials to span the spatial domain. The resultant set of coupled linear equations is then solved iteratively. The applicability of convergence acceleration techniques developed for the finite difference method is tested and implemented where appropriate. Finally, a number of numerical experiments are performed to evaluate the performance of the proposed method. The results are compared to results obtained by various established methods. In all cases, agreement is excellent. 16 figures, 7 tables. (auth)
Date: February 1, 1976
Creator: Tomlinson, E.T.; Robinson, J.C. & Vondy, D.R.
Partner: UNT Libraries Government Documents Department

Robustness to misspecifications of correlation models. Technical report No. 2

Description: Optimal linear interpolation between discrete observations in R/sup 2/ depends on the random function model assumed to generate the two-dimensional field. Sensitivity of the optimal solution to errors in specification of the model are studied. An illustration using second-order stationary models with a misspecified autocorrelation function is examined in detail. We also explore, by examples, the sensitivity procedure when more distant data points are omitted from the calculations. We have found that the optimal linear estimator is grossly insensitive to misspecifications of the autocorrelation function. However, if the misspecified autocorrelation function is used in the calculation of the squared interpolation error--then such error calculations may be grossly misleading.
Date: July 22, 1976
Creator: Sheshinski, R.
Partner: UNT Libraries Government Documents Department

INGEN: a general purpose mesh generator for finite element codes

Description: INGEN is a general purpose mesh generator for two- and three-dimensional finite-element codes. The basic parts of the code are surface and three-dimensional region generators that are linear-blending interpolation formulas. These generators are based on an i, j, k index scheme which is used to number nodal points, construct elements, and develop displacement and traction boundary conditions. 12 figures, 2 tables.
Date: January 1, 1977
Creator: Cook, W. A.
Partner: UNT Libraries Government Documents Department

Integrated system for production of neutronics and photonics calculational constants. Program LINEAR (Version 77-1): linearize data in the Evaluated Nuclear Data File/Version B (ENDF/B) format

Description: We have written a computer code called LINEAR that both converts evaluated cross sections in the ENDF/B format to linear-linear interpolatable form and thins those sections already in that form. The main advantage of the code is that it eliminates the need for any subsequent code to consider anything but linear-linear data.
Date: January 12, 1977
Creator: Cullen, D. E.
Partner: UNT Libraries Government Documents Department

User's manual for porgrams FILXYZ and FUNXYZ. [For computing functions of one, two, or three variables at equally spaced points, in extended FORTRAN for CDC 6600 computer]

Description: Program FILXYZ prepares an input file for program FUNXYZ by merging together subfiles of data for a specified test configuration or set of test conditions based upon one, two, or three independent variables. Program FUNXYZ computes the function of one, two, or three variables of a set of empirical or test data to provide a file with values that are equally spaced over the independent variables. The programs are written in FORTRAN for use on the CDC 6600. 2 figures
Date: February 1, 1977
Creator: Holbrook, E. D.
Partner: UNT Libraries Government Documents Department

Interpolation and Approximation

Description: In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and the least squares approximation (a special case of best approximation) is discussed. In the third chapter orthogonal polynomials as discussed as well as bounded linear functionals in Hilbert spaces, interpolation and approximation and approximation in Hilbert space.
Date: May 1977
Creator: Lal, Ram
Partner: UNT Libraries

Synthesis of approximation errors

Description: A method is developed for the synthesis of the error in approximations in the large of regular and irregular functions. The synthesis uses a small class of dimensionless elementary error functions which are weighted by the coefficients of the expansion of the regular part of the function. The question is answered whether a computer can determine the analytical nature of a solution by numerical methods. It is shown that continuous least-squares approximations of irregular functions can be replaced by discrete least-squares approximation and how to select the discrete points. The elementary error functions are used to show how the classical convergence criterions can be markedly improved. There are eight numerical examples included, 30 figures and 74 tables.
Date: July 1, 1977
Creator: Bareiss, E. H. & Michel, P.
Partner: UNT Libraries Government Documents Department

EVIDENCE FOR THE ITINERANT ELECTRON MODEL OF FERROMAGNETISM AND FOR SURFACE PHOTOEMISSION FROM ANGLE-RESOLVED PHOTOEMISSION STUDIES OF IRON

Description: Angle-resolved HeI photoemission spectra of Fe(001) are reported and interpreted within the framework of a direct transition model using Callaway's ferromagnetic band structure. The generally good agreement between predicted and experimental peak positions is taken to be strong support for the itinerant electron theory of ferromagnetism. Spectra taken with nearly grazing incidence p-polarized light emphasize the one-dimensional density of states peaks, supporting Kliewer's theoretical predictions of surface photoemission. The importance of electron refraction is noted, as is the value of interpolation calculations for interpreting ARP spectra.
Date: October 1, 1977
Creator: Kevan, S.D.; Wehner, P.S. & Shirley, D.A.
Partner: UNT Libraries Government Documents Department

VISCOSITY OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FROM 0 - 150o C

Description: A critical evaluation of data on the viscosity of aqueous sodium chloride solutions is presented. The literature was screened through October 1977, and a databank of evaluated data was established. Viscosity values were converted when necessary to units of centigrade, centipoise and molal concentration. The data were correlated with the aid of an empirical equation to facilitate interpolation and computer calculations. The result of the evaluation includes a table containing smoothed values for the viscosity of NaCl solutions to 150 C.
Date: October 1, 1977
Creator: Ozbek, H.; Fair, J.A. & Phillips, S.L.
Partner: UNT Libraries Government Documents Department