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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

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

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

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

Constructive polynomial approximation in Sobolev spaces

Description: A simple, constructive proof of the so-called Bramble--Hilbert Lemma is presented. This result is frequently used in establishing the approximation properties of finite-element function spaces, and several of the extensions studied here are directed to this type of application. Some examples of the uses of these results are presented.
Date: June 1, 1978
Creator: Dupont, T & Scott, R
Partner: UNT Libraries Government Documents Department

Some experiments with piecewise cubic interpolation

Description: An iterative refinement process for adjusting derivative values in the Hermite representation of a piecewise cubic function to produce visually pleasing interpolants is described. The difficulties encountered at various stages in the development of the algorithm are outlined, and future research directions are indicated. 22 figures.
Date: June 1, 1978
Creator: Fritsch, F.N.
Partner: UNT Libraries Government Documents Department

Piecewise cubic interpolation methods

Description: Interpolation of one-dimensional data using piecewise cubic interpolants is considered. Methods are presented for modifying the derivative values in the Hermite representation in order to eliminate the ''bumps'' and ''wiggles'' that frequently plague the more common cubic spline or Akima interpolants. The resulting interpolant is C/sup 1/, but generally not C/sup 2/. The report consists of a reproduction of a poster prepared for a meeting. 27 figures.
Date: November 1, 1978
Creator: Fritsch, F.N. & Carlson, R.E.
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 use linear-blending interpolation formulas. These generators are based on an i, j, k index scheme that is used to number nodal points, construct elements, and develop displacement and traction boundary conditions. This code can generate truss elements (2 modal points); plane stress, plane strain, and axisymmetry two-dimensional continuum elements (4 to 8 nodal points); plate elements (4 to 8 nodal points); and three-dimensional continuum elements 8 to 21 nodal points). The traction loads generated are consistent with the element generated. The expansion--contraction option is of special interest. This option makes it possible to change an existing mesh such that some regions are refined and others are made coarser than the original mesh. 9 figures.
Date: May 1, 1979
Creator: Cook, W.A.
Partner: UNT Libraries Government Documents Department

Estimation of random fields from network observations. Technical report No. 26

Description: When one has observed a random field Z at some points and recorded its values (network observations), a natural problem is to estimate Z at points where there are no observations. This dissertation deals first with this problem in an abstract setting, in m dimensions; later, it considers the estimation of a spatial two-dimensional random field. The problem then is one of constructing an estimated map of Z over a geographic area. For a given network of stations the quality of a map depends on the method of estimation. But for the given method of estimation the quality of a map depends on the choice of locations for the stations. This is the problem of network design. Both the study of methods of estimation and the problem of network design are addressed. 16 figures. (RWR)
Date: June 1, 1979
Creator: Cabannes, A F
Partner: UNT Libraries Government Documents Department

Misspecification of trend in spatial random-function interpolation with application to oxidant mapping. Technical report No. 28

Description: In epidemiological studies of the effects of air pollution it is desirable to obtain estimates of the exposure to various pollutants of persons living throughout a geographical region under study. It is typically the case that pollution levels are measured at only a few locations. The problems of interpolating these values and of determining the accuracy of interpolation are amenable to analysis by way of spatial stochastic models. Such models can lead to an optimal interpolation technique, in a manner which is reviewed here. Estimators based on a correctly and incorrectly specified constant mean are compared with estimators based on an unspecified constant mean. The ratios of the mean squared errors (MSE) decreases with decreasing correlation between observations, and are very close to one. Estimation done with a specified linear trend function to estimation are compared with an unspecified linear trend function. For interpolation, the MSE's tend to be close except for high underlying correlation models. For extrapolation - the MSE values can be very different. A biased partially constrained estimator versus a fully constrained universally unbiased estimator in the presence of a linear trend is discussed. The biased and unbiased estimators have similar performance, except for very steep linear slopes of the trend. The comparisons of these sections are made in the context of rather special and perhaps unrealistic model assumptions. The Kriging method is used for interpolating (mapping) values of oxidant levels from 1973 at 16 stations located in the San Francisco Bay Area. Constant and linear trends are used for the purpose. The method requires knowledge of the spatial covariance structure of the pollutant to which it is applied. Some difficulties encountered in estimating this for oxidant levels in the San Francisco Bay Area are mentioned.
Date: September 1, 1979
Creator: Faith, R & Sheshinski, R
Partner: UNT Libraries Government Documents Department

Program RECENT (version 79-1): reconstruction of energy-dependent neutron cross sections from resonance parameters in the ENDF/B format. [In FORTRAN IV for CDC-7600 and Cray-1]

Description: Program RECENT reconstructs energy-dependent neutron total, elastic, capture, and fission cross sections from a combination of resonance parameters and tabulated background cross sections in the ENDF/B format. Entire evaluations, not just cross sections, are written to the result file, which is in ENDF/B format. The output includes the original resonance parameters in a form that can be used in Doppler broadening and self-shielding calculations. A listing of the source deck is available on request. 5 figures, 5 tables.
Date: October 31, 1979
Creator: Cullen, D.E.
Partner: UNT Libraries Government Documents Department