16 research outputs found
Structure of the isotropic transport operators in three independent space variables
Based on the idea of separation of variables, a spectral theory for the three-dimensional, stationary, isotropic transport operator in a vector space of complex-valued Borel functions results in continuous sets of regular and generalized eigenfunctions
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Coupling 2-D cylindrical and 3-D x-y-z transport computations
This paper describes a new two-dimensional (2-D) cylindrical geometry to three-dimensional (3-D) rectangular x-y-z splice option for multi-dimensional discrete ordinates solutions to the neutron (photon) transport equation. Of particular interest are the simple transformations developed and applied in order to carry out the required spatial and angular interpolations. The spatial interpolations are linear and equivalent to those applied elsewhere. The angular interpolations are based on a high order spherical harmonics representation of the angular flux. Advantages of the current angular interpolations over previous work are discussed. An application to an intricate streaming problem is provided to demonstrate the advantages of the new method for efficient and accurate prediction of particle behavior in complex geometries
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Waukegan Station plume
In a previous report on effects of thermal discharges from power plants into the Great Lakes, we stressed the need for a statistical analysis of the spatial and temporal pattern of the thermal plume. The plume pattern is recognized as stochastic in nature and requires statistical analysis. A single realization of the Waukegan Station plume is studied with emphasis on its information content. Areas between isotherms at various depths are computed together with volumes of water in given temperature ranges above ambient; these measurements indicate the extent of the various parts of the plume together with the heat content of each part
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Flexible cubic spline interpolation
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
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Generalization of Spatial Channel Theory to Three-Dimensional x-y-z Transport Computations
Spatial channel theory, initially introduced in 1977 by M. L. Williams and colleagues at ORNL, is a powerful tool for shield design optimization. It focuses on so called ''contributon'' flux and current of particles (a fraction of the total of neutrons, photons, etc.) which contribute directly or through their progeny to a pre-specified response, such as a detector reading, dose rate, reaction rate, etc., at certain locations of interest. Particles that do not contribute directly or indirectly to the pre-specified response, such as particles that are absorbed or leak out, are ignored. Contributon fluxes and currents are computed based on combined forward and adjoint transport solutions. The initial concepts were considerably improved by Abu-Shumays, Selva, and Shure by introducing steam functions and response flow functions. Plots of such functions provide both qualitative and quantitative information on dominant particle flow paths and identify locations within a shield configuration that are important in contributing to the response of interest. Previous work was restricted to two dimensional (2-D) x-y rectangular and r-z cylindrical geometries. This paper generalizes previous work to three-dimensional x-y-z geometry, since it is now practical to solve realistic 3-D problems with multidimensional transport programs. As in previous work, new analytic expressions are provided for folding spherical harmonics representations of forward and adjoint transport flux solutions. As a result, the main integrals involve in spatial channel theory are computed exactly and more efficiently than by numerical quadrature. The analogy with incompressible fluid flow is also applied to obtain visual qualitative and quantitative measures of important streaming paths that could prove vital for shield design optimization. Illustrative examples are provided. The connection between the current paper and the excellent work completed by M. L. Williams in 1991 is also discussed