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Title: TRANSPORT THEORY AND SPECTRAL PROBLEMS

Abstract

A simple model of time-independent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non- linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic one-velocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)

Authors:
Publication Date:
Research Org.:
New Mexico. Univ., Albuquerque
OSTI Identifier:
4259132
Report Number(s):
SCR-88
NSA Number:
NSA-13-018477
Resource Type:
Technical Report
Resource Relation:
Other Information: Presented at American Mathematical Society Symposium on Reactor Theory, New York, April 1959. Orig. Receipt Date: 31-DEC-59
Country of Publication:
United States
Language:
English
Subject:
PHYSICS AND MATHEMATICS; CONFIGURATION; NEUTRON FLUX; NEUTRONS; NUMERICALS; SPECTRA; TRANSPORT THEORY; VARIATIONS; VELOCITY

Citation Formats

Wing, g. M. TRANSPORT THEORY AND SPECTRAL PROBLEMS. United States: N. p., 1959. Web. doi:10.2172/4259132.
Wing, g. M. TRANSPORT THEORY AND SPECTRAL PROBLEMS. United States. https://doi.org/10.2172/4259132
Wing, g. M. 1959. "TRANSPORT THEORY AND SPECTRAL PROBLEMS". United States. https://doi.org/10.2172/4259132. https://www.osti.gov/servlets/purl/4259132.
@article{osti_4259132,
title = {TRANSPORT THEORY AND SPECTRAL PROBLEMS},
author = {Wing, g. M.},
abstractNote = {A simple model of time-independent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non- linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic one-velocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)},
doi = {10.2172/4259132},
url = {https://www.osti.gov/biblio/4259132}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1959},
month = {5}
}