Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo

This paper presents results from the application of a Monte Carlo Markov Transition Rate Matrix Method to calculate forward and adjoint α eigenvalues and eigenfunctions of one-speed slabs, and perform eigenfunction expansion to approximate the time-dependent flux response to user-defined sources. Th...

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Bibliographic Details
Published in:Journal of computational and theoretical transport 2014-12, Vol.43 (1-7), p.38
Main Authors: Betzler, B. R, Martin, W. R, Kiedrowski, B. C, Brown, F. B
Format: Article
Language:English
Subjects:
Eigenvalues
Markov analysis
Monte Carlo simulation
Online Access:Get full text
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Description
Summary:This paper presents results from the application of a Monte Carlo Markov Transition Rate Matrix Method to calculate forward and adjoint α eigenvalues and eigenfunctions of one-speed slabs, and perform eigenfunction expansion to approximate the time-dependent flux response to user-defined sources. The formulation of this method relies on the interpretation that the operator in the adjoint α-eigenvalue problem describes a continuous-time Markov process, i.e., elements of this operator are rates defining particles transitioning among the position-energy-direction phase space. A forward Monte Carlo simulation tallies these elements for a discretized phase space, using careful bookkeeping during the random walk. We compare calculated eigenvalues and eigenfunctions to those obtained by the Green's Function Method for multiplying and non-multiplying multi-region slabs.
ISSN:2332-4309
2332-4325
DOI:10.1080/00411450.2014.909851