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...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue 1-7
container_start_page 38
container_title Journal of computational and theoretical transport
container_volume 43
creator Betzler, B. R
Martin, W. R
Kiedrowski, B. C
Brown, F. B
description 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.
doi_str_mv 10.1080/00411450.2014.909851
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_1816897509</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>4171568841</sourcerecordid><originalsourceid>FETCH-LOGICAL-g659-452cde657ae4245e5e8be841dbafa88f4642c95970babe75c608d97bbc09074e3</originalsourceid><addsrcrecordid>eNo9js9LwzAYQIMoOOb-Aw8Bz61f0qRJjlKnG2zsspvI-NJ-7TpiM_tD_30Hiqf3To_H2L2AVICFRwAlhNKQShAqdeCsFldsJrNMJiqT-vrfwd2yxTCcAECYzILVM7YuMJRTwLHtGv6G4XzEd75sG-q-MEw08FjzXUfJc_tB3dDGDgPfUtUi_27HI9_GbiReYB_iHbupMQy0-OOc7V-W-2KVbHav6-JpkzS5donSsqwo1wZJSaVJk_Vklag81mhtrXIlS6edAY-ejC5zsJUz3pfgwCjK5uzhN3vu4-dlcDyc4tRftoaDsCK3zmhw2Q_Sz08t</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1816897509</pqid></control><display><type>article</type><title>Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo</title><source>Taylor and Francis:Jisc Collections:Taylor and Francis Read and Publish Agreement 2024-2025:Science and Technology Collection (Reading list)</source><creator>Betzler, B. R ; Martin, W. R ; Kiedrowski, B. C ; Brown, F. B</creator><creatorcontrib>Betzler, B. R ; Martin, W. R ; Kiedrowski, B. C ; Brown, F. B</creatorcontrib><description>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.</description><identifier>ISSN: 2332-4309</identifier><identifier>EISSN: 2332-4325</identifier><identifier>DOI: 10.1080/00411450.2014.909851</identifier><language>eng</language><publisher>Philadelphia: Taylor &amp; Francis Ltd</publisher><subject>Eigenvalues ; Markov analysis ; Monte Carlo simulation</subject><ispartof>Journal of computational and theoretical transport, 2014-12, Vol.43 (1-7), p.38</ispartof><rights>Copyright © Taylor &amp; Francis Group, LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Betzler, B. R</creatorcontrib><creatorcontrib>Martin, W. R</creatorcontrib><creatorcontrib>Kiedrowski, B. C</creatorcontrib><creatorcontrib>Brown, F. B</creatorcontrib><title>Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo</title><title>Journal of computational and theoretical transport</title><description>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.</description><subject>Eigenvalues</subject><subject>Markov analysis</subject><subject>Monte Carlo simulation</subject><issn>2332-4309</issn><issn>2332-4325</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNo9js9LwzAYQIMoOOb-Aw8Bz61f0qRJjlKnG2zsspvI-NJ-7TpiM_tD_30Hiqf3To_H2L2AVICFRwAlhNKQShAqdeCsFldsJrNMJiqT-vrfwd2yxTCcAECYzILVM7YuMJRTwLHtGv6G4XzEd75sG-q-MEw08FjzXUfJc_tB3dDGDgPfUtUi_27HI9_GbiReYB_iHbupMQy0-OOc7V-W-2KVbHav6-JpkzS5donSsqwo1wZJSaVJk_Vklag81mhtrXIlS6edAY-ejC5zsJUz3pfgwCjK5uzhN3vu4-dlcDyc4tRftoaDsCK3zmhw2Q_Sz08t</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Betzler, B. R</creator><creator>Martin, W. R</creator><creator>Kiedrowski, B. C</creator><creator>Brown, F. B</creator><general>Taylor &amp; Francis Ltd</general><scope/></search><sort><creationdate>20141201</creationdate><title>Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo</title><author>Betzler, B. R ; Martin, W. R ; Kiedrowski, B. C ; Brown, F. B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-g659-452cde657ae4245e5e8be841dbafa88f4642c95970babe75c608d97bbc09074e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Eigenvalues</topic><topic>Markov analysis</topic><topic>Monte Carlo simulation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Betzler, B. R</creatorcontrib><creatorcontrib>Martin, W. R</creatorcontrib><creatorcontrib>Kiedrowski, B. C</creatorcontrib><creatorcontrib>Brown, F. B</creatorcontrib><jtitle>Journal of computational and theoretical transport</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Betzler, B. R</au><au>Martin, W. R</au><au>Kiedrowski, B. C</au><au>Brown, F. B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo</atitle><jtitle>Journal of computational and theoretical transport</jtitle><date>2014-12-01</date><risdate>2014</risdate><volume>43</volume><issue>1-7</issue><spage>38</spage><pages>38-</pages><issn>2332-4309</issn><eissn>2332-4325</eissn><abstract>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.</abstract><cop>Philadelphia</cop><pub>Taylor &amp; Francis Ltd</pub><doi>10.1080/00411450.2014.909851</doi></addata></record>
fulltext fulltext
identifier ISSN: 2332-4309
ispartof Journal of computational and theoretical transport, 2014-12, Vol.43 (1-7), p.38
issn 2332-4309
2332-4325
language eng
recordid cdi_proquest_journals_1816897509
source Taylor and Francis:Jisc Collections:Taylor and Francis Read and Publish Agreement 2024-2025:Science and Technology Collection (Reading list)
subjects Eigenvalues
Markov analysis
Monte Carlo simulation
title Calculating [alpha] Eigenvalues of One-Dimensional Media with Monte Carlo
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T15%3A46%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Calculating%20%5Balpha%5D%20Eigenvalues%20of%20One-Dimensional%20Media%20with%20Monte%20Carlo&rft.jtitle=Journal%20of%20computational%20and%20theoretical%20transport&rft.au=Betzler,%20B.%20R&rft.date=2014-12-01&rft.volume=43&rft.issue=1-7&rft.spage=38&rft.pages=38-&rft.issn=2332-4309&rft.eissn=2332-4325&rft_id=info:doi/10.1080/00411450.2014.909851&rft_dat=%3Cproquest%3E4171568841%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-g659-452cde657ae4245e5e8be841dbafa88f4642c95970babe75c608d97bbc09074e3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1816897509&rft_id=info:pmid/&rfr_iscdi=true