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Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and $k_\texttt{eff}$

hal.structure.identifierUniversity of Bath [Bath]
dc.contributor.authorCOX, Alexander
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
hal.structure.identifierUniversity of Bath [Bath]
dc.contributor.authorHORTON, Emma L.
hal.structure.identifierUniversity of Bath [Bath]
dc.contributor.authorKYPRIANOU, Andreas
hal.structure.identifierInstitut Élie Cartan de Lorraine [IECL]
hal.structure.identifierBiology, genetics and statistics [BIGS]
dc.contributor.authorVILLEMONAIS, Denis
dc.date.accessioned2024-04-04T02:43:28Z
dc.date.available2024-04-04T02:43:28Z
dc.date.issued2021-05-27
dc.identifier.issn0036-1399
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191338
dc.description.abstractEnThe Neutron Transport Equation (NTE) describes the flux of neutrons over time through an inhomogeneous fissile medium. In the recent articles [5, 10], a probabilistic solution of the NTE is considered in order to demonstrate a Perron-Frobenius type growth of the solution via its projection onto an associated leading eigenfunction. In [9, 4], further analysis is performed to understand the implications of this growth both in the stochastic sense, as well as from the perspective of Monte-Carlo simulation. Such Monte-Carlo simulations are prevalent in industrial applications, in particular where regulatory checks are needed in the process of reactor core design. In that setting, however, it turns out that a different notion of growth takes centre stage, which is otherwise characterised by another eigenvalue problem. In that setting, the eigenvalue, sometimes called k-effective (written $k_\texttt{eff}$), has the physical interpretation as being the ratio of neutrons produced (during fission events) to the number lost (due to absorption in the reactor or leakage at the boundary) per typical fission event. In this article, we aim to supplement [5, 10, 9, 4], by developing the stochastic analysis of the NTE further to the setting where a rigorous probabilistic interpretation of keff is given, both in terms of a Perron-Frobenius type analysis as well as via classical operator analysis. To our knowledge, despite the fact that an extensive engineering literature and industrial Monte-Carlo software is concentrated around the estimation of keff and its associated eigenfunction, we believe that our work is the first rigorous treatment in the probabilistic sense (which underpins some of the aforesaid Monte-Carlo simulations).
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enNeutron Transport Equation
dc.subject.enPrincipal eigenvalue
dc.subject.enSemigroup theory
dc.subject.enPerron-Frobenius decomposition
dc.subject.enR-theory for Markov processes
dc.title.enStochastic Methods for Neutron Transport Equation III: Generational many-to-one and $k_\texttt{eff}$
dc.typeArticle de revue
dc.identifier.doi10.1137/19M1295854
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1909.00581
bordeaux.journalSIAM Journal on Applied Mathematics
bordeaux.volume81
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02390745
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02390745v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Applied%20Mathematics&rft.date=2021-05-27&rft.volume=81&rft.issue=3&rft.eissn=0036-1399&rft.issn=0036-1399&rft.au=COX,%20Alexander&HORTON,%20Emma%20L.&KYPRIANOU,%20Andreas&VILLEMONAIS,%20Denis&rft.genre=article


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