Abstract

The neutron transport equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature, the NTE has had a somewhat scattered treatment in mathematical literature with a variety of different approaches. Within a probabilistic framework it has somewhat undeservingly received little attention in recent years; nonetheless, a few probabilistic treatments can be found. In this article our aim is threefold. First we want to introduce a slightly more general setting for the NTE, which gives a more complete picture of the different species of particle and radioactive fluxes that are involved in fission. Second we consolidate the classical c-semigroup approach to solving the NTE with the method of stochastic representation which involves expectation semigroups. Third we provide the leading asymptotic of our multi-species NTE, which will turn out to be crucial for further stochastic analysis of the NTE in forthcoming work (Cox et al. 2019; Harris et al. 2018; Horton et al. 2018). The methodology used in this paper harmonises the culture of expectation semigroup analysis from the theory of stochastic processes against c-semigroup theory from functional analysis. In this respect, our presentation is thus part review of existing theory and part presentation of new research results based on generalisation of existing results.

Original languageEnglish
Pages (from-to)425-455
Number of pages31
JournalJournal of Statistical Physics
Volume176
Issue number2
Early online date10 May 2019
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • Neutron transport equation
  • Perron–Frobenius decomposition
  • Principal eigenvalue
  • Semigroup theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Multi-species neutron transport equation. / Cox, Alexander M. G.; Harris, Simon C.; Horton, Emma; Kyprianou, Andreas.

In: Journal of Statistical Physics, Vol. 176, No. 2, 01.07.2019, p. 425-455.

Research output: Contribution to journalArticle

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