Multi-species neutron transport equation
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Publication:2315179
DOI10.1007/S10955-019-02307-2zbMATH Open1420.82027arXiv1809.00827OpenAlexW3101603000WikidataQ127888863 ScholiaQ127888863MaRDI QIDQ2315179
Author name not available (Why is that?)
Publication date: 1 August 2019
Published in: (Search for Journal in Brave)
Abstract: The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [9, 27]), the NTE has had a somewhat scattered treatment in mathematical literature with a variety of different approaches (cf. [8, 25]). Within a probabilistic framework it has somewhat undeservingly received little attention in recent years; nonetheless, probabilistic treatments can be found see for example [19, 26, 24, 29, 4, 3]. 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 c0-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 [6, 5]. The methodology used in this paper harmonises the culture of expectation semigroup analysis from the theory of stochastic processes against c0-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.
Full work available at URL: https://arxiv.org/abs/1809.00827
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