Multi-species Neutron Transport Equation
Multi-species Neutron Transport Equation
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DOI：
10.1007/s10955-019-02307-2
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发表时间：
2018-09
影响因子：
1.6
通讯作者：
A. Cox;S. Harris;E. Horton;A. Kyprianou
中科院分区：
文献类型：
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作者：
A. Cox;S. Harris;E. Horton;A. Kyprianou
中子输运方程（NTE）描述了中子在非均匀裂变介质中的通量。虽然在核物理文献中得到了很好的处理，但在数学文献中，NTE用各种不同的方法得到了一些分散的处理。近年来，在概率框架内，它受到的关注少得有些不应有；尽管如此，还是可以找到一些概率性的治疗方法。在这篇文章中，我们的目标有三个。首先，我们要介绍一个稍微更一般的NTE设置，它提供了一个更完整的画面，不同种类的粒子和放射性通量，涉及到裂变。其次，我们将经典半群方法与包含期望半群的随机表示方法结合起来解决NTE问题。第三，我们提供了我们的多物种NTE的主要渐近，这将对未来工作中NTE的进一步随机分析至关重要（Cox et al. 2019; Harris et al. 2018; Horton et al. 2018）。本文所使用的方法将随机过程理论中的期望半群分析文化与泛函分析中的反半群理论相协调。在这方面，我们的演讲部分是对现有理论的回顾，部分是基于现有结果的概括的新研究成果的介绍。
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-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-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.