2019/01/01 by Simon C. Harris, Harris, Simon C., E Horton +3 · 1 citation
Engineering · Mathematics · #60J75 #60J80 #60J99 #82D75 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Phase Equilibria and Thermodynamics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1901.00220
openalex publication_date 2019/01/01 · openalex created_date 2022/07/31 · openalex updated_date 2026/07/28
The neutron transport equation (NTE) describes the flux of neutrons across a\nplanar cross-section in an inhomogeneous fissile medium when the process of\nnuclear fission is active. Classical work on the NTE emerges from the applied\nmathematics literature in the 1950s through the work of R. Dautray and\ncollaborators, [7, 8, 19]. The NTE also has a probabilistic representation\nthrough the semigroup of the underlying physical process when envisaged as a\nstochastic process; cf. [7, 17, 18, 20]. More recently, [6] and [16] have\ncontinued the probabilistic analysis of the NTE, introducing more recent ideas\nfrom the theory of spatial branching processes and quasi-stationary\ndistributions. In this paper, we continue in the same vein and look at a\nfundamental description of stochastic growth in the supercritical regime. Our\nmain result provides a significant improvement on the last known contribution\nto growth properties of the physical process in [20], bringing neutron\ntransport theory in line with modern branching process theory such as [14, 12].\n
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