Stochastic methods for the neutron transport equation. I: Linear semigroup asymptotics
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Publication:2240469
DOI10.1214/20-AAP1567zbMATH Open1479.82116arXiv1810.01779OpenAlexW2894570655MaRDI QIDQ2240469
Author name not available (Why is that?)
Publication date: 4 November 2021
Published in: (Search for Journal in Brave)
Abstract: The Neutron Transport Equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatial Markov branching process which describes the process of nuclear fission, transport, scattering, and absorption. By reformulating the NTE in its mild form and identifying its solution as an expectation semigroup, we use modern techniques to develop a Perron-Frobenius (PF) type decomposition, showing that growth is dominated by a leading eigenfunction and its associated left and right eigenfunctions. In the spirit of results for spatial branching and fragmentation processes, we use our PF decomposition to show the existence of an intrinsic martingale and associated spine decomposition. Moreover, we show how criticality in the PF decomposition dictates the convergence of the intrinsic martingale. The mathematical difficulties in this context come about through unusual piecewise linear motion of particles coupled with an infinite type-space which is taken as neutron velocity. The fundamental nature of our PF decomposition also plays out in accompanying work [20, 9].
Full work available at URL: https://arxiv.org/abs/1810.01779
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