AbstractThis thesis concerns the study of the neutron transport equation, which describes how neutrons move through a fissile medium, such as a nuclear reactor. By studying various stochastic pro- cesses that model the behaviour of these neutrons, we address some of the criticality problems associated with such systems.
We first build a class of branching processes, whose behaviour mimics that of neutrons undergoing fission in a nuclear reactor. We then construct a class of weighted random walks, which are in some sense equivalent to the branching processes via a many-to-one formula. Anal- ysis of these two processes allows us to characterise the long-term behaviour of the underlying nuclear fission processes.
One of the parameters associated with characterising this asymptotic behaviour quantifies the average growth of particle numbers. A large part of this thesis is dedicated to what is known as the supercritical phase, which is where the average number of particles grows exponentially. In this regime, we consider both a spine and skeletal decomposition of the branching process in order to further describe the growth of the system through a law of large numbers result.
|Date of Award||4 Dec 2019|
|Supervisor||Alex Cox (Supervisor), Simon Harris (Supervisor) & Andreas Kyprianou (Supervisor)|