Application of the concept of hierarchical subordination to chain reactions in a nuclear reactor (2403.01462v1)

Abstract: Based on the theory of hierarchical structures, a correspondence has been established between the dynamics for the number of neutrons obtained from the theory of branching processes, the number of neutrons of the n-th generation, the number of nodes at the n-th level of the hierarchy, the rate of change in the probability of a chain reaction, the type of intensity and strength of the hierarchical connection, the degree reactor criticality, and neutron trajectories in the reactor. A connection has been found between the probabilities of the formation of a certain generation of the number of neutrons and the probability of the occurrence of a self-sustaining chain reaction of nuclear fission. It is shown that the Tsallis and R\'enyi distributions describing these processes are related by relations of deformed algebra, and under certain conditions can be accompanying with respect to each other.