Relationship between chain reactions in a nuclear reactor and multifractality

Abstract

A multifractal model of neutron evolution in a reactor is considered. For chain reactions, the dimension of the multifractal carrier, information and correlation dimensions, the entropy of the fractal set, the maximum and minimum values of the dimension, the multifractal spectrum function and other characteristics of multifractal neutron behavior are found. The use of geometric characteristics of a multifractal makes it possible to describe a stochastic system of hierarchically subordinate statistical ensembles, characterized by Cayley trees. A stationary distribution over hierarchical levels is established, which reduces to the Tsallis power law. Some possibilities for using fractal patterns in the theory of nuclear reactors are indicated.