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Application of boundary functionals of random processes in statistical physics
V. V. Ryazanov
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the…
Probabilistic assessment of the reactor vessel lifetime
V. V. Ryazanov
A simple and rapid method is proposed for assessing the reduction in the lifetime of steel walls of the reactor vessel under neutron irradiation. The method is based on modeling th…
Percolation, fractals and the critical point in a nuclear reactor
V. V. Ryazanov
The trajectories of neutrons in the reactor, the points of their fission of uranium nuclei, the points of neutron absorption, fission chains and chain reactions are considered from…
Application of the concept of hierarchical subordination to chain reactions in a nuclear reactor
V. V. Ryazanov
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 processe…
Percolation threshold and critical point of a nuclear reactor
V. V. Ryazanov
Neutrons in a nuclear reactor move along trajectories corresponding to Cayley trees associated with branching random processes. The probability of percolation, the appearance of su…
Relationship between chain reactions in a nuclear reactor and multifractality
V. V. Ryazanov
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 en…