The extinction probability in systems randomly varying in time

Nuclear Engineering and Technology

Lénárd Pál¹  Imre Pázsit²  M.M.R. Williams³ 

[1] Centre for Energy Research, Hungarian Academy of Sciences, H-1525 Budapest 114, POB 49, Hungary;Division of Subatomic and Plasma Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden;Mechanical Engineering Department, Nuclear Engineering Group, Imperial College of Science, Technology and Medicine, Exhibition Road, SW7 2AZ, United Kingdom;

关键词: Extinction probability;    Temporally varying medium;    Generating function;    Forward equation;    Backward equation;    Chebyshev-Gauss-Lobatto collocation algorithm;    Mathematica®;   

DOI  :  10.1016/j.net.2017.08.006

来源: DOAJ

【 摘 要 】

The extinction probability of a branching process (a neutron chain in a multiplying medium) is calculated for a system randomly varying in time. The evolution of the first two moments of such a process was calculated previously by the authors in a system randomly shifting between two states of different multiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than that of the moments, and it can only be achieved by pure numerical methods. The numerical results indicate that for systems fluctuating between two subcritical or two supercritical states, the extinction probability behaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is a crucial and unexpected deviation from the predicted behaviour. The results bear some significance not only for neutron chains in a multiplying medium, but also for the evolution of biological populations in a time-varying environment.

【 授权许可】

Unknown