Abstract
The average magnitudes of random values and their dispersions are for many processes known in science and engineering estimated by choosing the appropriate probabilistic processes. The instantaneous intensities of a process are then simulated. At the same time, mathematical expectations of random values and their dispersions can often be exactly or approximately presented in the form of analytical functions of translational intensities. This is a rather common approach, so it is evident that it can also be used in describing processes that occur during the interaction between neutrons and neutron-multiplying media in power reactors of various types. In this work, the above problem is solved for a thermal nuclear reactor.
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References
Galanin, A.D., Teoriya yadernykh reaktorov na teplovykh neitronakh (The Theory of Nuclear Reactors at Thermal Neutrons), Moscow: Atomizdat, 1959.
Levin, V.G., Yadernaya fizika i yadernye reaktory (Nuclear Physics and Nuclear Reactors), Moscow: Atomizdat, 1969.
Duderstadt, J.J. and Hamilton, L.J., Nuclear Reactor Analysis, New York: John Wiley and Sons, 1976.
Bartolomei, G.G., Bat’, G.A., Baibakov, V.D., and Altukhov, M.S., Osnovy teorii i metody rascheta yadernykh energeticheskikh reaktorov (Nuclear Energy Reactors: Foundations of Theory and Calculation Methods), Bat’, G.A., Ed., Moscow: Energoatomizdat, 1982.
Shirokov, S.V., Nestatsionarnye protsessy v yadernykh reaktorakh: Nauchnoe posobie (Nonstationary Processes in Nuclear Reactors. Scientific Tutorial Book), Kiev: Naukova Dumka, 2002.
Vladimirov, V.I., Prakticheskie zadachi po ekspluatatsii yadernykh reaktorov (Practical Problems of Nuclear Reactors Exploitation), Moscow: Energoatomizdat, 1986.
Bharucha-Reid, A.T., Elements of the Theory of Markov Processes and Their Applications, New York: McGraw-Hill, 1960.
Karlin, S., A First Course in Stochastic Processes, Howard Taylor, 1975.
Whittle, P., Probability, Penguin Books, 1970.
Kendall, D.G., Ann. Math. Stat., 1948, vol. 19, p. 1.
Dorogov, V.I. and Chistyakov, V.P., Veroyatnostnye modeli prevrashcheniya chastits (Probability Models for Particles Transformations), Moscow: Nauka, 1988.
Chistyakov, V.P., Kurs teorii veroyatnostei (Course of Probability Theory), Moscow: Nauka, Fizmatgiz, 1987.
E. Kamke, Differentialgleichungen: Losungsmethoden und Losungen, vol. 1: Gewohnliche Differentialgleichungen, Leipzig: B. G. Teubner, 1977.
Rudak, E.A. and Yachnik, O.I., Analytic expressions for neutron generations lifetime in multiplying medium by considering one of six groups of delayed neutrons, Preprint of B.I. Stepanov Institute of Physics Belarus National Acad. Sci., Minsk 2012, no. 749.
Rudak, E.A. and Yachnik, O.I., Izv. Nats. Akad. Nauk Belarus, Ser. Fiz.-Mat. Nauki, 2012, no. 4, p. 84.
Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady, elementarnye funktsii (Integrals and Series, Elementary Functions), Moscow: Nauka, Fizmatgiz, 1981.
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Original Russian Text © T.N. Korbut, A.V. Kuz’min, E.A. Rudak, 2015, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2015, Vol. 79, No. 4, pp. 503–511.
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Korbut, T.N., Kuz’min, A.V. & Rudak, E.A. A thermal nuclear reactor as an analog of ADS systems with internal sources of neutrons. Bull. Russ. Acad. Sci. Phys. 79, 461–469 (2015). https://doi.org/10.3103/S1062873815040206
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DOI: https://doi.org/10.3103/S1062873815040206