Email this article NUMERICAL-STATISTICAL INVESTIGATION OF SUPEREXPONENTIAL GROWTH OF THE MEAN PARTICLE FLUX WITH MULTIPLICATION IN A HOMOGENEOUS RANDOM MEDIUM
- Authors: Mikhailov G.A.1,2, Lotova G.Z.1,2
-
Affiliations:
- Institute of computational mathematics and mathematical geophysics SB RAS
- Novosibirsk State University
- Issue: Vol 514, No 1 (2023)
- Pages: 112-117
- Section: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/247103
- DOI: https://doi.org/10.31857/S2686954323600210
- EDN: https://elibrary.ru/CZXVJY
- ID: 247103
Cite item
Open Access
Access granted
Subscription Access
Abstract
The new correlative-grid approximation of a homogeneous random field is introduced for the effective numerically-analytical investigation of the superexponential growth of the mean particles flux with multiplication in a random medium. A complexity of particle trajectory realization is not dependent on the correlation scale. The test computations for a critical ball with isotropic scattering showed high accuracy of the corresponding mean flux estimates. For the correlative-grid approximation the possibility of Gaussian asymptotics of the mean particles multiplication rate when the correlation scale decreases is justified.
About the authors
G. A. Mikhailov
Institute of computational mathematics and mathematical geophysics SB RAS; Novosibirsk State University
Author for correspondence.
Email: gam@sscc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk
G. Z. Lotova
Institute of computational mathematics and mathematical geophysics SB RAS; Novosibirsk State University
Author for correspondence.
Email: lot@osmf.sscc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk
References
- Дэвисон Б. Теория переноса нейтронов. М.: Атомиздат, 1960, 514 с.
- Марчук Г.И., Михайлов Г.А., Назаралиев М.А. и др. Метод Монте-Карло в атмосферной оптике. Новосибирск: Наука, 1976. 283 с.
- Лотова Г.З., Михайлов Г.А. Численно-статистическое и аналитическое исследование асимптотики среднего потока частиц с размножением в случайной среде. Журнал вычислительной математики и математической физики. 2021. V. 61. № 8. P. 1353–1362. https://doi.org/10.31857/S0044466921060077
- Прудников А.П., Брычков Ю.А., Маричев О.И. Интегралы и ряды. М.: Наука, 1981.
- Larmier C., Zoia A., Malvagi F., Dumonteil E., Mazzolo A. Neutron multiplication in random media: Reactivity and kinetics parameters // Annals of Nuclear Energy. 2018. V. 111. P. 391–406. https://doi.org/10.1016/j.anucene.2017.09.006
- Ambos A.Yu., Mikhailov G.A. Solution of radiative transfer theory problems for ‘realistic’ models of random media using the Monte Carlo method // Rus. J. Num. Anal. Math. Model. 2016. V. 31. № 3. P. 1–10. https://doi.org/10.1515/rnam-2016-0013
- Gilbert E.N. Random subdivisions of space into crystals // Ann. Math. Statist. 1962. № 33. P. 958–972. https://doi.org/10.1214/aoms/1177704464
- Романов Ю.А. Точные решения односкоростного кинетического уравнения и их использование для расчета диффузионных задач (усовершенствованный диффузионный метод) // Исследование критических параметров реакторных систем. М.: Госатомиздат, 1960. С. 3–26.
- Ширяев А.Н. Вероятность. М.: Наука, 1980. 575 с.
Supplementary files
