Geodesic
On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
Applications of Mathematics, Tome 39 (1994) no. 4, pp. 269-286

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
DOI : 10.21136/AM.1994.134257
Classification : 45K05, 65C05, 65R20, 82C70, 82C80
Keywords: reactor kinetics; integral transport equation; Monte Carlo method 
Kyncl, Jan. On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method. Applications of Mathematics, Tome 39 (1994) no. 4, pp. 269-286. doi: 10.21136/AM.1994.134257
@article{10_21136_AM_1994_134257,
     author = {Kyncl, Jan},
     title = {On numerical solution to the problem of reactor kinetics with delayed neutrons by {Monte} {Carlo} method},
     journal = {Applications of Mathematics},
     pages = {269--286},
     year = {1994},
     volume = {39},
     number = {4},
     doi = {10.21136/AM.1994.134257},
     mrnumber = {1284101},
     zbl = {0812.65142},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134257/}
}
TY  - JOUR
AU  - Kyncl, Jan
TI  - On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
JO  - Applications of Mathematics
PY  - 1994
SP  - 269
EP  - 286
VL  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134257/
DO  - 10.21136/AM.1994.134257
LA  - en
ID  - 10_21136_AM_1994_134257
ER  - 
%0 Journal Article
%A Kyncl, Jan
%T On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
%J Applications of Mathematics
%D 1994
%P 269-286
%V 39
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134257/
%R 10.21136/AM.1994.134257
%G en
%F 10_21136_AM_1994_134257

[1] J. Mika, D. Obradovič, R. Stankiewicz: Spectral properties of a multigroup transport operator with delayed neutrons in plane geometry. Bulletin of the Boris Kidrič Institute of Nuclear Sciences 19 (1968).

[2] S. V. Shikhov: Problems of mathematical theory of reactors. Atomizdat, Moscow, 1973. (Russian)

[3] J. Kyncl: On Cauchy problem for the equations of reactor kinetics. Aplikace matematiky 34 (1989), 197–212. | MR

[4] M. B. Emmett: The MORSE Monte Carlo Radiation Transport Code System. ORNL – 4972 (1975); also ORNL – 4972 – R1 (1983) and ORNL – 4972 – R2 (1984).

[5] M. Borysiewicz, J. Mika: Time behaviour of thermal neutrons in moderating media. J. Math. Anal. Appl 26 (1969), 461–478. | DOI

[6] M. M. R. Williams: The slowing down and thermalization of neutrons. North-Holland publishing company, Amsterdam, 1966.

[7] A. Weinberg and E. Winger: The Physical Theory of Neutron Chain Reactors. Chicago, 1958. | MR

[8] G. V. Gnedenko: The theory of probability. Nauka, Moscow, 1973.

Cité par Sources :