Abstract
The paper considers the spectral problem associated with the study of local characteristics of weakly coupled systems in reactor physics. The method of associated invariant subspaces based on the matrix spectrum dichotomy method is described. With its help, distributions are found that reflect multiplicating properties of local areas in the system.
REFERENCES
I. M. Sobol’, Numerical Monte Carlo Methods (Nauka, Moscow, 1973) [in Russian].
F. B. Brown, S. E. Carney, B. C. Kiedrowski, and W. R. Martin, “Fission matrix capability for MCNP, Part I—Theory,” Proc. Int. Conf. Math. Comput. Methods Appl. Nucl. Sci. Eng. , 2828–2839 (2013).
R. J. Brissenden and A. J. Garlick, “Biases in the estimation of \( K_{\mathrm {eff}} \) and its error by Monte-Carlo Methods,” Ann. Nucl. Energy 13, 63–83 (1986).
T. Ueki, F. B. Brown, D. K. Parsons, and D. E. Kornreich, “Autocorrelation and dominance ratio in Monte-Carlo criticality calculations,” Nucl. Sci. Eng. 145, 279–290 (2003).
E. F. Mitenkova and T. V. Semenova, “Using the TDMCC software to solve problems with a close-to-one dominant ratio,” Vopr. At. Nauki Tekh. Ser. Mat. Model. Fiz. Protsess. (4), 3–13 (2015) [in Russian].
R. N. Blomquist, M. Amirshaw, D. Hanlon, N. Smith, Yo. Naito, J. Yang, Yo. Mioshi, T. Yamamoto, O. Jacquct, and J. Miss, Source Convergence in Criticality Safety Analysis. Phase I: Results of Four Test Problems (OECD/NEA, Paris, 2006).
G. E. Whitesides, “A difficulty in computing the \( k \)-effective of the World,” Trans. Am. Nucl. Soc. 14 (2), 26–40 (1971).
E. F. Mitenkova, D. A. Koltashev, and P. A. Kizub, “Distribution of the fission reaction rate in a weakly coupled system for testing the “checkerboard” model,” At. Energ. 116 (6), 421–427 (2014).
E. F. Mitenkova and T. V. Semenova, “Calculation of neutron distribution functions in slabs with extended heterogeneous fuel zones,” At. Energ. 126 (1), 16–20 (2019).
S. K. Godunov, Modern Aspects of Linear Algebra (Nauchn. Kniga, Novosibirsk, 1997) [in Russian].
T. V. Semenova, E. F. Mitenkova, and E. V. Solov’eva, “Fission matrix in the TDMCC program for calculating weakly coupled systems,” Vopr. At. Nauki Tekh. Ser. Yad.-Reakt. Konstanty (2), 31–35 (2019) [in Russian].
F. R. Gantmacher, The Theory of Matrices (AMS Chelsea Publ., reprinted by Am. Math. Soc., Providence, RI, 2000).
E. A. Biberdorf, E. F. Mitenkova, T. V. Semenova, and E. V. Solov’eva, “Method of associated invariant subspaces in problems of neutron distribution in weakly coupled systems,” Vopr. At. Nauki Tekh. Ser. Mat. Model. Fiz. Protsess. (2), 3–16 (2022) [in Russian].
V. G. Bun’kov, S. K. Godunov, V. B. Kurzin, and M. Sadkane, “Application of the new mathematical apparatus ‘One-dimensional spectral portraits of a matrix’ to solving the problem of aeroelastic vibrations of blade arrays,” Uch. Zap. TsAGI 40 (6), 3–13 (2009) [in Russian].
Funding
The work was carried out within the framework of state assignments of Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008, and Nuclear Safety Institute of the Russian Academy of Sciences, project no. FFGZ-2019-0005. No additional grants to carry out or direct this particular research were obtained.
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Translated by V. Potapchouck
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Biberdorf, E.A., Mitenkova, E.F. & Semenova, T.V. On the Spectral Problem of Modeling Neutron Distribution in Weakly Coupled Systems. J. Appl. Ind. Math. 18, 10–17 (2024). https://doi.org/10.1134/S1990478924010022
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DOI: https://doi.org/10.1134/S1990478924010022