Participation of V. S. Vladimirov in work on the USSR atomic project: a significant milestone in the development of the foundations of mathematical modeling of the processes of neutron physics. (English. Russian original) Zbl 1287.82028
Theor. Math. Phys. 174, No. 2, 173-177 (2013); translation from Teor. Mat. Fiz. 174, No. 3, 202-207 (2013).
Dedicated to the 90th anniversary of the birth of Vasilij Sergeevich Vladimirov, an excellent Russian mathematician, the authors review his activity in finding the good – and at that time calculable – method of solving the integro-differential form of the Boltzmann equation. The main purpose was to construct a numerical method, for a sufficiently stable and computationally not too demanding (think of the years around 1950!) solution of the kinetic equation for the neutron transport.
The procedure uses the method of characteristics. This method is shown here in short details. The ways of calculation were extremely important, and at that time were used in several variants for calculating the necessary theoretical steps of multilayer charges for the H-bombs. Though the results were important (at that time for military purposes), they also are fundamental in the theory of integro-differential equations. The young Vladimirov – together with N. N. Bogoliubov – was awarded the Stalin prize in 1953.
The procedure uses the method of characteristics. This method is shown here in short details. The ways of calculation were extremely important, and at that time were used in several variants for calculating the necessary theoretical steps of multilayer charges for the H-bombs. Though the results were important (at that time for military purposes), they also are fundamental in the theory of integro-differential equations. The young Vladimirov – together with N. N. Bogoliubov – was awarded the Stalin prize in 1953.
Reviewer: Iván Abonyi (Budapest)
MSC:
| 82D75 | Nuclear reactor theory; neutron transport |
| 81-03 | History of quantum theory |
| 01A60 | History of mathematics in the 20th century |
| 81V35 | Nuclear physics |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
Biographic References:
Vladimirov, Vasilii SergeevichReferences:
| [1] | V. S. Vladimirov, ”Numerical solution of the kinetic equation for the sphere,” Vychisl. Matem., 3, 3–33 (1958). |
| [2] | G. I. Marchuk, Methods for Calculations of Nuclear Reactors [in Russian], Atomizdat, Moscow (1961). |
| [3] | V. S. Vladimirov, Voprosy Atomnoi Nauki i Tekhniki, Ser. Matematicheskoe modelirovanie fizicheskikh protsessov, 4, 105–109 (1992). |
| [4] | V. A. Chuyanov, ”The Vladimirov method [in Russian],” in: Mathematical Encyclopedia, Vol. 1, Soviet Encyclopedia, Moscow (1977). |
| [5] | V. S. Vladimirov, I Am the Son of Working People [in Russian], FAZIS, Moscow (2007). |
| [6] | A. V. Nikiforova, V. A. Tarasov, and V. E. Troshchiev, USSR Comput. Math. Math. Phys., 12, 251–260 (1972). · Zbl 0281.65054 · doi:10.1016/0041-5553(72)90130-9 |
| [7] | V. E. Troshchiev, A. V. Nifanova, and Yu. V. Troshchiev, Dokl. Math., 69, 136–140 (2004). |
| [8] | V. E. Troshchiev and A. V. Nifanova, Mat. Model., 18, No. 7, 24–42 (2006). |
| [9] | A. V. Nifanova, ”Characteristic S n methods for kinetic equations of neutron transport in spherical systems [in Russian],” Candidate’s dissertation, TRINITI, Troitsk (2008). |
| [10] | V. S. Vladimirov, Priklad. Matem. i Mekhan., 19, No. 3, 315–324 (1955). |
| [11] | V. S. Vladimirov, Voprosy Atomnoi Nauki i Tekhniki, Ser. Matematicheskoe modelirovanie fizicheskikh protsessov, 1, 6–7 (2002). |
| [12] | A. D. Sakharov, Reminiscences [in Russian], Vol. 1, Prava Cheloveka, Moscow (1996). |
| [13] | V. S. Vladimirov, Proc. Steklov Inst. Math., 61 (1961). |
| [14] | Yu. N. Drozzinov, ”Vladimirov’s variational principle [in Russian],” in: Mathematical Encyclopedia, Vol. 1, Soviet Encyclopedia, Moscow (1977). |
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