A Guide to the Russian Academy of Sciences - University of Texas ...

Other important areas of research in the Department were the development of the method of
approximating Hamiltonian, problems of nonequilibrium Statistical Mechanics, the
theory of interaction of electromagnetic radiation with matter, problems of the
mathematical theory of phase transitions, theories of quasi-averages, the Green
functions method, and problems of radio waves transmission.
11. Department of Mechanics: After the Mathematical Institute had been organized
and moved to Moscow, two Mechanics departments were set up in it, the
Department of Elasticity Theory headed by N. I. Muskhelishvili and the Department
of Continuous Media headed by N. E. Kochin. These Departments were closed in
1939, when N. I. Muskhelishvili moved to Georgia and N. E. Kochin with his
colleagues moved to the newly organized Institute of Mechanics of the Academy of
Sciences of the USSR
The Department of Mechanics was set up again in 1944, with M. V. Keldysh as Head of
Department and has continued in existence. In 1953, after M. V. Keldysh moved to
the newly established Division of Applied Mathematics and then to the Institute of
Applied Mathematics, L. I. Sedov was appointed as Head of the Department and he
held that position until 1988. At different years, at the Department of Mechanics
many famous scientists worked who made important contributions to the
development of Mechanics. At present, the staff of the Department includes: L. I.
Sedov (since 1945), A. G. Kulikovskii (since 1958, Head of Department since
1988), V. V. Markov (since 1973), G. A. Alekseev (since 1975), A. T. Il'ichev
(since 1984). The research directions in the Department are in accordance with its
traditions which were introduced by its founders, and first of all by L. I. Sedov .
A traditional area of research is the theory of nonstationary gas motions and strong
explosions. After basis results of L. I. Sedov (presented in his monographs ``Plane
problems of hydrodynamics and aerodynamics'' and``Methods of the theory of
similarity and dimension in mechanics'', for which a State Prize was received in
1952) this topic was developed by members of the Department V. P.
Korobeinikov, N. N. Kochina, N. S. Mel'nikova(they received a State Prize in
1975). In subsequent years in this direction some phenomena were studied
connected with the process of chemical reactions, radiative transfer, with the
movement of solid and liquid particles in nonstationary currents. A number of
numerical results was obtained on non-one-dimensional and nonstationary
spreading of detonation fronts, initiation and extinction of detonation, and
movement of particles in streams (V. V. Markov ).
Another direction of research is the construction of new models of the mechanics of
continuous media using the basic variational equation (the L. I. Sedov equation).
The methods of description of interaction of continuous media with electromagnetic
fields in the framework of special and general relativity theory are developed (L. I.
Sedov, A. G. Tsypkin). A. G. Tsypkin worked at the Department from 1969 until
l1992. The problems of connection of space-time geometry and moving matter are
also studied. In the framework of general relativity theory, the problem of inertial
navigation was solved (in 1981, the International Astronautics Association awarded
L. I. Sedov the Karman Prize).
In the framework of general relativity theory, on the basis of modern theory of integrable
systems new methods of integration of nonlinear equations for interacting of
gravitational and electromagnetic fields, the Einstein-Maxwell equations, are
developed. Applications of the constructed new exact solutions to different
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