Department of Mechanics

After the foundation of Steklov Mathematical Institute in 1934, two departments of mechanics were organized: Department of Elasticity Theory headed by N. I. Muskhelishvili and Department of Continuous Media headed by N. E. Kochin. These departments were closed after the departure of N. I. Muskhelishvili to Georgia and N. E. Kochin's transition to a newly founded Institute of Mechanics of the Academy of Sciences.

Department of Mechanics at the Mathematical Institute was organized again in 1944 (headed by M. V. Keldysh). After M. V. Keldysh moved in 1953 to a newly founded Institute of Applied Mathematics, L. I. Sedov was appointed as the head of the department and he held this appointment till 1988. From 1988 to 2003 the department was headed by A. G. Kulikovskii, and from 2003 to 2011 by V. V. Kozlov. Art present the duties of the head of the department are fulfilled by S. V. Bolotin.

In 2002, the Department of Mechanics united with the Department of Statistical Mechanics which was established in 1969 under the leadership of N. N. Bogolubov (Jr). At present the staff of the Department includes members of RAS V. V. Kozlov and A. G. Kulikovskii, correspondent members of RAS N. N. Bogolubov and D. V. Treschev; doctors of phys.-math. sci. G. A. Alekseev, S. V. Bolotin, A. P. Chugainova, A. T. Il'ichev, V. V. Markov, D. P. Sankovich, candidate of phys.-math. sci. A. V. Soldatov.

• analytical methods and numerical simulation of nonlinear fenomena in various problems of mechanics of continuous media, stability of flows, propagation of wave fronts and shock waves of various structures in inhomogeneous and anisotropic media with dissipative and dispersive properties, interactions of nonlinear waves and shock waves (A. G. Kulikovskii and A. P. Chugainova);
• investigation with analytical and numerical methods of waves propagation in dispersive media, stability of localized wave structures and interfaces in various problems of hydromechanics, elasticity theory and theory of filtration (A. T. Il'ichev);
• numerical simulation of flows of continuous media with chemical reactions, radiation transport, movements of rigid and fluid particles in gas flows, propagation of nonstationary detonation fronts, initiation and extinction of detonation (V. V. Markov);
• theory of integrable space-time symmetry reductions of Einstein's, Einstein–Maxwell and other field equations of the gravitation theory and investigation of nonlinear properties of strong gravitational fields (G. A. Alekseev);
• mathematical methods of investigation of physical systems interacting with bosonic fields, including polaron-type systems and quantum low-dimensional systems (N. N. Bogolubov (Jr.), A. V. Soldatov);
• mathematically rigorous approach to the investigation of the thermodynamically equilibrium properties of strongly non-ideal Bose- and Fermi-systems on the basis of the correlation inequalities formalism; determination of the conditions under which various phase transitions can take place; rigorous proof of the Bose-condensation in the mentioned above quantum systems (D. P. Sankovich);
• nonequilibrium methods of statistical mechanics, including the method of the self-consistent projection operator and methods based on the exact evolution equations formalism, with the purpose of the electromagnetic field-matter interaction investigation with possible applications to problems of quantum optics;
• investigations of the irreversible evolution of quantum atomic systems interacting with the electromagnetic field with the purpose to obtain rigorous results regarding the nonequilibrium behavior (relaxation, decay) of such systems;
• mathematical methods of nonequilibrium statistical mechanics with applications to the problem of interaction of model atomic systems with external polychromatic electromagnetic fields; investigation of the spectroscopic properties of the composite quantum systems resulting from this interaction (N. N. Bogolubov (Jr.) and A. V. Soldatov);
• variational methods of classical mechanics (S. V. Bolotin, V. V. Kozlov);
• periodic and chaotic solutions of the 3 body problem (S. V. Bolotin);
• problem of integrability of the equations of motion (V. V. Kozlov, D. V. Treschev);
• nonholonomic mechanical systems and rolling of rigid bodies (V. V. Kozlov, D. V. Treschev);
• mathematical problems of statistical mechanics (V. V. Kozlov, D. V. Treschev);
• KAM theory and the problem of Arnold's diffusion (D. V. Treschev).