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    Vladimir Yanovsky

    pr. Lenina 60, Kharkov, 310001, Ukraine
    Institute for Single Crystals, National Academy of Sciences of Ukraine


    Kopp M. I., Tur A. V., Yanovsky V. V.
    Nonlinear dynamo theory
    2015, Vol. 11, No. 2, pp.  241-266
    Using the asymptotic method of multiple scales construct nonlinear theory of large-scale structures in stratified conducting medium in the presence of small-scale oscillations of the velocity field and magnetic fields. Such small-scale stationary oscillations are generated by small external sources at low Reynolds numbers. The nonlinear system of equations describing the evolution of largescale structure of the velocity field and the magnetic fields are obtained. The linear stage of evolution leads to the well known instability. We study the equations of non-linear instability and its stationary solutions.
    Keywords: stratified conducting medium, nonlinear system of equations, instability, large scale structures, multiscale method
    Citation: Kopp M. I., Tur A. V., Yanovsky V. V.,  Nonlinear dynamo theory, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 2, pp.  241-266
    Berezovoj V. P., Tur A. V., Yanovsky V. V.
    Proposed simple model movements thin tubes under the influence of fluid flow. Was obtained a nonlinear equation for the string with the flow. Demonstrated the possibility of tube vibrations under the influence of fluid flow and criterion was found linear instability at a constant flow rate. In the condition where the linear instability conditions are violated the possibility of oscillations detected during the presence of small periodic oscillation of flow.
    Keywords: string, fluid flow, the equation of motion, instability, parametric resonance
    Citation: Berezovoj V. P., Tur A. V., Yanovsky V. V.,  Dynamics of thin tubes under the influence of fluid flow, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  183-194
    Kulik K. N., Tur A. V., Yanovsky V. V.
    In this work considered the motion of a point dipole vortex in circular domain occupied by an ideal fluid. The motion equations for a dipole vortex in an domain bounded by solid wall, are obtained. These equations have the Hamiltonian form. Integrability in the quadratures of the motion equations for a point dipole vortex in a circular domain is proved. The character movement vortex is discussed.
    Keywords: point dipole vortex, Hamiltonian, motion equations
    Citation: Kulik K. N., Tur A. V., Yanovsky V. V.,  The evolution point dipole vortex in a domain with circular boundaries, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 4, pp.  659-669
    Naplekov D. M., Seminozhenko V. P., Yanovsky V. V.
    We consider a two-dimensional collisionless ideal gas in the two vessels. In one of them particles behavior is ergodic. Another one is known to be nonergodic. Significant part of the phase space of this vessel is occupied by islands of stability. It is shown, that gas pressure is uniform in the first vessel and highly uneven in second one. Distribution of particle residence times was considered. For nonergodic vessel it is found to be quite unusual: delta spikes on small times, then several sites of chopped sedate decay and finally exponential tail. Such unusual dependence is found to be connected with islands of stability, destroyed after vessels interconnection. Equation of gas state in the first vessel is obtained. It differs from the ordinary equation of ideal gas state by an amendment to the vessel’s volume. In this way vessel’s boundary affects the equation of gas state. Correlation of this amendment with a share of the phase space under remaining intact islands of stability is shown.
    Keywords: nonergodicity, ideal gas, equation of state, connected vessels, establishment of a stationary state
    Citation: Naplekov D. M., Seminozhenko V. P., Yanovsky V. V.,  The equation of state of an ideal gas in two connected vessels, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 3, pp.  435-457
    Bolotin Y. L., Slipushenko S. V., Yanovsky V. V.
    Targeting with external noise
    2010, Vol. 6, No. 4, pp.  719-736
    An influence of a low noise on the properties of the Hénon map chaotic modes is studied. The strong chaos and the intermittency mode are considered. We find the mechanisms of a significant influence of the low noise on the chaotic mode properties. The conditions which have impact on the Poincaré recurrences time are defined. We suggest the targeting stochastic scenario for taking the Hénon map under control. The physics and the efficiency of the proposed targeting method are considered.
    Keywords: dissipative dynamical systems, Hénon map, targeting, Poincaré recurrences, external noise
    Citation: Bolotin Y. L., Slipushenko S. V., Yanovsky V. V.,  Targeting with external noise, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  719-736

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