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Hydrodynamic Instabilities and Nonequilibrium Phase Transitions

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Abstract

For the laminar–turbulent transition, a model of reconstructing the initial stage of an instability treated as a nonequilibrium phase transition is developed. Its mechanism is based on diffusion stratification. It is shown that the Gibbs free energy of the deviation from the homogeneous state (with respect to the instability under consideration) is an analogue of the Ginzburg–Landau potentials. Numerical experiments concerning the self-excitation of a homogeneous state by applying a boundary control condition in the form of an increasing velocity were performed. Under an external influence (an increase in the velocity as input), the system exhibits a transition to chaos through period-doubling bifurcations similar to the Feigenbaum period-doubling cascade.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    E. V. Radkevich

  2. Research Institute “Geodesy”, 141292, Krasnoarmeisk, Moscow oblast, Russia

    E. A. Lukashev

  3. Moscow State University of Civil Engineering, 129337, Moscow, Russia

    O. A. Vasil’eva

Authors
  1. E. V. Radkevich
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  2. E. A. Lukashev
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  3. O. A. Vasil’eva
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Correspondence to E. V. Radkevich, E. A. Lukashev or O. A. Vasil’eva.

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Translated by I. Ruzanova

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Radkevich, E.V., Lukashev, E.A. & Vasil’eva, O.A. Hydrodynamic Instabilities and Nonequilibrium Phase Transitions. Dokl. Math. 99, 308–312 (2019). https://doi.org/10.1134/S1064562419030189

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  • DOI: https://doi.org/10.1134/S1064562419030189

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