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Contract number
Time span of the project

As of 30.01.2020

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scientific publications
General information

Name of the project: Development of mathematical theory of dynamic media and theory of differential equations applied to quantum mechanics and field theory, fundamental physics and dynamics of continuous media.

Strategy for Scientific and Technological Development Priority Level: а, в

Goals and objectives

Research directions: Mechanics, differential equations, mathematical physics

Project objective: Development of mathematical theory of dynamic systems and theory of differential equations in applications to quantum mechanics and field theory, fundamental physics, and continuous media.

The practical value of the study

  • Our researchers have investigated dynamics of liquid crystals and proven the theorem of existence and singularity of the solution for a periodical medium. On the basis of this theorem we have obtained similar results for limited regions.
  • We have studied movement of electric conductive liquid in tubes with complex configurations.
  • A method has been developed for computing energy necessary for overcoming the force of adhesion of solid particles on walls of pipes and studied features and parameters of movement of gas and oil mixture with admixture of sand in pipes with complex cross-sections.

Implemented results of research:

  • We have obtained a patent for a structure of pipes with self-cleaning during usage.
  • Achieved results contribute to development of fundamental problems of mechanics, dynamic systems theory and mathematical physics. In the future such tasks could be used in the domain of sport sports medicine, for giving sportsmen higher stability against falling and injuries (slalom), for learning new technical elements (figure skating).

Collaborations: V.A. Steklov Mathematical Institute of the Russian Academy of Sciences (Russia), École Polytechnique F´ed´erale de Lausanne (Switzerland), International Union of Theoretical and Applied Mechanics (France): joint research

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Romanov M.C., Ratiu T.S., Chechkin G.A.
Homogenization of the Equations of Dynamics of Nematic Liquid Crystals with Inhomogeneous Density. Journal of Mathematical Sciences 186(2) (2012).
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