Laboratory for Mathematical Modelling of Wave Phenomena

Wave processes in a loaded elastic shell are investigated. Such shells are actively investigated due to rich applications in engineering and construction.

Waves on the surface of a fluid are a common physical phenomenon; mathematical problems of wave theory arise in connection with important practical applications (first of all, calculation of hydrodynamic loads on submerged bodies).

Prof. A.P. Kiselev is a member of the organizing committee, the head of the program committee of the annual international conference Days of Diffraction. D.Sc. O.V. Motygin is a member of the program committee of the conference Days of Diffraction. A.P. Kiselev and O.V.

Research directions: Development of mathematical models and study of the nonlinear dynamics of nano- and microelectromechanical sensors based on the phenomenon of modal localization of oscillations in weakly coupled systems under electrostatic and laser thermo-optical excitation, taking into accoun

Research directions: Investigation of the behavior of various liquids during the flow in nanotubes. Three-dimensional modeling of the processes of molecular-dynamic interaction.

Research directions: Investigation of the dynamics of systems with time-varying stiffness and mass parameters. Dynamics of elastic structures interacting with moving ice cover. Detachment of the film from the substrate under external impact.

Nanofluidics (field of nanoliter liquids physics: 1 nL = 10−12 m3) is of great interest to researchers, because of the promising applications of these systems in biology, optoelectronics, and various sensors and actuators based on anisotropic molecular liquids and liquid crystal (LC) materials.

Direction of research: A study of non-stationary problems with free boundaries, governing the evolution of two viscous immiscible liquids with an unknown interface, on which surface tension is taken into account, in the framework of the Navier-Stokes model.

A plane nonlinear problem with a free boundary is studied, which describes steady waves on the surface of an ideal, incompressible fluid of finite depth, taking into account the vortex nature of its motion.

Direction of research.