### November 9, 2021

M.A. Bushmakova (SPbSU)

Evaluation of relaxation terms in state-to-state approachment problems using machine learning methods

Relaxation terms characterize the variation of vibrational level populations of molecules and molar fractions of atoms as a result of various types of energy exchange and chemical reactions. They are the right-hand sides of the set of differential equations for macroscopic gas parameters, describing the flows of multicomponent reacting gas mixtures under conditions of strong vibrational and chemical non-equilibrium. Conventional methods for calculating relaxation terms are computationally expensive, since they imply multiple summations, as well as the calculation of a large number of the rate coefficients of vibrational energy transitions and chemical reactions. In this work, a possibility of evaluating the relaxation terms by machine learning methods is assessed, and the efficiency of two models learned on datasets calculated with SSH and FHO methods is compared for the case of VT and VV relaxation in the mixture of O_{2}-O. Then the solution of zero-dimensional problem obtained by ML algorithms is compared to solution with SSH and FHO methods. It is shown that the k-nearest neighbours algorithm provides the best accuracy/efficiency ratio and can be recommended for further studies. It is also possible to decrease computational time by using ML algorithms.

**
Mariia A. Bushmakova ** – first year master student of the Department of Hydroaeromechanics at St. Petersburg State University. Project supervisor - Prof. E.V. Kustova.

### October 12, 2021

E.P. Nosov (SPbSU)

Study of the diffraction problem by the ray method for reflection of a plane wave from a parabolic surface

One of the methods for analysis of the diffraction problem is the ray method, the current concept of which was formed at the end of the last century. Nowadays, there is no general formula describing the reflection of a wave from an arbitrary surface. Therefore, special cases are considered. An example of such a case is the problem of external reflection from a parabolic surface. The purpose of this paper is a detailed study of that problem. In the current research the first two terms of the formal asymptotic series for the reflected plane monochromatic wave with constant velocity were found; the asymptotics and the residual were also calculated. It appears that the first term of the formal expansion gives sufficient accuracy for a number of problems.

**
Evgeny P. Nosov ** – first year master student of the Department of theoretical and applied mechanics at St. Petersburg State University. Project supervisor - Prof. I.V. Andronov.

### October 5, 2021

S.O. Bondarenko (SPbSU)

Motion of a horizontal dynamically unbalanced rotor in gravitational field.

A horizontal dynamically unbalanced rotor motion is considered. The motion equations of two systems are obtained: with two-plane automatic ball balancer and without it. Two rotor models are designed in MATLAB Simulink base on simplyfied equation systems for numerical solution. The whirling amplitude equations are obtained analytically for a rotor rotating at constant angular speed. The gravity is taken into account. Numerical and analytical results are compared.

**
Sergei O. Bondarenko ** – first year master student of the Department of theoretical and applied mechanics at St. Petersburg State University. Research area - rotordynamics. Scientific supervisior - Asso.Prof. A. S. Kovachev.