# Новости

## Section 3 - Track 1

On this page, talks in the format of posters are posted. They can be viewed during the whole time of the Conference. To send your question to the authors, please follow to Miro and write your question in the comments. You can also use the feedback form on our website. Authors will answer questions using Miro comments or via email. To get manual go to Instructions (eng / rus).

Mikhail Balabaev and Vladimir Sobolev * Phase flows geometry of autonomous dynamical models with singular perturbations *

In the framework of this paper we consider autonomous singularly perturbed dynamical models from the differential geometry point of view. We show the geometric interpretation of dynamical system phase flow; the correlation of stability solutions with the geometric peculiarities of the phase flow; geometrical meaning of various objects that are widely used in the analysis of integral manifolds of autonomous dynamical models with singular perturbations.

Michael Bolotov, Vadim Pechenin, Ekaterina Pechenina and Nikolaj Golev * Digital model of aircraft engine compressor rotor assembly optimization *

The article focuses on the problems of knowledge-intensive products assembly quality in aircraft engine industry. A mathematical model has been proposed to determine optimal conditions for mating assembly units of a low-pressure compressor (LPC) rotor of an aircraft engine. Parameters optimized include relative angular positions of parts in the rotor. Three optimization criteria have been considered: assembly geometry; imbalance value and integral criterion combining both above criteria. The model has been implemented in the MATLAB system. The calculations have been made using actual part models created based on measurements of the LPC parts geometry. The best optimization criterion has been selected.

Vladislav Lyubimov and Svetlana Kuznecova * Application of the method of integral manifolds to obtain low-frequency equations of motion of an asymmetric probe in the rarefied atmosphere *

The problem of uncontrolled descent of a space probe in the rarefied atmosphere is considered. We assume that the probe is a solid and it has a shape close to the body of rotation. A characteristic feature of the probe design is the presence of significant quantities of geometrical and aerodynamic asymmetries. The initial nonlinear system of equations of motion of the probe does not allow for an efficient asymptotic analysis of the evolution of the probe motion. For this reason, we need to lower the order of the original system of equations of motion of the probe. The aim of this work is to obtain low-frequency nonlinear equations of motion of the asymmetric probe performing uncontrolled descent in the rarefied atmosphere in this case, we apply the method of integral manifolds. The analysis of the slow fraction in the resulting low-frequency system of equations can be investigated, for example, by the averaging method.

Tatiana Shlyakova * Sound signal analysis using Morlet wavelet *

In this work, a comparative study and analysis of the features of an audio signal using a wavelet transform and Fourier transform, a comparison of the information content of the features. The spectral sequences obtained as a result of both transformations are compared according to the information content of the signs from the point of view of clustering of two types of voices: female and male.

Sergey Novikov and Mariya Fedina * On some problems and solutions in frame theory *

We define frames for a finite dimensional Hilbert space as the complete systems in. The basic frame families are classified such as tight and Parseval frames, equal norm frames and equiangular frames. The statements of some problems that have already become famous in the theory of frames are given. Considerable progress has been made in addressing some of them in recent years.

Dmitriy Novomeyskiy and Mikhail Piganov * Mathematical model of the interaction of a torch discharge with film elements *

The process of interaction of a flare discharge with a resistive film is described. The thermal balance equation is considered. Taking into account the exponential dependence of electrical conductivity on temperature a mathematical model of the interaction of a flare discharge with a resistive film is constructed based on this equation. Increasing the mathematical model accuracy for this interaction is considered.

Michael Bolotov, Vadim Pechenin, Nikolay Ruzanov and Iliya Grachev * Information model and software architecture for the implementation of the digital twin of the turbine rotor *

The location parameters of the actual profile of the blades of a gas turbine engine relative to its nominal position are used to assess the quality of manufacturing of these parts. The use of various methods for calculating the offset and rotation of the actual profile can lead to mismatching values, which raises the question of a reasonable choice of the methods used. This paper presents two methods for determining the geometric parameters of the location of the aerodynamic profiles of the blades, taking into account the features of their manufacture and the requirements of the existing industry standard. Also, the work evaluated the effectiveness of the proposed methods in determining the processing parameters of the blades of a gas turbine engine.

Arina Enikeeva and Ruslan Pikalov * The influence of climber motion on the dynamics of the orbital space elevator *

The paper deals with the motion of the orbital space elevator. The space elevator is designed to deliver payload to Earth orbit. It consists of the counterweight station and the lower docking module connected by the tether. The climber with payload moves on the tether. In the orbital space elevator, the lower end of the tether is not fixed to the Earth's surface, but is in low earth orbits. The space elevator is considered as a mechanical system consisting of three material points. The points are connected by elastic weightless rods of variable length. The first rod (lower segment) connects the lower docking module and the climber. The second rod (upper segment) connects the climber and the counterweight station. The motion of the climber is determined by the kinematic law, according to which the lower segment of the tether, as it climbing, increases in length, the upper segment – decreases. A mathematical model of the system is developed. A series of numerical experiments was carried out to study the influence of the climber motion on the dynamics of the orbital space elevator.

Ravil Uzyanbaev and Regina Yusupova * Mathematical modeling of mass-heat transfer processes on the grain of a catalytic cracking catalyst *

The catalytic cracking process is one of the most important processes. This is the largest tonnage process of oil production and takes the second place in oil production after its primary distillation. The study of processes on the catalyst grain is necessary to create effective catalytic systems. The calculations of the chemical process on the catalyst grain are carried out on the basis of solutions of the equations of balance of the mass of components and heat.

Gulshan Bikbova, Gulshat Mannanova and Irek Gubaydullin * Review of catalysts of catalytic cracking process and analysis of possibility of their calculation by universal kinetic model *

The catalytic cracking process is specific and depends on several technological factors such as temperature, type of catalyst and reactor, and contact time. This article presents a review of foreign industrial zeolite-containing catalysts RDM SWM, and Russian microspherical catalyst "Oktifayn", granular cracking catalysts "adamant". On the basis of experimental and production data it is possible to make mathematical modeling of catalytic cracking process, and to pick up a set of constants of rates of chemical transformations for each of types of catalysts.

Elena Shchepakina and Elena Tropkina * Order reduction for problems on travelling waves solutions to reaction-diffusion systems *

The paper is devoted to the order reduction for travelling wave problems in reaction-diffusion systems. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of the travelling wave of the original PDE system to the analysis of their profiles in ODE system with a lower order.

Albina Karamova * Program for modeling the kinetics of chemical reactions in the cascade of reactors *

Based on explicit and implicit numerical methods for solving the Cauchy problem, an algorithm is developed for solving the direct kinetic problem in a cascade of reactors. In the programming environment Borland Delphi implemented a software package. In the software package, it is possible to compile kinetic models of various catalytic processes based on the law of mass action. The software package can be used to simulate the kinetics of an industrial process in a cascade of reactors of ideal mixing of periodic action and ideal displacement.

Alexander Ryazhskikh, Igor Kachkin and Oleg Semenihin * Mathematical model of heat exchange in a descending stream of suspension in a vertical pipe under the boundary conditions of the second kind *

Andrei Pavelev and Vitalii Semin * Application of stochastic calculus for some classes of quantum models *

In this work, stochastic calculus is applied for describing open quantum systems. The suggested approach is based on a modified stochastic Schroedinger equation. We apply the approach to investigate a qubit relaxation in Markovian and non-Markovian regimes.