Posters

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.

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).

Valery Bogdanovich and Mikhail Giorbelidze
Mathematical modeling of features of heating of a cylindrical surface at plasma spraying
A mathematical model for determining the temperature in the coating-base system during plasma deposition of powder material on the inner cylindrical surface has been developed. The mathematical model takes into account the transformation of the Gauss heat source, the speed of relative motion of the plasma torch and the angle of the plasma jet with respect to the sputtered surface. The influence of technological parameters of sputtering on the heat stress of the process and the quality of plasma coatings is analyzed.

Andrey Agafonov, Ksenia Milanina, Anatolii Eremin and Vasiliy Gavrilov
Application of molecular dynamics for modeling processes in microfluidic devices
The article considers the possibility of using the molecular dynamics (MD) as part of multi-level models for describing processes in microfluidic devices. Much attention is paid to issues related to the use of MD to describe processes at a gas-solid interface.

Dmitriy Ivanov and Aleksandr Zhdanov
Numerically stable algorithm for identification of linear dynamical systems by extended instrumental variables
Instrumental variables are widely used to identify linear dynamical systems. The advantages of instrumental variables include low computational complexity, as well as the possibility of identification for different models of color noise. Often the method of instrumental variables leads to ill-conditioned problems, which significantly limits the application of this method. The paper proposes a solution to the problem of extended instrumental variables based on augmented normal equations. Test examples showed high accuracy of the proposed approach.

Andrey Dmitriev, Ilnur Madyshev, Aliya Khafizova and Andrey Nikolaev
Hydrodynamics in counterflow cooling tower with corrugated inclined contact elements
Packing for liquid cooling with counter flow of liquid and gas phases had developed by authors of paper. This packing is different from other devices in that it has quite simple design where self distribution of liquid in apparatus working area is organized. In paper an estimating calculations of packing operating mode with maximum efficiency of performed heat and mass transfer processes had conducted. The performed numerical study is showing that at mean gas velocity up to 4 m/s, contact device width equal to 0.1 m and liquid column height on contact stage – 0.02 m the share of liquid that forced through by gas flow is not more then 2 %. Decreasing of holes diameter on inclined contact elements results in increasing of bubbled liquid share.

Tatiana Mikhailova, Eldar Miftakhov, Vladimir Mikhailov and Sofia Mustafina
About an algorithm for modeling the isoprene polymerization process in the cascade of reactors using the Monte Carlo method
The article describes an algorithm for modeling the isoprene polymerization process based on the Monte Carlo method. The algorithm can be used to simulate polymerization processes carried out in batch or continuous mode. The possible polycentricity of the catalyst used is also taken into account. The model on the basis of this algorithm makes it possible to study the properties of the polymerization product and calculate the molecular weight distribution for different points in time.

Victor Ryazhskikh, Alexander Nikolenko and Dmitry Konovalov
On the structure of the orthotropic 3D permeability tensor of an anisotropic porous body in heat and mass transfer problems
The structure of a 3D permeability tensor with orthotropic properties is proposed to describe various heat and mass transfer processes in anisotropic porous media. This structure of the permeability tensor has advantages over the monoclinic and triclinic because of the minimum number of elements to be determined, which greatly simplifies the formulation, conduct and processing of the corresponding experiments. In addition, the confirmation of the operability of such a structure opens up new opportunities for the artificial creation of porous materials with specified properties and the required anisotropy architecture on 3D printers. Using the Jacobians of rotations in the Cartesian reference system, the matrix of rotations is found as a result of successive multiplication of Jacobians by different angles around the axes of the base coordinate system. The final form of the tensor is identified as the product of the orthotropic tensor on the left and right by the turn matrix and the transposed turn matrix, respectively. This representation allowed us to calculate the inverse permeability tensor and synthesize a mathematical 3D model of Darcy-Brinkman type of unidirectional flow in a porous channel of rectangular cross-section on the example of hydrodynamic filtration of a Newtonian fluid. It is shown that such linearization does not level the property of anisotropy in a porous medium, while maintaining three-dimensionality.

Vladimir Aslanov and Daria Andrievskaia
Delivery of a returned container from the surface of Phobos using electrostatic forces
The original scheme of delivery of a returned container with soil samples from the surface of Phobos to the orbital spacecraft is proposed. The scenario of this mission consists of two stages: the launch of the container from Phobos using a simple spring mechanism and capture of the container by the orbiting spacecraft using the Coulomb force. A mathematical model of the container's motion relative to the spacecraft has been developed. A motion analysis is carried out, based on which the following characteristics of the system are selected: initial velocity of the container, value of the Coulomb force, and height of the lift of the container.

Oleg Krol, Volodymyr Sokolov, Petko Tsankov and Olexandr Logunov
Modelling of machining center vibration stavility by the D-partitions method
The stability of operation, vibration-free processing of products various types at high-speed machining centers suggests the improvement of research in the field of the dynamics of machine tools and their main forming units. The three-dimensional models of the forming spindle node and the corner table of the machining center for the drilling-milling-boring type in the CAD environment KOMPAS-3D have been developed. An algorithm for analyzing the dynamic quality of the machine elastic parts based on the constructed static and frequency formular in the mathematical environment MAPLE is proposed. Programs have been developed and graphs of the main frequency characteristics and the hodograph of the transfer function for the spindle node in the specialized Signal Processing module have been obtained. The method of D-partitions using to estimate the vibration stability of the forming units on an example of 4 coordinate milling machining centers is introduced. Experiments on two variants of technological adjustments with different dimensions of the tool block (the cantilever part of the spindle assembly) were carried out. The analysis of stability in the plane of the cutting process optimized parameter (specific cutting force) was carried out. The region and the boundary of the stable functioning of the machine and, on this basis, the optimum modes of machining by the criterion of vibration stability are revealed.

Sergey Volgin, Maksim Ivanushkin and Ivan Tkachenko
Modelling of onboard systems operation of small satellites based on general logical-probabilistic method
An approach for simulating the operation of onboard systems of small satellites has been developed. The purpose of the technique is to simulate all possible combinations of malfunctions in the onboard systems of the small satellite, leading to the occurrence of abnormal situations during their operation. As a result of using the technique, a list of emergency situations is created, which is later used to create programs for complex testing of small satellite on-board equipment at the ground testing stage. The use of the technique leads to a reduction in time for the preparation of tests, provides support in making decisions on the management of the small satellites and reduces the response time to emergency situations that arise during operation.

Iliya Grachev, Michael Bolotov, Vadim Pechenin and Evgeny Kudashov
Comparative analysis of simulation options for the real geometry of the surfaces of gas turbine engine parts
Geometric deviations of parts surfaces inevitably occur during parts manufacture. It is known that the accumulated defects of parts surfaces and assembly units impact their functional characteristics throughout the entire product life cycle. Often, assembly simulation and dimensional ties analysis of products are performed by using the nominal geometry of parts without taking into account geometric deviations of the shape and location of parts surfaces. The accuracy of dimensional analysis without taking into account geometric deviations of the shape and location of parts surfaces is not sufficient to solve technological problems in digital production. The purpose of this article is the study of the influence of methods and models for constructing the real geometry on the accuracy of its reproduction. The subject of the research is the assembly unit of the rotor of a low-pressure turbine of an aircraft engine. The article considers three methods for constructing the real geometry, which are used to realize assembly virtual simulation. Comparative results of assembly simulation with the use of considered methods of real geometry constructing are presented, as well as their influence on the controlled assembly parameters is estimated.

Vadim Salmin, Vladimir Kurenkov, Sergey Safronov, Ivan Tkachenko, Artem Yakischik, Maksim Ivanushkin, Sergey Volgin and Anastasiia Krestina
Development of tools for computer-aided engineering and simulation of the remote sensing satellite systems, taking into account the requirements and limitations on customer resources
This article examines approaches to the selection of design parameters and modelling the functioning of the remote sensing satellite systems, taking into account the requirements and restrictions on customer resources. The objective of this research is to increase the efficiency of the use of space systems to solve urgent tasks of monitoring the earth's surface. Firstly, an analysis of the requirements for space imagery materials and consumer information support for solving regional problems was carried out, secondly, mathematical models of remote sensing equipment and onboard systems of small spacecraft, as well as the ground-based complex for receiving and processing information, were developed, and finally, a database with the technical characteristics of the onboard systems and remote sensing equipment of spacecraft, launch vehicles and ground-based reception and processing information facilities was created. As a result, software to determine main design parameters and modelling the functioning of cost-effective remote sensing satellite systems was developed.

Elena Demyanenko, Anastasia Kosolapova and Igor Popov
Modeling of the process of plastic deformation as applied to thin-walled shells of the type of bottoms
Disclosed is a method of producing bottom-type parts based on a flanging process. Results of physical modeling of equivalent-thickness parts of bottom type are presented. Parameters of rheological model of cold deformation are determined. The procedure of procurement calculation and simulation results are given.

Vadim Zinurov, Nailya Dubkova, Oksana Popkova and Oksana Dmitrieva
Influence of separation elements shape on device efficiency
A paper deals with the urgent problem of studying the separation process of gas flow from fine-dispersed particles. A device developed to intensify gas flow separation from fine-dispersed particles. The principle of operation of the device is given. The effect of the shape of separation elements, gas flow velocity, as well as size and density of particles on device efficiency has been investigated. As a result of the study, the maximum efficiency of gas flow separation (on average 85 %) is achieved at a gas velocity of 8 m/s. Moreover, the separation increases when the density and diameter of the particles begin to grow. The double-T shape of separation elements was demonstrated as the most effective types of geometry.

Andrey Parfiriev, Oksana Parfirieva and Igor Ishchuk
Quadcopter directorial control algorithm with the possibility of flying around obstacles
The article solves the problem of developing an autonomous flight control system that allows an unmanned aerial vehicle of a copter type, a quadrocopter, to fly along a given route with the possibility of flying around obstacles. The problem is solved by developing a detailed mathematical model of a quadrocopter with four propellers, taking into account the influence of the working environment and the algorithm for trajectory control of an unmanned aerial vehicle. The mathematical model is based on the basic law of dynamics for translational motion and the basic equation of dynamics for rotational motion. The trajectory control algorithm aimed at maintaining the required linear coordinates of the quadrocopter over the entire length of the route was developed using a proportional-integral-differentiating (PID) controller. A PID controller is also used to maintain angular coordinates. The coefficients of the PID controller are calculated by the tangential method or the Ziegler-Nichols method. The trajectory control algorithm is implemented in an object-oriented programming environment. The mathematical model is based on the basic law of dynamics for translational motion and the basic equation of dynamics for rotational motion.

Irina Papkova
On a static solution to the contact interaction of a flexible rectangular in plane of a microshell with a rectangular in plane of microplate
The mathematical model of the contact interaction of a flexible rectangular in plane of a spherical microshell and a flexible rectangular microplate is constructed. The material of the shell and plate is elastic isotropic and homogeneous. Kirchhoff hypotheses are taken into account. A system of nonlinear partial differential equations is derived from the Hamiltonian energy principle on the basis of a modified couple stress theory. The contact pressure function was determined according to the theory of B.Ya. Cantor. Contact interaction of sensitive elements of micromechanical sensors of inertial information in the form of a micro-shell and micro-plate is investigated. A micro-shell is affected by a static, uniformly distributed load. The static solution is determined by the establishment method. A new phenomenon related to the loss of stability is obtained.

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).

Ekaterina Serikova, Vladislav Kalaev and Olga Serikova
Using ROC analysis to confirm an algorithmically established diagnosis of lichen planus
The use of ROC analysis allowed the authors to determine cytogenetic criteria to confirm the diagnosis of lichen planus, obtained by selecting the most informative features and interpreting the micronucleus test in buccal epithelium, calculating their critical values, sensitivity and specificity for use as diagnostic tests. An increase in the number of cells with micronuclei in the lesion of lichen planus is a sign of genetic instability, which can trigger the process of their malignancy. Recognition of nuclear aberrations against the background of nuclear destruction makes it possible to diagnose lichen planus in patients.

Yuriy Vashukov
Mathematical modeling of hole formation with reinforcement in composite construction
With the help of the presented finite element model, studies of the deformed state of the process of setting the reinforcing sleeve in the hole of the part made of a polymer composite material are carried out. A mathematical model was developed to determine the force and operation of the setting process, as well as the dependence of the design parameters on the deformed state of the sleeve along the contour of the hole with reinforcement.

Klara Gabdrahmanova, Gulnara Izmailova and Lilia Samigullina
Mathematical modeling of geothermal energy extraction process by means of a well
The authors of the article examine the possibility of extracting geothermal energy to the Earth’s surface using the circulation of a heat carrier – water. For this purpose, an oil well is operated that is already suspended and is no longer used for its original purpose. A system of heat and mass transfer equations describing heat distribution in the ground around the well and in the coolant is presented. Various well depths, geothermal gradient, and water injection rate are considered.

Valery Kondrashchenko, Sergey Titov and Mong Thu Tran Thi
Mathematical model of a concrete mix rotational seal
A mathematical model is proposed for a throwing device in the form of two rotating cylinders with plates along their generators, which collect concrete mix portions and spray them in a mechanical way. A mathematical description of operation of such a device, interaction of individual particles with the blades and their flight in the space between rotors up to concrete mix compaction is given.

Vladimir Jordan, Igor Shmakov and Angelica Grigoryevskaya
Software implementation of the 3D-simulation procedure of SHS macrokinetics in the Ni-Al porous model medium with the closest packing of “mesocells”
The methodological features of the procedure for modeling the SHS macrokinetics in the model "etalon" structure of the densest packing of the so-called “mesocells” in the form of balls of the same radius are considered. In the center of the mesocell there is a spherical Ni particle (radius RNi = 30 μm), around which aluminum particles of radius RAl = 10 μm are contained in a spherical interlayer with a thickness of 20 μm. The etalon structure is formed by a program that takes into account the distribution of mesocells in the structure of the closest packing (alternating flat layers with square symmetry). A technique for numerical solution of the heat conduction equation using an implicit scheme of bicyclic splitting based on the symmetric Krank-Nicholson scheme is implemented. Together with the bicyclic splitting scheme, a procedure is implemented for numerically solving the diffusion kinetics equation in mesocells. For computational speedup, the parallelization schemes of cycles are used, which determine the main time costs for performing "runs" in grid computing schemes.

Aleksey Utkin, Albert Gareev and Asgat Gimadiev
Diagnostic method of a coil heat exchanger efficiency based on thermal and hydrodynamic processes modelling
The coolant quality is carefully monitored at thermal power plants using special devices, the input of which is a sample of superheated steam or condensate cooled by a coil heat exchanger. In the process of reducing the coolant temperature due to the content of impurities in the cooling water on the outer surface of the coil, scale deposits form, leading to a decrease in the efficiency of the heat exchanger and its failure due to blockage of the annulus by deposits. The use of parametric diagnostics of the heat exchanger efficiency, based on comparison of heat transfer coefficient of heat exchanger with and without deposits, will allow to set rational maintenance periods for the heat exchanger and reduce cooling water consumption. The paper presents a model for a subsystem of on-off automatic sample temperature control with a function for the heat exchanger efficiency diagnostic. The obtained simulation results with imitated deposits in the form of a multilayer coil wall show that with an increase in the thickness of deposits, the heat exchanger performance factor decreases almost linearly, confirming the rather high sensitivity of the proposed diagnostic method. The developed diagnostic method can be used in steam and water analyses system.

Angelica Grigoryevskaya, Pavel Gulyaev, Vladimir Jordan and Igor Shmakov
Spin instability criteria based on parametric identification of the node distribution in Trace transform direct image of the SHS combustion wave chronogram
The article gives examples of virtual chronograms of the propagation of a combustion wave in the diffusion, thermal, and spin instabilities of the SHS process. It is shown that the use of high-speed video recording allows one to reliably determine the moment of occurrence of the spin instability of the SHS combustion wave by differential chronoscopy methods. As a criterion for the recognition of spin instability, we selected the sign of the appearance of local maxima in the central transversal region of the spectrum of the trace transform. It is concluded that the spin instability is characteristic of the transition from the thermal to diffusion instability, in the presence of a hysteretic dependence of the burning rate on temperature.

Valery Berdnikov and Yakov Mostovoy
Analytical and numerical modeling of the formation of a programmable percolation route in the planning of two-phase operations
A swarm of robots, as a system of relatively simple interconnected controlled objects, fulfils a common task in a simultaneous and distributed manner. When planning swarm operations associated with the creation of a through frontal band in the service area from zones of target equipment operation – payload of the swarm objects, it becomes necessary to perform operational regrouping of the swarm, since at the time of planning the exact purpose of the swarm operation has not yet been determined or is a secret or is determined by a number of random circumstances. The execution of a swarm operation is advisable to carry out in two phases. The first phase starts even before resolving these uncertainties by creating a basic random network with a relatively small concentration of robots. At the second phase of the operation, a specific programmable percolation route is formed by local regrouping of the swarm objects, which provides a predetermined coverage of the target equipment of the swarm objects with operating zones in a certain service zone. In this case the time of the operation can be reduced significantly. This task is solved with the programmable percolation theory methods. The analytical dependences of the average quantity of the swarm objects from the stochastic base at the first phase of the operation, which are engaged in the formed programmable percolation route from the concentration of the swarm objects in the service zone, as well as the average quantity of the objects added to the inter-cluster intervals of the formed programmable percolation route depending on the concentration have been received. These dependences were confirmed by statistic modelling.

Valery Berdnikov and Yakov Mostovoy
Modification and training of ant algorithm for planning swarm operations of moving objects
A swarm of mobile robots, as a system of relatively simple interconnected controlled objects, fulfils a common task in a simultaneous and distributed manner. When planning swarm operations associated with the creation of a through frontal band in the service area from zones of target equipment operation – payload of the swarm objects, it becomes necessary to perform operational regrouping of the swarm, since at the time of planning the exact purpose of the swarm operation has not yet been determined or is a secret or is determined by a number of random circumstances. The execution of a swarm operation is advisable to carry out in two phases. The first phase starts even before resolving these uncertainties by creating a basic random network with a relatively small concentration of robots. At the second phase of the operation, a specific programmable percolation route is formed by local regrouping of the swarm objects, which provides a predetermined coverage of the target equipment of the swarm objects with operating zones in a certain service zone. This task is solved with the programmable percolation theory methods. A modified ant algorithm with evolutionary training has been considered and studied to solve quickly by the swarm the task of finding and forming the shortest through route via the service zone. In this case the time of the operation can be reduced significantly.

Valentina Burmistrova, Alexander Butov, Maksim Volkov, Mariya Moskvicheva, Yuliya Pchelkina, Boris Kostishko and Marina Yavtushenko
The change in the probability of aviation accidents “Collision of an aircraft with a bird” in accordance with of a change in the temperature cycle
This paper considers the possibility of predicting the most frequent aviation event "Collision of an aircraft with a bird", depending on the seasonality near the airfield. A model for determining the probability of this event is proposed, where the "time of year" is identified by the predicted air temperature near the airfield in question and the problem of determining the accumulated probability is solved. We consider the first approximation in which events are assumed to be independent (these are complex ecological and ornithological conditions and flaws of airfield’s ornithological support). Due to the first approximation of independence, the paper provides a possible way to determine the probability of the event "Collision of an aircraft with a bird". This method (in the form of a formula) determines the probability of intersection of events caused by hazard factors. The result of the simulation is the probability of long-term forecasting of the probability of an aviation incident due to an aircraft collision.

Larisa Stepanova and Ekaterina Mironova
Asymptotic stress fields near the crack tip in perfect plastic materials under mixed mode loading (plane strain conditions)
In the paper the asymptotic stress fields in the vicinity of the crack tip in perfectly plastic Mises materials under mixed mode loading for the full range of the mode mixities are presented. The salient point of the study is that the asymptotic solution is described by the same formulae for all values of the mixity parameter from 0.89 to 1 for plane strain. For plane stress conditions this segment can’t be observed.

Alexander Chekashov and Andrey Kramlikh
Research of optimality of the nanosatellite nominal reorientation trajectory
Nanosatellites have serious limitations on the onboard energy. Therefore, it is necessary to find a method of constructing a nominal reorientation trajectory that will optimally use the resources available on board. In this paper the process of constructing of nominal reorietation trajectory in the plane of nanosatellite orbit is considered. The problem of constructing a nominal reorientation trajectory was solved using the inverse dynamic problem method and Pontryagin maximum principle. A comparison of the results obtained using these two methods was made. As a result, it was noted that the solution obtained by the inverse dynamic problem method is close to the solution obtained using the Pontryagin maximum principle. This allows to speak about the optimality of the inverse dynamics problem method.

Anastasia Peksheva and Larisa Stepanova
Mixed mode fracture in perfect plastic materials for plane stress conditions
In the study the asymptotic stress fields in the neighbourhood of the crack tip in perfectly plastic Mises materials under mixed mode loading for the full range of the mode mixities are presented. This objective is engendered by the necessity of considering all the values of the mixity parameter for the full range of the mode mixities for plane stress conditions to grasp stress tensor components behaviour in the vicinity of the crack tip as the mixity parameter is changing from 0 to 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).

Evgeniya Tsarkova, Alexandr Belyaev and Elena Andreeva
Research of the mathematical model of the immune system
The paper considers a mathematical model describing the processes occurring in the human immune system. The algorithm of numerical solution of the problem by gradient descent method is developed. The dependence of the optimal control problem solution on the model parameters is investigated.

Vadim Salmin and Alexey Chetverikov
Algorithm for narrowing of the region of the final trajectory parameters deflection during the flight to geostationary orbit with low thrust engines
The article deals with the problem of control during the flight to the geostationary orbit of interorbital transport vehicles with low-thrust electric propulsion systems. The analysis of the influence on the final trajectory parameters of disturbing factors of various kinds, including the presence of a systematic error in the implementation of electric propulsion thrust. An algorithm for narrowing the area of deviation of the final trajectory parameters during the flight to geostationary orbit using low-thrust engines has been developed, which includes an algorithm for forming nominal programs for controlling the thrust vector and an algorithm for refining the amount of thrust created by an electric propulsion system, based on measurements of the actual period of circulation.

Vadim Salmin, Konstantin Peresypkin, Alexey Chetverikov and Ivan Tkachenko
Determination initial approximation in solving the problem of numerical optimization of a large-sized space structure using linear extrapolation of optimal solutions
The parameters of a large-sized space structure are determined using numerical optimization using the gradient method. The complexity of the boundary of design constraints makes the optimal solution poorly conditioned relative to the starting point of the iterative process. The starting point is selected based on the optimal solutions found with an incomplete set of design variables. The starting point is found by linear extrapolation of these optimal solutions. In the problem under consideration, this approach made it possible to obtain a better locally optimal solution than was possible with the help of an intuitive choice of the starting point.

Aurthur Vimalachandran Thomas Jayachandran, Andrey Tkachenko, Hewa Hussein Omar and Krishnakumar Aruljothi
Performance computing of an open cycle micro gas turbine powerplant using data aided modeling and simulation.
In this paper the study of the thermodynamic performance for a 6kW micro gas turbine power plant has been optimized by considering Air- fuel ratio at various altitudes along with fuel inlet temperature. The parametric analysis was performed to improve the overall efficiency of the power plant to obtain the required power needed by a multi-copter. The research deals with parametric optimization for determining realistic and practical combinations for improving the specific fuel consumption and overall efficiency of the Micro gas turbine power plant. The use of recuperators has not been beneficial for the micro gas turbine power system due to the increase in the total volume and weight of the engine. The fuel inventory should be decreased significantly to justify the addition of a recuperator system. The addition of heat exchangers improves the Specific fuel consumption that results in environmental friendly micro gas turbine engines. The result of this work helps to develop and design the micro gas turbine with high efficiency and at the optimized output. A model for a 6 kW micro gas turbine power plant was optimized for the application of primary power units for multi-copter or drones at low altitude conditions. To validate the model, JET CAT PHT3 shaft turbine design parameters were used and the results are compared with the experimental tests on this engine.

Aurthur Vimalachandran Thomas Jayachandran, Andrey Tkachenko, Krishnakumar Aruljothi and Hewa Hussein Omar
Modeling and parametric optimization for a solar-powered closed-cycle micro gas turbine for space applications.
The research describes the theory design and the modeling of a closed cycle micro gas turbine power plant (CMGTP). A computer simulation model in ASTRA is used to model specifically, for this cycle. The research is a feasibility study to examine the technology for Brayton-cycle based solar thermal power plants and to optimize the model in comparison with solar array photovoltaic cells to increase the power density by increasing the power generated per unit solar-collector area. A mathematical model for CMGTP was designed to power satellites in space environments. The goal is to provide electricity from a parabolic mirror acting as a heat source that is collected by pointing at the sun. The Closed Brayton Cycle power was simulated to produce an output of 6 kW at the generator terminal. The heat source generated from the sun was considered to be around 750 K to 1250 K. The vacuum at the space radiation environment was considered to be 200 K acting as a coolant sink. The CMGTP consists of a centrifugal compressor, a radial in-flow turbine on a single shaft powering a two- pole permanent magnet alternator.

Vadim Krysko
Nonlinear dynamics rectangular in plan nanoshells
Mathematical model of non-linear vibrations of rectangular in plan nano-shells on the basis of the first-order approximation of the Kirchhoff-Love theory under the action of a transverse sign-variable are proposed. The geometric non-linearity is introduced by means of the von Kármán shell theory and the shells are assumed to be shallow, elastic and isotropic. The governing equations are yielded by Hamilton–Ostrogradsky's variational principle, taking into account the modified couple stress theory. The continuous problem is reduced to the Cauchy problem by the finite-difference method of the second order accuracy. The Cauchy problem is solved via the fourth-order Runge–Kutta method with respect to time. We analyzed the convergence of these solutions depending on the step of integration over time and spatial coordinate. In particular, we found that taking nano-effects into account increases area of harmonic vibrations and leads to the appearance of as chaotic so hyperchaotic vibrations. Furthermore, we have detected the transition of vibrations from harmonic to chaotic according to Feigenbauman's scenario. We analyzed the character vibration using signs of spectrum the Lyapunov exponents. We found that hyperchaotic vibrations are characterized by two positive Lyapunov exponents and chaotic vibration by one positive Lyapunov exponent. For nano-shells, this phenomenon was discovered for the first time. The spectrum of Lyapunov exponents was determined by the methods of Wolf, Kanz, Rosenstein and Sawada to obtain reliable results. Computational examples of the theoretical investigations are given.

Hewa Hussein Omar, Venedikt Kuz’michev, Andrey Tkachenko and Aurthur Vimalachandran Thomas Jayachandran
Development of a mathematical model of the compact heat exchanger used for optimizing thermodynamic parameters of the aviation gas turbine engine
Nowadays, the task of increasing the economic and technical efficiency of the gas turbine engine and decrement of the specific weight and specific fuel consumption is one of the main targets in the development of the aviation gas turbine engine. A promising approach for decrement of specific fuel consumption and obtaining high thermal efficiency of the gas turbine engine (30% and above) is based on the concept of the recuperative cycle of the gas turbine engine. The article presents the computer-aided calculation for analysing the heat exchanger surface and developing novel mathematical models of heat exchanger in terms of weight goodness, flow passage goodness, and optimum weight and flow passage. 18 different heat transfer surfaces for heat exchanger cores have been evaluated and the results are presented. The same hydraulic diameter assumed for all heat transfer surfaces and only their thermo-hydraulic performances evaluated during the calculation design. To assess the reliability of the obtained models, the results of the design calculations of the developed models compared with the data of other authors and with the data of the existing gas turbine engine with heat exchanger. The obtained models focus on mathematical design calculation for optimizing the main thermodynamic parameters of a gas turbine engine coupled with a heat exchanger at the stage of conceptual design of aviation gas turbine engine with heat recovery of exhaust gas.

Valentina Burmistrova, Alexander Butov, Boris Kostishko and Marina Yavtushenko
The problem of optimal control of the intensities of processes with change-point
This article we consider the formulation of the problem of optimal control of processes with change-point. At the same time, for one important quotient, the problem of finding the optimal parameter value characterizing the intensity of the change-point is formed and solved. As a criterion, we consider a functional that takes into account the distribution of the moment of the first crossing fixed boundary by a process with a change-point with a controlled parameter.

Vladimir Volotsuev
A digital model of the density of the earth's residual atmosphere for ballistic analysis in the design of low-orbit spacecraft

Larisa Stepanova
A photoelastic and finite element study of the stress field in the vicinity of two interacting cracks: stress intensity factors, T-stresses and higher order terms
Multi-parameter stress field near the Mode I crack tip in an isotropic linear elastic material is presented. The coefficients of the Williams series expansion of the stress field in the vicinity of the Mode I crack in the isotropic linear elastic material are obtained by the digital photoelasticity technique and by finite element analysis. The main objective of this study is to determine first fifteen coefficients with good accuracy and to compare the numerical results with the analytical solution for the infinite plate with the central crack.

Larisa Stepanova and Oksana Belova
Determination of the higher-order coefficients of the Williams asymptotic expansion for notched semidiscs using the photoelasticity method and finite element analysis
The coefficients of the Williams series expansion in notched semidisks with different angles of the notch are obtained. The study is based on the experimental procedure of the photoelasticity method and the finite element analysis. The large series of experiments for semidiscs was performed. Digital photoelasticity method is used to analyze experimentally the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic cracked specimens under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtaining the stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens.

Hewa Hussein Omar, Venedikt Kuz’michev and Andrey Tkachenko
Optimization of the parameters of the working process of aviation turbofan engines with heat recovery
Improving the fuel efficiency of aircraft engines is the main global trend of modern propulsion engineering. One of the promising ways to further improve fuel efficiency is the use of complex thermodynamic cycles with heat recovery of exhaust gases and intermediate cooling in the process of air compression. An important task in the design of engines with heat recovery is to select the parameters of the working process that ensure maximum efficiency of the power plant - aircraft system. In the article presents the problem of optimization and selection of rational parameters of the working process of turbofan engines with heat recovery. Based on the developed method of multi-criteria optimization by means of numerical simulations conducted and presents the results of optimization of parameters of working process of turbofan engines with heat recovery system in passenger aircraft of type Airbus A310 on criteria such as the total mass of the power plant and fuel required for the flight, and the specific fuel consumption of the aircraft on a ton per kilometer. The developed mathematical model for calculating the mass of a compact heat exchanger, designed to solve optimization problems at the stage of conceptual design of the engine, is presented. The developed methods and models are implemented in the ASTRA program.

Elena Shchepakina
Order reduction for critical travelling waves problems
The paper deals with the order reduction for critical travelling waves problems. The specificity of such travelling waves is that they separate waves with qualitatively different behaviors. We show how the application of the geometric theory of singular perturbations allows us to reduce the problem of finding the travelling wave of the original PDE system to the analysis the projection of the system onto its slow invariant manifold. We illustrate this approach to the problem of finding the point-to-periodic travelling wave for the reaction-diffusion model.