The paper considers the results of modeling the cable system of the above-water cable-stayed transition of the main gas pipeline using a laboratory installation and computer modeling using finite element methods. The main characteristics of materials and structural elements used to create a computer and laboratory model are given. Various modes of tension of the cable system affecting the further operation of the model under consideration, allowing to determine the service life of the object, are studied. It is shown that with a slight weakening of the tension of one of the cables, in the cable system, the occurrence of stresses in the pipe body is observed, the magnitude of which, under certain conditions, greatly exceeds the operating values. A small imbalance of effort leads to a redistribution of effort and a distortion of the entire structure, which, under cyclic loads, can lead to a premature exit from the standing of the object in question.

Keywords: cable-stayed transition, effort, stress-strain state, cable system, finite element method, model, load, force.

This article suggests a mathematical apparatus for modeling quantitative indicators of social space and stratification. It describes formulas for calculating social status, radius and volume of power as characteristics of a separate social position and the magnitude of interaction between positions. The proposed formalization corresponds to the sociological theories of P.A. Sorokin and P. Bourdieu. It is offered to use simulation modeling to extend this approach to the regional level of analysis

Keywords: analytical and geometric analysis, simulation modeling, social space, social stratification

Mathematical modeling of processes in the crystal structures of the Gunn diode and modeling of the operation of the diode itself in various electrical circuits are relevant for monitoring the operation of electronic devices The paper investigates the effect of low-frequency pickups in the power supply circuit of the Gunn diode on the Fourier spectrum of the generated microwave signal. To study the processes of formation and motion of a domain in a crystal structure, the local field model of the Gunn diode is used, based on the assumption that the average drift velocity of electrons depends on the instantaneous value of the electric field, and the diffusion coefficient does not depend on the applied electric field. A serial circuit for switching on a diode with a power source and a resistive load is simulated. As a result of the simulation of the program, the distribution of stresses inside the crystal along its length at a selected moment of time is obtained; graphs of the movement of domains are plotted based on these data. Based on the data obtained, a Fourier transform is performed, and the resulting spectrum is constructed. The correctness of the program operation is confirmed by the spectrum obtained by the 3A703B diode on the S4-27 spectrum analyzer. The shape of the inhomogeneities in the crystal lattice, given the same width, does not affect the formation of domains. Rectangular, parabolic and gradient functions of dopant concentration variation are investigated. If the function changes more smoothly, then the maximum amplitude of the domain strengths will be greater, but the domain will take a little longer to form. The resulting model can be used to calculate fields with different loads in an electrical circuit.

Keywords: Gunn diode, microwave, simulation of physical processes, Fourier spectrum, radar systems

The trend in the development of information system design architectures is their complication and movement towards an increasing distribution of functions and components of the system. One of the options for developing decentralized systems are systems based on blockchain technologies. The article discusses an architectural template for applications developed on the basis of blockchain technology. The main elements of a multi-level architecture, which is the basis for building applications of this type, are considered. There are six layers that describe the infrastructure layer, data layer, network, consensus, application and representation. A brief analysis of the main features and differences of the implementation of each of the levels of the architectural template is carried out. According to the results of the analysis, the most specific components for blockchain-based systems are implemented at the level of consensus and data layers.

Keywords: decentralized application, blockchain platform, information system, multi-level architecture, pattern

Based on the review of methods for constructing distribution systems for microwave power amplifiers, a design of a spatial division-summation of power system in the Q-band and a power amplifier based on it is proposed.

Keywords: distribution system, microwave power amplifier, system of spatial division-summation of power

This article discusses the possibility of using ceramic materials with a high coefficient of thermal conductivity as a heat sink material to solve the problem of heat removal in heat-loaded elements of electronic equipment, which will significantly improve the thermal characteristics of the devices and the reliability of their operation.

Keywords: normal thermal mode, heat and mass transfer, high temperatures, thermal conductivity coefficient, ceramics

The article presents the results of a full-factor experiment and analyzesthe impact of various factors, such as the number of transitions a tape machine, the characteristics of an infrared laser diode and a the humidity of the material on the magnitude of the signal response when infrared radiation passes through the tape.

Keywords: fiber mixing quality, infrared estimation method, planning matrix, regression equation, model adequacy

The problem of data transformation in which calculations are carried out in parallel streams is considered. The goal is to draw up such a plan for the parallel assignment of data by performers, in which the conditions of validity, reliability, redundancy and adequacy of data suitable for further analysis will be satisfied. At the same time, taking into account the desire to complete data conversion cycles in the shortest possible time. The use of transport-type models is proposed for the solution. In contrast to two-dimensional minimax models by the criterion of time, the possibility of transformation of information is considered, both at source points and at destination points. The proposed model allows you to take into account the time of data delivery between processing sites. The influence of possible rules for moving information packets through intermediate points on the final value of the management quality indicator is shown.

Keywords: information chains, transport task, minimum time criterion, processing costs, data reliability

The given review of hygrothermal processes in the processing of grain crops, their features is presented from the standpoint of nanotechnology. It is shown that for the developed nanotechnologies in the production of agricultural products, it is necessary to apply non-traditional methods of process research, which is the method of similarity of the functioning of technical systems (SFTS). This method will allow for the processes of humidification, drying, wet-heat treatment in vacuum conditions to obtain generalized similarity criteria, determine their numerical values and obtain generalized criterion dependences of the intensity of the processes under consideration on the processing parameters. The implementation of the method will allow us to quantitatively describe the processes of hygrothermal grain processing in vacuum conditions, assign processing parameters and manage them. Mathematical models of hygrothermal processes have been developed based on the method of similarity of the functioning of technical systems depending on the parameters of the medium and the structure of capillary-porous grain shells.

Keywords: hydrothermal effects, grain crops, vacuum, nanotechnology, humidification, drying, wet-heat treatment, capillary-porous materials, microcapillary, the criterion of sublbiya, the method of similarity of the functioning of technical systems

The purpose of the study is to establish the regularities of a stable hydrodynamic regime by applying a fluoroplastic–containing composite polymer material to the support profile. Research methods: new models have been proposed describing the movement of a lubricant with truly viscous rheological properties in the laminar motion mode in the approximation for a "thin layer", in the working gap of a radial bearing with a support profile having a polymer coating with a groove, the continuity equation. A comparative analysis of the obtained results is carried out, confirming the approximation of the obtained model to practice. As a result of the study, a significant expansion of the possibilities for assessing the operational characteristics of the bearing has been achieved: the magnitude of hydrodynamic pressure, load capacity and coefficient of friction.

Keywords: radial bearing, increased wear resistance, antifriction polymer composite coating, groove, hydrodynamic mode, verification

The article considers the problem of optimizing the scheme of portages in a cutting area. The mathematical model of the cutting area is a polygon - a bounded closed broken part of the plane. The portage scheme corresponds to a root graph (forest, tree) of a special type. We have introduced the concept of covering a polygon with a rooted forest. The cover is interpreted as the possibility of cutting and collecting all the trees in the cutting area while moving the harvester and forwarder along the trails. The trails are laid according to the found covering root forest. Two variants of the algorithm for solving the problem are proposed, which are a modification of the local search. The first algorithm uses the greedy method we described earlier[18] to find the underlying solution. The second algorithm uses the branch and bound method to find the basic solution. Comparative experiments were carried out on polygons sized 12x12 and 18x18. Experimental results show that both modifications of the algorithm improve the basic solution. The first algorithm improves the solution by an average of 11% for a 12x12 polygon and by 24% for a 18x18 polygon.

Keywords: portage schemes, cutting area, polygon covering the root forest, local search, coverage

This paper presents the results of a study of the nature of lifting the tail lift of a truck with a hydraulic drive that supplies the working fluid to the cylinders in series for two positions of the center of gravity of the load on the lifting platform. A diagram of a hydraulic drive is presented, which supplies the working fluid to the hydraulic cylinders in series. Mathematical models describing the operation of the hydraulic drive are compiled according to the scheme. Simulation modeling was carried out using the MATLAB Simulink environment.

Keywords: wheel tyre, suspension module, wheeled vehicle, MATLAB Simulink, mathematical model, modeling

The article discusses the areas and prospects for the use of low-poly geometric models in the construction industry. Data on foreign researches in the considered area are given. The main differences of this type of models from the three-dimensional components of information models are listed, the difference in the methods of their development is described. An analysis of the currently relevant areas of application of these models in the construction industry was carried out, the key features that models should have to use them in these areas are named.

Keywords: civil engineering, low-polygon models, architectural and urban planning solutions, virtual reality, 3D cadastre, geoinformation systems

The article is devoted to the study of curves that are not representable by the intersection of two surfaces. In modern architectural practice, they very often depart from classical forms, replacing them with complex surfaces. Recently, there has been the development of such an architectural style as architectural bionics or bio-tech. Faced with the challenges of sustainable development and its impact on the environment, the construction sector faces the necessary need for innovation. Architecture is presented as one of the promising areas of knowledge use based on biological research. And it is able to respond to current environmental problems. Indeed, many species of animals and plants know how to apply adaptation strategies to the environment and its transformations, forming together with it a sustainable ecosystem. Technological advances in very small-scale observation allow for deeper knowledge of how nature works and offer a new source of knowledge and inspiration for architecture.

Keywords: architecture, spatial curves, axonometric projections of curves, narrowed curves, bionics, biomimicry, eco-innovation

Vector fields in ocean acoustics are the fields of particle velocity and power flow density. Vector analysis methods are used for theoretical analysis and classification of singular points in a hydroacoustic waveguide. Modeling of the power flow field is carried out as a product of the pressure fields and the components of the velocity particle field. The fields of pressure and velocity particles are calculated by the method of normal modes. The simulation of the power flow field in hydroacoustic waveguides with different sound velocity profiles and different acoustic properties of the bottom is carried out. Some regularities in the location of singular points are revealed.

Keywords: hydroacoustic waveguide, pressure field, particle velocity field, power flow field, singular points

TThe modeling of the process of distribution of profile oil pipes in a well by means of a cone punch is considered and the determination of the force necessary for its pushing is carried out on this basis. The normal force for one protrusion of the pipe profile was found. The change in the deformation resistance and profile geometry during distribution is taken into account. The optimal taper angle is determined and the geometric parameters of the punch are selected, including the largest and smallest diameters and its length. A numerical example of calculation based on the obtained formulas is given, which shows the technical feasibility of the process.

Keywords: distribution, oil profile pipes, protrusion force, equilibrium equation, deformation resistance, tool geometry, numerical example

The paper considers a mathematical model of the ion-beam etching process. A nonlinear differential equation of first-order ion-beam etching is considered. It has been established that the model equation for ion-beam etching can be reduced to a homogeneous Monge-Ampere equation. Some classes of exact solutions are presented for this equation. A power-law solution is obtained by the method of functional separation of variables, which depends only on a set of constants and does not contain arbitrary functions. Solutions are also found that linearly depend on arbitrary functions of the coordinate variable and the time variable. Assumptions and explicit conditions are formulated on how to select solutions from the families of solutions of the Monge-Ampere equation that correspond to the model process under consideration. A class of nonlinear equations in partial derivatives of the first order is indicated, which can also be reduced to the Monge-Ampere equation. Limitations on the etching rate are established, which allow the ion-beam etching equation to be reduced to a second-order linear hyperbolic equation, for which, by separation of variables, it is possible to obtain a solution in the form of a Fourier series.

Keywords: ion-beam etching equation, Monge-Ampere equation, model solutions, exact solutions

The water-chemical condition of the steam generators (SG) within the established limits are supporting by a purge. The purge is two kinds they are permanent and periodic. The main idea of the purge consists in taking part of the boiler water from the places of the most likely accumulation of sludge, corrosion products, salts, as well as water purification and its subsequent return to the circuit. The further way of boiler water which is taken from SG is the purge expander. The thermal-hydraulic sketch which is shown in the article and considered to be a mathematic model of the purge expander illustrated level changes in dynamic. Also the mathematic model of automatic control system for purge expander level control which includes a fuzzy governor is presented in the article. Both models are realized with use of software for technique system modelling called SimInTech. The technique implementation of level governor in the SG purge expander realized on the base of the standard software and hardware TPTS-EM which is used as grassroots automation for automatic control system in the technological process of NPP having water-water power reactor which power is 1000 megawatt.

Keywords: reactor, purge, steam generator, corrosion, erosion abrasion, heat carrier, purge expander, governor, model, fuzzy logic, level, pressure, consumption

The paper proposes a model of a circuit with a pulsating circulation of a liquid coolant for cooling an oil transformer and investigates the dependence of the heat transfer coefficient on the frequency of the liquid pulsation in the heated circuit. As a result of the experiments, it was found that the pressure amplitude remains practically unchanged up to a frequency of 0.45 Hz, then sharply decreases and at a frequency of 0.9 Hz it is approximately 12.5 kPa. It was also found that in the heated circuit (circuit 1) the temperature difference exceeds the temperature difference in the heating circuit (circuit 2), which is due to the fact that the fluid flow rate in the heating circuit exceeds the flow rate in the heated circuit. The theoretical calculation carried out showed that in the proposed model the heat transfer coefficient reaches its maximum at a pulsation frequency of 0.6 Hz and is 133.675 W/m2K.

Keywords: energy efficiency, oil transformer, heat recovery, heat exchanger, transformer cooling

The paper considers theoretical studies of the deformed state of the nagel joint with claw washers in LVL structures (from the English LVL – Laminated Veneer Lumber). A mathematical model of snow load has been developed. The method of theoretical calculations of creep from the action of periodic load on the basis of previously performed experiments is given.

Keywords: claw washer, LVL, connection, deformation, mathematical model, load, regression equation, humidity, creep

The regulation of the stress-strain state of the floor slab is considered in order to choose the optimal design solution for the frame of a unique building. Three variants of design solutions with varying reinforcement of the plate and cross sections of the vertical elements of the frame are proposed. The numerical experiment was performed by the finite element method using the Lira-CAD software package. To improve the accuracy of the results obtained, calculations were made taking into account the nonlinear operation of materials. The computational model of the floor slab includes physically nonlinear shell finite elements. Nonlinear loading was modeled taking into account the creep of concrete. Based on the results of the calculations, the analysis of the deflections of the floor slab and the consumption of materials was performed. The numerical experiment allowed us to propose an optimal design solution for the frame of a unique building.

Keywords: stress-strain state, finite element method, unique building, physical nonlinearity, deformation law, building frame

The method of numerical calculation of the parameters of the river channel in the arms is given. The method of nonlinear programming for analysis of dissipative systems with concentrated parameters is used. The technique is focused on computer modeling in the environment of engineering package MathCad. The results of the experiment are given.

Keywords: Distribution of water flow, calculation method, multi-node sections of rivers, water flow

The paper considers the problem of bringing vibrations of a flat membrane to rest, controlled by forces applied to the entire area of the membrane and limited in absolute value. Sufficient conditions are given for the initial data of the deviation and velocity of the membrane, under which a complete stop of motion in a finite time is possible. The resting time is also evaluated. The theorem on estimating the eigenfunctions of the Dirichlet problem for the Laplace equation used in the work makes it possible to refine the mentioned sufficient condition in comparison with the work of F.L. Chernousko. In this work, a similar problem is considered, and the method of expanding the unknown control and the corresponding solution in terms of eigenfunctions of the Dirichlet problem for the Laplace equation is also applied. In this paper, the problem of bringing various elastic oscillatory systems with distributed parameters (membrane, rod, plate, etc.) to a state of rest in a finite time is reduced by means of expansion into a Fourier series in the corresponding system of eigenfunctions to the study of the problem of stopping a counting system of pendulums, connected with each other only through the values of external control actions, the sum of the values of which should not exceed in absolute value some given constant. In order to fulfill this limitation, it is necessary to use estimates for the absolute values of the eigenfunctions, normalized in the mean square. In this paper, we use some estimates for the absolute values of eigenfunctions, previously obtained by Eidus D.M. This allows us to refine the results of F.L. Chernousko for sufficient conditions on the initial functions of the oscillatory system, under which we must dampen the oscillations. These conditions consist in the fact that the initial functions belong to Sobolev spaces with certain indices and in the fulfillment of some additional boundary conditions on the boundary of the domain in which the system is defined.

Keywords: control, wave equation, limited distributed force, Fourier method, counting system of harmonic oscillators

The article considers a model for identifying the parameters of an electric motor by the free run-out method by creating a model of acceleration and deceleration processes in the Scilab Xcos environment. The model is based on a simplified model of an electric motor in the form of an aperiodic link of the first order, which is supplemented by a model of a mechanical link connected to the shaft of an electric motor. Taking into account the inertia of electromagnetic processes makes it possible to adequately model the state and parameters of the electric motor. Identification allows you to determine the moment of inertia of the mechanical part of the electric motor. The model is based on a system of differential equations describing the dynamics of the processes of acceleration and braking of an electric motor. The scheme of the model includes blocks for solving a system of differential equations and blocks for calculating an identifiable parameter. Simulation modeling was carried out in the Scilab Xcos environment to evaluate the functionality of the resulting model scheme. The values of the desired moment of inertia are calculated from the beginning to the end of the simulation process, and the correct value is obtained, with the exception of a short section at the beginning of acceleration. The obtained graphical dependences allow us to visually illustrate the process of acceleration and deceleration of an electric motor in the form of transient functions for torques.

Keywords: electric motor, moment of inertia, electromagnetic moment, run-out method, parameter identification, torque, model diagram, transient function

The paper proposes a theoretical model of self-oscillators based on resonant tunneling diodes. Numerical modeling of the synchronization band of the oscillator was carried out on its basis. The effect of spreading resistance and resonator inductance on the synchronization band is analyzed. It is shown that at a low quality factor, as well as taking into account the nonlinearity of the capacitance and auto-bias, the frequency characteristics of the self-oscillator will be asymmetric and the instability regions of synchronous stationary oscillations will have a complex shape.

Keywords: theoretical model, numerical simulation, quality factor of an oscillatory system, synchronization bandwidth, capacitance nonlinearity, auto-bias, frequency characteristics, instability region, spreading resistance, resonator inductance