Journal articles - Siberian Aerospace Journal
All articles: 400
Scientific article
A mathematical model describing the dynamics of a resonant converter with a T-shaped oscillatory circuit in the mode of power supply from a current source, which is a simplified model of a solar battery, is analyzed. It is shown that increasing the output filter capacity to improve the quality of transients is an ineffective measure. As an alternative measure, it is proposed to supplement the output circuit of the converter with an additional low-pass filter. A linearized equivalent circuit of the upgraded converter has been developed. It has been found that the quality of the transients of the input and output circuits of the converter is practically independent of the inertial properties of the converting T-shaped oscillatory circuit due to the fact that the time constant of the input and output filters is much greater than the constant of the rise time of the circuit current. It is shown that the device in question is a current-to-voltage converter not only in statics, but also in dynamics, and the equivalent circuit of the input circuit of the converter, without taking into account the input filtering capacity, is described by an electrical circuit that is dual to the output circuit of the converter. The developed equivalent circuit makes it possible to increase the speed of computer simulation of transient processes in the converter tenfold. The adequacy of the proposed approach is confirmed by modeling the transients of a resonant transducer in the Matlab 2021b software package. It has been found that the use of an additional low-frequency output filter significantly reduces the time of transients, reduces the amplitude of the input voltage transition, and also improves the mass-dimensional characteristics of the converter.
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Scientific article
Today, the scope of application of electric propulsion systems for orbit correction and spacecraft’s attitude control is rapidly expanding due to their high efficiency compared to liquid jet systems. The main elements of electric jet systems are plasma or ion thrusters. To ensure power supply of such thrusters, complex electronic power processing systems – power processing units (PPU) – are used. These units are capable to operate for a long time (up to 15 years or more) in a high vacuum environment and generate sufficiently high accelerating voltages – from 300 V and higher. PPU’s comprise various EEE-parts, mainly in the case design. As a rule, the technology of their production is such that air or nitrogen is initially located inside the housing at atmospheric pressure. During the operation of the unit, the non-absolute hermeticity causes pressure decrease inside EEE housings. Due to high voltages applied, this can lead to electrical breakdowns between current-carrying ele-ments inside the parts, their failure with the subsequent failure of the functional blocks of the unit. The paper considers the physical principles of the breakdown occurrence inside EEE-parts cases. The results of non-hermiticity measurements of several types of HV EEE-parts are presented. The dynamics of the pressure drop to the values dangerous from the point of view of breakdown event and the relevant occurrence duration are esti-mated. It is shown that duration of being exposed to the pressure-dangerous conditions can be as long as space-craft service lifetime. It can make difficult to use packaged gas-filled EEE-parts at the level of units intended to operate in non-pressurized compartments of spacecraft. Recommendations are provided for selecting the design of EEE parts with an operating voltage of about 300 V or more, as well as circuit solutions used to develop high-voltage equipment intended to operate in vacuum environment.
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Scientific article
The rapid development of electric-powered aircraft (with electric and hybrid power plants, including unmanned ones) is determined by the following advantages: reduction of harmful effects on the environment, reduction of noise exposure, reduction of maintenance costs. However, the development of such aircraft is hindered, in addition to organizational and legal difficulties, also by technical ones, the key of which are: low power-to-weight ratio of the aircraft (compared to piston and jet aircraft), electrification, underdeveloped infrastructure of airports and airfields. One of the options for solving the problem of increasing the power and energy efficiency of an unmanned aerial vehicle (UAV) with electric traction is the installation on board of a chemical-kinetic energy storage (rotating battery packs), with the possibility of using static electrification to recharge batteries. This system allows you to implement a continuous consumption / recovery cycle during the flight. The design was developed and a simplified assessment of the energy and technical characteristics of a promising UAV based on the selection of static electricity was given. The principle of operation of the static electricity extraction system based on rotating battery packs is shown, the main advantages over traditional systems of energy storage / recovery of aircraft are given. The results of the calculation and research of a prototype (a promising unmanned aerial vehicle) are presented, showing the versatility of the design, high operational and technical characteristics, as well as recommendations for the practical application of the developed UAV design. The results obtained are the initial stage of promising work to improve unmanned aerial vehicles and electric-powered aircraft systems. The low weight and size characteristics, as well as the unusual principle of operation of the static electricity extraction system based on a rotating battery packs allows it to be used as an autonomous power source for unmanned aerial vehicles, which allows in the future to extend this principle of energy consumption for any electric-powered aircraft. This work is an important stage in the development of highly efficient power plants operating on unconventional principles of energy production, which, on the one hand, expands the field of research of storage/ recovery/ consumption systems in modern aircraft construction, on the other hand, gives a powerful impetus to the development of engineering and scientific thought in the field of unmanned aircraft construction.
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The use of the inverse transformation method for time series analysis
Scientific article
In modern conditions of technology development, signs of systemacity are manifested to one degree or another in all areas, so the use of system analysis is an urgent task. In this case, the main factors in this situation are data processing and prediction of the state of a system. Mathematical modeling is used as a prediction method for a given subject area. A mathematical model is a universal tool for describing complex systems representing the approximate description of the class of phenomena of the external world expressed by mathematical concepts and language. The mathematical model can be represented as a set of systematic components and a random component. In this article, the object of prediction is the irregular random component of a model, which reflects the impact of numerous random factors. The origin, nature and laws of variation of the random variable are known, therefore, to simulate its behavior or predict its future value, one needs high degree of certainty to establish the form of continuous distribution function of the random variable. The empirical distribution function is calculated using the sample of random variable values. This empirical function is close to the values of the desired unknown function of distribution. The resulting empirical function is discrete, therefore it is necessary to apply piecewise linear interpolation to obtain a continuous distribution function. The predicted random component of time series has been included in the initial regression model. In order to compare augmented and initial regression models, several values were excluded from the time series and new prediction was built. The value of the average approximation error for assessing the quality of the model is calculated. The augmented regression model proved to be more effective than the original one.
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Thermal emission and pyroelectric current in manganese chalcogenides
Scientific article
Manganese chalcogenides, which are promising for the manufacture of thermoelements, are being studied. The current is measured in the temperature range of 80–500 K, in the absence of external voltage, which can be caused by a temperature gradient (thermopower), a change in electrical polarization (pyroelectric current), piezoelectric current (when the sample is deformed, a potential difference arises) or thermionic emission (thermal emission current) . Temperatures of current anomalies and their relationship with thermionic current and polarization current are found. A change in electrical polarization with temperature will cause a pyroelectric current. Compensation for excess electrical charge will result in local electrical polarization. Partial decompensation will cause the formation of an electric field in the sample. The critical temperatures for the disappearance of electric polarization were determined for different concentrations. In the region of concentration of thulium ions flowing through the lattice, the activation nature of the thermionic current was established and the activation energy was found. The pyroelectric current has a smaller value compared to the thermionic current. The current mechanism is determined by the emission of electrons from deep traps and the temperatures of the maximum thermionic current correlate with the temperatures at which IR absorption disappears. The electric current density and its value depend on the type of substituted rare earth element are calculated.
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Three-component aerodynamic load cells
Scientific article
The article examines the effect of flow on models studied in wind tunnels. To determine the force effect of the flow on the model under study, a more accurate and reliable method of directly measuring forces and moments using aerodynamic strain gauge balances is proposed. When solving a plane problem for a symmetrical model at zero slip angle, a design of three-component scales is proposed that measures the lift force, the drag force and the pitching moment. To eliminate the interaction between the supporting devices and the model, which causes disturbances in the flow near the model, the scales are located outside the model and the working part of the wind tunnel. The components of the aerodynamic force and moment acting on the model are measured using resistance strain gauges, which convert the deformation of the elastic element into a change in electrical resistance, which is measured by an instrument connected to an appropriate measuring circuit. The choice of strain gauges as weight elements is due to their very small size and weight, the ability to measure very small relative deformations of elastic elements, low inertia, which makes it possible to measure not only static but also dynamic loads, and the possibility of remote measurements. To compensate for the influence of various sources of errors, increase sensitivity and ensure greater measurement accuracy, the strain gauges are connected via a bridge circuit and included in all four arms of the bridge. Deformation of the horizontal measuring beam causes a change in resistance not only in the strain gauges that measure the pitching moment, but also in the strain gauges designed to measure the lift force. Since the design of the scales does not allow for electrical separation of these components, the influence of the pitching moment on the magnitude of the lift force is determined during the calibration process and is assessed using a special influence graph constructed from the results of calibration data. In strain gauge measurements, the output values of forces and moments acting on the model under test are obtained in the form of corresponding readings from a device that measures electrical signals proportional to the applied forces. To convert instrument data into values of forces and moments, a joint calibration of scales and instruments is carried out in order to obtain calibration coefficients. Additional components of aerodynamic forces and moments created by the holder are determined by purging it in the presence of the model. Calculated dependencies for determining the components of the aerodynamic impact are given. The values of the coefficients of aerodynamic forces and moments are given in the flow coordinate system. The pledge has been given.
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Scientific article
Ensuring high reliability of unique high-critical products at the design stage is an actual task that the aerospace industry faces. For high reliability indicators, at the design stage, it is necessary to ensure the basic property of the product – its strength, with a high probability of non-destruction. It is provided by introducing the corresponding coefficients – «safety coefficient» and «margin of safety» into the strength calculations. The necessity in these coefficients is based on the spread of values of external loading factors: magnitude of forces, combination of forces, kind of actions, place of connection, etc. In this case, the safety coefficient is related to external factors. The margin of safety refers to internal factors: the spread of the mechanical characteristics of the product material, the spread of the geometric dimensions of the product, etc. To determine, with a given probability, the safety coefficient and margin of safety, it is necessary to know their dependence on the combination of spread of external and internal factors. The purpose of this work is to determine the mathematical connection between the internal factors of the spread and the safety coefficient, external factors of the spread and the margin of safety, the combination of these factors and the probability of non-destruction of structures. In this work the values of internal and external factors, which affect the strength and probability of non-destruction of the product and have the boundaries of the spread of their values, using the tools of probability theories, were characterized as random variables, the values of which are determined by the distribution density, expected value and variance. I this work there was found a high dependence of the product strength on the spread of its geometric characteristics and tools were defined to determine the total spread of the values of the main strength characteristics of the product with a given probability of non-destruction. The practical significance of the results of this work can be achieved in the aerospace industry, in particular, at the design stage of unique high-critical products.
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To the question of forecasting the technical condition of low-thrust liquid rocket engines
Scientific article
In the rapidly developing space and rocket industry, spacecrafts are being equipped with low-thrust liquid rocket engines. Нigh requirements are imposed on the reliability, efficiency and economy of fuel use for this type of rocket engine. To ensure monitoring of the characteristics of spacecrafts, a functional diagnostic system is used, which includes telemetry and analytical data processing. Telemetry performs the functions of receiving and transmitting information. Information processing is carried out in computer centers located on the spacecraft and the Earth. The most promising computing tool capable of predicting time series and classifying a large amount of interconnected data is considered an artificial neural network. In this regard, the subject of research in the work is data processing methods based on an artificial neural network. The purpose of the work is to develop a method for forecasting the technical condition of low-thrust liquid rocket engines using an artificial neural network. The relevance of research on the use of a neural network in the system of functional diagnostics of low-thrust liquid rocket engines for spacecraft is explained in the introduction. In the main part, an analysis of many telemetric data of the rocket engine is carried out and their strength in the forecast of the main diagnostic parameters is determined. It is proposed to use traction, specific impulse, and temperature of the structure as diagnostic parameters. The prognostic capabilities of the neural network were investigated and a schematic diagram of a method for predicting the technical condition of a low-thrust liquid rocket engine was developed. In the developed method, at the first stage, the neural network performs the approximation of the function and extrapolates the time series of telemetric data; the second stage determines the probable class of the technical condition of the engine. The conclusion outlines a plan for further experimental research in the study area and provides recommendations on the development and improvement of algorithms for functioning of artificial neural networks as part of the functional diagnostics system of the spacecraft. Due to the generalized nature of the methodological schemes, the results of the work can be applied to any type of rocket engines and used at all enterprises of the rocket and space industry of the corresponding profile.
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To the task of controlling a group of objects on the basis of information technologies
Scientific article
To participate the TPP with cross-section communications in the general primary frequency control, it is necessary to have a working main regulator. The main regulator is designed to maintain the steam pressure in the major steam line of the TPP at a given level, which is a difficult task. At the TPP with cross-connections, the steam produced by the boilers enters the major steam line. To maintain the pressure in the major steam line, it is necessary to control the heat load of the working boilers. Traditional solutions to construct the main regulator found no use, as have a number of disadvantages, not allowing exploiting a system of automatic control. Looking at the steam pressure control system in the major steam line from the bottom to up, it is possible to identify disadvantages that prevent the effective operation of the main regulator at each level. At the lower level of the main regulator, there are controllers of heat load of boilers, built according to the scheme task-heat. Heat load controllers are designed to maintain heat release in the boiler furnace at the required level. The heat signal is the sum of the signals for the steam flow of the boiler and the rate of change in the steam pressure in the boiler drum. Such a structure does not allow maintaining the invariance of the heat signal under external disturbances effectively, as sharp changes of the steam pressure in the major steam line lead to a "false" operation of the controllers. At the upper level there is the main regulator itself, which maintains the steam pressure in the major steam line at a given level and corrects the tasks to the controllers of the heat load of the boilers. The simultaneous identical effect on the heat load of the boilers cannot be optimal from the point of view of the criteria for assessing the quality of regulation, since the dynamic properties of the boilers, such as the gain, the transition time constant and the transport delay are individual for each boiler. However, in 2006–2008, the attempt to build an updated main regulator that takes into account the shortcomings of the traditional scheme was made. The basis of the structure of the main regulator is still parametric and, as a result of ten-years’ experience, shortcomings in the operation of the updated main regulator were identified. The shortcomings, in most cases, consist in need of frequent corrections of adjusting coefficients of system because of the change of dynamic properties of an object during the operation. In fact, the same problems related to the parametric structure of the regulator remain. Up-to-date information technologies made it possible to introduce adaptive process control systems that allow to count an extended number of signals entering the system and to form control actions, based on both current and historical data of the technological process. The use of the latest information technologies and modern hardware in the control of complex multi-connected units that solve not only the problems of process control, but also the problem of improving the economic and environmental performance of enterprises, should become a new step in the development of automatic control systems.
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Torsion of prismatic orthotropic elastoplastic rods
Scientific article
Conservation laws were introduced into the theory of differential equations by E. Noether more than 100 years ago and are gradually becoming an important tool for the study of differential equations systems. Not only do they allow you to qualitatively investigate the equation, but, as the authors of this article show, they also enable you to find exact solutions to the boundary value problems. For the equations of the iso-tropic theory of elasticity, the conservation laws were first calculated by P. Olver. For the equations of the theory of plasticity in the two-dimensional case, the conservation laws were found by one of the authors of this article and used to solve the main boundary value problems of the plasticity equations. Later it turned out that the conservation laws can also be used to find the boundaries between elastic and plastic zones in twisted rods, bent beams, and deformable plates. The proposed work found conservation laws for equations describing the orthotropic elastic state of the twisted straight-line rod. It is assumed that the remaining current depends linearly on the voltage tensor component. In the workit was also found an endless series of laws of preservation, which allows you to find an elastic-plastic boundary, which arises when twisting the orthotropic rod.
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Turn of an elastic-plastic rod under pressure that varies linearly along the forming
Scientific article
The article continues a series of articles devoted to the use of the method of conservation laws of differential equations for solving problems in the mechanics of deformable solids. Elastoplastic problems in the mechanics of a deformable solid take into account the nonlinear relation-ship between stresses and deformations under the influence of various loads. Such problems arise in structures where materials are characterized by different physical properties; taking into account elastic-plastic deformations is important for predicting the operation of structures, as well as for ensuring their durability. Currently, solutions to elastoplastic problems continue to be the focus of researchers' attention. New analytical approaches to solving these problems are emerging, and numerical methods are being improved. The authors contribute to solving the problems of mechanics of deformable solids using conservation laws. The use of conservation laws makes it possible to reduce the finding of the stress tensor components at each point to a contour integral along the boundary of the region under consideration, which makes it possible to construct a previously unknown elastoplastic boundary. The article considers an elastoplastic rod of constant cross-section, which is under the influence of li-near hydrostatic pressure and a pair of forces that twist it around a central axis coinciding with the oz axis. The lateral surface of the rod is stress-free and in a plastic state. The constructed conservation laws allow us to find the components of the stress tensor. The components of the stress tensor make it possible to determine the elastoplastic boundary in the rod under consideration.
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Scientific article
Autonomous navigation is very important in many fields and applications and it specifically depends on global positioning system (GPS) measurements which may not be accessible in some areas. This will directly affect the autonomous navigation and sequentially this will lead to problems according to the function of autonomous navigation. In this research, generalized regression neural network (GRNN) which is a variation to radial basis neural networks, was used to compensate global positioning system (GPS) measurements in case of GPS absences to increase accuracy of autonomous navigation parameters (basically location and velocity) of object. GRNN is integrated with loosely coupled Extended Kalman Filter (EKF). Location, velocity, orientation parameters and biases of sensors are estimated. The evaluation of this methods was conducted using dataset from Internet, two simulations for the GPS measurements outages were made (first outage periods were 35 and 60 seconds) to evaluate the behavior of GRNN, the results shows that using GRNN in GPS absence is effective and robust, it outperformed the only loosely coupled EKF method.
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Using of the contour method to solving the problem of optimal traffic distribution in the network
Scientific article
The purpose of this work is to create a method for solving the problem of optimal traffic distribution in a network using the contour data analysis method. In the first section of the work, the principle of converting any available network to a contour form is explained, and the case is considered both for networks without loss and for networks with losses. The second section shows in a general way the method of bringing the network in contour form to a system of non-linear inequalities, by solving which one can obtain a certain distribution of traffic in the system. In the final section, using the M/M/1/N queuing system as an example, the solution of the problem of optimal traffic distribution according to the loss minimization criterion is shown. The initial data for the task were the incidence matrix, service intensity and buffer dimension for communication channels. A feature of the proposed algorithm is the search for a contour matrix, for the compilation of which it is proposed to use loss edges as elements of the spanning tree of the graph, which allows you to immediately determine the contour matrix using the concept of a fundamental cycle of a graph. This approach to optimal traffic distribution reduces the number of variables used compared to the known methods based on loopless routes, and also does not require their preliminary search, since they are determined from the dimension of the incidence matrix of the simulated network graph.
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Using signals of navigation satellites in the monitoring of the Earth covers
Scientific article
The features and capabilities of remote sensing of earth covers by means of signals of navigation satellites are presented. The methods of reflectometry of the surfaces of earth covers and radioscopy of forest canopy are described. The options for using the signals of GLONASS, GPS systems are considered. Test measurements of interference diagrams were carried out on 5 test platforms from heterogeneous soil surfaces: salt marshes and asphalt; water surfaces of saline and freshwater bodies in summer, including ice cover of small thickness in the period of autumn freeze-up. The method of radioscopy helped obtain the data on the spatial and temporal characteristics of attenuated signals of the GLONASS and GPS satellites in the pine forest. Estimates of the linear attenuation coefficients of the signals passing through a forest canopy with a coordinate reference were made. The results obtained are the basis for the development of methods and technologies for continuous monitoring of the characteristics and state of earth covers by means of signals of navigation satellites for solving a wide range of applied tasks.
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Scientific article
Liquid gas generators (LGG) are additional firing units in the power system of liquid rocket engines (LPRE). The LGG ensure the operation of the power units of the turbopump unit (TPU) of the engine by feeding combustion products (CP) to the turbine drive. The main criteria for the efficiency of the generator gas is the complex (RT)gg and the thermodynamic properties of the mixture, depending on temperature, pressure, the degree of excess of the oxidizer and the enthalpy of the fuel, attributed to the conditions of supply to the nozzles of the GG. Changing the parameters of the generator gas leads to a change in the turbine power parameters due to its effect on the adiabatic operation of the Lad turbine. Depending on the engine circuit under consideration, CP GG can perform work in other units and elements of the engine, as well as influence many parameters of the LPRE. Among the main ones can be noted: the power of the booster gas turbine of the booster turbopump unit (BTPU) in the case of the selection of the generator gas after the GG or turbogas after the main turbine; the temperature of heating the refrigerant in the heat exchanger introduced in the GG; specific impulse of a liquid rocket propulsion system (LRPS), depending on the quantity and properties of the turbogas entering the exhaust pipe of the engine (for the engine circuit without afterburning the generator gas); mixing in the combustion chamber (CC) due to afterburning of turbogas entering the engine chamber after the turbine (for the engine circuit with afterburning of generator gas); parameters of the firing wall of the engine in the case of using a high-temperature gas curtain by blowing generator gas into the supersonic part of the nozzle. For many pairs of fuel during combustion in GG, the nonequilibrium of combustion products is characteristic (especially in hydrocarbon fuels).Due to the fact that the combustion products (CP) during the combustion of an oxygen-hydrogen mixture, due to the simplicity of the reaction, have time to form while staying in the GG (i.e., the time of chemical equilibrium of the CP is less than or equal to the time of stay in the GG), their thermodynamic parameters can be reliably determined using programs that simulate chemical equilibrium reactions. In this article, the issue of obtaining reliable results of thermodynamic calculations of generator gas at low and high coefficients of oxidant excess is investigated. Verification of parameters obtained in the programs “Astra” and “Rocket Propulsion Analysis” with calculated values was carried out. The most suitable program for performing engineering calculations and modeling the thermodynamics of liquid gas generators has been determined.
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Virtual imitation of a fueling panel for modern civil airplane
Scientific article
The article considers the design and development of a computer model of the fueling monitoring and control panel of the Sukhoi SuperJet 100 civil aircraft. The presented model is included in a simulator program for training technical specialists in aircraft maintenance skills under conditions of limited access to real or hardware-simulated equipment. In the process of designing of the presented simulation model, the refueling panel and the SSJ-100 aircraft refueling system sufficient components were considered and selected for further software implementation. The selection of the necessary components for the model was carried out using the decomposition method of the real system. First, the functional elements of the refueling panel itself were selected, after which the refueling system was disassembled into components that allow simulating the operation of the simulated panel. To implement the simulation model, software classes of objects and interactions between them were described. Software algorithms are implemented in the Unity environment using the C# language. The created program uses a three-dimensional graphic component and compiled for launching on a web browser. Software components have also been developed that allow studying the functions of the fueling panel both independently and in the mode of control of knowledge of the elements and algorithms for working with the fueling panel. The developed model is used as part of a practical simulator at the Reshetnev Siberian State University, and can be functionally expanded in the future.
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Volume temperature control at automated high-frequency processing of polymer and composite materials
Scientific article
The purpose of this work is to develop and justify a method for volumetric temperature control of a polymer and composite material in automated high-frequency processing. The developed method is implemented by in-troducing thermocouples into the prism-shaped or cube-shaped sample body according to a certain pattern of their location throughout the volume. This technique is cost-effective and easy to implement compared to expen-sive and specialized equipment with complex design, as well as to the cost of thermocouples having a simple de-sign. Methods to achieve the purpose of the research of the contact method of volumetric temperature of a polymer or composite sample control are development and outlining thermocouples throughout the volume so as to iden-tify the most accurate temperature spectrum of the polymer or composite sample during automated high-frequency processing. Another method to achieve this purpose is the method of finding out how it will affect the measurements accuracy of the heating sample temperature from the introduction of thermocouples by making holes in it for installation. For this, a finite-difference mathematical calculation of the dependence of the sample temperature on the number of holes for thermocouples in it was performed in the MSC Patran Sinda software package. The calculation results were summarized and presented on graphic data. Further, a general mathemat-ical calculation was performed according to the formulas for the process of heat and mass conductivity calcula-tion, the results of which were table and graphic data. At the end of the finite-difference and general mathematical calculation, a comparative analysis of the ob-tained error of temperature measurement from the introduction of thermocouples into the body of the sample was performed. Based on this analysis, the developed method is applicable for further research on automated high-frequency processing of polymer and composite materials, since the errors obtained do not exceed the permissi-ble 3 %.
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Scientific article
In the production of space rocket technology, electrochemical processes are used, as a result there is pollution of sewage by metal ions. The strict requirements of environmental authorities do not allow sewage, containing metal ions with concentration exceeding the maximum permissible values, to be discharged directly into reservoir or sewers. The greatest difficulties are caused by the purification of water from hexavalent chromium. The proposed methods for purifying from hexavalent chromium, electrocoagulation method, galvanocoagulation method, sorption methods, combined methods, have some disadvantages, such as: significant energy consumption, significant consumption of soluble metal anodes, passivation of the anodes, need for large excesses of reagent (iron salts), large amounts of precipitate and the complexity of its dehydration, high cost and scarcity of sorbents, high consumption of reagents for the regeneration of sorbents, and others. This work shows equipment for experiments, including a diaphragm electrolyzer with a coaxial arrangement of electrodes. Formulas for calculating the chromium ions flux due to migration and diffusion are presented. The difference between the calculated amperage from the practical one is 25 %, and the theoretical degree of purification from the real one is 4 %, which confirms the effectiveness of the proposed cleaning method. The concentration of chromium anions was determined by atomic absorption spectroscopy. The degree of purification of water from chromium ranged from 84 to 96 %. The highest degree of purification (96 %) was obtained with an electrolysis duration of 29 minutes.
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m-aperiodic words on three-letter alphabet
Scientific article
The work is devoted to the study of sets of aperiodic words over a finite alphabet. The set of aperiodic words can be considered as a dictionary of some finite formal language. The existence of infinite words in two-letter or three-letter alphabets that do not contain subwords that are third powers or, respectively, squares of other words was first discovered more than a hundred years ago. S.I. Adyan in 2010 constructed an example of an infinite sequence of irreducible words, each of which is the beginning of the next and does not contain word squares in a two-letter alphabet. S.E. Arshon established the existence of an n-digit asymmetric repetition-free sequence for an alphabet of at least three letters. In the monograph by S.I. Adyan proved that in an alphabet of two symbols there exist infinite 3-aperiodic sequences. In the works of other authors, generalizations of aperiodicity were considered, when not only the powers of some subwords were excluded. In the monograph by A.Yu. Olshansky proved the infinity of the set of 6-aperiodic words in a two-letter alphabet and obtained an estimate for the number of such words of any given length. The author previously considered the case of a three-letter alphabet only in the case of 6-aperiodic words. In this article, we prove the infinity of the set of m-aperiodic words in the three-letter alphabet at m 4 and obtain an estimate for the set of such words. The results can be applied when encoding information in space communications.
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Scientific article
Recently, there has been an increase of interest in satellite orbit raising using electric propulsion subsys-tems. Theoretic analyses and practical experience demonstrate that while orbit raising to the geostationary orbit (GEO) via a transfer orbit is feasible, it requires a certain amount of time due to the thrust of onboard electric thrusters being low (40-300 mN) and thus incomparable with that of propulsion systems of liquid propellant thrusters (22-400 N). Due to low thrust, orbit raising by electric thrusters is time-consuming. However, the associated increase in mass to GEO may counterbalance the long duration of satellite commis-sioning. Calculations demonstrate a potential added satellite mass on GEO of up to several hundred kilo-grams with orbit raising duration of about 6 months. In particular, with satellite mass not exceeding 2500 kg, coupled launch is possible using existing launch vehicles. ISS took into consideration the positive results ob-tained with Express-AM5, and Express-AM6 satellites to design the Express-80 and Express-103 with orbit raising in mind. Such approach allowed for a coupled launch on the Proton-M carrier rocked with a Breeze-M upper stage, and a twofold launch cost saving. To increase thrust during orbit raising and decrease its du-ration, coupled thruster operation in high thrust mode was implemented. The resulting total mass on GEO increase constituted over 700 kilograms with maneuver duration of up to 158 days. This allows performing coupled launches of heavier satellites with orbit raising by means of electric propulsion in a feasible timeframe.
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