Математическое моделирование тепловых процессов электроплазменного микродвигателя

This paper considers processes of electric arc damping by automatic switches in the short-circuit mode. Certain conditions for facilitating a successful short-circuit arc damping are shown, such as the limitation of the short-circuit current amplitude by its active resistance, the reduction of the phase shift between current and voltage, and the amplitude loss in returning and restoring voltages. The article features oscillograms of currents and voltages in the short-circuit mode. Anode heating processes are also described within the framework of the process of arc burning (heat saturation mode) and after the change of polarity current transition through zero processes at the cathode in the temperature equalization mode. Mathematical models of processes at the cathode took into account the thermal flows of the ionic component and evaporation. The calculations were carried out with the average values of thermal coefficients for copper, as the arc base moves from contacts to contact holders, which are made of copper and its alloys. The results of the calculations proved the validity of the considered mathematical models of thermal processes at both the cathode and the anode.

This article gives a brief description of the principles of organization of Internet education in the teaching of “Mathematical modeling of information technology and processes” to students on the basis of “Moodle LMS” system distance learning at the Tashkent Pharmaceutical Institute and shows its main features and advantages. Extensive use of educational technologies, optimization, humanization and innovation in the National Program of Personnel Training to solve the tasks of training and educating young people to be highly moral, spiritual and enlightened, conscientious at work, deeply aware of their responsibilities to society and family, competitive, qualified professionals. The organization, management and control of the learning process on the basis of methods is relevant. Nowadays, a wide range of opportunities are being created for students to have fast, plentiful, reliable information and to acquire knowledge independently. In particular, electronic systems allow students to use important information related to science at any distance, depending on their capabilities. “Moodle” open source software complex is a system designed specifically for the management of the educational process using the Internet (Learning management system - LMS). Distance learning is a modern form of organizing the learning process using distance learning technologies. Its development was due to the increase in the number of Internet users, the availability and quality of open learning electronic resources. The use of distance learning technologies undoubtedly has a wide range of advantages: the organization of the learning process in an Internet environment, so the student location does not prevent high-quality training, regardless of the location of the educational institution. Distance learning is based on the principle of independent preparation of students through teacher guidance and allows you to choose a convenient time for lessons. It includes interactive communication between teachers and students, information resources of the educational institution and information resources of the Internet, the rapid delivery of the Internet in electronic form.

Purpose of the study.The aim is to create a technique targeted at the development of simulation skills in higher education environment, where students are competent in applying information technologies in economics. The relevance of the research lies in the fact that the existing methodological developments often focus on a specific software tool or methodology that cannot respond to all economic problems. A specialist in simulation modeling should possess integrative interdisciplinary knowledge from related scientific fields, for example, probability theory and mathematical statistics, higher mathematics, be familiar with other methods of solving economic problems: linear, nonlinear, dynamic programming, optimization; show proficiency in structural and functional analysis; be able to explore complex processes and systems comprehensively.Materials and methods.The following pedagogical approaches and teaching methods were implemented in this research: ● a systematic approach to solving complex problems based on the modelling economic objects as systems operating in a certain environment, ● activity approach to develop students’ professional competences in the process of creation, debugging and optimization of computer models of economic systems; ● problem teaching method in the framework of research and analysis of educational problems of the subject area; ● implemented interactive teaching methods; ● multimedia methods in the content of teaching materials of the discipline, including electronic manuals, educational videos, as well as multimedia presentations. The research also utilized information technologies, in which computers, communication equipment and software environments are: ● means to provide educational material to students for the transfer of knowledge; ● tools for designing, developing and conducting simulation experiments. In addition, we used the following special professional technologies, methods and tools in the process of teaching students: ● structural and functional modeling methodology; ● discrete-event approach to simulation methodology; ● special software for development and research of simulation models of economic processes and systems: Arena 15.0, AnyLogic 8.3.2.According to the requirements of the new educational standards, the student must master a sufficiently large amount of general cultural, professional and specialized competencies included in the curriculum. The application of the proposed approaches and methods allows to provide effective development of skills of simulation modeling of educational programs for bachelors of «Applied Informatics» and «Business Informatics».Results.The study created a method of teaching students the skills of simulation modeling. The research also established the model of formation of readiness of the IT specialist to the development of simulation models of economic processes and systems in higher school. We also identified important methodological conditions for the formation of professional competencies of students in the field of modeling, such as: ● application of a systematic approach to the analysis of domain problems, as well as for the synthesis of mathematical simulation models of business processes and economic systems; ● practical orientation of the content of training (selection and research in the educational process of the most characteristic, typical problems of the economy); ● integration of interdisciplinary knowledge, methods and approaches to solve complex problems.Conclusion.The method can equip students with skills of simulation modeling with various areas of practical application. First, this technique can be used by university students who are engaged in pursuing practical skills and basic system knowledge in the field of simulation. Secondly, teachers can use it, conducting courses: “Computer modeling”, “Mathematical and simulation modeling”, “Modeling of processes and systems” in the educational process of the University to improve the professional competence of students training simulation modeling. Third, the outcomes may be of interest to managers of educational programs in the areas of: “Applied Informatics”, “Business Informatics”, etc. to improve the structure and sequence of disciplines of competence-oriented curricula. Finally, the application of the proposed methodology in the educational process of the University will enhance professional expertise of young specialists and undoubtedly address the needs of potential employers.

In this work a new nonlinear mathematical model of process of three level assimilation which is described by four-dimensional dynamic systems is offered. In case of constancy of coefficients special points of the dynamic system are found. The conditions on constant coefficients for which it is possible to find special points with all four coordinates non-negative are determined. Introducing some dependence among coefficients of the system, two first integrals are derived, and the four-dimensional system is reduced to a two-dimensional one.The sign-variable divergence theorem of a two-dimensional vector field in some one-coherent area of the first quadrant of the phase plane is proved. According to Bendixon’s criterion it is possible to have a closed integral curve completely lying in this area.Introduction. Mathematical modeling of physical processes has a long history. Mathematical modeling of physical processes involves the model adequacy, which is validated by Newton’s non-relative five laws of classical mechanics: mass conservation law; law of conservation of impulse; the law of conservation the momentum of impulse; the first law of thermodynamics, i.e. energy conservation law; the second law of thermodynamics, i.e. entropy conservation law [, , , , ].Creation of mathematical models is more original in social sphere, because, they are more difficult to substantiate [, , ].We created a new direction of mathematical modeling, i.e. “Mathematical Modeling of Information Warfare” [, , ]. In these models two antagonistic sides waging with each other information warfare and also the third peacekeeping side trying to extinguish information warfare are considered. Conditions on model parameters at which the third side will be able to force the conflicted sides to completion of information warfare are found.We also offered mathematical models of forecasting the results of political elections in case of two or three parties. Also models in case of change of selective subjects before the next elections have been considered [, , , , ].We proposed to create new nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or a country and its legal region) which consider economic or other type of cooperation between different parts of population aimed to the peaceful resolution of conflicts [, ].Taking into consideration the important tendencies in the world, it is important to study demographic and assimilation of social processes through mathematical modeling.In [] we considered a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world’s population are considered: a category that hinders and a category leading to the dominant position of the English language. With a positive demographic factor of the population, which prevents globalization or a negative demographic factor of the population contributing to globalization, it is shown that the dynamic systems describing these processes allow the existence of two topologically not equivalent phase portraits (a stable node, a limit cycle).It is known that, in the world, a social process of assimilation of languages is hidden. This process, as a rule, considers expansion of an area of the dominating languages (state languages of economically powerful states) at the expenses of less widespread languages (state languages economically of rather weak states).According to this point of view, today, for less widespread languages (including classic languages) the conditions under which there will be no disappearance of the major languages are important, i.e. there will be no full assimilation of people talking in these languages.

The article gives the review of works of employees of chair and laboratory of physical mechanics of St.Petersburg State University from the moment of its establishment in 1986 and till 2023 inclusive, that are devoted to modeling of the non-equilibrium processes in gas, fluid and solid. The basic attention is given several major results: 1) creation of model of adsorption layer for the description of locomotion of flying vehicles in near space and an upper atmosphere; 2) a theoretical and experimental substantiation of the general approach to modeling high-speed and short-duration processes in various mediums; 3) application of the specified general approach to studying of shock-induced processes in solid. The detailed substantiation of necessity of the integro-differential form of the transport equations for nonequilibrium processes is given. That is shown that time’s evolution of system, to which interaction of structural elements of medium on the mesoscale leads, is described by the cybernetic methods developed by A. L. Fradkov within the limits of the Control Theory of adaptive systems with feedback. Other results are given short enough.

One of the main directions for improving heat supply systems is the tendency to switch to low-temperature heating systems by using heat pump units is the tendency of implementation the low-temperature heating systems based on the use of heat pump units. In the work, the main attention is focused on the improvement of thermal parameters and circuit design features of elements of the heat pump system of heat supply using soil energy. For this purpose, the toolkit of mathematical modelling of processes in ground heat pumps is applied, taking into account the climatic conditions of Ukraine. The paper proves the technical possibility of creating an autonomous system of alternative heat supply for energy-saving technologies with the possibility of using ground energy, taking into account environmental requirements. It is substantiated that the use of the proposed systems is a promising direction for Ukraine, which is experiencing a shortage of its own energy resources, because it provides an opportunity to increase the share of organic fuel substitution and reduce the volume of heat emissions into the environment. A mathematical model of heat processes in the elements of the heat exchange equipment of the heat pump system based on renewable energy (soil energy) and secondary energy (wastewater) was developed, taking into account environmental requirements (preventing hypothermia of the soil during the operation of soil pipes and damage to vegetation, respectively), which allows choosing a rational mode of operation of the system under seasonal climatic changes and technological conditions. Numerical modelling of heat processes in elements of the heat exchange equipment of the heat pump system using groundwater and waste water was performed, and the energy and environmental efficiency of the system under variable climatic and technological factors was determined. Analysis and generalization of the calculation results of the heat pump heat supply systems using alternative energy based on the proposed mathematical model, taking into account environmental requirements (preventing thermal relaxation of the soil) allows to take into account the change in the temperature gradient around the soil heat exchanger and more accurately determine the heat flow from each section of the heat exchanger. It has been established that for heat pumps with soil heat exchangers, the maximum substitution ratio of the traditional fuel is 75 %, and the economically feasible quantity of soil heat exchangers is 9 units. Heat pumps using waste water can completely replace traditional heat supply systems. For individual consumers, it is possible to recommend heat pump units with soil heat exchangers, at the same time, it is necessary to provide a backup source of energy to increase the reliability of heat supply.

One of the main design parameters of multi-electrode furnaces, which largely determines their heat and eco-nomic indicators, is the ratio of the pitch circle diameter of electrodes to the bath diameter Dp/Db. The existing methods for choosing rational design parameters are more relevant to arc furnaces operating on alternating current of industrial frequency. For multi-electrode direct current furnaces, which use magnetohydrodynamic effects to improve mixing conditions and temperature homogenization of the melt, there is no relationship between the heat transfer parameters and the pitch circle diameter of electrodes. This work is a continuation of a number of patents and articles. Elsewhere, the design was justified, a mathematical model of magnetohydrodynamic and thermal processes in the melt of the furnace containing three roof arc and three bottom electrodes was developed, the model was verified through the results of physical experiments, and the parameters of heat transfer in the furnace at Dp/Db ≈ 0,2 were studied. The proposed type of furnace requires the study of the Dp/Db effect on the heat transfer parameters in the melt, which will allow a rational choice of the design parameter. The results were obtained using a three-dimensional mathematical model of magnetohydrodynamic and thermal processes in the steel melt constructed with the non-induction approximation and taking into account the k- turbulence model. The results were processed using methods of analysis of vortex structures and estimation of the integral parameters of hydrodynamic and thermal processes in the molten bath. Numerical experiments have been carried out with the design parameter Dp/Db varying from 0,2 to 0,5. New scientific data on the patterns of changes in the structure of flows and heat transfer parameters in the molten pool of a six-electrode furnace have been obtained. Dp/Db increase within the indicated range causes the increase of intensity of vertical vortex flows circulating between the axis of the corresponding electric arc and the axis of the bath and of the azimuthal flows circulating in horizontal sections of the bath. Vortex flows formed due to natural convection near the side walls of the furnace are suppressed. The maximum value zones of the effective thermal conductivity that reaches 1,8·105 W/(m·K) are redistributed to the central part of the bath, which contributes to increasing temperature distribution efficiency in the bath. The obtained results allow recommending a rational range of values of Dp/Db within 0,4–0,5, which decreases the volume of stagnant zones in the proposed six-electrode furnace by more than 40 % and increases the integral values of the Nusselt number over the depth of the horizontal section of the bath on average by more than 10 %. The obtained data revealing the possibility of improving the mixing conditions and increasing the heat transfer efficiency in the melt of the six-electrode furnace can be recommended for choosing the Dp/Db ratio when designing high power furnace.

The article presents the results of a study aimed at creating a mathematical model of thermodynamic processes in the intake manifold of a forced diesel engine, taking into account the features of simultaneous injection of fuel and water into the collector. In the course of the study, the tasks of developing a mathematical model were solved, it was implemented in the existing software for component simulation “Internal combustion engine research and development” (ICE RnD), created using the Modelica language, and verification was undertaken using the results of bench tests of diesel engines with injection fuel and water into the intake manifold. The mathematical model is based on a system of equations for the energy and mass balances of gases and includes detailed mathematical submodels of the processes of simultaneous evaporation of fuel and water in the intake manifold; it takes into account the effect of the evaporation of fuel and water on the parameters of the gas state in the intake manifold; it takes into account the influence of the state parameters of the working fluid in the intake manifold on the physical characteristics of fuel and water; it meets the principles of component modeling, since it does not contain parameters that are not related to the simulated component; it describes the process of simultaneous transfer of vapors and non-evaporated liquids between components; and it does not include empirical relationships requiring data on the dynamics of fuel evaporation under reference conditions. According to the results of a full-scale experiment, the adequacy of the mathematical model developed was confirmed. This model can be used to determine the rational design parameters of the fuel and water injection system, the adjusting parameters of the forced diesel engine that provide the required power, and economic indicators, taking into account the limitations on the magnitude of the mechanical and thermal loads of its parts.

The task of forming a plan for the development of a plant growing enterprise belongs to the non-trivial tasks of mathematical modeling of bioeconomic processes. When forming it, the decision-maker must systematically take into account the impact on the final result of at least three types of factors of different nature: agronomic, economic, organizational. This paper presents a system of mathematical models that forms the basis for optimizing the annual plan for the production of agricultural crops.

Application of two anaerobic digestion models to biofilm systems

Mathematical modelling of thermal and electrical processes during electrosurgical resection of colorectal polyps

The load distribution between 18 cable lines located in an underground cable channel is considered. It is found that a current distribution control system in the cable channel needs to be developed to optimize the load conditions, as well as prevent possible overheating. The possibility of using a mathematical model of heat and mass transfer processes in the channel to determining the optimal current loads of cable lines is considered. A mathematical model of heat and mass transfer processes in the cable channel is constructed that makes it possible to study the temperature conditions of the channel under different configurations and line loads. Search algorithms of optimal operating currents under varying loads are developed that take into account the requirements for permissible temperatures and categories of consumers. The unsteady condition of overload of one of the lines due to an emergency is investigated. The heating curves of current-carrying conductors of the emergency cable line and those adjacent to it are plotted. The value of the current is determined to which it is necessary to reduce the load in one of the lines to maintain the system operability.

Aspects of the mathematical modeling and computer prediction of deformation processes in polymeric parachute straps are examined. The computer methods developed on the basis of the mathematical model of viscoelasticity to predict relaxation and creep in the straps make it possible to calculate deformation and relaxation processes and the straps’ relaxational and deformational characteristics with a high degree of accuracy. Methods that were developed to divide total strain into its components also allow evaluation of the straps’ elastic and viscoelastic properties, which play an important role in choosing materials that have the requisite deformation properties.

Mathematical models of geomorphic processes can have value as both predictive tools and precise conceptual frameworks. Well-posed mechanistic models have great conceptual value because they link geomorphic processes to universal scientific principles, such as conservation of energy, momentum, and mass. Models without this linkage (e.g., models based exclusively on cellular rules or empirical correlations) have less conceptual value but offer logical methodology for making practical predictions in some circumstances. Clear tests of the predictive power of mechanistic models can be achieved in controlled experiments, whereas natural landscapes typically have uncontrolled initial and boundary conditions and unresolved geological heterogeneities that preclude decisive tests. The best mechanistic models have a simplicity that results from minimizing assumptions and postulates, rather than minimizing mathematics, and this simplicity promotes conclusive tests. Optimal models also employ only parameters that are defined and measured outside the model context. Common weaknesses in geomorphic models result from use of freely coined equations without clear links to conservation laws or compelling data, use of fitted rather than measured values of parameters, lack of clear distinction between assumptions and approximations, and neglect of the four-dimensional (space + time) nature of most geomorphic processes. Models for predicting landslide runout illustrate principles and pitfalls that are common to all geomorphic modeling.

Mathematical models of competitive processes in the economy using known universal models that describe the behavior of counterparties in the market are found in this article. The object of research is to build mathematical models of competitive processes in a pair – secondhand dealer, and to process and convert the economic parameters that are necessary for the models. The methods of research use analysing and solving equations for the known and improved universal models that describe the behaviour of contractors in the market. Mathematical package for construction of schedules of dependences is used. The goals are to construct and research the modified model on the basis of mathematical model by Lotka- Volterra and its further development, and to create software product for statistical processing the economic information. Results – the mathematical model manufacturer – secondhand dealer is created, its modified version is received, and with the help of mathematical package Mathcad, researches of models were done. Prospects of the further improvement of models are revealed. The software product is developed, allowing to process the statistical economic information. On the basis of mathematical model by Lotka-Volterra and its further development a mathematical model of several producers and one middleman is created. Its modified version is studied using mathematical package Mathcad. The nonstable behavior of the counterparties is found. For this model some prospects for further improvements is identified.