In the present paper, we study a source identification problem for hyperbolic-parabolic equation with nonlocal conditions. The stability estimates for the solution of this source identification problem are established...
In the present paper, we study a source identification problem for hyperbolic-parabolic equation with nonlocal conditions. The stability estimates for the solution of this source identification problem are established. Furthermore, we construct the second order of accuracy difference scheme for the approximate solution of the problem under consideration. The stability estimates for the solution of this difference scheme are presented.
In connection with the decreasing hydrocarbon reserves on land, the interest of researchers in new alternative methods of hydrocarbon production is growing. One of the actively developing areas is the production of hy...
In connection with the decreasing hydrocarbon reserves on land, the interest of researchers in new alternative methods of hydrocarbon production is growing. One of the actively developing areas is the production of hydrocarbons from deep-water deposits, in connection with which the share of developed deposits in the water area of the World Ocean is growing every year. However, this production method is not completely safe, since any damage to the production structure can lead to leakage of hydrocarbons. In this case, hydrocarbons are distributed in the form of a submerged jet. Predicting the behavior of submerged jets, calculating their trajectories and thermophysical parameters is important in the elimination of leakage. The article discusses an experimental study of a submerged jet. The results of the experiment will make it possible to verify the mathematical model describing the propagation of a submerged jet. The experiment was carried out to study the trajectory of the jet and its temperature. This paper presents the results on the analysis of the jet trajectory. In the experiment, gasoline or diesel fuel was used as a liquid, air was used as a gas. The work shows a diagram of the experimental setup, describes the process of the experiment, and also shows a photograph of the experiment and a comparison with the results of calculations.
The paper considers a mathematical model of the spread of a multiphase submerged jet, the flow of which is associated with a well damage during the development of a field or pipeline during oil transport. The jet cons...
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Due to possible hydrocarbon leaks that can occur when a well is damaged during deep-sea offshore oil production, it is important to study methods for eliminating leaks. The article deals with the mathematical model of...
Due to possible hydrocarbon leaks that can occur when a well is damaged during deep-sea offshore oil production, it is important to study methods for eliminating leaks. The article deals with the mathematical model of the device "dome-separator", which is used to eliminate deep-water leaks. The article also discusses the possibility of using and advantages of such a device. The paper presents a scheme of the device, a mathematical model that contains the basic equations. In the process of the computational experiments, the thermophysical characteristics of hydrocarbons accumulated inside the dome were determined, and the process of accumulation of hydrocarbons inside the dome was modeled.
Models of stochastic processes describe many phenomena in nature, technology, and economics. However, STEM and economics students usually do not have enough time to study this topic. When developing a course on stocha...
Models of stochastic processes describe many phenomena in nature, technology, and economics. However, STEM and economics students usually do not have enough time to study this topic. When developing a course on stochastic processes, a teacher faces some challenges. The task is to present sophisticated educational material, combining the mathematical severity of presentation and ease of understanding. Throughout several lessons, students should get a holistic understanding of the subject so that they can correctly and meaningfully apply models of stochastic processes in the field of their professional activities. The complicated nature of stochastic processes models requires understanding their multidimensionality, facilitated by various representation methods: formulas, tables, graphs, and computer simulation. The article discusses applying these techniques on the example of the formation of the concepts "stochastic process" "mathematical expectation and variance of a stochastic process."
In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in ℝ3 15; (0, T ). The main goal is to establish the regularity criterion via the gradient of one velocity componen...
In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in ℝ3 × (0, T ). The main goal is to establish the regularity criterion via the gradient of one velocity component in some multiplier spaces.
Artificial intelligence (AI) has recently seen transformative breakthroughs in the life sciences, expanding possibilities for researchers to interpret biological information at an unprecedented capacity, with novel ap...
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In the current research a model simulating a system consisting of DC-DC converter with fuel cell and supercapacitor is presented. The model is realized in MATLAB/Simulink environment. For energy storage device a super...
In the current research a model simulating a system consisting of DC-DC converter with fuel cell and supercapacitor is presented. The model is realized in MATLAB/Simulink environment. For energy storage device a supercapacitor is used. On the base of the developed model and the control system of the energy flows, a researches related with the necessary value of the supercapacitor with the basic purpose provision of the aforetime set load profile are realized. Another essential problem of the control system of the power converter is to provide operation mode with maximal efficiency of the power source – fuel cell. This research is useful for determination of the optimal value of the energy storage device, which has significantly meaning for economically efficiency of the system for decentralized production of the electrical energy.
A mathematical model of injection of liquid sulfur dioxide into a porous medium saturated with water and methane, accompanied by the formation of SO2 gas hydrate on the frontal surface is presented. The dependences of...
A mathematical model of injection of liquid sulfur dioxide into a porous medium saturated with water and methane, accompanied by the formation of SO2 gas hydrate on the frontal surface is presented. The dependences of the temperature and the coordinates for the formation front of sulfur dioxide gas hydrate on the pressure of the injection and the initial pressure of the layer are explored. It is established that at sufficiently high injection pressure values and the initial temperature of the layer, as well as the low values of the layer’s initial pressure, the temperature of the porous medium on the boundary of gas hydrate formation of sulfur dioxide may rise above the decomposition’s equilibrium temperature of the gas hydrate of sulfur dioxide. This corresponds to the appearance of a zone in a porous medium saturated with a mixture of water, sulfur dioxide and its gas hydrate, being in a state of phase equilibrium.
Relational DBMS are often used to store fuzzy values, but problems arise with putting such data in a tabular form. Moreover, there appears a problem of storing both the crisp and fuzzy data related to one subject doma...
Relational DBMS are often used to store fuzzy values, but problems arise with putting such data in a tabular form. Moreover, there appears a problem of storing both the crisp and fuzzy data related to one subject domain in one column of a relational table. This article considers the mechanism of storing crisp and fuzzy values and linguistic variables in the document-oriented Mongo DBMS. The data are stored in the collection as GeoJSON geometry; different geometries are used for different data options. The possibility of storing crisp scalar values, crisp value sets, crisp value intervals and fuzzy values in the collection documents is described. For data processing by means of SQL queries, the context-free grammar of the SQL subset is described, according to which lexer and parser are generated. In order to form the structure of an abstract syntactic tree, a corresponding object model has been implemented. A translator application has been developed, which allows converting SQL queries related to the crisp and fuzzy data into Mongo QL queries. The algorithm of fuzzy queries translation process is suggested; the geometrical interpretation of data comparison operations is described. The examples show the options of fuzzy comparison operations for different value options.
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