Mathematical Model Of Process Research Articles

Частная полумарковская модель как инструмент снижения сложности задачи оценивания устойчивости функционирования элементов информационной инфраструктуры, подверженной воздействию угроз

Decision-making on information infrastructure (II) security for its sustainable functioning in the face of threats requires a tool to assess the sustainability of its individual elements. The application of the semi-Markov model to assess the stability of the functioning of elements of II exposed to threats in a direct setting is associated with the increasing complexity of the description of the object of delineation (parametric space) in step progression from the number of the considered impacts, which reduces its practical significance. However, no studies have been found in the scientific literature to reduce the complexity of the semi-Markov model. The article presents an approach to reducing the complexity of modeling by adopting correct assumptions when forming the initial data. Given the conditions under which it is possible to take a series. It was a cost to limit the applicability of the model by significantly reducing the complexity of the modelling. The problem statement and the modified transition graph are given. The novelty of the problem statement is to take into account the limitations on the available resources for the restoration of functionality of the element. To explain the physical essence of the modeling process, a thought experiment with a model is introduced. To solve the problem, the following methods were used: a) expert methods for extraction of initial data; b) mathematical models of private semi-Markov processes; c) methods of transformation of Laplace; r) methods of planning of experiment. Illustrative examples and graphs accompany the task sequence demonstration. As a result of the experiment, the regularities of the studied process, the existence of which was proved formally. As a result of the experiment, the regularities of the studied process were revealed, the existence of which was officially proved. The results of the study broaden knowledge about the application of methods of Markov processes to assess the stability of the functioning of AI elements in relation to the conditions of the impact of threats.

Can physics-informed neural networks beat the finite element method?

Abstract Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other. In this work, we compare the methodologies in a systematic computational study. Indeed, we employ both methods to numerically solve various linear and nonlinear partial differential equations: Poisson in 1D, 2D, and 3D, Allen–Cahn in 1D, semilinear Schrödinger in 1D and 2D. We then compare computational costs and approximation accuracies. In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study. In some experiments, they were faster at evaluating the solved PDE.

Investigation of the transient change of the cutting force during the milling of C45 and X5CrNi18-10 steel taking into account the dynamics of the electro-mechanical measuring system

AbstractThe possible methods of determining the cutting force—due to the great practical importance of knowing the force—have long been and are still intensively studied areas of cutting theory. In milling, cutting is a series of successive short material removals. During force measurement in such cases, the transient process that can be detected at the beginning of the process can influence the nature of the entire cutting cycle. The present study reports on the research, the aim of which was to explore the dynamic process of cutting force measurement in intermittent cutting. The measurements were made during face milling of C-steel and highly alloyed steel (X5CrNi 18–10). The milling head contained a single insert, with which the disturbing interaction of the multiple cutting edges was eliminated. As a result of the work, a method suitable for examining the close relationship between the initial transient nature of the milling cycle and the decay, as well as a mathematical model for the decay process, was developed. The model was validated with cutting experiments and measurements. The achieved results can be used to better understand the process of chip removal and to determine the actual power requirements of milling works.

Physical Analysis and Mathematical Modeling of the Hydrogen Storage Process in the MmNi4.2Mn0.8 Compound.

The results of an experimental and mathematical study into the MmNi4.2Mn0.8 compound's hydrogen storage properties are presented in the present research. Plotting and discussion of the experimental isotherms (P-C-T) for different starting temperatures (288 K, 298 K, 308 K, and 318 K) were carried out first. Then, the enthalpy and entropy of formation (ΔH0, ΔS0) were deduced from the plot of van't Hoff. Following that, the P-C-T were contrasted with a mathematical model developed via statistical physics modeling. The steric and energetic parameters, such as the number of the receiving sites (n1, n2), their densities (Nm1, Nm2), and the energy parameters (P1, P2) of the system, were calculated thanks to the excellent agreement between the numerical and experimental results. Therefore, plotting and discussing these parameters in relation to temperature preceded their application in determining the amount of hydrogen in each type of site per unit of metal ([H/M]1, [H/M]2) as well as for the entire system [H/M] versus temperature and pressure besides the absorption energies associated with each kind of site (ΔE1, ΔE2) and the thermodynamic functions (free energy, Gibbs energy, and entropy) that control the absorption reaction.

Mathematical model for assessing the influence of vibrations for multicopter elements

The article discusses the problem of studying the probabilistic characteristics of vibrations of the propellermotor group of an unmanned aerial vehicle such as a multicopter. The results of the research are presented in the form of quantitative values of the vibration parameters of the propeller-motor group of the agrodrone at given values of the input parameters of the electric drive control system, taking into account the influence of external factors. It is shown that the values of the parameters characterizing the vibrations of the propeller-motor group of the agrodrone can be different depending on the operating modes of the engines and changes in external conditions.Based on the experimental studies carried out, sets of measured random vibration parameters were obtained, which made it possible, based on the application of mathematical statistics methods, to calculate the mathematical expectations and dispersions of the amplitudes and velocities of vibration processes. The obtained probabilistic characteristics make it possible to study emissions (crossing a given level) of processes, to evaluate the intensity and probabilistic characteristics of the process going beyond the given boundaries.A mathematical model of the vibration process is substantiated, which allows, on the basis of the obtained experimental data, to assess the influence of vibrations on the elements of equipment installed on a multicopter, to assess its performance and reliability, and to determine tolerances on equipment parameters. The computer modeling of the probabilistic characteristics of vibration processes clearly demonstrated the efficiency of the proposed research methodology.

Electric discharge process modelling when piston pins recovery in internal combustion engines

Introduction. The relevance of the topic of the presented article is determined by the improvement of the technology for repairing and restoring machine parts. Currently, the technology of restoring piston pins of internal combustion engines (ICE) by a high-energy method of plastic deformation of metal using the energy of a high-voltage pulse discharge in a liquid is widely used – the electrohydraulic effect, and on its basis electrohydraulic processing. The purpose of the article is to increase the efficiency of the method of restoring piston pins of internal combustion engines due to the use of the electrohydraulic distribution method.Materials and methods. The research methods such as the analysis of the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston fingers depending on the relevant material were used. The article discusses a mathematical model of the electric discharge process when restoring piston pins. The calculation method determines the modes and parameters of the process of electrohydraulic distribution of piston pins while maintaining their fatigue life, static strength and wear resistance.Results. In this work, the degree of influence of the electrical parameters of the electrohydraulic distribution process on the amount of deformation of the piston pins, depending on the product material used, is established. A mathematical model of the electric discharge process during the restoration of piston pins has been developed, and based on them, the modes and parameters of the process of electrohydraulic distribution of piston pins have been determined while maintaining their fatigue life, static strength and wear resistance.Discussion and conclusions. The studies have shown that exploding wires made of iron, copper, and tungsten are not effective in restoring piston pins with an internal radius of up to 10 mm. The pressure in the case of their use does not exceed 100 MPa. Exploding Al wires with a diameter of less than one millimeter have the greatest effect. In this case, the inductance of the circuit should be minimal, because this provides the largest share of the energy released in the discharge channel from all stored in the capacitor. This ensures the highest pressure in the channel. Based on the same considerations, the capacity should be limited to a range of 3-12 UF. This method can be applied to the restoration of other car parts.

A mathematical model of the copper plating process in restoration of road transport equipment parts

Introduction. The use of restored parts of motor vehicles makes it possible to reduce the financial costs of repairing equipment. The cost of the restored parts should not exceed 50% of the cost of the new part. Increasing the productivity (deposition rate) of an electrolytic copper coating during the restoration of parts of motor vehicles requires taking into account the technological and economic aspects of the restoration process. The study of the factors (deposition conditions) that most affect the deposition process of the copper coating, the analysis of the experimental results and its statistical processing made it possible to optimize the technology of restoration of copper parts to create the most appropriate deposition modes with maximum productivity, thus reducing the cost of restoration of parts of motor vehicles. The purpose of the research is to develop a mathematical model of the effect of deposition conditions (electrolyte temperature, cathode current density) and electrolyte composition (concentration of copper sulfate and sulfuric acid) on the performance of the deposition process of copper coating, for further development of the most productive technology for restoring collectors of electric motors of motor vehicles.Materials and methods. The studies on equipment that allows obtaining the necessary data with the required accuracy were carried out. Mathematical processing using modern statistical data processing tools that excluded possible errors, providing to obtain the dependence of factors with the necessary accuracy was carried out.Results. In the course of studies of copper sulfate electrolytes to obtain an electrolytic copper coating, with the further development of technology for the restoration of automotive parts, it became necessary to determine the effect of deposition conditions – “factors” (cathode current density, electrolyte temperature, copper sulfate concentration, sulfuric acid concentration) on the deposition rate – “response”. It was found that the factor “cathode current density” and the combination of factors “cathode current density” and “sulfuric acid concentration” are the most significant. The deposition conditions in order to obtain the most productive technology for restoring collectors of electric motors of motor vehicles by depositing a copper coating have been optimized. According to the obtained model, the optimal values of the deposition conditions for obtaining the maximum deposition rate are the electrolyte temperature of 35...40 ° C, the cathode current density of more than 5 A/Dm2, the concentration of copper sulfate 200...250 g/l, the concentration of sulfuric acid 40...70 g/l.

Method for expert evaluation of the technical con-dition of the cylinder-piston group of automotive engines after hydrolock

Problem: The study examines the thermogasdynamic process within an internal combustion engine cylinder during cold cranking mode while measuring compression. Analysis of various models and comparison of known data revealed unresolved challenges in constructing mathematical models of the engine operating cycle. The vast majority of practical data and recommendations for compression measurement in a cylinder are based on empirical knowledge, numerous experiments, and tests. Consequently, there arises a need for computational models of the compression measurement process and their theoretical justification, particularly in cases where engine damage occurs during hydrolock in a cylinder. Methodology. To address the identified issues, a mathematical model of the thermogasdynamic process within the cylinder during cold cranking while measuring compression was developed. Originality. Unlike existing models, this model describes the processes in the cylinder step by step, considering the real nature of intake-exhaust processes, air leakage through part interfaces, and heat exchange with the walls. Through modeling, the main patterns of compression changes depending on the modes and the nature of damage to associated parts of the valve mechanism and the cylinder-piston group were identified, including deformation of the connecting rod during hydraulic lock due to liquid entering the cylinder. Practical value. Based on the study results, it was concluded that the model's properties make it effectively applicable in diagnosing and monitoring the technical condition of automotive engines during operation.

Swelling kinetics of mixtures of soybean phosphatidylcholine and glycerol dioleate

Lipid-based drug delivery systems offer the potential to enhance bioavailability, reduce dosing frequency, and improve patient adherence. In aqueous environment, initially dry lipid depots take up water and form liquid crystalline phases. Variation of lipid composition, depot size and hydration-induced phase transitions will plausibly affect the diffusion in and out of the depot. Lipid depots of soybean phosphatidylcholine (SPC) and glycerol dioleate (GDO) mixtures were hydrated for varying time durations in a phosphate-buffered saline (PBS) buffer and then analyzed with Karl Fischer titration, magnetic resonance imaging (MRI) and gravimetrically. Mathematical modeling of the swelling process using diffusion equations, was used to estimate the parameters of diffusion. Both composition of lipid mixture and depot size affect swelling kinetics… The diffusion parameters obtained in Karl Fischer titration and MRI (with temporal and spatial resolution respectively) are in good agreement. Remarkably, the MRI results show a gradient of water content within the depot even after the end of diffusion process. Apparently contradicting the first Fick’s law in its classical form, these results find an explanation using the generalized Fick’s law that considers the gradient of chemical potential rather than concentration as the driving force of diffusion.

Study on aero engine thermal performance analysis using a new mathematical model of isentropic expansion (compression) process

At present, for the research of aero engine performance, it is necessary to calculate the overall thermal performance of the aero engine at the beginning of the research. For the mathematical model of the isentropic expansion (compression) process, most researchers use the ideal state value to calculate in the mathematical model, so that the calculated results have a certain error compared with the actual value. Therefore, the new isentropic expansion (compression) process mathematical model based on the Φ function is applied in this paper to the technical aero engine overall thermal performance calculation. After calculation and analysis, it is concluded that the calculation accuracy of the mathematical model provided in this paper is higher than that of the literature program for the overall thermodynamic performance parameters of the aero engine, whether it is the thrust of the aero engine, the unit fuel efficiency, or the thermal efficiency of the aero engine. It shows that it is feasible to revise and improve the mathematical model of isentropic compression and isentropic expansion process in this paper, more accurate calculation results can be obtained by using the new model in the performance analysis program, and more accurate numerical analysis can be carried out.

Mathematical modelling and techno-economic analysis of electric arc furnace steelmaking process with hot metal charging in China

Mathematical modelling and techno-economic analysis of electric arc furnace steelmaking process with hot metal charging in China

THE PROBLEM OF PROFESSIONAL TRAINING OF FUTURE IT SPECIALISTS IN THE RECEPTION ROOMS OF DOMESTIC SCIENTISTS OF THE LAST DECADE

In the article was analyzed the problem of professional training of future IT specialists in the receptions of domestic scientists of the last decade. It is found that the modern system of training specialists in higher education in Ukraine is focused on global trends in the development of higher education, such as globalization, integration, democratization, continuity, humanization, openness of education, academic freedom, autonomy, digitalization, etc., which leads to the transformation of training of highly qualified specialists, including IT specialists. It is proved that reception as a new methodological technology involves interpretation – one's own interpretation, addition to the previously created. Based on the analysis, it is determined that the professional training of future IT specialists involves the formation of their readiness to work and acquire relevant competencies in information technology, mathematical and computer modeling of processes and systems of various nature, forecasting, optimization, system analysis and decision-making, etc. The article characterizes the research of Ukrainian scientists related to the professional training of IT specialists in its multi-vector dimension over the past decade, such as I. Gerasymenko, A. Stryuk, A, M. Rassovutska, S. Semerikov, I. Tarasov, Y. Sikora, O. Glazunova, A. Kocharyan, S. Nikolayenko, V. Shynkaruk, V. Kovalchuk Y. Vasylenko, L. Dmytritsa, T. Bodnenko, V. Vlasenko, V. Bykov, A. Gurzhiy, M. Shyshkina, T. Voloshyna, T. Vakaliuk, T. Potapchuk, O. Malykhin, T. Yarmolchuk, S. Berezenska, N. Oliynyk, I. Varava, A. Kapiton, A. Schlichta, and others. It has been established that in the last decade, Ukrainian researchers have considered the professional training of future IT specialists in the context of their professional activities in a rather different way and have drawn certain analogies with the concept of competence as a person's ability to perform a certain type of activity

Working process model development of the gas turbine engine combustor fueling on methanol

The use of methanol as a fuel for aircraft and stationary gas turbine engines (GTE) is a priority direction in engine building. It is well known that when modeling the GTE performances using first-level mathematical models, there is an error in calculating specific fuel consumption, which is caused by the simplified description of the GTE combustor working process. The object of the study is the working process in the GTE combustor fueling on methanol. The peculiarity of the developed mathematical model of the working process of the GTE combustor is the use of enthalpy dependencies on temperature, pressure, and mixture composition. Enthalpy dependencies in this form implicitly account for the effect of thermal dissociation and allow for the correct formulation of the equivalent combustion reaction path. For two components (H2O and CO2), accounting for pressure leads to the fact that at standard temperature and partial pressures exceeding the saturation pressure, these components exist in a liquid state. This situation, with a constant enthalpy increment in the equivalent process of heating the combustion products from the standard temperature to the temperature at the end of adiabatic heat supply, decreases this temperature. Clarification of the temperature at the combustor outlet leads to changes in all calculated combustor performances, including the combustor fuel air ratio. The calculation results of the fuel air ratio are compared with known experimental data of the General Electric CF6-80A engine combustor (USA). The average calculation error of the fuel air ratio does not exceed 4 %. The developed model can be implemented in existing and developing mathematical models of gas turbine engines for temperatures at the end of the combustion process below 2,600 K

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Mathematical Model of an Electoral Process and Predicting of Outcome

We developed and analysed a mathematical model to study the dynamics of an electoral process and predict the outcome in Nigeria with three political parties as major actors. We model the ruling party; major opposition party and minority opposition parties. The model includes party campaigners of the three political parties and a class of eligible voters. The model also incorporates the Independent National Electoral Commission (INEC), electoral observers, judiciary, security personnel and thugs. The influx of voters into the system is determined by the registration rate of voter cards. The model’s interest lies in the measure of positive influence that the party campaigners who eligible voters to join their party. With this, the model mirrors election’s outcome and the movement of voters between the three groups of political parties involved. The model has proven that the pattern of election’s outcome for each political party is affected by the defection of party members and lack of policy consistency. We determine the equilibria analytically and discuss the stability of the system. Numerical simulations are graphed in combination with curve fitting to compare each party’s performances over the years. The result shows that no political party remains in power steadily from 2007 to 2019. Thus, the prediction of elections outcome to the political space of any region in Nigeria depends on political party structures and voters’ decisions.

Basics of calculation of a two-circuit air purification system for polydisperse dust

Purpose. To increase the level of environmental safety of enterprises by improving the quality of air purification from polydisperse dust in two-circuit closed systems, in particular, to obtain the basic design relations for the engineering calculation of such systems. Methodology. The aim of the study was realised by mathematical and numerical modelling of hydrodynamic processes in the elements of a closed double-circuit purification system. Findings. A methodology for hydraulic calculation of a closed two-circuit cleaning system was proposed by drawing up a pressure balance of individual circuits, and a dependence for the complex coefficient of hydraulic losses of the collection-return apparatus was determined. Originality. The hydraulic calculation of two-circuit closed cleaning systems is proposed to be carried out by compiling the pressure balance of individual circuits. To calculate a specific element of the system – the collection-return apparatus – the concept of a complex hydraulic loss coefficient is introduced, which takes into account both local pressure losses and losses along the length, and also indirectly reflects the effect of flow swirl on the hydraulic resistance of this element. For the complex coefficient of hydraulic losses, the quantitative results necessary for engineering calculations were obtained by numerical modelling of hydrodynamic processes of the swirling flow in an annular pressure channel. Practical value. The obtained results make it possible to design two-circuit closed cleaning systems for different production conditions, which, in turn, makes it possible to replace typical and inefficient direct-flow systems with a system in which the efficiency of polydisperse dust capture is significantly increased due to separate cleaning.

EXPLORING THE IMPACT OF PTH THERAPY ON BONE REMODELING: A MATHEMATICAL INVESTIGATION

The regulatory influence of the parathyroid hormone (PTH) is exerted on bone, which serves as a vital reservoir of calcium within the body. While various aspects of bone growth, turnover, and mechanisms operate independently of gonadal hormones, a crucial role is assumed by sex steroids, particularly estrogen, in maintaining bone equilibrium in adults. In order to unravel the underlying mechanisms of bone remodeling mediated by PTH, a distinguished mathematical model of this intricate process is presented. Subsequently, the temporal effects of Plasma PTH and PTH external dosages are investigated using the proposed mathematical model. Among the limited repertoire of approved and accessible anabolic treatments for severe osteoporosis, daily injections of PTH stand out. This pharmaceutical marvel possesses a unique dual action, capable of acting either anabolically or catabolically, contingent upon the mode of administration. The study aims to accurately predict osteogenic responses to introduced and endogenous PTH, incorporating factors such as [Formula: see text]-[Formula: see text], [Formula: see text], and bisphosphonates in osteoblast–osteoclast signaling, as well as considering PTH’s influence on the gland and the regulatory roles of [Formula: see text], [Formula: see text], and [Formula: see text] in osteoblast apoptosis and bone volume effects. Through diverse methods including illustrative depictions, numerical simulations, sensitivity analysis, and stability analysis, this work seeks to comprehend how PTH therapy impacts bone volume, enhancing its therapeutic relevance.

Determination of optimal technological parameters of a horizontal mixer of loose compound feeds

The quality of the compound feeds for animals and poultry directly depends not only on the components included in it but also on the type of mixer used. Horizontal mixers as compared to the vertical ones allow for a shorter period of time to obtain high-quality mixtures due to the intensification of the process of material movement by belt working bodies. The aim of the research is to determine optimal technological parameters of a horizontal mixer with a 0.3 m3 mixing chamber with a belt working body. The mixer is designed to produce mixed compound feeds of high uniformity in production lines, workshops or can be used as an independent machine for mixing loose components. The research was carried through multifactorial experiment. As the result, mathematical models of the mixer working process were obtained, two-dimensional cross sections of the response surfaces were built. The obtained mathematical models make it possible at the design stage to identify the dependence of qualitative and energy indicators on factors at the considered levels of variation. According to the results of the multifactorial experiment, it has been established that the best mixing quality of 94.8 % is achieved when the mixing chamber is loaded by 58 % at a speed of rotation of the mixer shaft of 30 min-1, mixing time of 6 minutes with simultaneous supply of the control and the main components. At the same time, the throughput is 0.78 t/h, and the specific energy consumption is 2.04 kWh/t.

Investigation of electromagnetic processes in the case of static eccentricity of a two-pole induction motor with a short-circuited rotor

Purpose. Correction of the mathematical model of electromagnetic processes in a two-pole induction motor with a short-circuited rotor, taking into account static rotor eccentricity to identify diagnostic correlations. Methodology. Analytical modeling using the method of specific magnetic conductivity, mathematical modeling of electromagnetic fields in a three-phase induction motor with a short-circuited rotor using methods of electromagnetic field theory and finite element methods. Obtained results. The necessity of improving mathematical models for induction motors with short-circuited rotors to establish new or refine connections between diagnostic features and diagnosed defects has been demonstrated. Refined mathematical expressions for calculating the specific conductivity of non-uniform air gaps in induction motors with static eccentricity are provided. Modeling was performed using the FEMM environment for a statically eccentric two-pole induction motor with a short-circuited rotor. It has been proven that the harmonic order values obtained using the numerical-field method are consistent with those obtained analytically. Findings. Based on the field approach and using the finite elements method, an analysis of the distribution of magnetic field in a two-pole induction motor with a short-circuited rotor was conducted. Harmonic analysis of the magnetic field in the air gap was performed to identify the fundamental harmonic and higher and lower-order harmonics when eccentricity occurs. The influence of static rotor eccentricity on the electromagnetic processes of the induction motor was analyzed. Practical value. The results of the study can be utilized for functional diagnosis of the rotor winding of induction motors based on the radial component of the magnetic field. This will contribute to enhancing the reliability of induction motors and enable the prevention of failure in induction motors with short-circuited rotors.

STUDY OF EFFECT TO COLD PILGER ROLLING PARAMETERS ON THE TEMPERATURE REGIME OF PROCESS

The research is aimed at determining the optimal parameters that affect the efficiency of rolling and the quality of the product. The relationship between various parameters such as heat transfer, ultimate strength, friction index and temperature regime is analyzed to improve the technological parameters of cold mill rolling and increase the quality of products. Mathematical modeling of cold mill rolling processes allows not only a deeper understanding of the physical processes occurring during rolling, but also provides an opportunity to analyze the influence of various parameters on the temperature regime and, in general, on the quality of the final product.