Mathematical Model Of Process Research Articles

Mathematical modeling of non-linear reaction-diffusion process in autocatalytic reaction: Akbari-Ganji method

A theoretical model of the electroreduction of halogen oxoanions via autocatalytic redox mediation by halide anions is discussed. This autocatalytic process depends upon a system reaction-diffusion equation including a nonlinear term for homogeneous reactions. This study solves these equations using the robust and user-friendly analytical technique, the Akbari-Ganji method. The current and the redox component concentration are presented in terms of the rate constant. The influence of variables on current is examined using sensitivity analysis. The most important factor affecting current is the ratio between the bulk concentrations of halogen molecules and non-electroactive halogen oxoanions. The theoretically predicted results are compared with the numerical results. These approximate results enhance our understanding of system behavior.

Моделирование работы газотурбинной установки SGT5-4000F с исследованием влияния режимных и климатических факторов на устойчивость горения в камере сгорания

When regulating gas turbine units, it is necessary to be confident in the stable combustion process in the combustion chambers, considering the dynamics of the processes and changes of external climatic factors. Many scientific studies are devoted to the problems of experimental research and mathematical modeling of processes in combustion chambers. The possibilities of flame failure, expansion of the lower limit of combustion, determination of the stable position of the flame front and other issues have been assessed. Even though the problem of design of mathematical models and their use remains relevant. The purpose of this research is to model and study the influence of operation and climatic factors on the stability of combustion in the combustion chamber of the SGT5-4000F gas turbine unit. The subject of the research is the SGT5-4000F gas turbine unit with a low-emission combustion chamber. The simulation model of the gas turbine unit has been developed in the environment of dynamic modeling of technical systems SimInTech. The research is carried out using theoretical methods of calculating fuel combustion, thermodynamic foundations of the theory of gas turbine engines, methods of mathematical and simulation modeling, as well as data from the archive of automated process control systems. A simulation model of SGT5-4000F gas turbine unit has been developed. It is distinguished by the ability to assess the proximity of the compressor operating mode to the stability limit and determine the boundaries of stable combustion procedure in the combustion chamber, considering environmental climatic factors. The authors have studied the stability of the compressor and combustion chamber. The results of the experimental studies of a gas turbine unit in the operating load range from 113 to 282 MW and in the range of outside air temperature from –12 to 30 °C have shown that the combustion process in the combustion chamber is unvarying over the entire operational stress spectrum. The results obtained are verified by comparing model values with technological parameters of a gas turbine unit taken from the archive of the power plant control system. The authors have assessed the influence of electrical load on the performance indicators of a gas turbine unit at outdoor temperatures of +30, +15 and –12 °C. According to the results of simulation modeling, the model of SGT5-4000F gas turbine unit is found to be adequate. The developed model can be used as a tool at the stage of functional and technological design of automated control systems for the development of effective automatic control systems.

Selecting a stirrer and optimizing the process of mixing the substrate in the fermenter of biogas unit

The relevance of the work is related to the problem of soil degradation as a result of pollution by livestock waste and the need for timely disposal of waste into effective organic fertilizer and biogas. Increasing the share of the use of organic fertilizers makes it possible to develop organic farming technologies, and accordingly leads to the production of healthy crop products. The work investigated the process of substrate mixing in the fermenters of an operating pilot biogas plant. The technological line is designed for processing liquid organic waste, mainly manure or litter, by anaerobic digestion to produce innovative environmentally friendly organic fertilizers on an industrial scale. The purpose of the study was to select a stirrer and optimize the conditions for mixing the substrate in the fermenters of a biogas plant. The physicochemical properties of the substrate were studied by laboratory methods. The mathematical model of the mixing process is based on a semi-empirical description of the hydrodynamics of flows in the reactor, modernized taking into account the current state of the issue under the conditions of a fermenter with specific geometric characteristics. As a result of the work carried out, the optimal options for the geometric dimensions of the stirrers were determined (three variants for three-blade stirrers intermittent with a blade angle of 30°, differing in the size of the impeller and rotation speed) and the parameters of the mixing process were calculated. Based on a laboratory experiment and the results of calculating the sedimentation rate, the frequency of turning on the stirrer (once a day) and the time of its continuous operation to homogenize the suspension were determined. The results of the work can be used in the design of mixing devices and substrate mixing modes in bioreactors.

Mathematical modeling of dynamic processes of agricultural mobile energy vehicles on an electric drive

The article considers the issues of modeling the processes of agricultural mobile energy vehicles (MEV) with electric drive (ED). A review of modern literature on the problem under study as well as questions on modeling the functional properties of mobile machines and improving the quality indicators of MEV work are presented. A mathematical model of the motion of the MEV with an electric motor is presented, as well as a description of the method used and a sequence of actions for conducting research. Preliminary theoretical studies of motion in different modes of operation have been carried out. The proposed model is convenient for implementation and calculation in any of the applied software products that support the modeling of dynamic systems with an electromechanical drive. The proposed model, the solution of which is based on the methods of numerical integration of systems in the Matlab Simulink software environment, made it possible to simulate the dynamic processes of electromechanical power transmission of MEV during various agricultural operations. With the help of this model, the analysis of electromechanical processes in transient and steady-state operating modes, as well as dynamic processes in the power transmission were carried out. Graphs of changes in the studied parameters of the MEV power transmission are obtained and elastic moments in the joints of the 5-mass design scheme are determined. The use of the model allows you to track the change in statistical characteristics when the conditions of the experiment change. The model has shown its operability when performing simulation of agricultural operations: fertilization, cultivation and sowing, and it can be used at the design stage to study the characteristics of dynamic processes of small-class traction MEV power transmissions with an electromechanical drive. With different parameters of the model, there is a change in the mathematical expectation of the angular velocity of the ED from 147.89 to 156.87 rad/s, a change in the mathematical expectation of the speed of the MES from 4.51 to 4.79 m/s.

Использование преобразованного уравнения электронейтральности при проведении технологических расчетов водоподготовки на ТЭС и АЭС

When performing technological calculations of water treatment units for thermal power plants (TPP) and nuclear power plants (NPP), it is necessary to determine the quality indicators of process water after the processing steps. The main difficulty is to calculate the concentrations of weak electrolytes since they are in chemical equilibrium with all forms of dissipation. Currently, for each type of processing, either simplified models or methods that solve a complex computational problem are used for calculations. It is necessary to develop a universal mathematical model that allows high accuracy to calculate the concentrations of weak electrolytes and the pH value for various types of water treatment. To develop the model the authors have applied the method of mathematical modeling of chemical-technological processes at thermal power plants and nuclear power plants. A mathematical model based on the transformed equation of electrical neutrality is proposed. It can be used to determine the equilibrium concentrations of dissociation forms of weak electrolytes (primarily water itself and carbonic acid) after various stages of water treatment. The proposed model allows, when conducting technological calculations of water treatment plants, to more accurately and universally calculate the concentrations of weak electrolytes and determine the pH value in process waters for various types of water treatment. The model can be used to determine the required doses of chemical reagents to ensure the required values of technological indicators (pH and Langelier index) in treated water.

DISCRETE GROUP METHOD FOR A MATHEMATICAL MODEL OF THE DIFFUSION IN SWELLING GELATIN

In this article, we will introduce the mathematical model of the diffusion process in a swelling medium that has already been modeled. The main purpose of this paper is introducing a new class of group transformations for solving the nonlinear emulsion equation. Thus, we introduce this method as the discrete group methods based on solvable class orbits. One of the crucial advantages of this method is that a transformation is sought, which reduces the equation being investigated to some standard form for which the methods of integration are known. In developing this approach, one may construct all canonical forms of solvable equations.

Implication of polymerase recycling for nascent transcript quantification by live cell imaging.

Transcription enables the production of RNA from a DNA template. Due to the highly dynamic nature of transcription, live-cell imaging methods play a crucial role in measuring the kinetics of this process. For instance, transcriptional bursts have been visualized using fluorescent phage-coat proteins that associate tightly with messenger RNA (mRNA) stem loops formed on nascent transcripts. To convert the signal emanating from a transcription site into meaningful estimates of transcription dynamics, the influence of various parameters on the measured signal must be evaluated. Here, the effect of gene length on the intensity of the transcription site focus was analyzed. Intuitively, a longer gene can support a larger number of transcribing polymerases, thus leading to an increase in the measured signal. However, measurements of transcription induced by hyper-osmotic stress responsive promoters display independence from gene length. A mathematical model of the stress-induced transcription process suggests that the formation of gene loops that favor the recycling of polymerase from the terminator to the promoter can explain the observed behavior. One experimentally validated prediction from this model is that the amount of mRNA produced from a short gene should be higher than for a long one as the density of active polymerase on the short gene will be increased by polymerase recycling. Our data suggest that this recycling contributes significantly to the expression output from a gene and that polymerase recycling is modulated by the promoter identity and the cellular state.

Spatial distribution model of thermal load for high-speed dry hobbing tool based on probability density function

High-speed dry hobbing is a clean and environmental-friendly gear machining process, but thermal dissipation inefficiency accelerates tool wear and shorten tool life which is difficult to be effectively inhibited due to its complex distribution characteristics. This paper proposes a thermal load distribution model based on probability density function, describing the spatial distribution of thermal load on tool and providing theoretical support for predicting the distribution of thermal load. Firstly, conducting a finite element simulation analysis based on a mathematical model of high-speed dry gear hobbing process; Secondly, the influence of various parameters on the constructed model is analyzed, and the Bayesian optimization algorithm is utilized to optimize the model parameters. Finally, the model is validated at the micro and macro level. The results show that the average coefficient of determination of the model is greater than 0.86 in micro level. And the average fitting error is less than 6 °C in macro level, besides, the average relative error is less than 15%. The description of the uneven thermal distribution on tool is obtained with probability density function, it provides a theoretical support for the prediction and further optimization of thermal load on tool under multiple parameters in the future.

МОДЕЛИРОВАНИЕ ТЕХНОЛОГИЧЕСКОГО ПРОЦЕССА ПРЕДОКРАСОЧНОЙ ОБРАБОТКИ КУЗОВНОЙ ОБШИВКИ ЖЕЛЕЗНОДОРОЖНОЙ ТЕХНИКИ

There are data on the mathematical modeling of the manufacturing process of gas dynamic treatment. The study objective is to obtain a mathematical apparatus that allows the calculation of the main manufacturing modes of gas dynamic treatment according to the destruction rate of operational pollution, as well as to the invasiveness of the body covering. To do this, the paper presents the main provisions of the mathematical model and the results of the research.

Steady-State simulation of cryogenic distillation used for helium isotope separation

Helium-3 (3He) is an invaluable and scarce resource with applications in various scientific and industrial fields. It is typically found mixed with helium- 4(4He) in natural gas and nuclear off-gas, which is industrial source of helium. Therefore, separation of the helium isotope is necessary. Cryogenic distillation is a preferred method of separation due to its higher separation coefficient and processing capacity. In this study, a numerical steady-state simulation of cryogenic distillation column for helium isotope has been conducted using programming. The mathematical model for the equilibrium-state cryogenic distillation process was established and solutions of the thermodynamic formulation was proposed. The simulation provided the distribution of 3He and 4He along each distillation column as well as the profiles of temperature and flow rates along the column, based on the designed specifications including the composition of the feeding mixture, feed flow rate and pressure. The required heat duty of the condenser and reboiler was also calculated, and the column dimensions were estimated. Besides, we have studied the effects of the reflux ratio and feed concentration of 3He on the final isotopic contents of the top and bottom products. The results demonstrated that the distillation simulation could provide crucial theoretical support for the smooth execution of future laboratory experiments.

Data‐driven identification of crystallization kinetics

AbstractA novel data‐driven methodology is presented for developing mathematical models for crystallization processes. The data‐driven approach is based on the sparse identification of nonlinear dynamics (SINDy) method, which iterates between a partial least‐squares fit and a sparsity‐promoting step leading to the discovery of sparse interpretable models. The performance of the SINDy methodology is characterized for the identification of crystallization kinetics in a mixed tank operated in a continuous mode, the isothermal crystallization of lysozyme in a batch stirred tank and cooling crystallization of paracetamol. The SINDy method is robust against noise. Good agreement is obtained between the data‐driven model and the data obtained from crystallization experiments. The presented data‐driven approach can be attractive for modeling industrial crystallization processes where process analytical technology tools are available for the measurement of process variables but functional forms of kinetic expressions are unknown.

Implementation of mDoE‐methods to a microcarrier‐based expansion processes for mesenchymal stem cells

AbstractThe need for advanced therapy medicinal products (ATMPs) has gained increased attention in recent years. In this respect, a well‐designed cell expansion process is needed to efficiently manufacture the required number of cells with the desired product quality. This step is challenging due to the biological complexity of the respective primary cell (e.g., mesenchymal stem cells (MSC)) and the usage of microcarrier‐based expansion systems. One accelerating approach for process design is model‐assisted Design of Experiments (mDoE) combining mathematical process models and statistical tools. In this study, the mDoE workflow was used for the development of an expansion processes with human immortalized mesenchymal stem cells (hMSC‐TERT) and the aim of maximizing cell yield assuming only a limited amount of prior knowledge at a very early stage of development. First, suitable microcarriers for expansion in shake flasks were screened and the differentiation of the cells was proven. Second, initial experiments were performed to generate prior knowledge, which was then used to set up the mathematical model and to estimate the model parameters. Finally, the mDoE was used to determine and evaluate the design space to be performed experimentally. Overall, a cell expansion process using microcarriers in a shake flask culture was successfully implemented and a significant increase in cell yield (up to 6,2‐fold) was achieved compared to literature.

Research of nonstationary dynamic models of the organizational and technological process of railway transport technical vehicles repair

The problems of analytical and computer research of dynamic models of repair and operation of technical vehicles used in railway transport are among the urgent problems related to ensuring safety and stability of traffic, with the development of digital twins and the improvement of monitoring and diagnostic systems. The analysis of models described by various types of multidimensional nonlinear differential equations requires the use of modern methods of dynamical systems theory, numerical optimization and computer algebra. The purpose of the article is to conduct a qualitative and numerical analysis of mathematical models of organizational and technological processes (OTP) in railway transport, as well as the synthesis of new controlled OTP models. Nonstationary generalizations of a two-dimensional dynamic model describing the repair process of railway transport equipment are proposed. Various cases of using constant and time-dependent parameters are considered. The case of linear and exponential dependences of parameters on time is studied. For the studied models, trajectories are obtained taking into account the variation of constant parameters and taking into account the choice of parametric dependencies, a comparative analysis of the results is presented. The formulation of the problem of optimal control of the number of repaired and repaired railway wagons is proposed. Promising methods for solving this problem using numerical optimization methods, including those inspired by nature, are described. The results can be used in the tasks of constructing and analyzing mathematical models of dynamic systems, in the tasks of numerical modeling of transport systems and technological processes, in the tasks of optimizing the number of vehicles and improving the transportation process, as well as in the tasks of creating digital counterparts in the transport industry.

Freezing and Thawing of Enclosing Structures and Foundation Soils Taking into Account the Effects of Solar Energy: Part 2. Problem Statement

Part 1 provides general information about some of the physical properties of water, ice, and snow necessary to understand the non-stationary processes of freezing and thawing of enclosing structures of wet foundation soils. Part 2 presents the physical and mathematical formulation of the problem of freezing of wet soil, the solution of Lyame and Clapeyron, the solution of Stefan, the physical and mathematical formulation of the problem of freezing of the ribbon foundation. The following are considered: description of the process of freezing of a single-layer enclosing structure considering the phase transformations of moisture in the material of the structure according to V.N. Bogoslovsky and the process of freezing of an unlimited plate considering the phase transformations of moisture in the material of the structure according to A.V. Lykov. Mathematical model of non-stationary heat transfer process in wet layered media. Based on the method of small-time intervals, solutions of boundary value problems for frozen and thawed zones in the region of large and small Fourier numbers are given. Prospects for the application of the proposed mathematical models to describe the processes of freezing and enclosing structures and foundation soils are outlined.

Development and Implementation of New Technologies Using Mathematical Modeling of the Rolling Process

Development and Implementation of New Technologies Using Mathematical Modeling of the Rolling Process

Solutions to the problem of differential games with electric oscillations by finite difference methods

The article deals with the issues of electromagnetic processes from the point of view of application technology. The problem of voltage normalization in lines in the presence of opposing external forces is studied. The process of realizing the solution of this problem is based on the introduction of a mathematical model of electromagnetic processes occurring in lines as a continuous differential pursuit game described by hyperbolic equations. The finite difference method transforms the continuous pursuit problem into a discrete game. Sufficient conditions are obtained getting into neighbourhood. And with the help of a well-known a priori estimate for the difference between the solutions of a continuous differential and the corresponding discrete game, sufficient conditions are obtained for the possibility of completing the pursuit of a continuous game. A pursuer outputs terminal set, which is voltage normalization.

Research on Hydrolithospheric Processes Using the Results of Groundwater Inflow Testing

The article considers a mathematical model of the hydrolithospheric process taking into account the skin effect. A methodology for using the results of groundwater inflow testing to determine the parameters of approximating models that take into account skin effects is presented. In addition, the problems of modeling hydrodynamic processes taking into account random factors are considered. A statistical analysis of well monitoring data was carried out and an algorithm for studying processes was developed. Using the obtained approximating models, a procedure for solving the problem of selecting the optimal number of production wells has been developed. Based on the results of the groundwater inflow testing, the prospects for the development and use of new aquifers can be determined.

Mathematical Modeling of Thermophysical Processes in a Thermoelectric Device for Cooling the Brain

Mathematical Modeling of Thermophysical Processes in a Thermoelectric Device for Cooling the Brain

Development of a dynamic gas lock inhibited model for EUV-induced carbon deposition.

The optical surface of extreme ultraviolet (EUV) lithography machines is highly vulnerable to contamination by hydrocarbons, resulting in the formation of carbon deposits that significantly degrade the quality and efficiency of lithography. The dynamic gas lock (DGL) has been proven as an effective approach to alleviate carbon deposition. However, the majority of existing studies on carbon deposition neglect the influence of the DGL. This paper is dedicated to investigating the phenomena of hydrocarbon adsorption, desorption, and cleavage with considering the effects of the DGL. A comprehensive mathematical model of the carbon deposition process is established, and the impact of radiation intensity, temperature, and hydrocarbon types on the depositing rate is considered. The results suggest that the primary cause of carbon deposition is the direct cracking of hydrocarbons induced by photons with a wavelength range between 12.5 and 14.5nm. Additionally, it has been observed that the carbon deposition rate decreases exponentially as clean gas flow increases when EUV radiation intensity exceeds 50 mW/mm2. Conversely, at low EUV radiation intensity, clean gas flow has little effect on the carbon deposition rate. An effective approach to mitigate carbon deposition is to elevate the temperature of the optical surface and employ light hydrocarbon materials in the EUV process.

Modeling of the removal of combustion products in the pipe of a low-rise building as a control object

The features of the formation and methods of preventing condensation in the chimney of an apartment low-rise building with an individual decentralized heat supply system are considered. A mathematical model of the technological process of removing flue gases from gas boilers in an apartment building through a collective chimney pipe as a multidimensional control object with distributed parameters, which is understood as a set of thermophysical processes occurring during the removal of combustion products. Numerical simulation of a collective chimney pipe is performed on the example of a three-storey apartment building with gas boilers installed in each apartment as a control object. A method of step-by-step experiments is proposed. At the first stage, the dependences of the distribution of the temperature field inside the chimney during non-stationary operation of boilers and changing ambient temperature are obtained. The phenomenon of condensate occurrence has been confirmed experimentally, and the most characteristic areas subject to its occurrence have been identified. During the second stage of research, it was found that it is most effective and economically feasible to prevent the formation of condensate by using a heating cable in the attic and chimney head sections. It is shown that the change of control actions has an effect on the temperature of adjacent sections of the chimney. The revealed non-stationarity is taken into account by inter-channel connections through the object in the block diagram. It is proved that, in relation to solving the problem of removing combustion products from the chimney, an object with distributed parameters can be represented by a model with concentrated parameters, for which the structure is synthesized and proper operators and operators of inter-channel connections are found in the form of transfer functions with variable parameters. The resulting model is problem-oriented to create a two-dimensional automatic temperature control system on the inner surface of the chimney in order to prevent the formation of condensate in the pipe.