Mathematical Model Of Process Research Articles

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.

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.

Specialists Training for the Radiation Type of Non-Destructive Testing Based on Digital Technologies

The purpose of research is the development of application software, including VR-technologies, to increase the number of trained specialists in radiation type of nondestructive testing by reducing the per capita load on radiographic laboratories while maintaining the amount of practical training, acquired competencies and formed relevant professional skills.Methods. Prerequisites for virtualization of the process of training specialists in nondestructive testing of structural materials and fabricated products are defined. The main factors of demand for industrial radiography simulator in relation to the practical part of the educational cycle on radiation type of nondestructive testing are considered. As a result of the analysis the most significant aspects of practical training, available for their virtual realization, are singled out. The results of software implementation of mathematical models of physical and physicochemical processes of ionizing radiation, attenuation and absorption of penetrating radiation within the scope of digital twin of radiographic image generation as a result of simulation of the technological process of radiation type of nondestructive testing are presented.Results. Performed practical implementation of didactic materials in the form of hardware and software VR-simulator as part of digital educational environment to solve the problems of training, retraining, preparation for certification of personnel and providing admission of specialists to work on radiation type of nondestructive testing at facilities. Physical and technological aspects are analyzed, modeling, algorithmization and software implementation of VR-simulator are performed. A comprehensive approach to the creation of a learning environment with the use of digital technologies is presented. Considered are the main components, their goals and objectives. The structure of a practical lesson and illustrations of the training process in a virtual environment are given. The results of approbation of training programs with integration of classes in VR-simulator of industrial radiography have shown that the total time of practice of trainees increases by 40-55% with simultaneous reduction of per capita radiographic laboratory load by more than 25%. The main directions of development and scaling of software and hardware solution using VR-technologies are given.Conclusion. The developed and tested hardware-software solution together with the results of scientific research suggests the possibility of application and development directions of the digital educational system with VR-environment. The proposed approach application will allow to reduce environmental and biomedical risks by reducing the requirements to safety of training with the use of software and hardware solution. Automation of testing task generation and knowledge control procedures on the basis of software tools and mathematical models application, including methods of artificial intelligence, will allow to achieve training term reduction and will contribute to further increase in the number of trained specialists in various types and methods of nondestructive testing. With the functional capabilities expansion and evolutionary development of hardware-software solution (industrial radiography simulator) on the basis of unified modular approach, software libraries and hardware-software interfaces, virtual simulator simplifies organization of the process of specialists training and knowledge control. Practical value of the digital virtual environment (VR-environment) development is revealed due to the transfer and scaling of the obtained hardware-software solution to other types and methods of nondestructive testing according to GOST R 56542-2019 " Non-destructive testing. Classification of types and method".

Research on Flexible Braking Control of a Crawler Crane during the Free-Fall Hook Process

Due to the large inertia and strong impact accompanying the free-falling hook process of crawler cranes, it is difficult to meet the demand for flexible and smooth braking control under different weight load conditions. Therefore, this paper takes the free-fall hook system as the research object and combines system operation characteristics and control theory to carry out research on flexible braking control of the free-fall hook system. Firstly, a joint simulation platform of MATLAB (version 2018b) and AMESim (version 2019.1) software is built to theoretically analyze the key components of the free-fall hook system (proportional pressure-reducing valve, winch reducer, and wet clutch). Secondly, a mathematical model of the braking process is established, and the pressure control demand is clarified to analyze the reasons for the existence of dead zones and hysteresis loops in the system. Meanwhile, it is found that the dead zones and hysteresis loops existing in the pressure output of the pressure-reducing valve are the main factors of flexibility with load braking. Then, in this paper, a closed-loop control strategy is formulated based on the automatic adaptation of the braking gear in combination with the fuzzy PID pressure. Finally, the effectiveness of the control strategy proposed in this paper is verified with simulation and experimental testing using the pressure hysteresis loop of the free-fall hook process and the load-braking acceleration as the judging criteria. The results show that the system pressure hysteresis loop is reduced by 50%–60% and the maximum braking acceleration is reduced by 24%–30% under the conditions of 6.44 tonnes and 10.44 tonnes, which improves the accuracy of pressure control and achieves flexible and smooth braking with loads for different tonnages of free-fall hooks.

Photocatalytic degradation of acid blue 74 by Co: WO3 nanoparticles: Kinetics and response surface methodology studies

Energy-efficient sol-gel synthesis was achieved through the microwave assisted self-combustion route to produce hexagonal Tungsten oxide semiconductor (WO3). The photocatalytic activity was enhanced by doping Cobalt (Co) into the crystalline structure of the nanoparticle, which were subsequently sintered at 400 °C for an hour. The structural and morphological properties of the Co-doped WO3 were revealed using X-ray diffraction (XRD) characterization. The nanoparticles exhibited an amorphous structure before annealing, due to the short heating time during combustion synthesis. Sintering the nanoparticle transformed the nanoparticle from a monoclinic phase to orthorhombic phase structure. Additional analysis techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy dispersive X-ray spectrum analysis (EDS).To assess the photocatalytic performance of these particles, Acid Blue 74 (AB 74) was employed in photodegradation experiments under UV light irradiation within a semi-continuous reactor.The photodegradation of dye molecules was evaluated utilizing a UV–Vis spectrophotometer, and the mineralization efficiency of the dye was determined through total organic carbon analysis (TOC). The results indicated that the dimension of the synthesized nano catalyst fell within the range of 70–120 nm, and it exhibited the ability to completely degrade a solution with an initial dye concentration of 20 ppm within 60 min. Various parameters affecting the photocatalytic reaction, including the photocatalyst dosage, initial dye concentration, pH and temperature of the dye solution were also investigated. The experiments were designed using Response surface methodology (RSM), through which a mathematical model for the dye removal process was developed.

Heat and mass transfer analysis of coal coking process in the coking chamber

ABSTRACT To study the coking heat mass transfer process and reveal the law of industrial-scale coal pyrolysis, the heat transfer characteristics of coal material in the coking process are analyzed based on coke oven temperature measurement experiments. A mathematical model of the coking process in the coking chamber was constructed based on the distributed activation energy model. The heat transfer process of the coal feed, generation of coke oven gas, and dynamic precipitation characteristics of each component during the coking cycle were further studied. The results show that tar and water are the earliest released and fastest precipitated pyrolysis products, respectively, which are completely precipitated at 800 K. The contents of the components of the inward and outward gases are obviously different, with CH4 and H2 accounting for 73.79% of the outward gas, while H2O and tar account for 77.80% of the inward gas. When the coal reaches 1200 K, all pyrolysis products except H2 are precipitated completely. The model can effectively predict the changes of raw coke oven gas composition during the coking process at different locations in the coking chamber.

Mathematical scheduling model of complex industrial process combining swarm intelligence algorithm and swarm dimension reduction technology

The swarm intelligence algorithm is widely used in scheduling problems due to its superior searchability and adaptability, but it faces high computational costs and low efficiency when dealing with high-dimensional complex data. To enhance the handling of large-scale and intricate data, as well as enhance the accuracy and efficiency of scheduling, this study develops a mathematical model for industrial scheduling. The model is based on swarm intelligence algorithms such as symbiotic evolution algorithms, grey wolf algorithms, cuckoo algorithms, population dimensionality reduction techniques, and resource optimal allocation calculation methods. The final test results showed that the accuracy of the model in calculating the objective function was about 80 % in cases of high complexity and about 90 % in cases of low complexity. Compared with other algorithms, its accuracy was improved by 7 %, error rate was reduced by 50 %, time cost was reduced by about 30 %, and conversion rate was fast and more stable on average after 200 generations. The experimental results indicate that the proposed mathematical scheduling model, which integrates multiple intelligent algorithms and population dimensionality reduction technologies, has certain practices and feasibility in large-scale and multi-dimensional production for enterprises. This study combines swarm intelligence algorithms with population dimensionality reduction techniques, which is an innovative attempt at complex industrial scheduling problems.

Mathematical modeling and simulation of generation milling process to manufacture complex face gear surface through multi-axis machine kinematics

Manufacturing of face gear is a complex process, due to its varying geometry, hence the application is not wide as conventional gear geometry. The developments in analytical tools and kinematics of the CNC machine tools motivate researchers to explore the manufacturing process and associated applications. This article presents an efficient method for the generation milling of spur face gear utilizing a nutating head multi-axis CNC machine tool where the tool swings about an arbitrary axis in an inclined plane. The mathematical model of the disk milling cutter and face gear geometry were derived from the shaper geometry by applying the theory of gearing, equation of meshing and coordinate transformation. The cutter location (CL) data was evaluated by aligning the tool orthogonal unit vector and the tooth surface normal vector at the contact point by calculating the appropriate transformation matrices. The evaluation of machine coordinates on a multi-axis CNC milling machine was analyzed with respect to the machine pivot point and the axes movement during generation milling for the face gear drive was studied on the nutating head machine. The NC data is derived from the CL data using the inverse kinematics and the machining simulation was carried out using suitable software. The tooth surface deviation of a maximum of 43.5 μm was observed between the simulated model and the theoretical model, which is well within the requirement of roughing. The generation milling process with the proposed machine configuration is concluded as a profound face gear manufacturing technique.

Branching Models in Practice: Tackling Real-Life Challenges Beyond Theoretical Constructs Using Python Programming

The mathematical modeling of branching processes finds its origin in attempts to model reproduction patterns in species. For systems with replicating and dying components (like cells or particles), branching process theory provides the mathematical tools for understanding their probabilistic progression.. They are used to describe random systems such as chain reactions, survival of family names, pest eradication, population development and gene propagation. This study showcases clear illustrations of the likelihood of extinction, the duration until extinction, and the probability related to the entire offspring. Observations of past elite families often highlight their eventual decrease, leading to myriad speculations. Through Python-based modeling, it was found that if every person, on average, yields slightly over one offspring, there is no absolute guarantee of family extinction. However, if the mean number of offspring per individual  is one or less, the process is guaranteed to become extinct.

Formation of students' research skills and abilities with the help of Mobile Learning in the course of general physics

Relevance. The relevance of this research work is to investigate the impact of mobile learning methods on students' academic performance in the course of general physics based on university-level physics laboratories, since similar studies show that allowing students to solve mathematical models of physical processes exclusively on their smartphones rather than on traditional personal computers tends to improve students' academic performance.Purpose. The purpose of this research work was set, which is to study the impact of mobile learning on the formation of research skills and abilities in the study of general physics course, and in particular in the construction of mathematical models, which include methods of differential and integral calculus.Methodology. To achieve the goal of this research work empirical methods of research were used, which consist of observation, direct experiment, generalization and analysis of the results obtained. For the research two groups of students were formed � control and experimental, who studied the same physics disciplines, only the control group did it on personal computers, and the experimental group did it on smartphones.Results\Conclusions. The results of the experiment showed that the use of smartphones in the building of mathematical models in the course of general physics increases the academic performance of students. The results of this research work have prospects for use in the development of new techniques in education, in particular for the course of general physics and other research subjects. The results are also in demand for the analysis of student results obtained in mobile learning, which can be used to improve the academic performance of students.