Mathematical Modeling Simulation Research Articles

Dynamic model of magnetic transmission

In the work, a non-contact electromechanical energy converter with permanent magnets, which is known as magnetic transmission, is studied. Magnetic transmissions have certain structural advantages compared to mechanical transmissions, namely: high reliability, efficiency, lower losses, non-contact transmission of mechanical power, no maintenance costs, and simplicity of construction. The use of magnetic transmissions for systems of conversion of low-potential mechanical energy into electrical energy is especially relevant: wind energy, water energy, energy of mechanical vibrations, etc. The use of magnetic gearboxes in autonomous wind power plants can be more promising from an economic and technical point of view compared to traditional mechanical transmissions. A numerical simulation mathematical model of magnetic transmission with permanent magnets has been developed. The use of magnetic transmission, for example, for autonomous wind power systems allows to increase the reliability of the operation of such installations, reduce operating costs and increase the efficiency of their operation. In emergency modes of operation, the use of magnetic transmission allows to avoid destruction or emergency shutdowns of electrical equipment. The developed simulation model of magnetic transmission takes into account the pulsations of the electromagnetic moment due to the discrete structure of the magnetic transmission and the change of the model parameters when the input moment changes: pulsations, losses in the magnetic core and permanent magnets, the change of the load angle and the transmitted electromagnetic moment. A feature of the developed model of the magnetic transmission system is that a change in the load of the electric power source leads to a change in the operating point on the mechanical characteristics of the rotor of the wind turbine. Conversely, when the wind parameters change, the output parameters of the source of electrical energy change: power, voltage, current and electromagnetic moment.

Simulation of the Effect of N2O on DNA Damage by Ionizing Radiation

Damage to the DNA molecule by ionizing radiation can be influenced by the presence of certain chemicals in the cell during irradiation. These substances can be both radioprotective and radiosensitive. In this paper, we will discuss the effect of N2O, widely used in medicine, on the chemical stage of the radiobiological mechanism. N2O in the cell during irradiation with ionizing radiation results in more significant damage to the DNA molecule because N2O reacts with hydrated electrons 𝑒𝑎𝑞 − to form aggressive OH radicals. A mathematical simulation model developed using hybrid Petri nets is used to analyze this dynamic process. Hybrid Petri nets allow us to quickly create a mathematical simulation model and explore the system under study to obtain detailed information for practical applications.

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester’s vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

A hybrid evaluation of the intestinal absorption performance of compounds from molecular structure.

Intestinal absorption of compounds is significant in drug research and development. To evaluate this efficiently, a method combining mathematical modeling and molecular simulation was proposed, from the perspective of molecular structure. Based on the quantitative structure-property relationship study, the model between molecular structure and their apparent permeability coefficients was successfully constructed and verified, predicting intestinal absorption of drugs and interpreting decisive structural factors, such as AlogP98, Hydrogen bond donor and Ellipsoidal volume. The molecules with strong lipophilicity, less hydrogen bond donors and receptors, and small molecular volume are more easily absorbed. Then, the molecular dynamics simulation and molecular docking were utilized to study the mechanism of differences in intestinal absorption of drugs and investigate the role of molecular structure. Results indicated that molecules with strong lipophilicity and small volume interacted with the membrane at a lower energy and were easier to penetrate the membrane. Likewise, they had weaker interaction with P-glycoprotein and were easier to escape from it and harder to export from the body. More in, less out, is the main reason these molecules absorb well.

Numerical simulation and mathematical modeling of biomechanical stress distribution in poroelastic tumor tissue via magnetic field and bio-ferro-fluid

Based on scientific evidence, it seems that bio-magnetic systems can change the process of cancer cell death by affecting the distribution of pressure and mechanical stress in the tumor tissue. Already most of the research has been done experimentally and few mathematical modeling and numerical simulations have been done to investigate the relationship between the magnetic parameters and the mechanical stress of the tumor tissue. This is despite the fact that in order to be able to make new equipment with the help of medical engineering methods, it is definitely necessary that the mathematics governing the problem and changes in the effective magnetic parameters (such as the shape of the magnetic source, magnetic flux density, magnetic source distance and ferro-fluid volume fraction) should be studied as much as possible. In this research, using numerical simulation and mathematical modeling, four common geometrical shapes (rectangular and circular) of the static magnetic field source were used to investigate the relationship between the change of the effective magnetic parameters and the mechanical stress created in the tumor tissue. The results of this research showed that when the magnetic flux density and ferro-fluid volume fraction and also the distance between the magnet and the tissue are kept constant, as well as without spending any extra energy, for a rectangular magnet, just by changing the way the source is placed on the tissue, the average biomechanical stress inside the tumor tissue causes a 25% change. Also, for a circular magnet, just by doubling the radius of the magnet, the average biomechanical stress inside the tumor tissue causes a 73% change.

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester’s vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

Special issue: “Integrated approaches for the mechanics of masonry structures: Novel strategies for experimental characterization, mathematical modelling and computer simulations”

Special issue: “Integrated approaches for the mechanics of masonry structures: Novel strategies for experimental characterization, mathematical modelling and computer simulations”

Modeling and sensitivity analysis of a supersonic inductive Magnetohydrodynamic (MHD) generator

This study presents the supersonic inductive Magnetohydrodynamic (SIMHD) generator and simulates its model through the use of COSMOL Multiphysics. This generator, as an inductive MHD generator, is suggested to address the problems associated with the conventional MHD generator. Since the proposed generator does not require a moving part to convert thermal energy to electrical energy, it is categorized as a direct energy convertor. The SIMHD generator consists of a converging-diverging duct and is divided into two sections at the diverging part by means of a diaphragm. Both of these sections are diverging, which makes it possible to obtain a high Mach number. In this regard, the performance of the SIMHD generator is studied by its mathematical modeling and numerical simulation using the finite element method. In addition, a sensitivity analysis is carried out on the design parameters. The results indicate that the proposed SIMHD duct design will increase the speed from 160 to 1300 m⁄s, and decrease the temperature from 2100 to 1300 K. Moreover, considering a charge generation equation, the produced power for the resistive load 50 Ω equals 25.3 kW. This generator also has the potential to be used in scramjets and ramjets.

Discrete Dynamic System Modeling for Simulated Moving Bed Processes

Although the simulated moving bed (SMB) process boasts advantages such as high productivity and low consumption, the cost of obtaining optimized parameters through practical experiments to control the separation process can be enormous due to its complex nonlinear characteristics. Consequently, the successful transformation of the SMB separation process into a mathematical dynamic model for computer simulation would greatly reduce the research costs associated with experimental studies. In this study, the Crank–Nicolson method was employed to discretize and dynamize the SMB process, enabling the simulation of processes under both linear and Langmuir isotherms. The results of the simulation experiments demonstrated the feasibility and high efficiency of this approach, thereby establishing a solid foundation for further advancements in online control strategies.

Fractional mathematical modeling of breast cancer stages with true data from Saudi Arabia

This research focuses on the development, analysis, and simulation of fractional mathematical models to investigate the transmission dynamics of different phases of breast cancer. The suggested breast cancer model incorporates three often-used fractional operators in epidemiology: Caputo, Caputo–Fabrizio–Caputo, and Atangana–Baleanu–Caputo operators. In this study, the determination of the equilibrium point and its stability analysis is conducted using the Routh–Hurwitz criterion. Additionally, we examine the existence and uniqueness of solutions for the fractional system using Krasnoselskii’s and Banach fixed-point theory. Moreover, the global stability is discussed via the Ulam–Hyres criterion. Furthermore, the fractional models are being verified using reported occurrences of stage IV breast cancer among females in Saudi Arabia from 2004 to 2016. The real data is used to determine the values of the parameters that are fitted using the least squares error-minimizing methodology. Also, residuals and efficiency rates are computed for the integer as well as fractional-order models. Graphical representations are used to illustrate numerical results by examining different choices of fractional order parameters. Then, the dynamic characteristics of various stages of breast cancer are analyzed to demonstrate the impact of fractional order on breast cancer progression and how the rate of chemotherapy influences its behavior. We provide graphical results for a breast cancer model with effective parameters, resulting in fewer future incidences in the population of stages III and IV. Chemotherapy often raises the risk of cardiotoxicity, and our proposed model output reflects this. The goal of this study is to reduce the incidence of cardiotoxicity in chemotherapy patients while also increasing the pace of patient recovery. This research has the potential to significantly improve outcomes for patients and provide information on treatment strategies for breast cancer patients.

Permeability Prediction in Nonwoven Geotextiles Using Mathematical Modeling and Numerical Simulation

The vertical permeability coefficient is a pivotal hydraulic index of needle-punched nonwoven geotextiles. The accurate determination of the permeability coefficient is important for assessing engineering properties. This study employed mathematical modeling, numerical simulations, and physical experimentation to investigate the permeability behavior of nonwoven geotextiles. Mathematical modeling relies on the fiber and pore size characteristics of the geotextiles extracted through two-dimensional image analysis. The numerical simulation method was based on a pore network model acquired through three-dimensional image analysis. The results of the physical experiments served as benchmarks for evaluating the precision of the two methods. These findings underscore the efficacy of mathematical modeling and numerical simulation in predicting the permeability characteristics of nonwoven geotextiles.

Construction of the mathematical model of magnetic transmission for an autonomous wind power plant

Construction of the mathematical model of magnetic transmission for an autonomous wind power plant

Optimizing heat transfer rate with sensitivity analysis on nonlinear radiative hydromagnetic hybrid nanofluid flow considering catalytic effects and slip condition: Hamilton–Crosser and Yamada–Ota modelling

AbstractIn current investigation the optimization of heat transportation rate in a nonlinear radiative buoyancy‐driven hydromagnetic carbon nanotube (CNT) hybrid nanofluid flow is analysed. The proposed catalytic effects and slip condition is accounted for the real‐world complexities of the system. The Hamilton–Crosser (HC) and Yamada–Ota (YO) models are employed to characterize the behaviour of the nanofluid. The primary objective is to enhance the heat transmission rate, which is crucial for various engineering applications such as thermal management, energy systems and so forth. To achieve this, sensitivity analysis is performed to identify the most influential parameters affecting heat transfer in the system. By understanding the sensitivity of these parameters, the performance of the system can be improvised. The study focuses on the interplay between key factors including radiative heat transfer, buoyancy‐driven flow, magnetic field influence, catalytic effects, and slip condition. The presence of CNTs in the nanofluid adds another dimension to the complexity of the system that explores the effects of varying the concentration and size of CNTs on the heat transfer rate. By utilizing advanced mathematical modelling and numerical simulations, the performance of the system under different scenarios and identify the optimal conditions for maximizing heat transfer rate is evaluated. The findings of this research provide valuable insights into the design and optimization of heat transfer systems involving nanofluids with nonlinear radiative and hydromagnetic effects. The observation shows that, irrespective to single wall and multi wall CNT nanoparticles the fluid velocity attenuates significantly whereas it favours in enhancing the fluid temperature. Further, the comparative analysis reveals that the heat transfer augments in the case of HC model than that of YO model.

Performance map and theoretical analysis of Carnot battery technology via novel reversible Rankine-based cycle

Carnot battery technology offers a good solution for storing the energy for later use. There are various types of Carnot batteries, and the Rankine-based cycle stands out due to its efficiency in power generation. Carnot battery can be configured as a stand-alone system, in which the heat pump and heat engine are installed separately. This approach, though, necessitates additional components, leading to high initial investment costs. As an alternative approach, a reversible system that reduces the number of components can be a promising alternative. This article reported the analysis of the Carnot battery implemented via a novel reversible Rankine-based thermodynamic cycle (so-called RRTC). This RRTC system is designed using one expander for both the organic Rankine cycle and heat pump modes (i.e., a throttle valve in the heat pump mode is replaced by an expander). The mathematical modeling simulation and its results are described, highlighting the performance map of the RRTC. Simulations were made for nine selected working fluids, focusing on their thermal properties. Among nine working fluids studied, R152a emerged as the most promising for RRTC applications due to its superior power-to-power performance of 1.57, surpassing other working fluids for which performances below 1.50 were obtained. The results show that a relative difference below 10% was likely observed between simulation results with and without Baumann's correlation. Moreover, Ba(OH)2·8 H2O and acetamide offer a less phase change material mass required in the storage system, achieving thermal energy storage mass sizing ratio of 0.35–1.55 and 0.39–1.71, respectively.

Force analysis of the planetary-type mechanisms of the enhanced vibration exciters

The planetary-type vibration exciters are relatively novel and prospective types of actuators for various vibratory technological equipment. Numerous research papers substantiated the possibilities of implementing such exciters for generating circular, elliptical, and rectilinear oscillations of the working members of different technological machines. The present research continues the authors’ previous investigations dedicated to kinematics and dynamics of planetary-type vibration exciters and is focused on the analysis of forces, moments, and torques acting upon the elements of the corresponding actuating mechanisms. The research methodology contains the development of the simplified dynamic diagrams of two different designs of planetary-type mechanisms, derivation of the analytical expressions describing force parameters of the considered mechanical systems, performing the mathematical modeling and computer simulation of the mechanism motion in order to analyze the corresponding forces, moments, and torques. The obtained results present the time dependencies of the mentioned force parameters under different operational conditions and design parameters of the planetary-type mechanism. The major scientific novelty of the paper consists in defining the minimal required torque of the motor needed to be applied for driving the mechanism at different conditions. The research outcomes can be effectively used by engineers while developing new and improving existent vibratory technological machines equipped with the considered planetary-type vibration exciter.

NEURAL NETWORK MODELING OF PLASMA-CHEMICAL PROCESSES OF OBTAINING NANOSYSTEMS

Plasma-chemical technology is a new area of industrial chemical technology. Chemical processes in low-temperature plasma, the regularities of reactions, and the basis of plasma-chemical technology will require computer simulation. Building adequate simulation models of plasma-chemical processes for developing nanosystems and computer simulations with them allows the development of applied research studies in this subject area. Computer intelligence technologies provide an opportunity to use non-classical approaches to building mathematical models of chemical processes. Neural network technologies make it possible to create mathematical simulation models of various processes.

Service life estimation of electric vehicle lithium-ion battery pack using arrhenius mathematical model

Durability is a desired characteristic for all battery packs in Electric Vehicles. In this study, the service life of the EV battery pack under real-world operating conditions is projected using an Arrhenius mathematical simulation model. The model comprises a 39.2 kWh EV Lithium-Ion battery pack integrated with a three-phase inverter to convert the battery pack’s Direct Current output to Alternating Current. In addition, the Alternating Current output is coupled to a 100 kW permanent magnet synchronous motor, which is regarded as the load. A field-oriented controller provides pulse width-modulated output signals that are supplied back to the inverter to generate the correct driving current. Variable conditions of charge rate (C-rate: 1.25C − 4C), discharge rate (C-rate: 0.5C − 4C), temperature (25°C–60°C), and depth of discharge (30%–90%) are evaluated to determine the battery pack’s service life. Under a 4C charge rate/0.5C discharge rate and 50% depth of discharge, the modeling results indicate the battery pack has a service life of approximately 6,000 h at low temperatures (25°C) and roughly 3,000 h at high temperatures (60°C). The model has been validated by comparing the results with experimental data from the literature.

Impact of Shelf-Life Extension on Platelet Availability: Results from an Inventory Management Modeling Study

<b><i>Introduction:</i></b> In Germany, demand for platelet transfusion is maintained or even increasing, despite a decrease in whole blood donations observed in the last decade. The shelf-life of platelet concentrates (PCs) in Germany is 4 days, which can be extended to 5 days if appropriate safety measures are used. This short shelf-life leads to decreased PC availability. <b><i>Methods:</i></b> We investigated the impact of PC shelf-life extension on PC shortage, using a mathematical simulation model based on the PC production and delivery statistics of the Frankfurt Institute of the German Red Cross Transfusion Service of Baden-Württemberg-Hessen. We used a 2.2-year dataset for PC production and delivery as input data for a Monte Carlo inventory management simulation, focusing on PC shortage. The model generated the daily stock (expressed as mean number of PC units ± standard deviation), mean PC age at release, mean number of expired PC units, and shortage rates (i.e., requiring the release of more PCs than available), overall and by PC blood group. <b><i>Results:</i></b> Over 2.2 years, a total of 74,322 PC units were produced and 62,178 units were released at the Frankfurt Institute; the overall overproduction rate was 19.5%. Shortage rates decrease with an increase in PC shelf-life and/or increase in overproduction rates. At an overproduction rate of 20%, shortage rates would be reduced from 2.8% for a 4-day shelf-life to 0.7%, 0.3%, and 0.2%, for shelf-life lengths of 5, 6, and 7 days, respectively. Extending the PC shelf-life to 6 or 7 days would eliminate shortages almost entirely, including for rare bloods. <b><i>Conclusion:</i></b> These results can inform blood services and regulatory authorities on the potential medical and economic impact of extending PC shelf-life to 6 or 7 days.

Сравнительная оценка энергетических затрат при перемещениях кранов-штабелеров

Within the framework of the put forward hypothesis that energy costs of working movements of the links of racking stacker cranes are inextricably linked to the shape of the working area of the warehouse in which the crane operates, to reduce energy costs, it was pro-posed to use a rotating boom in the design of the stacker crane. With the help of program implementations of mathematical models of stacker cranes of traditional bicycle design and the proposed design with a rotating boom, it became possible to determine the average energy costs for all possible movements of loads of the same mass within the corresponding working areas of these designs. For this purpose, systems of differential equations in Cauchy form were developed, where dissipation of energy was taken into account. The total value of work of crane drives during acceleration and braking was determined. The latter were carried out with constant accelerations, and the movement after acceleration — with constant speeds. The developed simulation mathematical models of cranes of traditional design and the proposed design with a rotating boom allow to determine the energy costs in the drives when moving the crane links along the given trajectories. According to the criterion of average total energy costs, adopted for all possible combinations of movements within areas of the same capacity of one hundred square meters, the stacker crane of the proposed design has an advantage over the crane of traditional design. This makes it possible to significantly reduce energy costs when using such cranes in warehouses and hangars. It is reasonable to recommend the use of a stacker crane of the developed design in warehouses of round shape — it will allow to reduce significantly the energy costs when using such cranes in warehouses and hangars.

Mathematical modelling, analysis and numerical simulation of social media addiction and depression.

We formulate a mathematical model of social media addiction and depression (SMAD) in this study. Key aspects, such as social media addiction and depression disease-free equilibrium point (SMADDFEP), social media addiction and depression endemic equilibrium point (SMADEEP), and basic reproduction number (R0), have been analyzed qualitatively. The results indicate that if R0 < 1, the SMADDFEP is locally asymptotically stable. The global asymptotic stability of the SMADDFEP has been established using the Castillo-Chavez theorem. On the other hand, if R0 > 1, the unique endemic equilibrium point (SMADEEP) is locally asymptotically stable by Lyapunov theorem, and the model exhibits a forward bifurcation at R0 = 1 according to the Center Manifold theorem. To examine the model's sensitivity, we calculated the normalized forward sensitivity index and conducted a Partial Rank Correlation Coefficient (PRCC) analysis to describe the influence of parameters on the SMAD. The numerical results obtained using the Fourth-order Runge-Kutta (RK-4) scheme show that increasing the number of addicted individuals leads to an increase in the number of depressed individuals.