Mathematical Modeling Simulation Research Articles

Mathematical Modeling and Numerical Simulation of Drug Consumption Dynamics in Burkina Faso

In this paper a mathematical model of drug consumption dynamics is proposed and analyzed. The model is based on the principle of the epidemiological model and takes into account the biological and environmental factors of exposed individuals, treatment and sensitization. The Jacobian determinant method is used to determine the basic reproduction function R0 of the model. The drug-free equilibrium points and the endemic equilibrium of the model were then identified, and their stabilities were analyzed based on the value of R0. A sensitivity analysis was performed to assess which parameters have the greatest influence on the dynamics of drug consumption. The numerical simulation was carried out using data from the Burkinabe population in 2020, aged between 11 and 65 years. The numerical results show that sensitization and treatment do not have much effect if the individual evolves in a favorable environment.

STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT

Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculated the disease-free and endemic equilibrium points and the basic reproduction number ( ) of the model. Model parameters were obtained using data from BPS Bengkalis Regency and UPTD Puskesmas Mandau. The calculation resulted in one disease-free equilibrium point and one endemic equilibrium point. If < 1, then the disease-free equilibrium point is asymptotically stable, and if > 1, then the endemic equilibrium point is also asymptotically stable. Based on the results of the data analysis, the value of. This value is less than 1, so the equilibrium point obtained is a disease-free and asymptotically stable equilibrium point. This means that the population will be free from diphtheria and the level of migration affects the presence of diphtheria disease in Mandau District.

Separation Time of Aluminothermic Reduction Products for Sustainable Silicon Production.

This work was carried out within the framework of the SisAl Pilot project, which is devoted to the environmentally friendly production of silicon. This new method relies on the aluminothermic reduction of quartz in slag, offering a more sustainable alternative to the traditional reduction of silica with carbon in submerged arc furnaces. The process takes place in a rotary kiln producing silicon (Si) and alumina slag (actually, a CaO - Al 2O 3 slag), which must be separated at the end to extract the silicon. This separation process is analyzed through mathematical modelling and numerical simulation, as it is of industrial interest to know how much time it takes for Si and CaO - Al 2O 3 slag to separate once the process has ended. Generally, a multiphase flow model is used to estimate the separation time of the two components once aluminothermic reduction has ended. Several scenarios are considered for the numerical simulation of the separation time, namely different initial configurations and material properties of both fluids are covered. Moreover, the separation times obtained with two distinct multiphase flow models -VOF (volume of fluid) and Eulerian- are compared. The separation times resulting from simulations using the multiphase Eulerian model are more realistic compared to those from the VOF model, which clearly tends to underestimate separation times. Furthermore, apart from the selected multiphase flow model, the density difference between silicon and alumina slag plays a critical role in determining the separation time.

Mathematical Modeling and Numerical Simulation of the Dynamics of Human Papillomavirus (HPV) and Cervical Cancer in Burkina Faso

Mathematical Modeling and Numerical Simulation of the Dynamics of Human Papillomavirus (HPV) and Cervical Cancer in Burkina Faso

Algorithm performance study pulse suppression of auto-oscillation phenomena in the electromechanical system of the electric traction drive in braking mode electric traction drive system in braking mode by methods of simulation modeling

Research relevance. Modes accompanied by increased sliding of a wheel with negative viscous friction, characterized by reduction of friction force at growth of sliding speed, can arise at the movement of the vehicle. In these cases, a loss of stability may occur, resulting in the excitation of auto-oscillation phenomena in the electromechanical system (road-wheel-mechanical drive-electric motor). The emergence of this process sharply increases the dynamic load of the system, which can lead to its failure or breakdown. As a consequence, the development of suppression methods of auto-oscillation phenomena is considered to be an urgent task.Purpose of the research. Verification of operability and efficiency of the suppression method of auto oscillations in the electromechanical system of wheel drive during braking of the vehicle.Materials and Methods. With the help of Lyapunov’ function analysis for the electromechanical system of wheel drive the suppression method of auto oscillation phenomena is substantiated. The study of the algorithm performance has been carried out with the use of MATLAB Simulink program complex.Research results. The operability and efficiency of the algorithm is proved by methods of simulation mathematical modeling, which allows its further use in the development of traffic control systems. In case of braking of the vehicle equipped with antilock braking system with the function of suppression of auto oscillations on a slippery support base the reduction of amplitudes oscillation of angular velocities of wheels by 80% and braking moments by 96% is observed. When this vehicle is braked on a high adhesion base, the amplitudes are reduced by 98% in angular velocities and 81% in torques. In simulation modeling of vehicle braking dynamics on a support base with low adhesion properties it has also been shown that in these cases the evasive maneuver can be performed, which indicates on the increase in controllability and active safety of the vehicle.Conclusion. The practical value of the study lies in the possibility of using the developed algorithm for suppressing auto oscillations in practical application as part of vehicle control systems. The developed algorithm can be used on vehicles of different classes equipped with individual traction electric drive of driving wheels.

MATHEMATICAL MODELING AND NUMERICAL SIMULATION OF THE AFRICAN EDUCATION SYSTEM

In this paper, we focus on mathematical modeling and numerical simulation of the African education system. The aim is to create a mathematical model that can take into account the various parameters required for better governance of the education system in African countries. This is an ongoing problem in African educational establishments, both public and private. The aim is to provide decision-makers with a useful decision-making tool. For this resolution, we have chosen the simplex table method to arrive at the optimal solution.

Simulation of a Reverse Electrodialysis–Absorption Refrigeration Integration System for the Efficient Recovery of Low-Grade Waste Heat

The absorption refrigeration system (ARS) stands as a remarkable device that is capable of efficiently harnessing low-grade thermal energy and converting it into cooling capacity. The reverse electrodialysis (RED) system harvests the salinity gradient energy embedded in two solutions of different concentrations into electricity. An innovative RED–ARS integration system is proposed that outputs cooling capacity and electric energy, driven by waste heat. In this study, a comprehensive mathematical simulation model of a RED–ARS integration system was established, and an aqueous lithium bromide solution was selected as the working solution. Based on this model, the authors simulated and analyzed the impact of various factors on system performance, including the heat source temperature (90 °C to 130 °C), concentrated solution concentration (3 mol∙L⁻1 to 9 mol∙L⁻1), dilute solution concentration (0.002 mol∙L⁻1 to 0.5 mol∙L⁻1), condensing temperature of the dilute solution (50 °C to 70 °C), solution temperature (30 °C to 60 °C) and flow rate (0.4 cm∙s⁻1 to 1.3 cm∙s⁻1) in the RED stacks, as well as the number of RED stacks. The findings revealed the maximum output power of 934 W, a coefficient of performance (COP) of 0.75, and overall energy efficiency of 33%.

Модель для контроля качества магнитопроводов линейных электродвигателей на стадии изготовления

The article presents the results of implementing an integrated approach to quality control of linear electric motor inductors at the production stage. The approach is based on the use of mathematical modeling methods and computational experiment. To assess the quality of inductors, it is proposed to use two types of indicators: differential and integral. Differential indicators are determined by conducting a series of experiments with each tooth division of the inductor. Integral indicators allow us to assess the quality of the inductor magnetic circuit as a whole, for which criterion relationships are used. To test the effectiveness of the proposed approach and the reliability of the obtained indicators, a simulation mathematical model of an electric motor inductor with detailing down to one tooth division was developed. Based on this model, an algorithm and a computer program were created that implement the proposed method of quality control during technical testing. The program is written in the Maple software product’s own interpreted programming language and requires the user to enter the parameters of the inductor and power source. As a result of the program, the user receives a conclusion on the quality of the inductor magnetic circuit, as well as numerical values of the differential and integral quality indicators. The materials of the prototype inductor with a high-quality and low-quality magnetic core were used to test the quality criteria using mathematical modeling and computational experiment methods. The results of the experiment confirmed the feasibility of implementing the proposed approach and showed that it adequately reflects the technical quality of inductor magnetic cores. The software product created as a result of the study is intended for technical control of inductor magnetic cores during their production and information support for measures to improve their quality.

Mathematical bounds on r 2 and the effect size in case-control genome-wide association studies.

Case-control genome-wide association studies (GWAS) are often used to find associations between genetic variants and diseases. When case-control GWAS are conducted, researchers must make decisions regarding how many cases and how many controls to include in the study. Depending on differing availability and cost of controls and cases, varying case fractions are used in case-control GWAS. Connections between variants and diseases are made using association statistics, including χ 2 . Previous work in population genetics has shown that LD statistics, including r 2 , are bounded by the allele frequencies in the population being studied. Since varying the case fraction changes sample allele frequencies, we extend use the known bounds on r 2 to explore how variation in the fraction of cases included in a study can impact statistical power to detect associations. We analyze a simple mathematical model and use simulations to study a quantity proportional to the χ 2 noncentrality parameter, which is closely related to r 2 , under various conditions. Varying the case fraction changes the χ 2 noncentrality parameter, and by extension the statistical power, with effects depending on the dominance, penetrance, and frequency of the risk allele. Our framework explains previously observed results, such as asymmetries in power to detect risk vs. protective alleles, and the fact that a balanced sample of cases and controls does not always give the best power to detect associations, particularly for highly penetrant minor risk alleles that are either dominant or recessive. We show by simulation that our results can be used as a rough guide to statistical power for association tests other than χ 2 tests of independence.

Advanced self-sensing road stud: integrating deep learning-based speed detection and energy harvesting

Abstract This study introduces a self-powered and self-sensing vehicle speed detection sensor, representing a significant advancement in transportation. The system employs mechanical components like a slider crank, bevel gears, and one-way bearings for unidirectional rotation, converting translational motion into electrical energy upon the impact of vehicle tyres on road studs. The electrical power generation module, including a DC generator, rectifier, and battery circuit, captures and stores this energy. In addition to energy harvesting, the system integrates a deep learning model using long short-term memory (LSTM) networks to precisely calculate vehicle speed from the displacement signals of the road studs. Displacement data from an ultrasonic distance sensor (SR-04) is processed and fed into the LSTM network, achieving a classification accuracy of 98.90% for vehicle speed categories of low, medium, high, and overspeed. A mathematical model and MATLAB Simscape simulations were developed, followed by experimental validation using a mechanical testing and sensing system under laboratory conditions. Lab-scale testing, a maximum output power of 3.72 W and an efficiency of 62.7% were recorded at 8 Hz. Field tests were performed at various vehicle speeds. A peak voltage output of 10 V was recorded for a single phase of a three-phase DC generator at 15 km h−1. The displacement sensor beneath the road stud was used to record the relative time signal between adjacent peaks to calculate vehicle speed. The sensor is sustainable in energy and easily installable without infrastructure changes, enhances transportation efficiency, and is useful for traffic management, road safety, and smart transportation networks.

Kinetic Modelling of Ralstonia eutropha H16 Growth on Different Substrates

Due to environmental pollution and the depletion of fossil fuels, there is growing interest in the development and use of biofuels as environmentally friendly alternatives. One of the most promising biofuels is biohydrogen, hydrogen produced through sustainable processes using microorganisms such as bacteria and algae. One of the most interesting bacteria for hydrogen production is Ralstonia eutropha H16, known for its ability to produce oxygen-tolerant hydrogenases. These enzymes play a crucial role in biohydrogen metabolism and production. The aim of this work was to determine the optimal conditions (reactor type and synthetic medium composition) for the cultivation of R. eutropha H16. The culture media contained different concentrations of fructose and glycerol (mono- or double-substrate cultivation) and the experiments were carried out in a batch reactor. The initial experiments were carried out with 4 g/L fructose or glycerol in the culture medium at pH 7, T = 30 °C, and 120 rpm. The mathematical model, consisting of the growth kinetics (described by the Monod’s model) and the corresponding mass balances, was proposed. The developed model was validated using two independent experiments with different initial substrate concentrations: 2 g/L glycerol and fructose in one medium and 4 g/L fructose and 1 g/L glycerol in the second. In order to propose the optimal cultivation procedure for future research, the mathematical model simulations were performed for different reactor types (batch, fed-batch, and continuous stirred tank reactors) and different initial substrate concentrations. The most successful experiment was the one with 4 g/L glycerol, where γX = 0.485 ± 0.001 g/L of biomass was achieved. Further calculations showed that the most biomass would be produced at higher glycerol concentrations (at γG = 6.358 g/L, γX = 1.311 g/L should be achieved after 200 h of cultivation) and when using a fed-batch reactor (γX = 0.944 g/L after 200 h of cultivation).

Стохастическая модель процесса распространения препаратов платины в опухолевых тканях

Purpose: The study of the kinetics of the spatio-temporal distribution of cisplatin, as an agent capable of increasing the effectiveness of chemo-radiation therapy of solid tumors. Material and methods: The material was the data of literature on the results of experiments of various groups of authors who studied the content of platinum in tissues on biopsy materials. The method of simulation mathematical modeling (in silico) is used, based on the biological patterns of tumor growth, morphofunctional changes in the structure of tumor cells and tissues. Model is based on reaction-diffusion equation system, coefficients of which are random functions of space and time. The model takes into account the sequence of processes from intravenous administration of cisplatin and its spatial distribution in various tissues, until the excretion of its addicts from the cell. Results: The heterogeneity of the distribution of the concentration of platinum atoms in the tumor is shown. Perhaps this is due to the varying degree of vascularization of tissues, the rate of metabolism of the tumor occurring in the outer layer and in its hypoxic core. These processes lead to significant errors when evaluating the biopsy data obtained in the experiments and the analysis of platinum content in the biopsy. Conclusions: The calculation assessments of the distribution of platinum atoms in the tumor are consistent with the literature on the concentration of cisplatin in biopsy samples for carcinoma. The results of the calculations on the described model are fair, taking into account the morphological type, the size of the tumor and the plan of the administration of the drug. For other conditions (cancer types, treatment regimens, etc.), new calculations are necessary. To increase the efficiency of combined chemo-radiation therapy, cisplatin should be introduced at least 72 hours before the start of radiation therapy.

Modeling, Control and Validation of a Three-Phase Single-Stage Photovoltaic System

The central inverter topology presents some advantages such as simplicity, low cost and high conversion efficiency, being the first option for interfacing photovoltaic mini-generation, whose shading and panel orientation studies are evaluated in the project planning phase. When it uses only one power converter, its control structures must ensure synchronization with the grid, tracking the maximum power generation point, appropriate power quality indices, and control of the active and reactive power injected into the grid. This work develops and contributes to mathematical models, the principles of formation of control structures, the decoupling process of the control loops, the treatment of nonlinearities, and the tuning of the controllers of a single-stage photovoltaic system that is integrated into the electrical grid through a three-phase voltage source inverter. Using the parameters and configurations of an actual inverter installed at the power plant CRESP (Reference Center for Solar Energy of Petrolina), mathematical modeling, implementation, and computational simulations were conducted in the time domain using MatLab® software (R2021b). The results of the currents injected into the grid, voltages, active powers, and power factor at the connection point with the grid are presented, analyzed, and compared with real measurement data during one day of operation.

MODERN METHODS OF QUANTITATIVE ASSESSMENT OF THE STRUCTURE OF HYDROCARBON RESOURCES OF LARGE PETROLEUM BASINS

The article discusses modern methods of quantitative assessment of the elements of hydrocarbon resource structure in large oil and gas (petroleum) basins. The assessment is based on the law of mass distribution of hydrocarbon accumulations, i.e., the truncated Pareto distribution. The procedure developed is used for: estimation of the truncated Pareto distribution parameters and cumulative hydrocarbon volumes concentrated in pools, prediction of their number and size distribution and total resources within each size-class interval; simulation of spatial distributions of hydrocarbon accumulations with transformation of a population of HC pools into a population of fields; prediction of the number and size-class distribution of total HC resources in pools and fields, and fields distribution by the number of HC pools. The involved analytical approach based on the simulation mathematical modeling is described.

Separation Time of Aluminothermic Reduction Products for Sustainable Silicon Production

Background This work was carried out within the framework of the SisAl Pilot project, which is devoted to the environmentally friendly production of silicon. This new method relies on the aluminothermic reduction of quartz in slag, offering a more sustainable alternative to the traditional reduction of silica with carbon in submerged arc furnaces. Methods The process takes place in a rotary kiln producing silicon (Si) and alumina slag (actually, a CaO – Al2O3 slag), which must be separated at the end to extract the silicon. This separation process is analyzed through mathematical modelling and numerical simulation, as it is of industrial interest to know how much time it takes for Si and CaO – Al2O3 slag to separate once the process has ended. Generally, a multiphase flow model is used to estimate the separation time of the two components once aluminothermic reduction has ended. Results Several scenarios are considered for the numerical simulation of the separation time, namely different initial configurations and material properties of both fluids are covered. Moreover, the separation times obtained with two distinct multiphase flow models -VOF (volume of fluid) and Eulerian- are compared. Conclusions The separation times resulting from simulations using the multiphase Eulerian model are more realistic compared to those from the VOF model, which clearly tends to underestimate separation times. Furthermore, apart from the selected multiphase flow model, the density difference between silicon and alumina slag plays a critical role in determining the separation time.

Modeling and Dynamic Characteristics of Tracked Vehicle Equipped with Symmetrical Suspensions Based on Multi-Body Dynamics and Discrete Element Coupling Method

For improving the adaptability of a tracked vehicle equipped with a symmetrical suspension system on complex hilly terrain, based on the coupling method of multi-body dynamics (MBD) and discrete element method (DEM), an MBD-DEM coupling model was built and verified to explore its dynamic behaviors on soil. Firstly, according to the basic parameters of the tracked vehicle equipped with a symmetrical suspension system, a corresponding MBD model was built in Recurdyn V9R4 software. Based on the Euler–Lagrange method, the mathematical structure of the symmetrical suspension system was analyzed, and a corresponding mathematical simulation model was built in Matlab2016/Simulink to verify the MBD model. Secondly, based on the DEM theory and the parameter of the soil in a hilly area, a granular pavement model was built. Then, based on the coupling method of MBD and DEM, the corresponding MBD-DEM coupling model was built. Finally, using the MBD-DEM coupling model, the dynamic behaviors of the tracked vehicle equipped with a symmetrical suspension system under horizontal condition, the climbing condition and the obstacle crossing condition were obtained and discussed. The study results show that the proposed MBD-DEM coupling model could be used effectively to analyze the dynamic characteristics of the tracked vehicle. In addition, according to the analysis of the dynamic characteristics of the proposed tracked vehicle, the tracked vehicle equipped with a symmetrical suspension presents good adaptabilities under various working conditions.

Optimizing alkalinity control in recirculating aquaculture systems (RAS): A dynamic modelling approach

Maintaining good water quality is essential for successful fish production in land-based recirculating aquaculture systems (RAS). Numerous interdependent factors influence water quality parameters, making it difficult to evaluate which operational strategies are most favorable. Mathematical models and model simulations have proven to be powerful tools to evaluate how RAS design and operation are linked to RAS dynamics, but these models rarely implement pH and carbonate species as dynamic variables. Here, we present a dynamic model for RAS (dynRAS) that combines rates of TAN (total ammonia nitrogen) removal, fish growth, and CO2 and TAN excretion, with a reaction model for pH and the carbonate system formulated based on the law of mass action. A novel aspect of our approach is the incorporation of a dosage system modelled by a Hill-function, enabling the exploration of diverse dosing strategies for pH and alkalinity management. The model was validated based on empirical data from a pilot scale RAS system operated with a feeding regime involving 12 h of feeding per day. We found that model simulations could be used to accurately predict diurnal cycling patterns in RAS water quality parameters. Furthermore, we made use of simulations to assess how diurnal cycling varies with changing pH and alkalinity levels. Model results emphasize the complexity of pH and alkalinity control in RAS in relation to overall water quality management. Based on our simulations, we argue that what should be considered as optimal pH and alkalinity in RAS depends on the state of the system. Accordingly, optimal pH and alkalinity thresholds may vary between different RAS units and between different time points of a rearing cycle. More generally, we demonstrate how modelling and model simulations can be an effective way of getting insights into the dynamics of complex RAS interactions and provide a valuable tool to efficiently explore effects of different operational strategies on water quality parameters.

Simulation optimization and experimental validation of hydraulic impact in pruning machines

Abstract This study addresses the instability caused by hydraulic shocks in fruit tree pruning machines during operation and proposes an optimization scheme that combines simulation with experimentation. We investigated the mechanisms of load shock in the hydraulic system through mathematical modeling and LS-DYNA simulation analysis. The optimal operating parameters were determined using mechanical and orthogonal analyses: a forward speed of 4 km h−1, a pruning tool angle of 60°, and a saw blade rotation speed of 1200 r min−1. Additionally, we employed AMESim simulation to optimize the hydraulic system of the pruning machine by designing a dual accumulator configuration to effectively suppress hydraulic shocks. We validated the optimized system through simulations and experimental tests, demonstrating significant reductions in pressure fluctuations, with cutting efficiency improved by 30% and pressure fluctuations reduced by 26.7%. This study not only presents an innovative dual accumulator design but also validates its effectiveness in pruning machines through simulations and experiments, thereby enhancing the operational efficiency and stability of agricultural machinery.

Mathematical Modeling and Simulation of 1,3-Propanediol Production by Klebsiella pneumoniae BLh-1 in a Batch Bioreactor Using Bayesian Statistics.

Mathematical modeling and computer simulation are fundamental for optimizing biotechnological processes, enabling cost reduction and scalability, thereby driving advancements in the bioindustry. In this work, mathematical modeling and estimation of fermentative kinetic parameters were carried out to produce 1,3-propanediol (1,3-PDO) from residual glycerol and Klebsiella pneumoniae BLh-1. The Markov chain Monte Carlo method, using the Metropolis-Hastings algorithm, was applied to experimental data from a batch bioreactor under aerobic and anaerobic conditions. Sensitivity analysis and parameter evolution studies were conducted. The root-mean-square error (rRMSE) was chosen as the validation and calibration metric for the developed mathematical model. The results indicated that the average tolerance of glycerol was 174.68 and 44.85 g L-1, the inhibitory products was 150.95 g L-1 for ethanol and 35.56 g L-1 for 1,3-PDO, and the maximum specific rate of cell growth was 0.189 and 0.275 h-1, for aerobic and anaerobic cultures, respectively. The model presented excellent fits in both crops, with rRMSE values between 0.09 - 33.74% and 3.58 - 31.82%, for the aerobic and anaerobic environment, respectively. With this, it was possible to evaluate and extract relevant information for a better understanding and control of the bioprocess.

Frictional loss and permeability estimation of sediment in salt cavern: A combined approach of mathematical model, experimental validation, and numerical simulations

Harnessing gas storage in sediment voids presents a promising trajectory for the future construction of large-scale underground gas reservoirs in low-grade salt mines. This approach not only augments the effective gas volume but also enhances the stability of the cavern. In contrast to traditional gas injection and brine discharge process, where brine is expelled from the upper pure brine space without involving brine seepage in sediment voids, gas storage in sediment voids entails expelling brine from these spaces, thus necessitating an understanding of the brine seepage characteristics in the sediment, which remains unclear. This study presents a comprehensive approach for estimating sediment frictional loss and permeability in interconnected wells, integrating mathematical modeling, experimental validation, and numerical simulation. The mathematical principles governing sediment behavior during in-situ gas/brine injection and brine discharge tests are theoretically elucidated, accompanied by derived formulas. Experimental verification is conducted in the horizontal interconnected wells (Ha4-5) of the Huaian salt mine in Jiangsu, yielding the sediment frictional loss (0.53 MPa) and permeability (6.9 × 10−11 m2). Subsequently, a 2D cross-sectional numerical model is established using the COMSOL software, considering the measured and predicted well morphologies. The model provides insights into the relationship between sediment frictional losses and permeability, yielding an inverse calculation of the average permeability (1.016 × 10−10 m2). Simulation results depict laminar brine flow characteristics in the cavern during gas/brine injection and brine discharge processes, with frictional loss occurring as brine passes through sediment. Examination of the brine seepage and pressure fields in the sediment reveals consistent brine flow velocity after passing through the sediment. This combined approach focuses on investigating the seepage characteristics of sediment at the bottom of salt caverns, offering valuable insights for estimating frictional losses and permeability in similar salt mines.