Nonlinear Mathematical Model Research Articles

Modelling the leadership role of police in controlling COVID-19

Abstract During the recent Coronavirus disease (COVID-19) pandemic, different parts of the globe faced indefinite lockdowns. To maintain the lockdown measures, government authorities deployed security forces and police. The primary role of the police is to monitor the movement of the people and advise/guide them to follow the lockdown. In the current work, we propose a nonlinear mathematical model to study the role of police and security personnel in controlling COVID-19. It is observed that the proposed model possesses two equilibria, namely, trivial and non-trivial. We performed the stability analysis of the non-trivial equilibrium point by using the compound matrix technique. Finally, we perform a detailed numerical simulation to investigate the feasibility of the theoretical results. The current study demonstrates that police forces played a significant role in controlling the pandemic.

Non-linear super-resolution computed tomography imaging algorithm based on a discrete X-ray source focal spot model

Spatial resolution is one of the critical metrics for evaluating the performance of a computed tomography (CT) system. Traditional methods often neglected the influence of the focal spot size of the X-ray source, leading to data inconsistency and degrading the spatial resolution of the reconstructed images. Thus, this study introduces what we believe to be a novel non-linear super-resolution CT reconstruction method based on the characteristics of the X-ray source’s focal spot. The proposed method employed a discrete focal spot model and utilized measured focal spot information to formulate a non-linear mathematical model for CT imaging. Building on this model, a high-precision iterative solution method was developed. The proposed approach achieved improved data consistency during the forward projection process and employed a highly accurate solution method in the inversion process. As a result, this approach reconstructed images of higher quality compared to other methods, revealing more detailed structural information.

Mathematical modeling and computational analysis of hepatitis B virus transmission using the higher-order Galerkin scheme

Abstract Hepatitis B, a liver disease caused by the hepatitis B virus (HBV), poses a significant public health burden. The virus spreads through the exchange of bodily fluids between infected and susceptible individuals. Hepatitis B is a complex health challenge for individuals. In this research, we propose a nonlinear HBV mathematical model comprising seven compartments: susceptible, latent, acutely infected, chronically infected, carrier, recovered, and vaccinated individuals. Our model investigates the dynamics of HBV transmission and the impact of vaccination on disease control. Using the next-generation matrix approach, we derive the basic reproduction number R 0 {R}_{0} and determine the disease-free equilibrium points. We establish the global and local stability of the model using the Lyapunov function. The model is numerically solved using the higher-order Galerkin time discretization technique, and a comprehensive sensitivity analysis is carried out to investigate the impact of all physical parameters involved in the proposed nonlinear HBV mathematical model. A comparison was made of the accuracy and dependability with the findings produced using the Runge–Kutta fourth-order (RK4) approach. The findings highlight the critical need for vaccination, particularly among the exposed class, to facilitate rapid recovery and mitigate the spread of HBV. The results of this study provide valuable insights for public health policymakers and inform strategies for hepatitis B control and elimination.

Dual-Sliding-Surface Robust Control for the PEMFC Air-Feeding System Based on Terminal Sliding Mode Algorithm

The proton exchange membrane fuel cell (PEMFC) is the most widely used fuel cell, but it also has some limitations. One of the research pain points is controlling the oxygen content in PEMFCs. A moderate excess of oxygen boosts electrochemical reaction efficiency, while an appropriate oxygen content ensures system stability. In this paper, a fourth-order nonlinear mathematical model of a PEMFC stack air supply system is established to solve the problem of optimal oxygen excess ratio (OER) control under dynamic load conditions. Based on the model, a nonsingular terminal sliding mode controller (NTSMC) based on a sliding mode observer (SMO) is proposed. The NTSM exhibits superior robustness and performance compared to other sliding mode structures. Meanwhile, the SMO accurately predicts system states, facilitating precise control actions. Additionally, the dual sliding mode surfaces enhance system stability against parameter uncertainties and external disturbances. Our results demonstrate that the proposed controller outperforms traditional ones in terms of robustness and performance, which significantly enhances PEMFC system efficiency and stability.

Sugarcane, corn silage and concentrate levels in cattle diet

This study evaluated two roughage types (sugarcane and corn silage) and two concentrate feed levels (0 and 25% of the total dry matter) in the cattle diet, in a 2x2 factorial design, and compared passage rate measurements (indicator and rumen evacuation). Four Holstein-Zebu heifers cannulated in the rumen and ileum were evaluated, in a 4x4 Latin square design. Stool samples (8th - 10th day) and rumen fluid (8th day) were collected and the rumen was emptied (14th and 16th day). Treatments were compared by contrast, evaluating the effects of roughage, concentrate feed and interaction between these factors. Dry matter (DM) intake and neutral detergent fiber corrected for ash and protein (apNDF) were highest for animals fed corn silage, and DM and organic matter (OM) intake were highest when fed concentrate. There was no roughage effect on ruminal mass, but concentrate decreased ruminal NDF in the total digesta mass. The coefficients of total digestion of crude protein (CP), apNDF and non-fiber carbohydrates (NFC) were higher for sugarcane than corn silage. Concentrate feed improved the total digestibility of OM and NFC. Passage rates evaluated by the marker technique and rumen evacuation were similar. Corn silage or 25% concentrate in the cattle diet improved consumption, intake rate and nutrient digestibility. The particle passage rate can be estimated by rumen evacuation or by adjusting a nonlinear mathematical model.

Coordinated Optimization and Management of Oxygen Content and Cathode Pressure for PEMFC based on Hybrid Nonlinear Robust Control

Cathode inlet and exhaust management remains a significant challenge in proton exchange fuel cell (PEMFC). Achieving optimal oxygen content in real-time through precise control of the inlet gas is crucial for maintaining optimal output. Additionally, coordinating the air inlet and exhaust to ensure consistent cathode and anode pressures is essential for balancing the internal stack pressure and preventing nitrogen penetration, thereby enhancing PEMFC’s stability and lifespan. This paper addresses these challenges by introducing a mixed control strategy based on a fifth-order nonlinear mathematical model of the PEMFC stack cathode. Two non-singular fast terminal sliding mode structure controllers are combined as control system to optimize oxygen content and pressure control under dynamic loading conditions. The non-singular terminal sliding mode structure ensures finite-time convergence while mitigating potential singularity issues associated with traditional terminal sliding modes. The results showcase the robustness and effectiveness of the proposed control method in managing load variations, external disturbances, and PEMFC uncertainties.

Chemically reactive stagnated third‐grade magnetized nanomaterial considering modern diffusion approaches

AbstractAn incompressible boundary‐layer third‐grade nanomaterial stagnated flow confined by stretchy regime is formulated. The laminar magnetized thermal and solutal flow features the aspects of Brownian diffusion, generalized thermal‐flux, thermophoresis, and generalized solutal‐flux. The dimensionalized third‐grade steady‐state model is obtained by implementing appropriate variables. The subsequent nonlinear mathematical model is analytically computed by utilizing homotopy algorithm. The graphics demonstration of nondimensional fields (i.e., velocity, concentration, and temperature) for distinct physical variables is exhibited. The outcomes for the skin‐friction coefficient are calculated and confirmed to be precise. The analysis reveals that augmented values of material parameters escalate nanomaterial velocity while the Hartman number exhibits lower velocity. The temperature field displays a decaying trend for Prandtl number and thermal relaxation variable while contrary effects for nanoscale parameters (i.e., thermophoresis diffusive and Brownian diffusive) are reported. Besides, the nanomaterial concentration shows a decreasing trend with respect to the Schmidt number, Brownian motion, and solutal‐relaxation variable while thermophoresis parameter exhibits opposite effects. Furthermore, this study could be valuable for the design of various lab‐on‐a‐chip and thermal microfluidic devices in the field of biomedicine. Besides contributing to the creation of new devices, they may also be advantageous for performing genetic testing and developing innovative tools.

Impact of elevated carbon dioxide and temperature on crop yield: A study of autonomous and nonautonomous systems.

Agricultural crops are vital for human survival, forming the backbone of global food supply. However, the rising atmospheric carbon dioxide (CO2) level and the increasing temperature relative to the pre-industrial level are poised to impact the yields of essential staple food crops significantly. In this research, we propose and analyze a nonlinear mathematical model to investigate the effects of elevated CO2 and temperature on crop yield. Our model assumes that rising CO2 levels elevate the global average temperature, and the surface temperature initially boosts the growth rate of crops until a threshold is reached, after which the growth rate declines. We also incorporate seasonal variations into the model and perform a comprehensive analytical and numerical analysis of both the autonomous and associated nonautonomous systems. Our findings reveal a critical threshold for anthropogenic CO2 emissions, beyond which the crop yield starts to decrease. Notably, crops with high-temperature tolerance demonstrate higher yields even under elevated CO2 conditions, suggesting a viable strategy for mitigating climate change impacts: developing or utilizing crop varieties with enhanced temperature tolerance. Moreover, our analysis of the nonautonomous system uncovers periodic solutions when the corresponding autonomous system is stable. The nonautonomous system also exhibits complex dynamics, including higher-period oscillations and chaos, when the autonomous system undergoes limit-cycle oscillations. This study provides valuable insights into the interplay between CO2 level, global average surface temperature, and crop yield, offering potential strategies for safeguarding agricultural productivity in the face of climate change.

Development of mathematical models of heat conductivity for modern electronic devices with elements containing foreign inclusions

This paper considers the heat conduction process for an isotropic medium containing a foreign half-through inclusion and heated by a locally concentrated heat flow. Linear and non-linear mathematical models for determining the temperature field have been built to establish the temperature regimes for the effective operation of electronic devices. The coefficient of thermal conductivity of a non-uniform structure is represented as a whole, using asymmetric unit functions, which automatically provides the conditions of ideal thermal contact on the surfaces of materials. This results in solving one heat conduction equation with discontinuous and singular coefficients. A linearizing function was introduced to linearize the nonlinear boundary value problem. Analytical-numerical solutions of linear and nonlinear boundary-value problems have been obtained in a closed form. A linear temperature dependence of the coefficient of thermal conductivity of structural materials was chosen for a heat-sensitive medium. As a result, an analytical-numerical solution was derived, which determines the temperature distribution in this medium. On this basis, a numerical experiment was performed, the results of which are graphically displayed and confirm the adequacy of the constructed mathematical models to a real physical process. The materials of the plate and inclusion are silicon and silver. The results for these materials based on the linear and non-linear model differ by 7 %. Their slight difference is explained by the fact that the values of the temperature coefficient of thermal conductivity are small. The models built make it possible to analyze the given environments in terms of their thermal resistance. As a result, it becomes possible to improve it, and protect structures from overheating, which could lead to the failure of individual nodes and their elements and the entire electronic device

Self-financing model for cabbage crops with pest management

Smallholder farmers rely on their farm earnings to cover operating costs and generate income. That is not an easy task because of the pests, which reduce yields and generate plant protection costs. The farm yield and plant protection depend on the budget capacity of the farmer. In this work, we want to explore conditions for a sustainable and self-financing cabbage farm. We propose then a non-linear mathematical model for cabbage crops by considering the current account of the plantation as a dynamic variable. We assume that this variable increases due to the sale of cabbages, and provides for the seedling purchase, the plant protection costs, and the grower’s income. In the first part, we analyze the model without pest management. We determine how the budget must be spent and we show the existence of a double transcritical bifurcation. We quantify the seasonal yield and income, and estimate the damage due to pest herbivory. In the second part, we analyze a slightly simplified version of our model and obtain the existence of a backward bifurcation. Furthermore, we show that botanical pesticides can be used to prevent pest spread with relatively low plant protection costs.

Measurement Verification of a Developed Strategy of Inrush Current Reduction for a Non-Loaded Three-Phase Dy Transformer

This article presents the measurement verification of a novel strategy for inrush current reduction in an unloaded three-phase Dy transformer. The strategy combines appropriate pre-magnetization of transformer cores with an original control switching system using initial phase values of the supply voltage as control variables. Measurements were recorded for primary voltages and currents as well as secondary voltages during transient states at start-up under no-load conditions. Various inrush scenarios were examined across the full angular spectrum of initial phase angles, both polarities, and in regard to different pre-magnetization current values. A detailed analysis of the inrush currents was performed using proprietary automated software based on the recorded data. A comparative study with a nonlinear mathematical model of the transformer was also conducted. Additionally, key technical aspects of the designed system for implementing the proposed pre-magnetization strategy with controlled voltage energization are discussed.

Modelling pressure dynamics of oil–gas two-phase flow in double-porosity media formation with permeability-stress sensitivity

Pressure dynamics can reflect the basic characteristics of fluid flow through underground porous formation. In this research, the oil–gas two-phase flow model for a double-porosity media formation with permeability-stress sensitivity was first established for three kinds of outer boundaries. The unified governing equation was deduced by utilizing the H function. The nonlinear mathematical model in consideration of permeability-stress sensitivity was linearized by implementing the canonical perturbation transformation and then solved by using the Laplace transformation. After that, a sequence of typical log–log curves of pressure dynamics influenced by various model parameters were plotted and analyzed. These curves reflect the typical characteristic of a V shape caused by the inter-porosity fluid flow from matrix toward natural fractures. Oil saturation and permeability-stress sensitivity coefficient have much influence on the pressure dynamics. Ultimately, the established model of oil–gas two-phase flow was validated through a well-test fitting interpretation for a real condensate gas well in a sandstone formation. This research can offer insights into the pressure dynamics dominated by the oil–gas two-phase flow in naturally fractured formations and the permeability-stress sensitivity effect.

Characterization and Hygroscopic Behavior of Mentha crispa Powder Obtained by Foam-Mat Drying

Objective: Characterize and determine the hygroscopic behavior of Mentha crispa powder by obtaining adsorption isotherms and fitting nonlinear regression mathematical models. Theoretical Framework: Mentha crispa is an economically important species in the industry that, due to its perishability, is subjected to drying to increase its shelf life. Hygroscopicity is linked to physical, chemical and microbiological stability and it is necessary to understand its behavior to enable the use of biological products in regions with different climatic characteristics. Method: The powder was characterized according to water content, yield, water solubility index, pH, soluble solids, particle size and color. The adsorption isotherms were obtained by the indirect static method at a temperature of 25 °C. The BET, linear BET, Chung and Pfost, GAB, Halsey, Henderson, Langmuir, Oswin and modified Peleg models were adjusted to the experimental data. Results and Discussion: The results obtained revealed that the increase in drying temperature caused a darkening and degradation of the green hue of the powder. The powder isotherms presented type III behavior, with a sigmoidal shape common to food products. The Oswin and Henderson models are the ones that best represent the adsorption isotherms of Mentha crispa powders under the conditions studied. Research Implications: The research contributes to the literature with practical information on the hygroscopic behavior of the material. Originality/Value: Highlights the importance of adjusting nonlinear regression models to the adsorption isotherms of biological products. The models help to predict the behavior of a material during storage, informing the water content under a given environmental condition.

Assessing the multifaceted repercussions of chemical insecticides on vegetable yield and human population: A modeling study

Vegetables stand out as invaluable reservoirs of essential vitamins, minerals, antioxidants, and vital dietary elements, yet their production faces a considerable threat due to insects. To tackle this challenge, farmers spray chemical insecticides to enhance vegetable yields by controlling the insect population. Nevertheless, the presence of insecticide residues in vegetables stands as a primary contributor to acute illnesses and chronic health conditions in humans. In the present research work, we formulate a novel nonlinear mathematical model meticulously designed to scrutinize the multifaceted repercussions of chemical insecticides on vegetable yield and the human population. In our model formulation, we adopt a dynamic approach where insecticide application on vegetables in agricultural fields correlates with the insect population. However, we acknowledge the consequential impact of insecticide usage on human health, which in turn reduces the growth rate of the human population. This study determines the critical value of the spraying rate of insecticide at which the human population reaches its maximum, ensuring that human needs for vegetables are met while minimizing the adverse effects of insecticide. Since various species of insects attack vegetables in the field and different insect species have different natural mortality rates, therefore we also identify the range of natural mortality rates of insects for which vegetable yield is minimal and fluctuates with time. Further, our research reveals that if the natural mortality rate of insects in a certain crop field lies within this identified range, then farmers should increase the insecticide spraying rate to avoid this upheaval situation and stabilize vegetable yield at a higher level.

The Frank-Wulf method in modeling information systems

Subject of research: the process of choosing the best option for the structure of an information system under given conditions at the design stage. Purpose of research: to increase the efficiency and quality of the validity of decision-making, to reduce time and financial costs when choosing the structure of an information system at the design stage. Methods and objects of research: the object of research is an information system. The problem of nonlinear programming is formulated. A mathematical model of choosing the optimal variant of an information system is presented. By the method of expert assessments, information system projects with point values are determined. Information system projects with maximum values of scores are selected to determine the optimal option. The method of the conditional Frank-Wolf gradient determines the optimal solution of a nonlinear mathematical model. The essence of gradient methods is a sequential change in the value of the objective function when moving from the starting point of the domain of acceptable solutions to the optimal value of the function. The algorithm of the Frank-Wulff method includes the following steps: determining the initial value of the point of the domain of acceptable solutions, calculating the gradient, determining the optimal solution to a linear programming problem, moving to a new point, checking the condition for the end of the iterative process. The iterative process of determining the optimal solution ends when the calculated value of the calculation accuracy is less than the given value. Main results of research: preliminary projects of the information system were determined using the method of expert assessments, the optimal solution of the mathematical model of nonlinear programming by the Frank-Wolf method was found. A mathematical model for determining the optimal design of an information system will improve the efficiency and quality of the validity of decisions made, reduce financial costs and design time of information systems. The results obtained can be used in further research on this topic.

Bernstein operational matrix of differentiation to analyze the conductive, convective, and radiative non-linear sublimation model with temperature-dependent internal heat generation

Theoretical modeling of solid-vapor phase change process, known as sublimation, is of much interest in the pharmaceutical industry and freeze-drying technology. While past theoretical studies on sublimation assume that the phase change material (PCM) remains in direct contact with the heat source or sink with no heat loss due to the surrounding temperature, in most practical scenarios, PCM experiences less heat on its surface due to the loss of some amount of heat in the surrounding environment. Considering the impact of heat radiation on the porous surface is essential for ensuring the precision of the phase change process. The present study reports a theoretical model of a sublimation problem where heat generation is in proportion to the local temperature and loss of heat due to thermal radiation occurs in the porous medium. In connection with thermal radiation, a convective boundary condition is assumed at the surface of the porous body. The solution of the non-linear mathematical model is determined numerically via the Bernstein operational matrix of differentiation method. It is found that temperature-dependent heat generation enhances the temperature within the porous medium and thus, the rate of sublimation increases, while it is delayed due to heat loss through the radiation.

Analysis of a Simplified Predictive Function Control Formulation Using First Order Transfer Function for Adaptive Cruise Control

This paper presents a formulation and analysis of a low computation Predictive Functional Control (PFC), which is a simplified version of the more advanced Model Predictive Control (MPC) for an Adaptive Cruise Control (ACC) system by using a representation of first order closed-loop transfer function. In this work, a non-linear mathematical model of vehicle longitudinal dynamics is considered as a control plant. Then, a simple Proportional Integral (PI) controller is employed as an inner loop to identify the first-order relationship between its actual and desired trajectory speed according to the reasonable time constant based on the logical response of pedals pressing. To directly control the whole plant, the PFC is formulated as an outer loop to track the desired speed together with the convergence rate based on a user preference while satisfying constraints related to acceleration and safe distancing. Since PFC is formulated based on the first-order transfer function, the prediction and tuning processes are straightforward and specific to this system. The simulation results confirm that the proposed controller managed to track the desired speed while maintaining a comfortable driving response. Besides, the controller also can retain safe distancing during the car following application, even in the presence of unmeasured disturbance. In summary, this framework can avoid the need to formulate an inverse non-linear model that is typically used when deploying a hierarchical control structure to compute the throttle and brake pedals pressing as it has been replaced with an inner loop PI controller. The performance also is comparable yet more conservative due to the simplification. These findings can become a good reference for designing and improving the ACC controller, as the framework can be easily generalized for any type of vehicle for future work.

Study and Experimental Verification on Anti-Disturbance Control Strategy for Electro-Mechanical Servo Systems

With technological advances and industrial upgrading, electro-mechanical actuators (EMAs) have gradually replaced traditional hydraulic actuation systems. During operation, force servo systems inevitably suffer from external force or position disturbances, thus affecting the output performance of the system. Therefore, it is of significant engineering application value to develop EMA anti-disturbance control strategies that exhibit strong robustness and are more easily applicable to engineering practice. In this study, an open-loop transfer function of the system with command signals and disturbance signals as inputs was established based on the nonlinear mathematical models built for the core components of EMAs. To overcome the impact of external position disturbances on the motion performance of the force servo system, a proportional integral derivative (PID) controller was introduced and a high-order transfer function associated with various parameters such as speed and acceleration was derived and obtained as feedforward compensation based on the mathematical model. By incorporating a three-loop PID controller, the impact of external disturbance forces on the motion performance of the position servo system was overcome and the tracking accuracy of the system was also improved. Finally, simulation models were built using AMESim software (AMESim 2020, LMS Imagine.Lab, Roanne, France) and a dual-channel EMA performance testing system was developed. Simulation and test results indicated that both anti-disturbance control methods exhibited strong robustness and excellent anti-disturbance performance, with the control accuracy and dynamic performance almost unaffected by disturbances. This verified the correctness of the single-channel EMA anti-disturbance control strategy and the usability of the simulation model.

Integrating the triple bottom line of sustainability, resilience strategies, and product perishability consideration to design a pharmaceutical supply chain network: A COVID-19 case study

This paper aims to design a resilient and sustainable pharmaceutical supply chain network under the perishability of medicine in which a multi-objective nonlinear mathematical model is formulated. To this end, four objective functions seek to minimize total cost, maximize the social indicators, minimize CO2 emission and minimize de-resilience measures. Moreover, the three main categories of resilience strategies are integrated to mitigate the severe impacts of disruption. In order to solve the model, lexicographic goal programming is applied for small-scale problems, and NSGA-II is utilized for large-scale problems. The applicability of the proposed model is demonstrated by implementing it in a real case study during the COVID-19 situation. Also, a set of sensitivity analyses is conducted to validate the model and show the behavior of the objective functions. The results reveal the superiority of the resilient model with integrated strategies. Eventually, the Pareto front solutions are provided to quantify the trade-offs in satisfying the conflicting objective functions.

A reliable Bayesian regularization neural network approach to solve the global stability of infectious disease model

The purpose of this study is to perform the numerical results of the global stability of infectious disease mathematical model by using the stochastic computing scheme. The design of proposed solver is presented by one of the efficient and reliable schemes named as Bayesian regularization neural network (BRNN). The global stability of infectious disease mathematical nonlinear model is categorized into susceptible, infected, recovered and vaccinated. The construction of dataset is performed through the Runge-Kutta scheme in order to lessen the mean square error (MSE) by dividing the statics as training 74 %, while 13 % for both testing and endorsement. The proposed stochastic process contains log-sigmoid merit function, twenty neurons and optimization through RBNN for the numerical solutions of the global stability of infectious disease mathematical system. The best training values for each model's case are performed around 10–11. The scheme's correctness is performed by the matching of the results and the minor calculated absolute error performances. Moreover, the regression, state transmission, error histogram and MSE indicate the trustworthiness of the designed solver.