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Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]

Ecologists and evolutionary biologists have revealed that adaptive microevolution (i.e., allele frequency changes through time) and behavioral changes occur rapidly enough to affect contemporary ecological dynamics, and we can consider rapid adaptation for better conservation and management of wild populations. However, previous studies tended to focus on adaptation that increases population densities (e.g., evolutionary rescue), and did not pay attention to adaptation that decreases population densities (e.g., evolutionary suicide). Here, we demonstrate that controlling trait adaptation may be potentially important for decreasing population densities. One possibility is introducing "selfish" genotypes to populations. If the genotypes increase their reproductive success at the expense of population growth (e.g., cheaters in subsocial ants or coercive males in damselflies), we can decrease population densities (intraspecific adaptation load). The other possible option is diverting trait values of animals from the value that maximizes population growth (ecological trap). For example, we may be able to change behavior of a deer population by hunting so that they will not approach the best habitat with ample resources (landscape of fear). Then, we can consider the optimal allocation of our effort to directly decrease their population densities and control their trait values. However, we should carefully conduct controlling trait adaptation because it may result in unintended outcomes through modified genetic compositions and behaviors, such as increasing genetic variation of the focal population that enhances adaptation to changing environments by introducing selfish genotypes or a transient increase of population densities by modified behaviors. [ABSTRACT FROM AUTHOR]

Cellulose material is a dielectric with intricate microscopic relaxation processes due to its complex structure. However, conventional models and curve fitting methods used for tracing and analyzing these processes often fail to capture crucial dielectric information. This paper aimed to extract the Distribution of Relaxation Time (DRT), the most fundamental and effective dielectric information providing the time scale and relative contribution of all microscopic relaxation processes. First, a distributed extended Debye model with infinite branches was constructed based on the microscopic nature of dielectric relaxation. Then, an implicit equation of the DRT function was established, inspired by the mathematical principles of infinite subdivision and summation. To obtain the numeral solution of the DRT function, a regularization method was proposed and validated. Finally, the approach was applied to cellulose insulating paper with varying degradation degrees. The relaxation process with a long time constant played a significant role, and variations during the degradation process were attributed to reduced activation energy. With clear physical interpretation and robust mathematical foundation, our method sheds light on the intricate dielectric relaxation processes in cellulose. This not only enhances the theoretical understanding and practical application of cellulose materials but also provides valuable insights for the analysis and application of other materials. [Display omitted] [ABSTRACT FROM AUTHOR]

The pulp and paper sector is the fourth largest industrial sector in terms of energy use in the world. Of the numerous processes involved in paper-making by a paper machine, the dryer section is the process that consumes the largest amount of energy. A model-based method for estimating energy-saving potentials of the dryer section was put forward in the present study. It was done by four steps: establishing a mathematical model about energy consumption, determining the model parameters, benchmarking the drying performance to obtain the corresponding energy-saving measures, and estimating the energy-saving potentials by using the mathematical model. In a case study, a multi-cylinder dryer section was selected to illustrate the method. After a fundamental field test and observation, several operating problems that restricted the energy performance of paper drying were found. And then several reasonable energy-saving measures were suggested to the operators. Finally, applying the mathematic model, it was found that 0.32 ton of steam will be saved when producing 1 ton of paper in recommended operating conditions. With the designed capacity of 200,000 tons/year, the annual steam-savings will be 64,000 tons. Generally, the price of steam is 130–150 Chinese Yuan (about US$21–24) in China, and the annual economic benefits will be 8.32–9.60 million Chinese Yuan (about US$1.344–1.536 million). [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. [ABSTRACT FROM AUTHOR]

In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]

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 planetarytype 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. [ABSTRACT FROM AUTHOR]

In the ship's electrical power system, the largest percentage of a load powered by an induction machine (IM) can be represented through the fan load characteristics. Likewise, it is well known that, from the point of view of the current load, the "most problematic" way of starting the induction machine is the direct start. This paper deals with a novel analytical modeling of the IM direct start-up speed–time curve under fan load. The derived analytical expressions have been used for modeling the start of induction machines of different powers and voltage levels. Also, the obtained results have been compared with the corresponding results provided by using the realized MATLAB/Simulink model of the induction machine coupled with fan load. Moreover, the results obtained have been compared with the methods presented in the literature as regards the modeling of start-up characteristics. The experimental validation of the proposed analytical expressions for modeling the direct start of IM driving fan load has also been carried out on a 300 W machine in a laboratory environment. Both the simulations and experimental verification have demonstrated an exceptional accuracy of the derived analytical expressions. The paper also provides the implemented MATLAB code for determining the speed–time curve of IM during direct start under fan-type load. [ABSTRACT FROM AUTHOR]

The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction–diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The classes are found by translating biological knowledge into mathematical conditions and the analysis of the models further constrains the classes. Numerical simulations allow comparing single models out of the model family with available qualitative information on the solutions from observations. The method provides insight into a hierarchical order of the mechanisms. The method is applied to the clinics for liver inflammation such as metabolic dysfunction-associated steatohepatitis or viral hepatitis where reasons for the chronification of disease are still unclear and time- and space-dependent data is unavailable. [ABSTRACT FROM AUTHOR]

This paper conducts an extensive comparative analysis of numerical methods employed in modeling blood flow through arteries with Magnetohydrodynamics (MHD) and hybrid nanofluids. The study investigates the effectiveness and precision of distinct numerical approaches: Akbari Ganji's Method (AGM), Fourth-Order Runge–Kutta (RK4), Finite Volume Method (FVM), and the Finite Element Method (FEM). These methods are essential for comprehending the intricate fluid dynamics that arise in the presence of magnetic fields and hybrid nanofluids a phenomenon relevant in numerous medical applications. Blood flow is subjected to a homogeneous magnetic field in a radial direction while the magneto-hemodynamics effect is taken into account. A variety of medical, physiological, and surgical procedures, as well as the regulation of blood pressure, heat distribution, wound healing, diagnostic imaging, and drug discovery, depend on blood flow through arteries to carry out vital functions such as oxygen and nutrition delivery, organ maintenance, and wound healing. Our findings highlight that while each method has strengths, their applicability varies based on the problem's characteristics and computational resource constraints. This analysis aids researchers and practitioners in selecting the most suitable method for their modeling requirements, advancing numerical techniques for complex fluid dynamics involving MHD and hybrid nanofluids. [ABSTRACT FROM AUTHOR]

This paper examines the relationship between the magnetization behavior and crystal lattice orientations of Fe–Si alloys intended for magnetic applications. A novel approach is introduced to assess anisotropy of the magnetic losses and first magnetization curves. This method links the magnetocrystalline anisotropy energy of single crystal structures to the textures of polycrystalline materials through a vectorial space description of the crystal unit cell, incorporating vectors for external applied field and saturation magnetization. This study provides a preliminary understanding of how texture influences magnetic loss rates and the first magnetization curves. Experimental results from Electron Back-Scattered Diffraction (EBSD) and Single-Sheet Tests (SSTs), combined with energy considerations and mathematical modeling, reveal the following key findings: (i) a higher density of cubic texture components, whether aligned or rotated relative to the rolling direction, decreases magnetic anisotropy, suggesting that optimizing cubic texture can enhance material performance; (ii) at high magnetic fields, there is no straightforward correlation between energy losses and polarization; and (iii) magnetization rates significantly impact magnetization loss rates, highlighting the importance of considering these rates in optimizing Fe–Si sheet manufacturing processes. These findings offer valuable insights for improving the manufacturing and performance of Fe–Si sheets, emphasizing the need for further exploration of texture effects on magnetic behavior. [ABSTRACT FROM AUTHOR]

Cervical intraepithelial neoplasia (CIN) is the development of abnormal cells on the surface of the cervix, caused by a human papillomavirus (HPV) infection. Although in most of the cases it is resolved by the immune system, a small percentage of people might develop a more serious CIN which, if left untreated, can develop into cervical cancer. Cervical cancer is the fourth most common cancer in women globally, for which the World Health Organization (WHO) recently adopted the Global Strategy for cervical cancer elimination by 2030. With this research topic being more imperative than ever, in this paper, we develop a nonlinear mathematical model describing the CIN progression. The model consists of partial differential equations describing the dynamics of epithelial, dysplastic, and immune cells, as well as the dynamics of viral particles. We use our model to explore numerically three important factors of dysplasia progression, namely, the geometry of the cervix, the strength of the immune response, and the frequency of viral exposure. [ABSTRACT FROM AUTHOR]

In this paper, the author proposes and studies a mathematical model for the spread of coronavirus 2019. The effect of preventive programs on the control of disease is also considered. The basic reproduction number R0$$ {R}_0 $$ was computed and the results showed that forward bifurcation occured. Local and global stability of the equilibrium points of the model was studied by geometric stability method and Lyapunov function. Finally, the particular data of China which was reported for Covid‐19 were used for numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents an in‐depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters are estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (Tuberculosis and COVID‐19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high‐quality treatment, and precise isolation measures. [ABSTRACT FROM AUTHOR]

This paper introduces a groundbreaking method, Homotopy-based Fourier transform, integrating Fourier transform and Homotopy perturbation for refined nonlinear problem-solving. The modification enhances solution technique efficiency, notably accelerating convergence, particularly in solving the Korteweg–de Vries equation. Demonstrating versatility, the method effectively addresses ordinary and partial differential equations, showcasing its applicability across diverse mathematical scenarios. Moreover, the approach is extended to nonlinear dynamical systems, illustrating its robustness in handling complex dynamic behaviors. This method proves especially suitable for highly nonlinear differential equations, offering an efficient and effective tool for scientists and engineers dealing with intricate mathematical models. By significantly improving convergence rates, the Homotopy-based Fourier transform stands out as a valuable asset in unraveling the complexities of nonlinear systems across various scientific and engineering applications. [ABSTRACT FROM AUTHOR]

This paper focuses on the urgent issue of minimising the impact of pollutants on aquatic life in river ecosystems. Our innovative approach involves the integration of mathematical modelling and strategic control methods to counteract the negative consequences of industrial and agricultural activities. The model, developed in a one-dimensional context, captures the complex dynamics of species population and pollutant concentration. Using an optimisation framework, we strive to achieve a harmonious balance that limits pollution, enhances species diversity and optimises control expenditure. Ultimately, we seek to harmonise industrial progress with ecological vitality, promoting the sustainability of river ecosystems for generations to come. [ABSTRACT FROM AUTHOR]

Biofiltration is a method of pollution management that utilizes a bioreactor containing live material to absorb and destroy pollutants biologically. In this paper, we investigate mathematical models of biofiltration for mixing volatile organic compounds (VOCs) for instance hydrophilic (methanol) and hydrophobic (α -pinene). The system of nonlinear diffusion equations describes the Michaelis-Menten kinetics of the enzymic chemical reaction. These models represent the chemical oxidation in the gas phase and mass transmission within the air-biofilm junction. Furthermore, for the numerical study of the saturation of α -pinene and methanol in the biofilm and gas state, we have developed an efficient supervised machine learning algorithm based on the architecture of Elman neural networks (ENN). Moreover, the Levenberg-Marquardt (LM) optimization paradigm is used to find the parameters/ neurons involved in the ENN architecture. The approximation to a solutions found by the ENN-LM technique for methanol saturation and α -pinene under variations in different physical parameters are allegorized with the numerical results computed by state-of-the-art techniques. The graphical and statistical illustration of indications of performance relative to the terms of absolute errors, mean absolute deviations, computational complexity, and mean square error validates that our results perfectly describe the real-life situation and can further be used for problems arising in chemical engineering. [ABSTRACT FROM AUTHOR]

There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations. [ABSTRACT FROM AUTHOR]

Microscale robotics has emerged as a transformative field, offering unparalleled opportunities for innovation and advancement in various fields. Owing to the distinctive benefits of wireless operation and a heightened level of safety, magnetic actuation has emerged as a widely adopted technique in the field of microrobotics. However, factors such as Brownian motion, fluid dynamic flows, and various nonlinear forces introduce uncertainties in the motion of micro/nanoscale robots, making it challenging to achieve precise navigational control in complex environments. This paper presents an extensive review encompassing the trajectory from theoretical foundations of the generation and modeling of magnetic fields as well as magnetic field-actuation modeling to motion control methods of magnetic microrobots. We introduce traditional control methods and the learning-based control approaches for robotic systems at the micro/nanoscale, and then these methods are compared. Unlike the conventional navigation methods based on precise mathematical models, the learning-based control and navigation approaches can directly learn control signals for the actuation systems from data and without relying on precise models. This endows the micro/nanorobots with high adaptability to dynamic and complex environments whose models are difficult/impossible to obtain. We hope that this review can provide insights and guidance for researchers interested in automated magnetic microrobot control. [ABSTRACT FROM AUTHOR]

The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on Mathematical Modeling and Problem Solving at PDPTA'23, the 29th International Conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas. [ABSTRACT FROM AUTHOR]

This paper investigates a mathematical model of a star formation system, including in-fall of gas from the local environment and out-flow of gas due to supernovae explosions and perturbations. In particular, the objective is to study how the variable density of interstellar components of the system namely atomic, molecular, and stellar components, interact in the star formation cycle. Under special parametric conditions, both limit cycle and stationary state behavior are observed. This indicates a stable star formation cycle in discrete episodes and an unstable star formation cycle converging to a stationary state. Observations of duty cycles under various parameters with varying intensity of supernovae shockwaves for dwarf galaxies, showed that the system adopts a self-regulatory oscillation state beyond a particular value. Analysis of giant galaxies showed decreased oscillatory periods for higher values. This is implied by the low production rate of supernovae in dwarf galaxies, increased production of cold gas, continuation of the cyclic behavior for a longer time. Stronger shockwaves increase the rate of dissipation of gases, resulting in shredding of mass, to get transferred into a precipitous lower mass. Star-forming rate (SFR) of high-mass star systems was found to vary against higher-order perturbations of supernovae shockwave but remained the same in the case of low-mass star systems. [ABSTRACT FROM AUTHOR]

In this paper, we delve into the analysis of the Hepatitis B model, specifically the S E I A I C R model, within the scope of the Caputo–Fabrizio fractional operator. A new state variable the number of vaccinated individuals is also added to the model. This addition enriches the scope of the hepatitis B model inviting a deeper exploration of the subject matter. Our study proves the existence of a disease-free fixed point within the proposed compartmental model. To ensure the existence and uniqueness of the fixed point, we employ a fixed-point result in the b-complete b-dislocated quasi-metric space, utilizing a Geraghty-type contraction mapping. This approach establishes the fixed point of a disease-free state within the model. Furthermore, we employ a two-step Adams–Bashforth numerical scheme, serving as a validation of both the significance of fractional-order derivatives and the validity of our obtained theoretical results. Together our research presents an innovative perspective on the S E I A I C R hepatitis B model pushing the boundaries of understanding and shedding light on the dynamics of disease transmission with the impact of vaccine. [ABSTRACT FROM AUTHOR]

The sustainable implementation of resources and the transition to low-carbon construction is on the world's daily agenda. This paper describes the development of criteria for the efficient management of material resources in low-carbon construction. Net income, gross profit, balance sheets, and equity are proposed as indicators that serve as criteria for assessing the efficient use of resources. Nonlinear regression models were the methodological basis for the establishment of cause-and-effect relationships of the volume of construction of transport structures. It was established that since construction companies do not purchase materials for storage, the cost of materials for use in low-carbon technological construction work is directly proportional to the cost of construction. The volume of production in the construction industry is determined by construction costs. More efficient use of low-carbon materials reduces cost and construction waste. In this paper, we have established the relationship between the indicator of efficiency for the functioning of the construction enterprises in Ukraine and the use of low-carbon materials for the construction of transport structures. The practical value of the obtained results for low-carbon construction management lies in proving the relationship between the performance indicators of the construction enterprise (net profit, gross profit, output volume, balance sheets, and equity capital) and the use of low-carbon material resources. Our results form the basis for future research into the use of a cost-based model for low-carbon economy transition in municipalities and regions. [ABSTRACT FROM AUTHOR]

This paper presents research on the impact of the material microstructure on the performance of Molten Carbonate Fuel Cells (MCFC). The study is motivated by the need to increase the operation time of MCFC stacks. As the MCFC stacks are mainly composed of porous materials, the paper shows the impact of the porosity on both fuel cell performance and degradation rate. The study is based on the mathematical model, validated through experiments with varying microstructure parameters, achieving an overall relative error of 8%. The study evaluated the performance of MCFC using anodes with different porosity and found that increasing anode porosity from 40% to 70% led to a nearly two-fold increase in maximum power density. However, from both the degradation test and polarization curves, the optimal level of porosity for the anode is around 55%. The porosity level at 55% ensures the highest catalytic surface of the electrodes and is a compromise between the mechanical properties of the electrode and its electrochemical properties. • New approach of 0D model of MCFC including materials microstructure influence is proposed. • The new model is prepared in MS Excel and Aspen HYSYS environments. • Experimental investigation for materials with predefined microstructire parameters was performed for model validation. • Variant analysis is presented for different porosity, tortuosity and constrictivity of MCFC anode. • An optimal scenario is suggested based on modleing results. [ABSTRACT FROM AUTHOR]

When the converter transformer core is grounded at multi-points, a fault loop will be formed and a circulation will be generated, leading to local overheating of the magnetic core and decomposition of insulating oil. Therefore, the converter transformer core will be single point grounded. As a rare internal lead of converter transformer, the ground current on the core ground lead can often reflect the running state of converter transformer. In this paper, theoretical analysis, modeling simulation and experimental research are carried out on the ground current of converter transformer at one point. Firstly, according to the structure characteristics of converter transformer, the analytical modeling of ground current is carried out. Secondly, based on the structure characteristics of oil paper insulation, the equivalent capacitance of converter transformer is calculated. Then, the analytical and finite element simulation model of converter transformer is established, and the ground current of converter transformer is calculated. Finally, the correctness of the proposed scheme is verified by measuring the grounding current of converter transformer core. [ABSTRACT FROM AUTHOR]

The growing use of hydrogen as an energy carrier in the context of a renewed energy landscape is showing very promising potential. Most notably, polymer electrolyte membrane fuel cells (PEMFCs) are at the heart of the energy revolution and provide an efficient alternative to fossil fuels. The need for accurate modeling to analyze and develop the performance of PEMFCs has prompted many researchers to make major efforts in this area. This paper proposes a new approach based on an enhanced version of the bio-inspired metaheuristic salp swarm algorithm (ESSA) to identify the unknown parameters of the PEMFC model. This innovative approach was implemented by the combination of the merits of four approaches, namely the opposition-based learning, the new category of salps, referred to as exploration salps, the crossover and mutation operators, and the survival of the fittest mechanism. The newly introduced mechanisms succeed to overcome the problem of low population diversity of the SSA algorithm, accelerate its speed of convergence, strengthen the salp exploration capabilities, and improve its convergence accuracy. The performance of this technique has been tested and validated experimentally on the voltage–current characteristic on two commercial PEMFC stacks, such as 250 W and BCS500 W. The found results are compared to those of the original SSA and six recently published competitive metaheuristic algorithms simulated in various conditions as well as nine other well-cited methods from the literature. The performance comparison involved the calculation of the sum of squared errors (SSE), Standard Deviation (STD), computational speed, and statistical measurements. In this context, the best SSE and STD values obtained for Case I range 2 were 0.60132 and 1.0597 E − 14 , while those of Case II were 0.01167 and 1.1127E−15, respectively. Based on the results, the ESSA-based approach demonstrates superior performance in determining PEMFC parameters from experimental measurements, offering enhanced stability, faster convergence speed, and greater accuracy. This method thus emerges as a highly promising avenue for PEMFC parameter estimation, providing a valuable tool for optimizing fuel cell performance and design. • Modeling and parameter extraction methods for PEMFC models are investigated. • A new ESSA is proposed to tackle the parameterization problem of PEMFC. • ESSA uses OBL, exploration salps, crossover and mutation operators, and survival of the fittest mechanism. • Experimental tests show ESSA's best accuracy, convergence speed, and stability for 250 W and BCS500 W PEMFC. • ESSA is useful to develop precise simulators, and master PEMFC design and control. [ABSTRACT FROM AUTHOR]

The objective of this paper was to study the sCO2 cycle as a waste heat recovery system for a 180 kW biogas engine. The research methodology adopted was numerical simulations through two models built in different programs: Aspen HYSYS and GT Suite. The models were used to optimize the design and thermodynamic parameters of a CO2 cycle in terms of system power, system efficiency, expander, and compressor efficiency. Depending on the objective function, the sCO2 cycle could provide additional power ranging from 27.9 to 11.3 kW. Based on the calculation performed, "Recuperated cycle at maximum power" was selected for further investigation. The off-design analysis of the system revealed the optimum operating point. The authors designed the preliminary dimensions of the turbomachinery, i.e., the rotor dimension is 16 mm, which will rotate at 100,000 rpm. [ABSTRACT FROM AUTHOR]

The paper proposes approaches to the analytical structural modeling of polymers used in additive manufacturing. A comparative analysis of the empirical and analytical approaches to modeling the kinetics of the formation of a functional surface fluorine and oxygen-containing layer in polymers based on the calculation of the properties of the material using experimental data and analytical calculations has been carried out. [ABSTRACT FROM AUTHOR]

The paper proposes directed surface chemical and morphological (by gas-phase oxyfluorination) and volumetric (by photochromes) structuring of polymers of extrusion additive prototyping (polyethylene terephthalate and polyethylene terephthalate glycol) carried out in order to model and control functional, incl. transport, properties of microfluidic devices. [ABSTRACT FROM AUTHOR]

The reconfiguration problem (DPSR) in electrical distribution systems is a critical area of research, aimed at optimizing the operational efficiency of these networks. Historically, this problem has been approached through a variety of optimization methods. Regarding mathematical models, a key challenge identified in these models is the formulation of equations that ensure the radial operation of the system, along with the nonlinear equations representing Kirchhoff's laws, the last often necessitating complex relaxations for practical application. This paper introduces an alternative representation of system radiality, which potentially surpasses or matches the existing methods in the literature. Our approach utilizes a more intuitive and compact set of equations, simplifying the representation process. Additionally, we propose a linearization of the current calculation in the power flow model typically used to solve DPSR. This linearization significantly accelerates the process of obtaining feasible solutions and optimal reconfiguration profiles. To validate our approach, we conducted rigorous computational comparisons with the results reported in the existing literature, using a variety of test cases to ensure robustness. Our computational results demonstrate a considerable improvement in computational time. The objective functions used are competitive and, in many instances, outperform the best reported results in the literature. In some cases, our method even identifies superior solutions. [ABSTRACT FROM AUTHOR]

The paper proposes a two-dimensional thermokinetic model of the composite synthesis process in the mode of dynamic thermal explosion taking into account the structurization of the synthesis product. Structurization in the model is understood as a transition from amorphous to crystalline state. The model takes into account the heating of the reactor walls by thermal radiation from the device, the temperature of which can vary at different rates. Chemical reactions are described by a summary scheme that corresponds to the synthesis of Ni3Al composite. The kinetic law takes into account a possible strong inhibition of the rate of the reaction with the accumulation of the synthesis product, which is typical for reactions controlled by diffusion at the particle level. The effective thermophysical properties of the components of mixture and reaction products in the reactor depend on the properties of the constituents of the initial mixture and the fraction of reaction product. The properties of the latter also depend on the degree of structurization. The structurization process is described by a special additional parameter whose evolution is modeled by a reversible reaction. It is assumed that the structurization process starts from the moment of product appearance and continues during the cooling of the system. It is shown that synthesis results in the formation of a composite containing the initial components and the reaction product with the matrix partly in the amorphous state and partly in the structured state. The dynamics of synthesis and structurization are influenced by heating conditions and reactor size. [ABSTRACT FROM AUTHOR]

The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in-stent procedures, root growth, deep-drilling, and more. In this paper, we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a nonlinear springy wall, i.e., a wall that is laterally pushed by the beam against a nonlinear spring. Based on a simplified mathematical model, we obtain closed-form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as the transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments. [ABSTRACT FROM AUTHOR]

Two-phase flows under microgravity conditions play a crucial role in Space technology and science. Studying the behavior of dispersed droplets suspended in a gas flow and their influence on the characteristics of the carrier flow is the main task of computational modeling of turbulent two-phase flows. To understand the features and predict the behavior of such flows, along with experimental studies, it is necessary to develop mathematical models, which adequately describe all the basic physical and chemical processes in a gas-droplet environment at different scales. In this paper we obtain solutions for the problem of two droplets collision, using solutions for cumulative jets, and propose droplet collision outcome criterion. This research will focus on the process of two interacting droplets coalescence into one and coalescence with subsequent separation into two or more droplets. A semi-analytical method has been developed for application of the solution of the cumulative jet problem to the problem of droplet collision. A differential equation has been obtained that describes the following possible outcomes of droplet collision: coalescence and coalescence with subsequent separation. A criterion for determining the outcome of on-head droplet collision has been obtained. In accordance with the developed criterion, the number and size of formed droplets are obtained. The effect of collision on moving droplet evaporation in a heated atmosphere was regarded. • Solutions for the problem of two droplets collision and fragmentation are obtained. • A differential equation has been obtained that describes droplet coalescence or atomization. • A criterion for droplet fragmentation has been obtained. • The effect of collision on moving droplet evaporation in a heated atmosphere was regarded. [ABSTRACT FROM AUTHOR]

Time of day affects how well the immune system responds to viral or bacterial infections. While it is well known that the immune system is regulated by the circadian clock, the dynamic origin of time-of-day-dependent immunity remains unclear. In this paper, we studied the circadian control of immune response upon infection of influenza A virus through mathematical modeling. Dynamic simulation analyses revealed that the time-of-day-dependent immunity was rooted in the relative phase between the circadian clock and the pulse of viral infection. The relative phase, which depends on the time the infection occurs, plays a crucial role in the immune response. It can drive the immune system to one of two distinct bistable states, a high inflammatory state with a higher mortality rate or a safe state characterized by low inflammation. The mechanism we found here also explained why the same species infected by different viruses has different time-of-day-dependent immunities. Further, the time-of-day-dependent immunity was found to be abolished when the immune system was regulated by an impaired circadian clock with decreased oscillation amplitude or without oscillations. [ABSTRACT FROM AUTHOR]

The static charges and induced voltages from extra-high-voltage alternating current transmission lines (EHVACTLs) on parallel oil pipelines (POPLs) raise the risk levels for people and animals. Thus, the objective of this paper was to reduce and/or mitigate the electric field which is concentrated on POPLs by using grounded shield wires under EHVACTLs. Three techniques are employed to reduce the electric field effects on POPLs of two distinct types of transmission lines (TLs), 500 kV and 220 kV. The first technique involves raising the tower's height to improve the clearance space between the POPLs and the TL conductors. The second technique is increasing the horizontal distance between the POPLs and the nearest stressed conductors of the TL. The third technique involves placing shield wires beneath the stressed conductors of the EHVACTLs. The electric field under the EHVACTLs is calculated with and without the grounded shield wires using charge simulation method. The results of the first technique revealed that with increasing the tower height from 10 m to 15, 20, 25, and 30 m, the electric field decreased by 43.75%, 62.5%, 68.75%, and 75%, respectively. Herein, employing the second technique, the electric field intensity is reduced by 20% and 21% depending on the POPL placed at a distance from the right stressed conductor equal to the horizontal clearance between conductors of 500 kV and 220 kV, respectively. Besides, the results of the third technique proved that the shield wires under the EHVACTLs reduced the electric field intensity on the POPLs by 17.65% and 24.71% for 500-kV and 220-kV TLs, respectively. [ABSTRACT FROM AUTHOR]

Cardiovascular illnesses are a primary global health concern because they are frequently brought on by arterial stenosis. The complicated hemodynamics of blood flow via elliptically shaped arteries with numerous stenotic lesions along their top and bottom walls are examined in this paper. Carreau fluid model is used with Navier–Stokes equations in this study. The complete comparative study is done by using the Finite Element and Finite Volume Methods. This study uses commercial software to examine blood flow velocity, pressure and temperature distributions under various physiological situations at Reynolds number 30. Our results illuminate the interaction between flow dynamics, stenosis characteristics, and arterial geometry. The novelty of the work is to investigate how stenosis size, shape, and location affect pressure gradients, and flow disturbances. These observations provide helpful direction for understanding disease progression, designing treatments, and possibly new stent designs. The future direction of this research may involve further exploration of the interplay between hemodynamics and arterial stenosis by incorporating advanced computational models. Additionally, studies focusing on in vivo validation and clinical applications could enhance the translational impact of the findings. Collaborations between researchers, clinicians, and engineers may pave the way for personalized treatment strategies and innovations in cardiovascular care based on a deeper understanding of the intricate dynamics within diseased arteries. [ABSTRACT FROM AUTHOR]

Nanoparticles tethered with vasculature-binding epitopes have been used to deliver the drug into injured or diseased tissues via the bloodstream. However, the extent that blood flow dynamics affects nanoparticle retention at the target site after adhesion needs to be better understood. This knowledge gap potentially underlies significantly different therapeutic efficacies between animal models and humans. An experimentally validated mathematical model that accurately simulates the effects of blood flow on nanoparticle adhesion and retention, thus circumventing the limitations of conventional trial-and-error-based drug design in animal models, is lacking. This paper addresses this technical bottleneck and presents an integrated mathematical method that derives heavily from a unique combination of a mechanics-based dispersion model for nanoparticle transport and diffusion in the boundary layers, an asperity model to account for surface roughness of endothelium, and an experimentally calibrated stochastic nanoparticle-cell adhesion model to describe nanoparticle adhesion and subsequent retention at the target site under external flow. PLGA-b-HA nanoparticles tethered with VHSPNKK peptides that specifically bind to vascular cell adhesion molecules on the inflamed vascular wall were investigated. The computational model revealed that larger particles perform better in adhesion and retention at the endothelium for the particle sizes suitable for drug delivery applications and within physiologically relevant shear rates. The computational model corresponded closely to the in vitro experiments which demonstrates the impact that model-based simulations can have on optimizing nanocarriers in vascular microenvironments, thereby substantially reducing in vivo experimentation as well as the development costs. [ABSTRACT FROM AUTHOR]

The financial system of production-sharing contracts has more complications in comparison with other oil contracts, especially production participation contracts. The financial system and the conditions governing the payment and repayment of production-sharing contracts can be modeled at various times during the implementation of these contracts, and by using this modeling, the profitability of the plan for the parties of the contract can be evaluated, and an optimal decision can be made based on the results of the modeling In the research literature, the economic analysis of oil production-sharing contracts in the middle stages of contract implementation has not been done or very little has been done from the perspective of the investor. In this paper, economic mathematical modeling of oil production-sharing contracts with the aim of maximizing the investor's internal rate of return is presented. In this model, the data is derived from a real contract that has been delayed for approximately 30 months, as well as payment and repayment forecasts for the next 56 months. To optimize the model, we have simulated monthly payments and repayments were generated by observing their minimum and maximum values in 2000 times and each time, the rate of return was calculated, and the optimal payment and repayment amount was determined. Results specify that if the contract has been delayed, the investor can improve the internal rate of return by managing the timing of payments. [ABSTRACT FROM AUTHOR]

Cystic fibrosis (CF) is a genetic disease caused by the mutations of cystic fibrosis transmembrane conductance regulator (CFTR), the cystic fibrosis transmembrane conductance regulator gene. Cftr is a critical ion channel expressed in the apical membrane of mouse salivary gland striated duct cells. Although Cftr is primarily a Cl− channel, its knockout leads to higher salivary Cl− and Na+ concentrations and lower pH. Mouse experiments show that the activation of Cftr upregulates epithelial Na+ channel (ENaC) protein expression level and Slc26a6 (a 1Cl−:2 HCO 3 − exchanger of the solute carrier family) activity. Experimentally, it is difficult to predict how much the coregulation effects of CFTR contribute to the abnormal Na+, Cl−, and HCO 3 − concentrations and pH in CF saliva. To address this question, we construct a wild-type mouse salivary gland model and simulate CFTR knockout by altering the expression levels of CFTR, ENaC, and Slc26a6. By reproducing the in vivo and ex vivo final saliva measurements from wild-type and CFTR knockout animals, we obtain computational evidence that ENaC and Slc26a6 activities are downregulated in CFTR knockout in salivary glands. NEW & NOTEWORTHY: This paper describes a salivary gland mathematical model simulating the ion exchange between saliva and the salivary gland duct epithelium. The novelty lies in the implementation of CFTR regulating ENaC and Slc26a6 in a CFTR knockout gland. By reproducing the experimental saliva measurements in wild-type and CFTR knockout glands, the model shows that CFTR regulates ENaC and Slc26a6 anion exchanger in salivary glands. The method could be used to understand the various cystic fibrosis phenotypes. [ABSTRACT FROM AUTHOR]

• Reviews the mathematics of the EOQ/EPQ-based reverse logistics models. • It provides a condensed review of the works that stemmed from the work of Schrady (1967). • It identifies significant research gaps and provides future research directions. This paper reviews the mathematics of the economic order/production quantity (EOQ/EPQ)-based models in the reverse logistics (RL) literature. It starts with the seminal work of Schrady (A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, 14(3), 1967, 391–398) up until December 31, 2022. It provides researchers with a road map of how the mathematics has evolved since the work of Schrady and saves them time and effort by avoiding the need to review the entire RL literature. As it unifies the notations for all reviewed models, it also provides some research pointers for promising topics to be pursued. [ABSTRACT FROM AUTHOR]

The paper presents research on identifying a biomechanical parameter from a theoretical model of changes during osteoarthritis. In vitro experiments were carried out on quasi-3D chondrocyte cultures seeded on corn-starch hydrogel materials and subjected to mechanical stress on a designed and constructed stand. The results were adapted to a mathematical model and calculated on a simplified two-dimensional specimen. Numerical simulations have been performed to illustrate the growth of bone spurs. The observed changes of variables which determine osteophytes are qualitative and more correlated to the real-life observations. [ABSTRACT FROM AUTHOR]

Inter-turn faults (ITFs) are one of the most common types of faults that affect the operation of induction motors. This paper presents an ABC frame-based model to simulate the induction motor with ITFs. The proposed model is capable of representing the induction motor in both health and faulty conditions considering the introduced unbalance by ITFs in the machine circuit. The performance of the proposed model is thoroughly investigated using a detailed simulation in MATLAB/Simulink environment. Different fault cases with a variety of motor loading conditions are considered and compared with the experimental results obtained from a specially wounded 3-phase induction motor. The simulation current response of the proposed model shows good correlation with the experimentally obtained response under the same conditions. Also, a comparison between the proposed ABC model and a DQ-model is established demonstrating ABC model superior performance in simulating ITFs in induction motor. [ABSTRACT FROM AUTHOR]

Objective: The role of cerebral microvasculature in cognitive dysfunction can be investigated by identifying the impact of blood flow on cortical tissue oxygenation. In this paper, the impact of capillary stalls on microcirculatory characteristics such as flow and hematocrit (Ht) in the cortical angioarchitecture is studied. Methods: Using a deterministic mathematical model to simulate blood flow in a realistic mouse cortex, hemodynamics parameters, including pressure, flow, vessel diameter‐adjustable hematocrit, and transit time are calculated as a function of stalling events. Results: Using a non‐linear plasma skimming model, it is observed that Ht increases in the penetrating arteries from the pial vessels as a function of cortical depth. The incidence of stalling on Ht distribution along the blood network vessels shows reduction of RBCs around the tissue near occlusion sites and decreased Ht concentration downstream from the blockage points. Moreover, upstream of the occlusion, there is a noticeable increase of the Ht, leading to larger flow resistance due to higher blood viscosity. We predicted marked changes in transit time behavior due to stalls which match trends observed in mice in vivo. Conclusions: These changes to blood cell quantity and quality may be implicated in the development of Alzheimer's disease and contribute to the course of the illness. [ABSTRACT FROM AUTHOR]

In the realm of cementitious materials, integrating nanoclay shows promise in enhancing properties relevant to additive manufacturing. This paper presents a novel mathematical model that combines simple empirical dissolution/nucleation Avrami-like kinetics with a thixotropic kinetics equation. To analyze the initial exothermic peak, two sets of the calculation parameter function are built to describe the exothermic rate as a function of time, following an exponential pattern. This allows for the prediction of the changes in cumulative heat and heat rate during hydration, considering different concentrations of nanoclay. In the rheological aspect, the relationship between shear stress, shear rate, and time is modeled as a combination of exponential dependencies. This enables the prediction of the variations in shear stress with one variable while holding the other constant (either time or shear rate). By integrating these aspects, this model effectively describes both the first exothermal peak and the rheological behavior during cement hydration with the inclusion of nanoclay. Validated against experimental results, these models demonstrate good accuracy (overall below 3% error), reliability, and applicability. The findings offer valuable insights into the thermal and rheological aspects of concrete printing, enabling informed design decisions for both scientific and industrial applications. [ABSTRACT FROM AUTHOR]

Abstract—To describe secular geomagnetic variation on geological timescales, statistical models have been widely used in recent decades. Currently, the most popular among these is the TK03 model (Tauxe and Kent, 2004). As other statistical models, TK03 numerically characterizes the amplitude of secular geomagnetic variation and the shape of the distribution of paleomagnetic directions which are thought to directly reflect the directions of the geomagnetic field on the considered interval of geological time. For this purpose, three main parameters are used: the scatter Sb (or S) of the virtual geomagnetic poles, the elongation E of the distribution of paleomagnetic directions, and the elongation direction of the distribution of paleomagnetic directions. The correct use of these parameters to describe paleosecular variation requires the fulfillment of certain, sometimes rather strict conditions. These conditions for parameters Sb and E were considered in a number of previous publications, while the limits and conditions of application of have not been studied in detail so far. The results of mathematical modeling presented in this paper allow us to evaluate the stability of the calculated parameter values as a function of sampling latitude, the number of samples used to determine this parameter, the length of the time series from which this parameter is estimated, as well as the inclination shallowing and the degree of averaging if is estimated from sedimentary rocks. We also consider the extent to which the parameter can be sensitive to the presence and characteristics of the equatorial dipole component in the total geomagnetic field. [ABSTRACT FROM AUTHOR]

Along with the developing technology, obesity and diabetes are increasing rapidly among people. The identification of diabetes diseases, modeling, predicting their behavior, conducting simulations, studying control and treatment methods using mathematical methods has become of great importance. In this paper, we have obtained numerical solutions by considering the glucose-insulin fractional model. This model consists of three compartments: the blood glucose concentration (G), the blood insulin concentration (I) and the ready-to-absorb glucose concentration (D) in the small intestine. The fractional derivative is used in the sense of Caputo. By performing mathematical analyzes for the Glucose-Insulin fractional mathematical model, numerical results were obtained with the help of the Euler method and graphs were drawn. [ABSTRACT FROM AUTHOR]

In this paper, the variational iterative method (VIM) with the Laplace transform is utilized to solve the nonlinear problems of a simple pendulum and mass spring oscillator, which corresponds to the Duffing equation. Finding the Lagrange multiplier (LM) is a significant phase in the VIM, and variational theory is frequently employed for this purpose. This paper demonstrates how the Laplace transform can be utilized to locate the LM in a more efficient manner. The frequency obtained by Laplace-based VIM is the same as that defined in the already existing methods in the literature in order to ensure the clarity of the results. Numerous analytical techniques can be used to solve the Duffing equation, but we are the first to do it using a Laplace-based VIM and a distinctive LM. The fundamental results of my paper are that LM is also the same in the Elzaki transformation. In the vast majority of instances, Laplace-based VIM only requires one iteration to arrive at an answer with high precision and linearization, discretization or intensive computational work is required for this purpose. Comparing analytical results of VIM by Laplace transform to the built-in Simulink command in MATLAB which gives us the surety about the method's applicability for solving nonlinear problems. Future work on the basic pendulum may examine the effects of nonlinearities and damping on its motion and the application of advanced control mechanisms to regulate its behavior. Future research on mass spring oscillators could examine the system's response to random or harmonic input. The mass spring oscillator could also be used in vibration isolation to minimize vibrations from one building to another. [ABSTRACT FROM AUTHOR]

Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]