Mathematical Modeling Approach Research Articles

Effect of Pulsed Electric Fields on the Shelf Stability and Sensory Acceptability of Osmotically Dehydrated Spinach: A Mathematical Modeling Approach.

This study focused on the osmotic dehydration (OD) of ready-to-eat spinach leaves combined with the pulsed electric field (PEF) pre-treatment. Untreated and PEF-treated (0.6 kV/cm, 0-200 pulses) spinach leaves were osmotically dehydrated at room temperature for up to 120 min. The application of PEF (0.6 kV/20 pulses) prior to OD (60% glycerol, 25 °C, 60 min) lowered water activity (aw = 0.891) while achieving satisfactory product acceptability (total sensory hedonic scoring of 8). During the storage of the product (at 4, 8, 12, and 20 °C for up to 30 d), a significant reduction in total microbial count evolution was observed (9.7 logCFU/g for the untreated samples vs. 5.1 logCFU/g for the PEF-OD-treated samples after 13 d of storage at 4 °C). The selection of these PEF and OD treatment conditions enabled the extension of the product shelf life by up to 33 d under chilled storage. Osmotically treated spinach could find application in ready-to-eat salad products with an extended shelf life, which is currently not possible due to the high perishability of the specific plant tissue.

A simplified mathematical modeling approach for thermal runaway of Li(Ni0.8Co0.1Mn0.1)O2 pouch cells based on thermal runaway experimental data

Currently, the numerical modeling methods used to characterize the thermal runaway and propagation mechanisms in NCM811 pouch batteries still face numerous challenges. This is primarily due to the uncertainties in thermal runaway reactions and the immense computational demands encountered when modeling begins at the granular level of the cell. To address this issue, this study designed a series of experiments for an NCM811 pouch battery. By employing experimental data, reasonable assumptions were made regarding the combined effects of solid-state thermal conduction, electrochemical heating, and fluid-solid heat transfer through gas jet streams. A simplified thermal runaway mathematical modeling method based on experimental data was proposed, effectively tackling the problem. This framework was then applied to thermal runaway experiments on a single NCM811 battery used in this study, providing essential input parameters for three-dimensional numerical modeling of modules composed of multiple batteries in multiphysics simulation software. The simulation results derived from the proposed method were in good agreement with experimental data. This study can characterize the thermal runaway and thermal propagation characteristics of battery modules using single-cell thermal runaway experiments. Moreover, the proposed modeling approach not only predicted the experimental outcomes of the NCM811 pouch battery with reasonable accuracy but also provided smoother data, elucidating the highly fluctuating trends observed in experimental data. This method also offers guidance for designing fire prevention and smoke exhaust systems for battery packs. This study presents a novel approach for the mathematical modeling of thermal runaway and thermal propagation in battery modules using NCM811 pouch batteries, contributing to the ongoing development of lithium-ion battery module design.

Optimization and sensitivity analysis of heat transfer for Powell–Eyring fluid between rotating rolls with temperature-dependent viscosity: A mathematical modeling approach

This study explores the flow of a non-Newtonian fluid between two rolls that are counter-rotating at the same speed and of equal size. The fluid's viscosity depends on temperature, and we investigate its theoretical impact on the thickness of the sheet and other engineering parameters relevant to the process. We derive non-dimensional mass and momentum balance equations using suitable transformation and the lubrication approximation theory. The expressions for velocity distribution, pressure gradient, flow rate, temperature profile, and pressure fields have been obtained by utilizing the perturbation method. After obtaining these expressions, we compute engineering quantities such as the roll separation force, streamline, Nusselt number, and the power input required to drive both cylinders based on the system's kinematical and geometrical parameters. We also obtain numerical solutions using the finite difference method and built-in (BVP method) in Maple. Further, we use response surface methodology and analysis of variance to determine what the mathematical models mean and whether they are good enough for sensitivity and optimization analysis of the heat transmission and roll separation force. Using statistical tools such as the R2, we determine that our Nusselt number and roll separation force provide the best solution for the considered model. Additionally, it has been observed that as the Weissenberg number increases, velocity tends to rise; conversely, velocity decreases with a higher velocity ratio. Also, the temperature profile is notably influenced by the Brickman number and increases with the increase in the Brickman number. It has also been noted that as the values of velocities ratio increase, the separation points shift toward the nip region, while concurrently, the coating thickness decreases. Furthermore, we also demonstrate that compression between analytical and numerical solutions for the considered problem of fluid flow, which suggests that the results presented here are reasonable. Finally, we compare our work with published studies to validate our findings. Hence, these factors help in an efficient fluid coating process and improve the substrate life.

Measuring BIM Implementation: A Mathematical Modeling and Artificial Neural Network Approach

Measuring BIM Implementation: A Mathematical Modeling and Artificial Neural Network Approach

Integrating Computational Fluid Dynamics for Maneuverability Prediction in Dual Full Rotary Propulsion Ships: A 4-DOF Mathematical Model Approach

To predict the maneuverability of a dual full rotary propulsion ship quickly and accurately, the integrated computational fluid dynamics (CFD) and mathematical model approach is performed to simulate the ship turning and zigzag tests, which are then compared and validated against a full-scale trial carried out under actual sea conditions. Initially, the RANS equations are solved, employing the Volume of Fluid (VOF) method to capture the free water surface, while a numerical simulation of the captive model test is conducted using the rigid body motion module. Secondly, hydrodynamic derivatives for the MMG model are obtained from the CFD simulations and empirical formula. Lastly, a four-degree-of-freedom mathematical model group (MMG) maneuvering model is proposed for the dual full rotary propulsion ship, incorporating full-scale simulations of turning and zigzag tests followed by a full-scale trial for comparative validation. The results indicate that the proposed method has a high accuracy in predicting the maneuverability of dual full-rotary propulsion ships, with an average error of less than 10% from the full-scale trial data (and within 5% for the tactical diameters in particular) in spite of the influence of environmental factors such as wind and waves. It provides experience in predicting the maneuverability of a full-scale ship during the ship design stage.

Sampling, quantification and mathematical modeling in agricultural spray drift: A review

An effective spray of agrochemicals is inevitable for crop production for viable agriculture. Spraying inherently suffers from drift, which has always been one of the major concerns in agriculture, affecting the intent of agrochemical spraying and posing serious environmental hazards. Complete elimination of spray drift is impractical under field conditions but can be minimized using precision spraying techniques. Agricultural spray drift has several detrimental effects, such as environmental damage, polluting water bodies, human and animal health risks, chemical exposure, and economic losses, and may also lead to conflicts between neighboring farmers. Hence, the assessment of spray drift is a salient part of the design process of plant protection equipment to achieve maximum deposition in both chemical and biological pesticide applications. The different methods used to study the drift of a sprayer include test bench, wind tunnel and phase Doppler particle analyzer (PDPA) methods. In the field-level assessment, the fluorometric tracer sampling method conforming to ISO-22866:2005 was used. Plume dispersion, particle tracking and computational fluid dynamics (CFD) are the major mathematical modeling approaches for spray drift simulation studies. Among various methodologies and techniques, an appropriate method for spray drift assessment should be adopted in accordance with factors such as crop parameters, mode of application, and environmental conditions.

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

A Systematic Review of Sustainable Supply Chain Network Design: Optimization Approaches and Research Trends

In response to the ever-increasing pursuit of competitiveness among organizations in today’s global business landscape, the subject of supply chain management has become a vital domain encompassing a wide range of sectors and industries across the economy. The growing concern about sustainable development has prompted public and private supply chain players to incorporate the three pillars of sustainability, namely, economic, environmental, and social, into the design of their supply chain networks. This study reviews and examines the content of 102 relevant papers to discuss the mathematical models, modeling approaches, and solutions that have been explored in the existing literature on forward sustainable supply chain network design. This paper also investigates the sustainability elements and supply chain network peculiarities including design factors and decision levels. In this review, several limitations in the current literature on sustainable supply chain network design optimization models are highlighted. According to the analysis, it was found that a better understanding of the industry and its sustainability requirements and priorities is essential for designing sustainable supply chain networks that are tailored to the needs of a specific industry rather than achieving general sustainability objectives. In addition, integrating strategic, tactical, and operational decision levels in the design of supply chain networks is critical for evaluating their impact on each other in terms of sustainability. More sophisticated mathematical solution methods for dealing with real-life scenarios including nonlinearity and uncertainty sources are required. The paper concludes with new prospects of research to promote a better integration of sustainability into supply chain networks.

Flight dynamic modeling and stability of a small-scale side-by-side helicopter for Urban Air Mobility

This paper aims to explore the development of a flight dynamics model for a small-scale side-by-side helicopter and describe its trim and stability characteristics. The helicopter is considered a suitable candidate for Urban Air Mobility (UAM) solutions, because of its reliable design and low noise characteristics, but still very small knowledge is present on the mathematical modeling approaches and dynamic properties. A 14 degrees of freedom nonlinear mathematical model is developed and semi-analytical models are employed to account for the presence of the shrouds. An iterative trim routine is developed and applied with a suitable control mix that allows the use of classic helicopter controls. To control the vertical speed and roll rate, the paper assumes an equal collective pitch and lateral cyclic in the two rotors, while a uniform plus a differential longitudinal cyclic is adopted for pitch and yaw maneuvers. The paper discusses unique characteristics of the side-by-side configuration as obtained from the stability analysis: an unstable high-frequency mode, governed by the vertical velocity and pitch angle arises when the center of gravity (CG) of the vehicle is aligned or placed in front of the two main rotors. Similarly, both lateral phugoid and roll subsidence modes are sensitive to the CG location. The side-by-side configuration presents also a stable spiral mode which needs to be carefully designed.

CNS Viral Infections-What to Consider for Improving Drug Treatment: A Plea for Using Mathematical Modeling Approaches.

Neurotropic viruses may cause meningitis, myelitis, encephalitis, or meningoencephalitis. These inflammatory conditions of the central nervous system (CNS) may have serious and devastating consequences if not treated adequately. In this review, we first summarize how neurotropic viruses can enter the CNS by (1) crossing the blood-brain barrier or blood-cerebrospinal fluid barrier; (2) invading the nose via the olfactory route; or (3) invading the peripheral nervous system. Neurotropic viruses may then enter the intracellular space of brain cells via endocytosis and/or membrane fusion. Antiviral drugs are currently used for different viral CNS infections, even though their use and dosing regimens within the CNS, with the exception of acyclovir, are minimally supported by clinical evidence. We therefore provide considerations to optimize drug treatment(s) for these neurotropic viruses. Antiviral drugs should cross the blood-brain barrier/blood cerebrospinal fluid barrier and pass the brain cellular membrane to inhibit these viruses inside the brain cells. Some antiviral drugs may also require intracellular conversion into their active metabolite(s). This illustrates the need to better understand these mechanisms because these processes dictate drug exposure within the CNS that ultimately determine the success of antiviral drugs for CNS infections. Finally, we discuss mathematical model-based approaches for optimizing antiviral treatments. Thereby emphasizing the potential of CNS physiologically based pharmacokinetic models because direct measurement of brain intracellular exposure in living humans faces ethical restrictions. Existing physiologically based pharmacokinetic models combined with in vitro pharmacokinetic/pharmacodynamic information can be used to predict drug exposure and evaluate efficacy of antiviral drugs within the CNS, to ultimately optimize the treatments of CNS viral infections.

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration.

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1's contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration.

Strategic Planning and Ecological Safety Evaluation of University Campuses on Green Marketing Principles

Strategic planning of university campuses (UC) aims to harmonize nature, humans, and architectural complexes, enhancing the positive university image through specialized green and recreation zones. Highly urbanized UC areas, particularly with nearby roads, encounter increased technogenic load and pose additional health hazards. The purpose of the paper is the evaluation of the environmental safety level of the UC recreational territories on the example of campuses of Kyiv universities, located nearby highly loaded roads, using a complex of express methods of analysis, mathematical modeling and criterion-based approach, considering the main green economy principles. The scientific novelty of the paper and the authors’ contribution is in the assessment of the environmental safety level of city-type UC recreational territories being under the significant technogenic load from vehicle emissions. Such express analysis methods as densimetry, viscometry, stalagmometry, conductometry, potentiometry and optical methods, and in particular, refractometric studies have been used to assess the impact of vehicle emissions. The mathematical modeling and computational experiment have been carried out for dispersion fields of the main vehicle emissions pollutants. Ecologically acceptable distances from the road considering the specifics of recreational territory have been determined using the integral index of technogenic load. Propositions for minimizing human health hazards and improving the system of environmental monitoring of such territories have been provided and substantiated. The study also confirms the positive effects of environmental management and green marketing principles synergy, benefiting both nature and humans as well as the university image. Obtained results can be used for the design and reconstruction of UC and their recreational areas, as well as for planning roads located nearby the campuses, improving traffic on them. It is also convenient to foresee the enhancement of the environmental activities in the student research work and create student communities for monitoring the UC environmental state and the development of eco-startup projects.

Understanding the spread of typhoid fever: Combining vaccination and sanitation methods for better public health policies

Typhoid fever remains a major public health concern, affecting over nine million individuals globally each year. Mathematical modeling approaches can provide valuable insights into typhoid transmission dynamics and inform preventive strategies. In this study, we developed a compartmental model incorporating key features of typhoid epidemiology and two crucial interventions: vaccination and sanitation practices. The model stratifies the population into susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered compartments and tracks the bacterial load in the environment. We established a disease-free equilibrium and basic reproduction number R0. We also identified the endemic equilibrium and analyzed its existence. Numerical simulations demonstrated the critical impact of enhanced sanitation and vaccination in curtailing infections. Our model underscores the need for multifaceted control measures that encompass vaccine coverage, sanitation enforcement, and healthcare capacity building to mitigate typhoid in high-risk regions. This study provides a comprehensive framework to model the intricate transmission dynamics of typhoid fever, supporting informed public health policies and decision-making.

A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival

In this paper, we introduce a mathematical model given by
 \begin{equation}
 { }^c \mathfrak{D}_t^\alpha u = \nabla \cdot \mathrm{D} \nabla u + \rho f(u) \quad \text{in } \Omega,
 \end{equation}
 where $f(u)=\frac{1}{1-u/\mathrm{K}}, \, u/\mathrm{K} \neq 1, \, \mathrm{K} > 0$, to enhance established mathematical methodologies for better understanding glioblastoma dynamics at the macroscopic scale. The tumor growth model exhibits an innovative structure even within the conventional framework, including a proliferation term, $f(u)$, presented in a different form compared to existing macroscopic glioblastoma models. Moreover, it represents a further refined model by incorporating a calibration criterion based on the integration of a fractional derivative, $\alpha$, which differs from the existing models for glioblastoma. Throughout this study, we initially discuss the modeling dynamics of the tumor growth model. Given the frequent recurrence observed in glioblastoma cases, we then track tumor mass formation and provide predictions for tumor visibility timing on medical imaging to elucidate the recurrence periods. Furthermore, we investigate the correlation between tumor growth speed and survival duration to uncover the relationship between these two variables through an experimental approach. To conduct these patient-specific analyses, we employ glioblastoma patient data and present the results via numerical simulations. In conclusion, the findings on tumor visibility timing align with empirical observations, and the investigations into patient survival further corroborate the well-established inter-patient variability for glioblastoma cases.

A mathematical modeling approach to analyzing and addressing customer service inefficiencies in an international company

This paper presents a novel and in-depth mathematical approach to analyzing the inefficiencies and shortcomings of customer service in an international company based in China. By employing advanced mathematical concepts such as set theory, graph theory, probability theory, and stochastic processes, we develop a comprehensive and multi-faceted model that captures the various aspects of customer service, including unfairness, bureaucracy, failure to perform duties, irresponsibility, untruthfulness, and untrustworthiness. Our findings suggest that these issues are deeply rooted in the company's organizational structure and culture, and we propose potential solutions to address these problems. We also introduce new mathematical techniques, such as the use of hypergraphs and multi-objective optimization, to provide a more nuanced understanding of the complex dynamics at play within the customer service department.

Quantifying in vitro B. anthracis growth and PA production and decay: a mathematical modelling approach

Protective antigen (PA) is a protein produced by Bacillus anthracis. It forms part of the anthrax toxin and is a key immunogen in US and UK anthrax vaccines. In this study, we have conducted experiments to quantify PA in the supernatants of cultures of B. anthracis Sterne strain, which is the strain used in the manufacture of the UK anthrax vaccine. Then, for the first time, we quantify PA production and degradation via mathematical modelling and Bayesian statistical techniques, making use of this new experimental data as well as two other independent published data sets. We propose a single mathematical model, in terms of delay differential equations (DDEs), which can explain the in vitro dynamics of all three data sets. Since we did not heat activate the B. anthracis spores prior to inoculation, germination occurred much slower in our experiments, allowing us to calibrate two additional parameters with respect to the other data sets. Our model is able to distinguish between natural PA decay and that triggered by bacteria via proteases. There is promising consistency between the different independent data sets for most of the parameter estimates. The quantitative characterisation of B. anthracis PA production and degradation obtained here will contribute towards the ambition to include a realistic description of toxin dynamics, the host immune response, and anti-toxin treatments in future mechanistic models of anthrax infection.

A Risk-Structured Model for the Transmission Dynamics of Anthrax Disease

Anthrax, a zoonotic disease with serious public health consequences, has been the subject of rigorous mathematical and statistical modeling to better understand its dynamics and to devise effective control techniques. In this study, we propose a novel mathematical risk-structured model for anthrax disease spread that includes both qualitative and quantitative evaluations. Our research focuses on the complex interplay between host–anthrax interactions and zoonotic transmission. Our mathematical approach incorporates bifurcation analysis and stability considerations. We investigate the dynamic behavior of the proposed model under various settings, shedding light on the important parameters that determine anthrax transmission and persistence. The normalized forward sensitivity analysis method is used to determine the parameters that are relevant to reducing Rc and, by extension, disease spread. Through scenario simulation of our model, we identify intervention techniques, such as enlightenment of the populace, that will effectively minimize disease transmission. Our findings provide insights into anthrax epidemiology and emphasize the importance of effective disease management. Bifurcation investigations reveal the existence and stability of numerous equilibria, allowing for a better understanding of the behavior of the system under various scenarios. This study adds to the field of anthrax modeling by providing a foundation for informed decision-making regarding public health measures. The use of a mathematical modeling approach improves our ability to anticipate and control anthrax epidemics, ultimately helping to protect both human and animal populations.

Collaboration of thermal sensors and drones in fighting wildfires; Mathematical model and heuristic approach

The forest temperature is monitored utilizing thermal sensors. In the event of a temperature increase, these sensors promptly notify firefighters, enabling timely intervention against fires. Drones offer a potential solution for fire containment by swiftly addressing them in their nascent stages, as identified by temperature fluctuations detected by these sensors. Alternatively, if left unchecked, the situation may necessitate protracted aerial operations like the deployment of fixed-wing air tankers, helicopters, smokejumpers, and rappellers. Regrettably, such measures consume invaluable time that could be better spent combating the blaze. Recent literature on wildfires underscores the significance of collaborative approaches and the seamless integration of contemporary technologies in mitigating the expenses associated with forest fires. This study builds upon the temperature data acquired through thermal sensors to propose an all-encompassing mathematical framework designed to identify and facilitate the early extinguishment of fires using drones. The initial step involves formulating the problem through a mixed-integer linear programming model. To solve the model within expansive dimensions, a heuristic approach inspired by Clark and Wright is posited. The efficacy of this algorithm is gauged through the resolution of diverse scenarios. Promisingly, the results show the viability of collaboration of thermal sensors and drones to accurately pinpoint and extinguish forest fires. The outcomes underscore not only the protective capabilities of the suggested methodology but also its cost-effectiveness. Moreover, the approach's pioneering nature is underscored as it offers a fiscally prudent strategy that rapidly curbs uncontrollable fires.

The analysis of a novel COVID-19 model with the fractional-order incorporating the impact of the vaccination campaign in Nigeria via the Laplace-Adomian Decomposition Method

This study underscores the crucial role of COVID-19 vaccinations in managing the pandemic, with a specific focus on Nigeria. Employing a fractional-order mathematical modeling approach, the research assesses vaccination efficacy, minimum effectiveness, and duration. The model’s numerical solution is derived through the Laplace Adomian Decomposition Method (LADM), utilizing rapidly converging infinite series. Simulation results illustrate the impact of COVID-19 transmission and vaccination rates. The study concludes that implementing a vaccination strategy in an integer order proves to be the most effective approach to controlling the spread of COVID-19. These findings have significant implications for researchers, policymakers, and healthcare workers. They emphasize the central role of fractional calculus in facilitating vaccine implementation in the ongoing battle against COVID-19. The study calls for global efforts to maximize vaccination implementation for the overall benefit of public health.

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.