Mathematical Modeling Techniques Research Articles

Metaphorical meaning dynamics: Identifying patterns in the metaphorical evolution of English words using mathematical modeling techniques

Abstract Conceptual metaphor theory has been criticized due to its emphasis on concepts instead of words and its top-down direction of analysis. In response to these criticisms, this paper employs a new strategy, utilizing established mathematical modeling methods to allow a systematic, quantitative analysis of the entire dataset produced by the Mapping Metaphor project at the University of Glasgow. This dataset consists of 9609 words performing 18916 metaphorical mappings between 414 domains. The data is represented as a network consisting of 414 nodes, the domains, connected by shared words. Words are represented by groups of directed mappings between all domains in which they occur. This is made possible by the use of a directed hypergraph representation, a tool commonly used in discrete mathematics and various areas of computer science but not previously applied to the metaphorical meanings of words. Examining the dataset as a whole, rather than focusing on individual words or metaphors, allows global patterns of behavior to emerge from the data without pre-filtering or selection by the authors. Outcomes of the analysis relating to the distributions of source and target domains within the network, the growth mechanisms at work in the spread of metaphorical meanings and how these relate to existing concepts in CMT are discussed.

Mathematical models for sustainable fisheries management in U.S. waters: Balancing economic growth and conservation

Sustainable fisheries management is critical for balancing the dual objectives of economic growth and environmental conservation, particularly in U.S. waters where overfishing, habitat degradation, and fluctuating marine ecosystems pose significant challenges. This review explores the role of mathematical models in addressing these challenges and guiding fisheries management decisions. Various models, including population dynamics, bioeconomic, and ecosystem-based approaches, are examined for their utility in setting sustainable catch limits, assessing stock health, and predicting ecosystem changes. Through case studies of U.S. fisheries, the paper highlights how these models have been implemented within the framework of federal regulations, such as the Magnuson-Stevens Act, to achieve sustainable yields while supporting economic growth. The review also identifies trade-offs between short-term economic gains and long-term conservation goals, emphasizing the need for adaptive management strategies. Finally, it explores emerging innovations in mathematical modeling techniques, such as artificial intelligence, and provides policy recommendations to enhance the integration of these models into sustainable fisheries management. This paper underscores the importance of mathematical models as essential tools in ensuring the future viability of U.S. fisheries, balancing economic prosperity with the preservation of marine ecosystems.

Experimental and numerical investigation of heat transfer characteristics of radiator using Graphene Amine-based nano coolant

This work presents experimental and numerical investigations on enhancing the heat transfer performance of automobile radiators with nano-coolant flowing with different mass flow rate and at different inlet temperatures conditions. Thermal management is critical as it dictates a system's overall power output, performance, efficiency and energy utilisation. Radiators and Thermal management systems for batteries are vital in keeping automobiles operating under optimal conditions. Conventional coolants lack the ability to keep up with the increasing performance requirements of thermal management systems. Nanocoolants represent a cutting-edge advancement in heat transfer fluid, boosting conductivity without compromising essential fluid dynamics of the cooling solutions. Several investigators have worked on various nanocoolants, but less work is done on radiators. In view of this, experimental and numerical investigations were done on radiator heat transfer performance using Graphene Amine based nanocoolant with varied coolant temperatures (50 °C–80 °C) and flow rates (3 l/min to 9 l/min). Thermophysical properties of nanocoolants, such as density, thermal conductivity, viscosity, specific heat, and Prandtl number, were determined by experimental and mathematical modelling techniques and were comparable with an average deviation of 5 %. Compared to the base fluids of De-ionised water and ethylene glycol combinations, Graphene Amine based nanocoolant has exhibited advancements in heat transfer properties, showing elevated Nusselt numbers, heat transfer coefficients and heat transfer rates. The investigation into the thermal transfer properties of nanocoolants utilizing theoretical and real-world experiments shows consistency with an average deviation of 20 %. Maximum heat transfer enhancement of 154.3 % and maximum heat transfer coefficient of 3209.52 W/m2K was found for Graphene Amine at 80 °C with coolant flowing at 9 l/min, which is 83.1 % higher when compared to De-ionised Water.

Advanced Modeling of Hydrogen Turbines Using Generalized Conformable Calculus

This article addresses critical challenges in the transition to clean energy sources by highlighting the importance of advanced mathematical modeling and computational techniques in turbine design and operation. Specifically, we extend and generalize the work of Camporeale to advance the modeling of hydrogen turbine systems. By utilizing conformable calculus, we develop dynamic equations that analyze key aspects of turbine performance, including temperature variations in turbine blades, angular velocities of rotating shafts, and mass--energy balances within the plenum and combustion chamber. Furthermore, we incorporate Kirchhoff's equation in its generalized conformable integral form, enhancing the precision of energy balance calculations and improving the representation of heat transfer processes in the combustion chamber. This methodology introduces novel perspectives in hydrogen turbine research, contributing to the advancement of sustainable and efficient technologies. Our comprehensive approach aims to provide more accurate and efficient predictions of turbine behavior, thereby impacting the design and optimization of hydrogen-based clean energy systems.

Exploring arteriolar atherosclerosis: laminar blood flow across stenosis with fluid-structure interaction and gravitational effects

Abstract In response to the unanswered relevant questions surrounding atherosclerosis, it becomes imperative to investigate arterioles using sophisticated mathematical modelling techniques to shed light on critical stress and strain patterns influenced by gravity. The primary objective of this study is to scrutinize flow characteristics and probe stress and strain distributions experienced by the intima layer of arterioles, encompassing coronary, renal, cerebral, mesenteric, and pulmonary arteries, under gravitational forces. This investigation employs a fluid-structure interaction methodology utilizing arbitrary Eulerian–Lagrangian formulation. The study delves into blood flow characteristics within coronary, renal, cerebral, mesenteric, and pulmonary arterioles using the fluid-structure interaction technique, employing an arbitrary Eulerian–Lagrangian formulation. It thoroughly examines various biomechanical parameters such as the Cauchy–Green stress tensor, Principal strain, Piola–Kirchoff stress tensor, deformation tensor, and volume strain along the intima layer under the gravitational influence, elucidating vulnerable regions prone to endothelial dysfunction. Higher values of δV are found at the left shoulder and in the intima’s post stenosis area due to the pressure gradient along the flow channel, whereas other intima regions show a null volume strain. A thorough understanding of stress distribution is essential to create focused therapies to lessen vascular health problems. The stress in the post-stenosis region seems to affect the endothelial layer to a significant extent.

Designing resilient supply chain networks: a systematic literature review of mitigation strategies

AbstractWith increased globalisation supply chain (SC) disruption significantly affects people, organisations and society. Supply chain network design (SCND) reduces the effects of disruption, employing mitigation strategies such as extra capacity and flexibility to make SCs resilient. Currently, no systematic literature review classifies mitigation strategies for SCND. This paper systematically reviews the literature on SCND, analysing proposed mitigation strategies and the methods used for their integration into quantitative models. First to understand the key failure drivers SCND literature is categorised using geography, with local, regional or global disruptions linked to vulnerable sections of a SC. Second, the strategies used in mathematical models to increase SC resilience are categorized as proactive, reactive, or SC design quality capabilities. Third, the relative performance of mitigation strategies is analysed to provide a comparison, identifying the most effective strategies in given contexts. Forth, mathematical modelling techniques used in resilient SCND are reviewed, identifying how strategies are integrated into quantitative models. Finally, gaps in knowledge, key research questions and future directions for researchers are described.

Maximizing Onboard Hydrogen Storage Capacity by Exploring High-Strength Novel Materials Using a Mathematical Approach.

Hydrogen fuel holds promise for clean energy solutions, particularly in onboard applications such as fuel cell vehicles. However, the development of efficient hydrogen storage systems remains a critical challenge. This study addresses this challenge by exploring the potential of high-strength novel materials, including glass, to maximize onboard hydrogen storage capacity. A mathematical approach was employed to evaluate the feasibility and efficacy of various high-strength materials for hydrogen storage. This study focused on capillary arrays as a promising storage medium and utilized mathematical modeling techniques to estimate the storage capacity enhancement achievable with different materials. The analysis revealed significant variations in storage capacity enhancements in different high-strength novel materials, with glass having promising results. Glass-based materials demonstrated the potential to meet or exceed US Department of Energy (DOE) targets for both gravimetric and volumetric hydrogen storage capacities in capillary arrays. By leveraging a mathematical approach, this study identified high-strength novel materials, including glass and polymers, capable of substantially improving onboard hydrogen storage capacity: 29 wt.% with 40 g/L for quartz glass and 25 wt.% with 38 g/L for Kevlar compared to 5.2 wt.% with 26.3 g/L from a conventional type IV tank. These findings underscore the importance of material selection in optimizing hydrogen storage systems and provide valuable insights for the design and development of next-generation hydrogen storage technologies for onboard applications.

Determining the coordinates of unmanned aerial vehicles

The purpose of the work was to develop a method for determining unmanned aerial vehicles’ (UAVs) coordinates, trajectory and parameters of their spatial movements by means of kinematic projection. The paper analyses the use of technologies for determining coordinates and spatial movements of aircraft trajectories. The principle of the kinematic scheme of fixing moving objects by means of orthogonal and kinematic design has been developed. The principle scheme of determining UAV coordinates by kinematic projection was studied. The theoretical mathematical dependencies of the determination and calculations of the coordinates of spatial movements of unmanned aerial vehicles have been practically verified. The main object of research in this work was the theory of kinematic design as a means of graphically displaying the patterns of spatial movements of objects. The subject of the study was the specific features of searching and recording the trajectories of spatial movements of unmanned aerial vehicles in order to determine the coordinates of their instantaneous location in space. In the process of conducting theoretical and experimental research, methods and techniques of physical and mathematical modelling of fast-moving processes and mathematical statistics of analysis and classification of their results were used. The basis of the experimental study was the theory of mapping coordinates and trajectories of spatial movements of moving objects by means of graphic geometry when combining classical orthogonal design with dynamic features of kinematic design. For an objective assessment of the results of the theoretical and experimental study of the dynamics of objects moving in space, the classical theory of research planning with a mathematical apparatus for processing their results was used. Graphical models of UAV coordinate fixation were made with the use of computer technology and the AutoCAD graphic editor software.

Potential for eliminating COVID-19 in Thailand through third-dose vaccination: A modeling approach.

The COVID-19 pandemic continues to pose significant challenges to global public health, necessitating the development of effective vaccination strategies to mitigate disease transmission. In Thailand, the COVID-19 epidemic has undergone multiple waves, prompting the implementation of various control measures, including vaccination campaigns. Understanding the dynamics of disease transmission and the impact of vaccination strategies is crucial for guiding public health interventions and optimizing epidemic control efforts. In this study, we developed a comprehensive mathematical model, termed $ S{S}_{v}I{H}_{1}C{H}_{2}RD $, to elucidate the dynamics of the COVID-19 epidemic in Thailand. The model incorporates key epidemiological parameters, vaccination rates, and disease progression stages to assess the effectiveness of different vaccination strategies in curbing disease transmission. Parameter estimation and model fitting were conducted using real-world data from COVID-19 patients in Thailand, enabling the simulation of epidemic scenarios and the exploration of optimal vaccination rates. Our results showed that optimizing vaccination strategies, particularly by administering approximately 119,625 doses per day, can significantly reduce the basic reproduction number ($ {R}_{0} $) below 1, thereby accelerating epidemic control. Simulation results demonstrated that the optimal vaccination rate led to a substantial decrease in the number of infections, with the epidemic projected to be completely eradicated from the population by June 19, 2022. These findings underscore the importance of targeted vaccination efforts and proactive public health interventions in mitigating the spread of COVID-19 and minimizing the burden on healthcare systems. Our study provides valuable insights into the optimization of vaccination strategies for epidemic control, offering guidance for policymakers and healthcare authorities in Thailand and beyond. By leveraging mathematical modeling techniques and real-world data, stakeholders can develop evidence-based strategies to combat the COVID-19 pandemic and safeguard public health.

DYNAMICS AND STABILITY OF EMERGENCY VEHICLES ON DIFFICULT TERRAIN

This research paper examines the nuances of the dynamics and stability of emergency vehicles when maneuvering over complex terrain, offering a multifaceted analysis that combines theoretical modeling and empirical research. Central to the considerations is the study of the interaction between vehicle design and features of various landscapes, including mountain, forest and urban environments. The research uses a synergistic approach that interweaves advanced mathematical modeling techniques such as computational fluid dynamics and finite element analysis with experimental validation in real-world conditions. The methodology clarifies the critical role of vehicle design parameters, such as suspension tuning and aerodynamic properties, in determining vehicle performance in challenging environments. The study highlights the relevance of terrain-dependent speed limits and maneuvering strategies, advocating for modular vehicle designs and terrain-independent technologies. The paper not only makes a significant contribution to the optimization of emergency vehicles, but also paves the way for future research in the areas of artificial intelligence-driven control systems, sustainable propulsion technologies, and predictive performance modeling. Integrated solutions in this area re key to improving the efficiency and safety of rescue operations in diverse and challenging environments.

Optimizing faade shading design for public buildings in China's hot and humid regions: A comprehensive analysis

This paper presents a comprehensive analysis of faade shading design methods tailored for public buildings in Chinas hot and humid regions. Through a multidisciplinary approach integrating climatic analysis, quantitative modeling, and architectural principles, the study investigates the critical role of shading in enhancing energy efficiency and occupant comfort. Highlighting the climatic characteristics and solar radiation impact specific to hot and humid areas, the analysis underscores the necessity of tailored shading solutions. A review of traditional and modern shading strategies, alongside case studies, elucidates successes, limitations, and emerging trends. The paper also delves into mathematical modeling techniques for optimizing shading efficiency and explores the integration of shading with architectural design and renewable energy systems. The findings advocate for a holistic approach to faade shading, emphasizing its significance in achieving sustainable building practices in hot and humid climates.

SUSTAINABLE COVID-19 CONTROL MEASURES: A MATHEMATICAL MODELLING STUDY

Mathematical modelling techniques have become essential in predicting the consequences of viral disease outbreaks and in planning sustainable preventative measures to curb their transmission dynamics. To better understand the sustainable evolution of the control measures’ impacts on COVID-19 transmissions, a reaction-diffusion system is employed to describe the epidemiological phenomenon through two processes: (i) A reaction process of SEIRS-type (Susceptible, Exposed, Infected, Recovered, and Susceptible) kinetics; and (ii) a diffusion process that models local dispersal of individuals through the incorporation of spatial dimension. Optimal control theory and numerical simulation studies are performed to examine the combined effects of reinfection, spatial dispersal process, and distinct control measures on the severity of the outbreaks. The results indicate the effectiveness of implementing adequate control measures vaccination and treatments to prevent further disease outbreaks and minimise the number of infected cases. The insights from these modelling studies benefit different stakeholders, e.g., public health practitioners and policymakers in devising sustainable COVID-19 management plans to prepare for endemicity and deal with large-scale disease outbreaks in the future.

Analysis of decentralized drone control model and interception trajectory calculation

Subject matter: This article is devoted to the study of applying the innovative Cascade DataHub method for optimizing the management of automated mobile systems, especially unmanned aerial vehicles. The work analyzes both theoretical and practical aspects of implementing this method across various application sectors. Goal: The objective of the study is to conduct a comprehensive analysis of contemporary models and methods for managing a group of drones, focusing on decentralized approaches. Additionally, the study aims to develop effective algorithms for optimizing the interception trajectory, with the goal of enhancing the accuracy and reliability of managing complex automated systems through increased real-time data integration. The research is directed towards identifying the potential advantages of this method in reducing system response times and improving decision-making accuracy. Tasks: The main tasks of the research include the development of comprehensive algorithms for rapid processing and analysis of large volumes of data from various sources, creating reliable communication protocols to ensure connection stability under extreme conditions. Another important task is the integration of these developments into practical applications, which will increase their effectiveness in real operational conditions. Methods: To achieve the set goals, advanced techniques of mathematical modeling, statistical analysis, machine learning, and deep learning are used. The application of these techniques ensures high accuracy and reliability of the management systems. Results: During the research, it was found that the Cascade DataHub method significantly reduces the response time of systems to commands, increases the accuracy of task execution, and decreases data loss during their transmission. The implementation of this method also contributes to a more efficient distribution of resources among automated units, which is critically important for missions requiring high coordination and time synchronization. Conclusions: A comprehensive analysis of contemporary models and methods for managing a group of drones with a focus on decentralized approaches has been conducted. Effective algorithms for optimizing the interception trajectory have been developed, aimed at enhancing the accuracy and reliability of managing complex automated systems through real-time data integration. The study revealed the potential advantages of the proposed method in reducing system response times and improving decision-making accuracy, contributing to the more efficient functioning of automated systems.

AN ENGINEERING APPROACH TO THE STUDY OF THE PROCESSES OF DOUGH FLOW IN THE PRODUCTION OF PASTA AT AGRO-INDUSTRIAL ENTERPRISES

Background. In modern conditions, the provision of domestic pasta produced from durum wheat varieties on modern technological equipment is becoming important. At the same time, the quality of the finished pasta is also determined by the rheological properties of the pasta dough when passing through the pasta press matrix, which determined the purpose of the study to develop a method of computational evaluation for calculating the relationship between the speed parameters of the flow of pasta dough in the cylindrical sections of the channels of the molding matrix with pressure drops to overcome viscous resistance, the dimensions of the structural elements of the channel, as well as with indicators of the rheological properties of pasta dough. Materials and methods. To study the flow of pasta dough, baking flour of the highest grade M-54 28 was chosen as a raw material in stepped cylindrical channels. The applied rheological model is described and a technique for mathematical modeling of the flow parameters of pasta dough in cylindrical channels is given. Due to the small contribution of the pasta dough shear strength to the total pressure loss, a rheological model of a nonlinear-viscous medium is used, which is described by a power equation containing physically determined constants. Neglecting the elastic deformations of the dough due to their smallness, we assumed the condition of constancy of the volumetric productivity for each cross section of the channel. Results. Analytical dependencies are presented that relate the change in velocity over the channel cross section to the pressure developed necessary to overcome the viscous resistance, as well as to the radii and length of the channel, and to the rheological properties of the pasta dough. These dependences formed the theoretical basis of the method for calculating the parameters of pasta dough flow in cylindrical channels. Conclusion. On the example of an industrial matrix of a pasta press, made in the form of a system of cylindrical channels of a stepped-variable diameter in the preforming zone, calculations were made to determine the average and maximum flow rates of pasta dough in each section of the channel and the developed pressure. The results of the research can be used in engineering practice when designing new matrices for forming pasta dough and in the production processes of enterprises to calculate their production capacities.

A Mathematical Model of the Dynamics of the Transmission of Monkeypox Disease Using Fractional Differential Equations

AbstractThis study presents a comprehensive analysis of the dynamics of Mpox viral transmission using a compartmental mathematical model. The model incorporates the impact of immunization, isolation, and hospitalization on disease management, as well as the interaction between humans and rodents. Through numerical simulations, the study highlights the effectiveness of isolation in mitigating disease transmission and emphasizes the significance of mathematical modeling and simulation techniques in understanding disease dynamics. The utilization of Caputo's fractional differential equation in the human dynamical model is shown to be effective in regulating disease in all compartments. Sensitivity analysis is conducted to identify the most influential parameters in virus transmission. The findings contribute valuable insights for public health strategies and provide a foundation for further research in disease control and management.

Efficient bioreduction of 4-phenyl-2-butanone to drug precursor (S)-4-phenyl-2-butanol by a whole-cell biocatalyst using a novel hybrid design technique

Asymmetric synthesis is a critical tactic in pharmaceutical industries for creating chiral medications as it allows an enantiomer to be obtained in synthetic chemistry. The asymmetric bioreduction processes by biocatalysts have shown significant potential in producing chiral alcohols. The amount of substrate and the production method of the biocatalytic synthesis of (S)-4-phenyl-2-butanol ((S)-2) are not still desired levels. Furthermore, the biocatalytic asymmetric reduction of 4-phenyl-2-butanone (1) to (R)- or (S)-4-phenyl-2-butanol did not use any mathematical modeling techniques. In this study, the asymmetric bioreduction of 1 was carried out in this work employing Lactobacillus paracasei BD71 biocatalyst and a novel hybrid design-based optimization approach. By using the hybrid design technique, the optimal circumstances were discovered to be pH = 7, temperature = 29 °C, incubation period = 66 h, and agitation speed = 189 rpm. Also, the enantiomeric excess (ee) and conversion could be 99.15 % and 98.19 %, respectively. Next, (S)-2 was acquired to be ee: 99 %, conversion: >99 %, and yield: 97 % from the optimum bioreduction conditions. Furthermore, 14.08 g of 1 under optimal conditions was entirely transformed into (S)-2 (13.84 g, 97 % isolated yield). This study is the first research attempt to use a biocatalyst and an innovative and new hybrid design-based optimization approach to fabricate enantiopure (S)-2 at a high gram scale. This work has successfully demonstrated that the new hybrid design-based optimization technique is applicable to biocatalytic asymmetric reduction processes.

Mathematical modeling and optimization technique of anticancer antibiotic adsorption onto carbon nanocarriers

This study employs a combination of mathematical derivation and optimization technique to investigate the adsorption of drug molecules on nanocarriers. Specifically, the chemotherapy drugs, fluorouracil, proflavine, and methylene blue, are non-covalently bonded with either a flat graphene sheet or a spherical C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} fullerene. Mathematical expressions for the interaction energy between an atom and graphene, as well as between an atom and C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} fullerene, are derived. Subsequently, a discrete summation is evaluated for all atoms on the drug molecule utilizing the U-NSGA-III algorithm. The stable configurations’ three-dimensional architectures are presented, accompanied by numerical values for crucial parameters. The results indicate that the nanocarrier’s structure effectively accommodates the atoms on the drug’s carbon planes. The three drug types’ molecules disperse across the graphene surface, whereas only fluorouracil spreads on the C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} surface; proflavine and methylene blue stack vertically to form a layer. Furthermore, all atomic positions of equilibrium configurations for all systems are obtained. This hybrid method, integrating analytical expressions and an optimization process, significantly reduces computational time, representing an initial step in studying the binding of drug molecules on nanocarriers.

Evaluation of the Microbiological Quality of Some Marketed Spices in Lomé (Togo)

This comprehensive study delves deeply into the intricate process of optimizing fish product distribution routes in the expansive Western Kenya region, with an explicit focus on understanding and refining the operational strategies employed by Victory Farm Limited. Leveraging the Hungarian Method, celebrated for its unparalleled effectiveness in the realm of combinatorial optimization, the research endeavors to meticulously evaluate and fine-tune the shortest and most efficient transportation routes for seamlessly ferrying fish products from Kisumu Logistic Center to a myriad of distribution depots and retail markets scattered across the Western Kenya region's diverse landscape. Through an exhaustive analysis that spans road networks, logistical constraints, and the ever-evolving dynamics of market demand, this study systematically identifies and delineates optimal routes that not only minimize the distance traversed but also significantly mitigate associated transportation costs, all while steadfastly adhering to stringent standards for punctuality and product quality. Furthermore, by synergistically integrating sophisticated mathematical modeling techniques, meticulously executed through Python programming, with a robust foundation of real-world data meticulously sourced from Victory Farm Limited, this research endeavors to provide invaluable insights and pragmatic recommendations aimed at fortifying and enhancing the overall efficiency and profitability of fish product distribution operations throughout Victory Farm Western Kenya depots. In essence, the anticipated outcomes of this study transcend the realm of theoretical conjecture, poised instead to catalyze tangible advancements in the sustainable development of the region's burgeoning aquaculture sector, thereby fostering a lasting legacy of economic prosperity and environmental stewardship for generations to come.

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

On the efficacy of facial masks to suppress the spreading of pathogen-carrying saliva particles during human respiratory events: Insights gained via high-fidelity numerical modeling.

Respiratory fluid dynamics is integral to comprehending the transmission of infectious diseases and the effectiveness of interventions such as face masks and social distancing. In this research, we present our recent studies that investigate respiratory particle transport via high-fidelity large eddy simulation coupled with the Lagrangian particle tracking method. Based on our numerical simulation results for human respiratory events with and without face masks, we demonstrate that facial masks could significantly suppress particle spreading. The studied respiratory events include coughing and normal breathing through mouth and nose. Using the Lagrangian particle tracking simulation results, we elucidated the transport pathways of saliva particles during inhalation and exhalation of breathing cycles, contributing to our understanding of respiratory physiology and potential disease transmission routes. Our findings underscore the importance of respiratory fluid dynamics research in informing public health strategies to reduce the spread of respiratory infections. Combining advanced mathematical modeling techniques with experimental data will help future research on airborne disease transmission dynamics and the effectiveness of preventive measures such as face masks.