Mathematical Model Research Articles

Machine learning-based optimal temperature management model for safety and quality control of perishable food supply chain

The management of a food supply chain is difficult and complex because of the product's short shelf-life, time-sensitivity, and perishable nature which must be carefully considered to minimize food waste. Temperature-controlled perishable food supply chain provides the highly crucial facilities necessary to maintain the quality and safety of the product. The storage temperature is the most vital factor in maintaining both the quality and shelf-life of a perishable food. Adequate storage temperature control ensures that perishable foods are transported to the end-users in good quality and safe to consume. This paper presents perishable food storage temperature control through mathematical optimal control model where the storage temperature is regarded as the control variable and the deterioration of the perishable food’s quality follows the first-order reaction. The optimal storage temperature for a single perishable food is determined by applying the Pontryagin's maximum principle to solve the optimal control model problem. For multi-temperature commodities supply chain, an unsupervised machine learning (ML) method, called k-means clustering technique is used to determine the temperature clusters for a range of perishables. Based on descriptive analysis, it is observed that the k-means clustering technique is effective in identifying the best suitable storage temperature clusters for quality control of multi-commodity supply chain.

Variable viscosity and activation energy aspects in convection heat transfer over gravity driven solar collector plate for thermal energy storage

Variable viscosity, activation energy and microgravity effects on Darcy nanofluid for the thermal performance improvement in thermal energy storage systems through stretching flat plate solar collector is the focus of this research. Thermal energy storage (TES) can be improved though solar collectors, phase change materials and photovoltaic cells using nanofluid in the base liquid. To increase the reaction rate in nanoparticles, the activation energy and solar radiations are used for the efficiency of TES. The viscosity of nanofluid improves the heat and mass transmission. Due to solar radiations, nanofluid plays prominent role in TES applications such as heat exchangers, electronic cooling devices and solar power generation through solar plate collector. Solar energy based mathematical model is developed to execute the frequency of oscillating heat transfer in TES numerically. Primitive and Stokes coefficients are used for feasible programming. Finite difference analysis is performed to display oscillatory thermal energy using Gaussian-elimination matrix scheme. Steady velocity, surface temperature and concentrations are plotted and utilized in oscillatory formula to perform oscillatory skin friction, oscillatory heat transfer and oscillatory mass transfer along π⁄4 angle. Fluid velocity enhances but temperature and concentration variation decreases as viscosity decreases. High amplitude in velocity, temperature and concentration is sketched as activation energy and microgravity increases. Steady heat and mass transmission enhances as thermophoretic and Brownian motion enhances. Amplitude and frequency of oscillations in heat transport, skin friction and mass transport enhances as Prandtl and Schmidt component enhances. In validation of results, the 0.00064% percentage error for heat transport and 0.00102% percentage error for mass transmission are deduced.

Central place foragers, prey depletion halos, and how behavioral niche partitioning promotes consumer coexistence

Many seabirds congregate in large colonies for breeding, a time when they are central place foragers. An influential idea in seabird ecology posits that competition during breeding results in an area of reduced prey availability around colonies, a phenomenon known as Ashmole's halo, and that this limits colony size. This idea has gained empirical support, including the finding that species coexisting within a colony might be able to do so by foraging on a single prey species but at different distances. Here, we provide a comprehensive mathematical model for central place foragers exploiting a single prey in a two-dimensional environment, where the prey distribution is the result of intrinsic birth and death, movement in space, and mortality due to foraging birds (we also consider a variant tailored toward colonial social insects). Bird predation at different distances occurs according to an ideal free foraging distribution that maximizes prey delivery under flight and search costs. We fully characterize the birds' ideal free distribution and the prey distribution it generates. Our results show that prey depletion halos around breeding colonies are a robust phenomenon and that the birds' ideal free distribution is sensitive to prey movement. Furthermore, coexistence of several seabird species on a single prey easily emerges through behavioral niche partitioning whenever trait differences between species entail trade-offs between efficiently exploiting a scarce prey close to the colony and a more abundant prey far away. Such behavioral-based coexistence-inducing mechanism should generalize to other habitat and diet choice scenarios.

Malaria treatment for prevention: a modelling study of the impact of routine case management on malaria prevalence and burden

BackgroundTesting and treating symptomatic malaria cases is crucial for case management, but it may also prevent future illness by reducing mean infection duration. Measuring the impact of effective treatment on burden and transmission via field studies or routine surveillance systems is difficult and potentially unethical. This project uses mathematical modeling to explore how increasing treatment of symptomatic cases impacts malaria prevalence and incidence.MethodsLeveraging the OpenMalaria stochastic agent-based transmission model, we first simulated an array of transmission intensities with baseline effective treatment coverages of 28%, 44%, and 54% incorporated to reflect the 2023 coverage distribution across Africa, as estimated by the Malaria Atlas Project. We assessed the impact of increasing coverage to as high as 60%, the highest 2023 estimate on the continent. Subsequently, we performed simulations resembling the specific subnational endemicities of Kenya, Mozambique, and Benin, using the Malaria Atlas Project estimates of intervention coverages to reproduce historical subnational prevalence. We estimated the impact of increasing effective treatment coverage in these example settings in terms of prevalence reduction and clinical cases averted in children under 5 years old and the total population.ResultsThe most significant prevalence reduction – up to 50% – was observed in young children from lower transmission settings (prevalence below 0.2), alongside a 35% reduction in incidence, when increasing effective treatment from 28% to 60%. A nonlinear relationship between baseline transmission intensity and the impact of treatment was observed. Increasing effective treatment coverage to 60% reduced the risk in high-risk areas (prevalence in children under 5 years old > 0.3), affecting 39% of young children in Benin and 20% in Mozambique previously living in those areas. In Kenya where most of the population lives in areas with prevalence below 0.15, and case management is fairly high (53.9%), 0.39% of children were estimated to transition to lower-risk areas.ConclusionsImproving case management directly reduces the burden of illness, but these results suggest it also reduces transmission, especially for young children. With vector control interventions, enhancing case management can be an important tool for reducing transmission intensity over time.

The Effect of Network Delay and Contagion on Mobile Banking Users: A Dynamical Analysis

This paper analyses how network contagion affects the acceptance or rejection of mobile banking, emphasizing the risk of contagion that hinders the growth of users among bank clients. As a research method, a mathematical model based on the Susceptible, Infected, and Recovered framework is used within a nonlinear dynamic system with a distributed time delay and the optimal control strategy. The approach aims to find the behaviour dynamics of mobile banking users, non-users, and undecided ones. Our model adds value to the existing literature by employing a qualitative dynamic analysis, as opposed to other studies that study contagion empirically. The steady states and their conditions for stability are found, and the critical value for time delay causing oscillatory is determined. The optimal control strategies are identified to enlarge the number of mobile banking users and decrease the number of non-users. Numerical simulations support the theoretical findings. The research has practical implications given that the model predicts mobile banking user behaviour in assisting policy decision-making and addresses the possible policy measures that aim to increase the number of mobile banking users. The conclusions suggest that financial inclusion can contribute to the expansion of mobile banking users.

Opinion response functions are key to understanding the tipping of social conventions

Abstract The extent to which committed minorities can overturn social conventions is an active area of research in the mathematical modeling of opinion dynamics. Researchers generally use simulations of agent-based models (ABMs) to compute approximate values for the minimum committed minority size needed to overturn a social convention. In this manuscript, we expand on previous work by studying an ABM’s mean-field behavior using ordinary differential equation models and a new tool, namely opinion response functions (ORFs). Using this method allows for formal analysis of the deterministic model, which can provide a theoretical explanation for observed behaviors, e.g. coexistence or overturning of opinions. In particular, ORFs are a method for characterizing equilibria in our social model. Our analysis confirms earlier numerical results and supplements them with a precise formula for computing the minimum committed minority size required to overturn a social convention.

Study on type of magnetic suspension rotor groove and wear of drop touchdown bearing

The active magnetic bearing (AMB) is widely used in the field of flywheel energy storage system (FESS) in wind power generation. This study mainly studies the magnetic suspension rotor groove (MSRG) of FESS and the wear of drop touchdown bearing (DTB). The mathematical model of air gap magnetic field waveform on stator surface and Plath equation of control in air gap region were established. Contrastive analysis of conventional, second harmonic and third harmonic ‘petal-shaped’ MSRG in AMB. The life test of DTB on magnetic suspension rotor was carried out for 24000r/min and lasted for 1500 h. The second harmonic ‘petal-shaped’ MSRG could not only generate reluctance torque and increased the torque density of the motor, but also increased the fundamental component and excitation torque component by reducing the peak value of the magnetic field. The temperature ranges of front and rear DTB were ‘30℃–46℃’ and ‘26℃–40℃’, respectively. After service, the maximum thickness of metamorphic layer in the DTB raceway was 6 μm. After service, the content of Fe in the metamorphic layer of DTB raceway decreased by 10.11% and the content of C increased by 2.41%. Raceway hardness of DTB after service was 59.67 HV higher than that before service.

Digital Rights Management (DRM) technologies and legal research: Applications and regulations of encryption, digital watermarking, and copyright protection systems

Abstract. This paper explores the intersection of technology and law in Digital Rights Management (DRM) systems. By examining the application and regulation of encryption technologies, digital watermarking, and comprehensive copyright protection systems, this study provides a detailed understanding of how these technologies prevent unauthorized copying, distribution, and use of digital content. The paper introduces mathematical models to quantify the effectiveness of encryption and watermarking, offering insights into their practical applications and implications for intellectual property law. The comprehensive DRM effectiveness model combines these individual models, accounting for user inconvenience, to provide a holistic view of DRM system performance. Key case studies illustrate the implementation of DRM technologies in various industries, highlighting best practices and regulatory compliance. The study concludes with recommendations for future research and policy development to enhance the effectiveness and legal robustness of DRM technologies. This work contributes to the academic and practical understanding of DRM, offering a framework for optimizing DRM strategies in a dynamic digital landscape.

APPLICATION OF OPTIMIZATION METHOD IN MULTIDIMENSIONAL SPACE TO THE PROBLEM OF DETERMINING FULLERENE CONCENTRATION IN FULLERENE-CONTAINING MIXTURE

The work proposes a method for the quantitative processing of experimental data from ultraviolet spectroscopy of substituted fullerene mixtures, taking into account errors in the experimental data. This task can be written as a system of Vierordt equations (a system of linear equations). The coefficients of the system are the extinction coefficients of individual substituted fullerenes, which are difficult to measure accurately. Therefore, the mathematical model of the problem contains significant errors that affect the reliability and stability of the solution. To minimize the influence of errors, the work [1] proposes a method, which involves reducing the considered system of linear equations to a linear programming problem. This study generalizes the work [1] and proposes to use linear programming problems to find interval values of correction factors for parameters containing errors. Since decreasing the discrepancy reduces the solution error only for well-conditioned coefficient matrices, the values of correction coefficients that minimize the condition number of the coefficient matrix are found in the obtained intervals. The found correction values allowed to significantly improve the conditionality of the system coefficient matrix and obtain a more accurate solution. By using the refined extinction coefficients, the distribution of molar fractions of fullerene fragments and fullerene-containing compounds in the mixture of products formed by the attachment of cyanoisopropyl radicals was obtained, as well as the distribution of molar fractions of fullerene fragments of different degrees of substitution for samples of fullerene-containing polymethyl methacrylate and the distribution of molar fractions of fullerene fragments of different degrees of substitution for samples of fullerene-containing polystyrene. The results are correct and consistent with the theory, both for low-molecular-weight mixtures and for fullerene-containing polymers.

Effect of Coupling Impedance on Stability Assessment of Grid-Forming Converters Under Various Grid Conditions

The phenomenon of frequency coupling is widely observed in grid-forming (GFM) converters due to the presence of asymmetrical controls and nonlinear blocks. However, the factors influencing frequency coupling have not been thoroughly explored. This paper introduces a systematic small-signal impedance model of GFM converters that intuitively reflects the factors affecting frequency coupling and provides a detailed analysis of how coupling impedance affects stability. It is demonstrated that the influencing factors of coupling impedance are an active power loop and reactive power loop. Specifically, the active power loop influences coupling impedance characteristics near the fundamental frequency, while the reactive power loop impacts the entire frequency range. This paper first reveals that the reactive power loop has a more pronounced effect on frequency coupling than the active power loop. Additionally, the variation in the steady-state operating points also affects the degree of frequency coupling of the GFM converters, primarily affecting the coupling impedance characteristics beyond the fundamental frequency, and the low operating points tend to affect system stability adversely. Finally, simulation results validate the accuracy of the mathematical model and theoretical analysis.

Harnessing computational techniques to analyze and enhance fandom engagement through interaction ritual chains

Abstract. This study explores the application of Interaction Ritual Chains (IRC) theory and computational techniques to analyze and enhance fandom engagement within the Chinese Australian community. By integrating sentiment analysis, social network analysis, and gender-based language analysis, this research provides a comprehensive understanding of how emotional energy, shared focus, and bodily synchronization contribute to fan interactions. We employ a predictive mathematical model to quantify these IRC components and their impact on engagement, leveraging data mining, natural language processing (NLP), and machine learning. The findings reveal the dynamics of fan behavior and offer insights into personalized content recommendations, gamification, and virtual reality experiences to foster deeper emotional bonds and sustained engagement. This study bridges the gap between theoretical frameworks and practical applications, providing a robust foundation for future research on digital fandoms.

Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality

In this paper, we studied a mathematical model for honeybee population diseases under the influence of seasonal environments on the long-term dynamics of the disease. The model describes the dynamics of two different beehives sharing a common space. We computed the basic reproduction number of the system as the spectral radius of either the next generation matrix for the autonomous system or as the spectral radius of a linear integral operator for the non-autonomous system, and we deduced that if the reproduction number is less than unity, then the disease dies out in the honeybee population. However, if the basic reproduction number is greater than unity, then the disease persists. Finally, we provide several numerical tests that confirm the theoretical findings.

FORECASTING FIRE RISK VALUES USING MACHINE LEARNING AND TIME SERIES ANALYSIS

The probability of occurrence of emergencies and their consequences can be minimized by predicting events that contribute to the emergence of such a situation. An optimal and useful tool for such prediction and forecasting can be modeling, which can be carried out on the basis of information technology using computer programs.The methods of modeling and forecasting emergencies related to fires are the same as for other emergencies, but there are some specifics. The forecast of emergencies related to fires is aimed at three main stages: 1. forecasting the probability of occurrence with the determination of the place of the highest probability of fire occurrence, time and factors contributing to it; 2. forecasting the development of the situation and the spread of the fire (direction, speed) when it occurs, the process itself; 3. forecasting the consequences of a fire at a specific facility.The forecast is made based on the analysis of all possible unfavorable factors, their fields of action, features of the facility, its fire hazard and other data.The use of machine learning methods and time series analysis for forecasting fire risk values is substantiated. The possibility of using statistical methods of mathematical modeling of fire occurrence as the basis of the machine learning model is noted. This approach enables the machine learning model to process and analyze a large amount of statistical information for specific time periods and issue forecasts.

Effect of forced lateral vibration on flow and heat transfer performance within an annular fuel element

The investigation into the thermo-hydraulic characteristics of fuel elements under forced vibration conditions is of paramount importance in the design and application of offshore nuclear power platforms. This study employs a mathematical model of fluid-solid coupling and applies the theory of multi-field synergy to numerically analyze the flow and heat transfer features in an annular fuel element with internal and external double-sided cooling under forced lateral vibration conditions. The synergistic relationship of each flow field parameter is scrutinized for vibration conditions with frequencies ranging from 0 to 10 Hz and amplitudes from 0.005 to 0.2 m. The results demonstrate that increased amplitude and frequency contribute to enhancing the homogeneity of the temperature and velocity field distributions. Notably, the field synergy angles α, β, ψ, and γ attain minimal values at the gaps (X = 8 mm, X = 25 mm). Furthermore, the variation of vibration frequency and amplitude decreases the mean synergistic angle ψ by 5.14 % and 7.9 % and increases the mean field synergistic angle θ by 23.18 % and 31.21 %, respectively. It indicates that the vibration parameters have the least effect on the synergistic angle ψ and the greatest effect on the synergistic angle θ.

The Warburg Effect is the result of faster ATP production by glycolysis than respiration

Many prokaryotic and eukaryotic cells metabolize glucose to organism-specific by-products instead of fully oxidizing it to carbon dioxide and water-a phenomenon referred to as the Warburg Effect. The benefit to a cell is not fully understood, given that partial metabolism of glucose yields an order of magnitude less adenosine triphosphate (ATP) per molecule of glucose than complete oxidation. Here, we test a previously formulated hypothesis that the benefit of the Warburg Effect is to increase ATP production rate by switching from high-yielding respiration to faster glycolysis when excess glucose is available and respiration rate becomes limited by proteome occupancy. We show that glycolysis produces ATP faster per gram of pathway protein than respiration in Escherichia coli, Saccharomyces cerevisiae, and mammalian cells. We then develop a simple mathematical model of energy metabolism that uses five experimentally estimated parameters and show that this model can accurately predict absolute rates of glycolysis and respiration in all three organisms under diverse conditions, providing strong support for the validity of the ATP production rate maximization hypothesis. In addition, our measurements show that mammalian respiration produces ATP up to 10-fold slower than respiration in E. coli or S. cerevisiae, suggesting that the ATP production rate per gram of pathway protein is a highly evolvable trait that is heavily optimized in microbes. We also find that E. coli respiration is faster than fermentation, explaining the observation that E. coli, unlike S. cerevisiae or mammalian cells, never switch to pure fermentation in the presence of oxygen.

Lessons learned from COVID-19 modelling efforts for policy decision-making in lower- and middle-income countries

IntroductionThe COVID-19 pandemic had devastating health and socioeconomic effects, partly due to policy decisions to mitigate them. Little evidence exists of approaches that guided decisions in settings with limited pre-pandemic...

Flocs as vectors for microplastics in the aquatic environment

AbstractMicroplastics (MPs) are an important component of suspended particulate matter in aquatic environments with two main transport modes, that is, as individual entities or in flocs. Despite its importance to MP pollution management, understanding and predicting MP flocculation remains a challenge. In this Article, we combined a meta-analysis of published data (>2,000 measurements) with new experimental data (>4,000 measurements) to investigate which size fraction of MPs can be incorporated into and transported by flocs in the aquatic environment. The size relationship between MPs and flocs can be used to predict the flocculation of MPs in various aquatic environments, and we have proposed a mathematical model to show that small MPs (<162 µm) are predominantly transported as flocs, regardless of the physicochemical characteristics of the MPs or water body. This provides valuable information to predict the transport modes of MPs, presenting a critical insight for multiple environmental settings and future pollution control strategies.

Numerical study of the influence of temperature data error on the determination of frictional heat generation

Subject of research: determination of the friction torque and functions of the specific intensity of heat generation in system of sliding bearings. The purpose of the study: To develop a method for determining the friction torque in sliding bearings using temperature data. Based on computational experiments, study the influence of errors in temperature data on the solution of the inverse problem. Methods and object of research: A system of sliding bearings made of a polymer composite material on which a rotating shaft rests is considered. A mathematical model of the thermal process in the considered system of friction units is presented, taking into account the spatial distribution of temperature and its change over time. The temperature is measured at several points in each bearing. Frictional heat generation is determined by solving the inverse heat conduction problem from the condition that the measured and calculated temperatures are close. To ensure continuous data processing and determine the friction torque during long-term tests, the inverse problem of determining the friction torque from temperature data is solved at successive short time intervals. Then the resulting solutions are «glued together». The main results of the study: With such a restoration, the discrepancy between the specified and restored functions of the specific intensity of heat generation is 10–15 % with an error level in temperature data of 10 %. The developed algorithm for solving the inverse problem of thermal conductivity can be used to determine the friction torques in real systems of self-lubricating sliding bearings.

Multi-strain modeling of influenza vaccine effectiveness in older adults and its dependence on antigenic distance

Influenza vaccine effectiveness (VE) varies seasonally due to host, virus and vaccine characteristics. To investigate how antigenic matching and dosage impact VE, we developed a mechanistic knowledge-based mathematical model. Immunization with a split vaccine is modeled for exposure to A/H1N1 or A/H3N2 virus strains. The model accounts for cross-reactivity of immune cells elicited during previous immunizations with new antigens. We simulated vaccine effectiveness (sVE) of high dose (HD) versus standard dose (SD) vaccines in the older population, from 2011 to 2022. We find that sVE is highly dependent on antigenic matching and that higher dosage improves immunogenicity, activation and memory formation of immune cells. In alignment with clinical observations, the HD vaccine performs better than the SD vaccine in all simulations, supporting the use of the HD vaccine in the older population. This model could be adapted to predict the impact of alternative virus strain selection on clinical outcomes in future influenza seasons.

Topological Anderson insulators by homogenization theory

. A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in different topological phases. A topological Anderson Insulator is an insulator whose topological phase is induced by spatial fluctuations. This article proposes a mathematical model of perturbed Dirac equations and shows that for sufficiently large and highly oscillatory perturbations, the system is in a different topological phase than the unperturbed model. In particular, a robust asymmetric transport indeed appears at an interface separating perturbed and unperturbed phases. The theoretical results are based on careful estimates of resolvent operators in the homogenization theory of Dirac equations and on the characterization of topological phases by the index of an appropriate Fredholm operator.