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With the rapid development of the photovoltaic industry, flexible photovoltaic supports are increasingly widely used. Parameters such as the deflection, span, and cross-sectional dimensions of cables are important factors affecting their mechanical and economic performance. Therefore, in order to reduce steel consumption and cost and improve application value, it is crucial to design and optimize their initial morphology. In this paper, the mechanical behavior of a single-cable structure is introduced, and the simplified analytical formulations for internal force and displacement are deduced based on the geometric nonlinear characteristics and small strain assumption of the flexible photovoltaic supports. On this basis, the analytical expressions for the cable force and displacement of a convex prestressed double-layer cable truss flexible photovoltaic support structure under a uniform load are derived, and the correctness of the analytical formulations is verified by comparing the values with the finite element analysis results. In order to reduce the construction costs of the flexible photovoltaic support, a mathematical model for optimizing the initial structure's morphology is established according to the analytical formulations. The initial morphology of the double-layer cable truss flexible photovoltaic support is optimized, and the optimization results of different deflection deformation limits and whether the lower load-bearing cable is allowed to relax are compared. The results indicate that the errors of the displacement formulation and cable force formulation, when compared with the finite element results, are less than 3% and 4%, respectively, which verifies the accuracy of the analytical formulations. By analyzing the cable force and displacement of the structure under static action, it is suggested that the deflection limit of the double-layer cable truss structure should be 1/100 of the single span. The lower load-bearing cables of the double-layer cable truss flexible photovoltaic support are highly susceptible to relaxation under wind suction loads, and, by comparing the optimization results, it is suggested that slack should be allowed in the lower load-bearing cables for a better economic effect. When choosing the most economical structure morphology, it is recommended that the total height of the mid-span struts should be 1/20~1/15 of the single span. The analytical formulation and the mathematical model for the optimization of the initial morphology proposed in this paper can provide certain theoretical references and bases for the design of practical engineering projects and play an important role in promoting its application and promotion. [ABSTRACT FROM AUTHOR]

This paper presents an innovative mathematical model of solid fuel gasification, which is not described in the available literature. The calculation of the components of the heterogeneous phase (including both solid and gaseous phases) as well as the calculation of the homogeneous phase (only gaseous components) is based on the balance of the total amounts of carbon, oxygen, hydrogen, and nitrogen entering the reactor space. Additionally, this paper introduces a new method for calculating the composition of the gaseous phase, based on reducing the heterogeneous mixture (composed of solid and gaseous phases) to a homogeneous gaseous phase. This approach to calculating the gaseous phase composition in the solid fuel gasification process has not been found by the authors in the cited literature. This paper also presents a model for calculating the heterogeneous and gaseous phases using the number of moles that participate in the assumed chemical reactions of the solid fuel gasification process. This approach to calculating the composition of the heterogeneous and gaseous phases of the solid fuel gasification process is also not represented in the cited literature. For comparison with the literature data, municipal solid waste (MSW) and cashew nut shell (Cashew Shell Char (CNSC)) were used as fuels in the calculation of gasification composition. The results of the calculation of the gaseous phase composition using the model presented in the paper show good agreement with the data from the literature. The calculation of the composition of the heterogeneous mixture during the steam gasification of MSW (α = 0.4) shows the presence of a solid phase (carbon) up to approximately 735 °C. At that temperature, the synthetic gas contains only gaseous components: CO = 33.10%, H2 = 52.70%, CH4 = 2.54%, CO2 = 4.97, H2O = 5.93% and N2 = 0.76%. Increasing the temperature above 735 °C eliminates the solid phase from the equilibrium mixture. The literature data on solid fuel gasification generally do not consider the proportion of the solid phase (carbon) in the equilibrium mixture. To satisfy the material balance at the input and output of the gasification reactor, it is necessary to determine the proportion of the solid phase (carbon) in the equilibrium mixture. Since the proportion of the solid phase (carbon) in the heterogeneous equilibrium mixture can only be determined through measurement, the development and application of a mathematical model in engineering practice is of great importance, so this developed model can be considered a useful tool for simulating the influence of process parameters on gas characteristics. [ABSTRACT FROM AUTHOR]

This paper proposes an electric vehicle routing problem, considers the states of charging stations and suggests solution strategies. The charging of electric vehicles is a main issue in the field of electric vehicle routing. There are many studies that find the locations of charging stations, recharging functions for the batteries of vehicles, and so on. However, the state of charging stations significantly affects the routes of electric vehicles, which is not much explored. The states may include open or closed charging stations, occupied or empty charging slots, and so on. This paper investigates how the states of charging stations are estimated and how routing strategies are determined. We formulate a mixed integer programming model and suggest how to solve the problem with an exact method. Numerical examples provide the optimal routing strategies of electric vehicles for the changing environments regarding the states of charging stations. [ABSTRACT FROM AUTHOR]

Batteries play a crucial role in the domain of energy storage systems and electric vehicles by enabling energy resilience, promoting renewable integration, and driving the advancement of eco-friendly mobility. However, the degradation of batteries over time remains a significant challenge. This paper presents a comprehensive review aimed at investigating the intricate phenomenon of battery degradation within the realm of sustainable energy storage systems and electric vehicles (EVs). This review consolidates current knowledge on the diverse array of factors influencing battery degradation mechanisms, encompassing thermal stresses, cycling patterns, chemical reactions, and environmental conditions. The key degradation factors of lithium-ion batteries such as electrolyte breakdown, cycling, temperature, calendar aging, and depth of discharge are thoroughly discussed. Along with the key degradation factor, the impacts of these factors on lithium-ion batteries including capacity fade, reduction in energy density, increase in internal resistance, and reduction in overall efficiency have also been highlighted throughout the paper. Additionally, the data-driven approaches of battery degradation estimation have taken into consideration. Furthermore, this paper delves into the multifaceted impacts of battery degradation on the performance, longevity, and overall sustainability of energy storage systems and EVs. Finally, the main drawbacks, issues and challenges related to the lifespan of batteries are addressed. Recommendations, best practices, and future directions are also provided to overcome the battery degradation issues towards sustainable energy storage system. [ABSTRACT FROM AUTHOR]

The work in this paper is applied to the Zhangbei Power grid. In the flexible direct current (DC) power system, the fault current rises extremely fast when a DC fault occurs. The requirements for the peak of breaking current and fault energy absorption of DC circuit breakers (DCCBs) increase linearly, which significantly increases the cost of the equipment. Therefore, in order to reduce the design difficulty of DCCBs, this paper proposes a strategy to control energy after the fault occurs. Firstly, the energy dimension is added on the basis of the traditional vector control of MMC, which constitutes a three-dimensional energy direct control. Subsequently, the architectures of energy fluctuation control and feedforward control are proposed. The influencing mechanisms for the peak fault current, peak fault voltage and energy dissipation are analyzed. Finally, the simulation of energy fluctuation control and feedforward control is constructed on PSCAD/EMTDC. The simulation results show that the energy fluctuation control is obviously better than the conventional three-dimensional energy control, and the feedforward energy control is further improved on this basis. Compared with the conventional vector control, the peak energy is reduced by 45.43% and the peak current is reduced by 25.39%, which helps to simplify the equipment design and reduce the equipment cost. [ABSTRACT FROM AUTHOR]

Rolling mill bearings are prone to wear, erosion, and other damage characteristics due to prolonged exposure to rolling forces. Therefore, regular inspection of rolling mill bearings is necessary. Ultrasonic technology, due to its non-destructive nature, allows for measuring the oil film thickness distribution within the bearing during disassembly. However, during the process of using ultrasonic reflection coefficients to determine the oil film thickness and distribution state of rolling mill bearings, changes in bearing temperature due to prolonged operation can occur. Ultrasonic waves are susceptible to temperature variations, and different temperatures of the measured structure can lead to changes in measurement results, ultimately distorting the results. This paper proposes using density and sound speed compensation methods to address this issue. It simulates and analyzes the oil film reflection coefficients at different temperatures, ultimately confirming the feasibility and effectiveness of this approach. The paper establishes a functional relationship between bearing pressure and reflection coefficients, oil film thickness, and reflection coefficients. This allows for the compensation of reflection coefficients under any pressure conditions, enhancing the accuracy of oil film thickness detection. The proposed method provides technical support for the maintenance of plate rolling processes in the steel industry. [ABSTRACT FROM AUTHOR]

One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils. [ABSTRACT FROM AUTHOR]

The transient characteristics of pressure in the condenser under fault conditions have a crucial impact on the safe operation of the entire nuclear power plant. In order to ascertain whether the condenser pressure of a HPR1000 nuclear power unit meets the requirements of the steam generator, this paper establishes a mathematical model of the condenser, along with the connected steam turbine bypass steam system and circulating water system, based on Apros. The accuracy of the simulation model is verified by comparing the coasting curve of the circulating water pump with the flow change curve under the pump-tripping condition in Apros. Under the initial CCR condition and the half-side operating condition of the condenser, simulation analyses were conducted for two transient sequences involving the loss of normal external power and the simultaneous tripping of two circulating water pumps. The corresponding changes of pressure in the condenser under the transient sequence were obtained. The study reveals that, under different initial conditions and transient sequences, the condenser pressure of the unit can meet the requirements of a 12 s steam discharge to the condenser before the internal pressure of the condenser reaches the "unavailable" set value when the turbine bypass system is under the fault condition. The research findings of this paper can provide reference data for the design, commissioning, and operation of subsequent HPR1000 nuclear power plants. [ABSTRACT FROM AUTHOR]

To facilitate a direct comparison of the differences in network resources among countries worldwide, this paper proposes a method for quantifying the relationship between autonomous systems and territorial networks from the perspective of network topology. Using global router-level network topology data as the foundational data for the network resources of various countries, we abstract the dual mapping information of router geographic distribution and operational ownership into a matrix-form mathematical model. By employing relevant indicators from both network scale and border connectivity, we compare matrix model data from different periods to quantitatively assess changes in the network structures of countries globally. The study results show that internet resources are concentrated in the United States, which owns 38.04% of the global routers, distributed across 87.88% of the countries, significantly impacting the global network. Compared to the average quantitative indicators of each country, 67.00% of the countries exhibit higher deployment consistency, 37.30% show higher border connection consistency, 23.81% perform prominently in terms of impact, and 46.20% have outstanding border node degrees. From a continental perspective, the analysis indicates that Asian and African countries have a closer relationship between AS and territorial networks, while Europe's connections are relatively sparse. Over time, we observe a slight decline in deployment consistency in Asia, Africa, and Europe, a slight increase in border connection consistency in Asia, Africa, and North America, and enhanced impact in Asia, Africa, Europe, and South America. These trends suggest that the integration between AS and territorial networks is intensifying in most countries. [ABSTRACT FROM AUTHOR]

Thrombus formation plays a crucial role in the clinical treatment of certain diseases. In conditions such as aortic dissection and cerebral aneurysm, complete thrombus occlusion in the affected region is desired to reduce blood flow into the false lumen or aneurysm sac, leading to a decrease in the tension exerted on the vascular wall and making it less likely to rupture. However, desired thrombosis sometimes fails to occur. Predicting thrombus formation can provide valuable information in such cases. This article offers a comprehensive review of conventional methods for predicting thrombus formation. In reviews conducted from the year 2000 to the present, the number of published related papers every five years has increased more than tenfold. We also found that the predictive methods can be classified into two categories: those based on the hemodynamic evaluation parameters and those based on hemodynamic and mathematical models that simulate the transport and reaction of blood components. Through our discussions, we identified several challenges that need to be resolved, including predictions based on patient-specific condition, model validation, multi-scale problems, the mechanisms of thrombus formation, and ensuring cost effectiveness. This review aims to guide researchers interested in exploring thrombus formation prediction within clinical treatments. [ABSTRACT FROM AUTHOR]

During the anaerobic digestion (AD) of fruit and vegetable waste (FVW), excessive particle size reduction can lead to the overproduction and inhibition of methanogenic microorganisms. This paper presents an in-depth analysis through experimental assays, modeling, and response surface analysis of the effect of particle size on methane production. A simple model was proposed considering the inhibition of the growth of methanogenic microorganisms and surface-based hydrolysis kinetics. The model parameters were estimated using experimental data from batch systems fed with FVW of varying particle sizes (ranging from 1.8 to 1000 μm). Response surface methodology establishes a statistical model for estimating methane production based on particle size and concentration. Numerical and statistical analyses were conducted using Matlab R2024a and Minitab 24 software. A model with an R2 of 0.89 was obtained, which determined an optimal concentration of 8.2 k g · m − 3 and a particle size of 742.3 μ m , yielding a methane production of 303.3 m 3 · k g − 1   V S , similar to the experimentally obtained range of 300.95 to 316.7 m 3 · k g − 1   V S . [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis. [ABSTRACT FROM AUTHOR]

The Zika virus has been shown to infect glioblastoma stem cells via the membrane receptor α v β 5 , which is activated by the stem-specific transcription factor SOX2. Since the expression level of SOX2 is an important predictive marker for successful virotherapy, it is important to understand the fundamental mechanisms of the role of SOX2 in the dynamics of cancer stem cells and Zika viruses. In this paper, we develop a mathematical ODE model to investigate the effects of SOX2 expression levels on Zika virotherapy against glioblastoma stem cells. Our study aimed to identify the conditions under which SOX2 expression level, viral infection, and replication can reduce or eradicate the glioblastoma stem cells. Analytic work on the existence and stability conditions of equilibrium points with respect to the basic reproduction number are provided. Numerical results were in good agreement with analytic solutions. Our results show that critical threshold levels of both SOX2 and viral replication, which change the stability of equilibrium points through population dynamics such as transcritical and Hopf bifurcations, were observed. These critical thresholds provide the optimal conditions for SOX2 expression levels and viral bursting sizes to enhance therapeutic efficacy of Zika virotherapy against glioblastoma stem cells. This study provides critical insights into optimizing Zika virus-based treatment for glioblastoma by highlighting the essential role of SOX2 in viral infection and replication. [ABSTRACT FROM AUTHOR]

In the everchanging landscape of human mobility and commerce, efficient route planning has become paramount. This paper addresses the open vehicle routing problem (OVRP), a major logistical challenge in route optimization for a fleet of vehicles serving geographically dispersed customers. Using a heuristic approach, we explore the complexities of OVRP, comparing the results with advanced optimization methods. This study not only highlights the effectiveness of mathematical modeling, but also explores the practicality of heuristic algorithms such as Greedy, Nearest Neighbor and 2-opt to provide quality solutions. The findings highlight the nuanced interplay between solution quality and computational efficiency, providing valuable insights for addressing real-world logistics challenges. Recommendations delve into optimization opportunities and the integration of emerging technologies, ensuring adaptable solutions to the intricate the problem of open vehicle routing. [ABSTRACT FROM AUTHOR]

Pressure ulcers are a frequent issue involving localized damage to the skin and underlying tissues, commonly arising from prolonged hospitalization and immobilization. This paper introduces a mathematical model designed to elucidate the mechanics behind pressure ulcer formation, aiming to predict its occurrence and assist in its prevention. Utilizing differential geometry and elasticity theory, the model represents human skin and simulates its deformation under pressure. Additionally, a system of ordinary differential equations is employed to predict the outcomes of these deformations, estimating the cellular death rate in skin tissues and underlying layers. The model also incorporates changes in blood flow resulting from alterations in skin geometry. This comprehensive approach provides new insights into the optimal bed surfaces required to prevent pressure ulcers and offers a general predictive method to aid healthcare personnel in making informed decisions for at-risk patients. Compared to existing models in the literature, our model delivers a more thorough prediction method that aligns well with current data. It can forecast the time required for an immobilized individual to develop an ulcer in various body parts, considering different initial health conditions and treatment strategies. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the stability of a special class of single-channel slow-rotating homing missiles using the Frank–Wall stability criterion. To achieve this, starting from the model of a slow-rolling missile with six degrees of freedom (6 DOFs) in the body frame, a 6-DOFs model in the Resal frame is obtained, which is used to linearize the coupled commanded motion. Based on the linearized model, we obtain the structural scheme of the commanded object and define the flight quality parameters. The obtained linear model has a complex representation (with real and imaginary parts) due to the coupling between longitudinal channels for the rolling missile. Then, the kinematic guidance equations, the seeker equations and the actuator relations using a switching function, specific to the slow-rolling single-channel missile, are defined. The guidance kinematic equations, the seeker equations and the actuator model are linearized in the Resal frame, and the structural diagram of the homing missile is constructed. Starting from this, the characteristic polynomial having complex coefficients is determined and then analyzed with the Frank–Wall stability criterion. Based on the analysis, a stability range is determined for the navigation constant (k) , and a minimum and possibly a maximum limit for the time to hit the target t g o is obtained. The stability range defined for the navigation constant in the linear model is finally validated in the nonlinear model in the body frame. [ABSTRACT FROM AUTHOR]

The paper proposes an equivalent optical scheme of an in-line digital holographic system for particle recording and a mathematical model that establishes a one-to-one correspondence between the dimensional and spatial parameters of a digital holographic image of a particle and the imaged particle itself. The values of the model coefficients used to determine the real size and longitudinal coordinate of a particle according to its holographic image are found by calibration. The model was tested in field and laboratory conditions to calibrate a submersible digital holographic camera designed to study plankton in its habitat. It was shown that four calibration measurements are sufficient enough to determine the model coefficients, and the developed design of the submersible digital holographic camera makes it possible to perform these measurements during the recording of each hologram. In addition, this neither requires data on the refractive index of the medium with particles nor on the parameters of the optical elements of the scheme. The paper presents the results of marine experiments in the Kara Sea and the Laptev Sea, as well as in fresh water in laboratory conditions and in Lake Baikal. The error in measuring the particle size in seawater without the use of the model is 53.8%, while the error in determining their longitudinal coordinates is 79.3%. In fresh water, the same errors were 59% and 54.5%, respectively. The error in determining the position of a particle with the use of the designed mathematical model does not exceed 1.5%, and the error in determining the size is 4.8%. The model is sensitive to changes in the optical properties of the medium, so it is necessary to perform calibration in each water area, and one calibration is quite sufficient within the same water area. At the same time, the developed design of the submersible holographic camera allows, if necessary, calibration at each holographing of the medium volume with particles. [ABSTRACT FROM AUTHOR]

This paper presents the results of an investigation of the possibility of the reliable determination of the residual stress–strain state in polymers and composites using a combination of bridge curvature, optical scanning, and finite element methods. A three-factor experiment was conducted to determine the strength of printed PLA plastic products. The effect of the residual stresses on the strength of the printed products was evaluated. By comparing the values of the same strength stresses, a relationship between the nature of the stresses and the strength of the samples was found. A tendency of the negative influence of tensile stresses and the opposite strengthening effect of compressive stresses was obvious, so at the same values of tensile strength, the value of residual stress of 42.9 MPa is lower than that of the fibre compression at the value of 88.9 MPa. The proposed new methods of the residual stress determination allow obtaining a complete picture of the stressed state of the material in the investigated areas of the products. This may be necessary in confirming the calculated models of the residual stress–strain state, clarifying the strength criteria and assessing the quality of the selected technological modes of manufacturing the products. [ABSTRACT FROM AUTHOR]

The effective operation of model-based control strategies in modern energy systems, characterized by significant complexity, is contingent upon highly accurate large-scale models. However, achieving such precision becomes challenging in complex energy systems rife with uncertainties and disturbances. Controlling different parts of the energy system poses a challenge to achieving optimal power system efficiency, particularly when employing model-based control strategies, thereby adding complexity to current systems. This paper proposes a novel model-independent control approach aimed at augmenting transient stability and voltage regulation performance in multi machine energy systems. The approach involves the introduction of an optimized model-free fractional-order-based excitation system stabilizer for synchronous generators in a multi machine energy system. To overcome the limitations associated with complex system model identification, which add degrees of simplification at defined operating conditions and assume the system model remains fixed despite high uncertainty and numerous disturbances, an optimal model-independent fractional-order-based excitation control strategy is introduced. The efficacy of the proposed approach is validated through comparative numerical analyses using the MATLAB/Simulink environment. These simulations were conducted on a two-area, 12-bus multi-machine power system. Simulation results demonstrate that the presented excitation system stabilizer outperforms conventional controllers in terms of transient and small-signal stability. It also suppresses the low-frequency electromechanical oscillations within the multimachine energy system. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. [ABSTRACT FROM AUTHOR]

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model's potential to develop effective strategies for combating misinformation related to COVID-19. [ABSTRACT FROM AUTHOR]

Diffusion processes in operations involving polymeric materials are of significant interest. Determining experimental values for diffusion coefficients is often challenging. Estimating these coefficients in concentrated polymer solution, polymer films, and membranes relies on experimental tests where the polymer is brought into contact with certain components/solvents. The diffusion coefficient values depend on the diffusion type, which is affected mainly by the nature of the polymer, concentration, and temperature. The literature presents an extensive amount of information regarding the diffusion phenomenon. This paper makes a particular contribution by showing how experimental data obtained from different applications can be processed to determine diffusion coefficients. The manuscript addresses some aspects regarding solvent diffusion in polymers, and illustrates how to determine the diffusion coefficients from experimental data. For specific cases of diffusion, several models for the predictive estimation of diffusion coefficients are also presented. Polymer–solvent systems such as polyvinyl alcohol (PVA)–water, cellulose acetate (CA)–tetrahydrofuran (THF) and cellulose triacetate (CTA)–dichloromethane (DCM) are investigated, with their diffusion mechanisms influenced by changes in structure caused by variations in concentration and temperature. The experimental data obtained through a gravitational technique allow for the highlighting of the diffusion mechanism and the selection of an appropriate mathematical model. A change in the structure of the polymer during the experiment leads to diffusion anomalies. Modeling the experimental data yielded diffusion coefficient values that vary based on the type of system investigated, composition and temperature. Thus, in the case of the CTA-DCM system, the diffusion coefficient at 303 K, at various concentration values, is in the range of 4.5 and 8·10−11 m2/s; for the PVA-H2O system, D = 4.1·10−12 m2/s at 303 K, and D = 6.5·10−12 m2/s at 333 K; while for the CA-THF system, the solvent–polymer diffusion coefficient has a value of 2.5∙10−12 m2/s at 303 K, and D = 1.75∙10−11 m2/s at 323 K. Mathematical models can be useful in studies regarding the drying of polymer films with complex structures, providing knowledge for designing or selecting suitable equipment. [ABSTRACT FROM AUTHOR]

As society continues to age, people are becoming more concerned about their health care. This has led to an increase in the demand for medical products in urban areas, emphasizing the need for regular and prompt deliveries. However, the existing logistics centers are located in the suburbs of Seoul, a metropolitan city, which makes it challenging to ensure timely delivery. To address this issue, this study aims to establish new logistics centers in urban areas, particularly in Seoul, while minimizing CO2 emissions from delivery vehicles in alignment with sustainability efforts. The scientific gap addressed in and the novelty of this paper is that the input parameters are prepared based on actual data from a medical company in Korea to reflect reality, and the mathematical model-based optimization technique is applied to determine the optimal location of a new logistics center. The genetic algorithm is developed to solve the proposed mathematical model by deriving optimal or near-optimal solutions. Furthermore, the numerical experiment examined the impact of establishing a new logistics center in one of the candidate areas of local governments in Seoul by considering environmental impact. As a result, the new logistics network can reduce CO2 emissions by approximately 66.74% compared to the existing logistics network. [ABSTRACT FROM AUTHOR]

Controlling the distribution of water and wastewater between industrial processes is vital to rationalize water usage and preserve the environment. In this paper, a mathematical technique is proposed to optimize water–wastewater networks, and a nonlinear program is introduced to minimize the consumption of freshwater and, consequently, the flowrate of wastewater discharge. A general mathematical model, able to handle industrial plants containing up to eight sources and eight sinks, is developed using LINGO optimization software to facilitate dealing with complex case studies. The introduced model can handle single-contaminant networks as well as multiple-contaminant ones. The optimal water network is synthesized through two steps; the first step involves the introduction of the case study data into the developed mathematical model. The second step considers using the optimal solution produced after running the developed LINGO model as feed data for a pre-designed Excel sheet able to deal with these results and simultaneously draw the optimal water–wastewater network. The proposed mathematical model is applied to two case studies. The first case study includes actual data from four fertilizer plants located in Egypt; the water resources and requirements are simultaneously integrated to obtain a sensible cutting in both freshwater consumption (lowered by 52.2%) and wastewater discharge (zero wastewater discharge). The second case study regards a Brazilian petrochemical plant; the obtained results show noticeable reductions in freshwater consumption by 12.3%, while the reduction percentage of wastewater discharge is 4.5%. [ABSTRACT FROM AUTHOR]

The principal economic sector devoted to the breeding, raising, and production of farm animals is known as the livestock industry. There are precise standards for making high-quality feed in animal husbandry. Precision livestock feeding is a crucial component, with the potential to significantly impact the profitability of livestock; it permits the provision of diets to animals that are precisely tailored to their specific daily nutritional needs. Through simulation modeling, a single model can be created for automated systems to determine daily rations for farm animals. For the purposes of this document, precision livestock feeding refers to the practice of tailoring feed to individual animals or groups of animals, taking into account their changing nutritional needs over time and individual differences in terms of nutritional requirements. The practice aims to optimize animal health and performance while reducing feed waste. This paper presents a formal model for determining the quantities of components needed to achieve a minimum cost mixture that satisfies compositional and quantitative criteria. The present research calculates the amount of hay and silage required to feed an animal per day at the most economical cost by applying an optimization approach that involves defining and solving an optimization problem. The problem is solved using a well-known software package, which is necessary for the practical application of the resulting model. Real data from livestock production in Bulgaria are used to numerically test the model. [ABSTRACT FROM AUTHOR]

Deep soil moisture data have wide applications in fields such as engineering construction and agricultural production. Therefore, achieving the real-time monitoring of deep soil moisture is of significant importance. Current soil monitoring methods face challenges in conducting the large-scale, real-time monitoring of deep soil moisture. This paper innovatively proposes a real-time prediction approach to deep soil moisture combining GNSS-R data and a water movement model in unsaturated soil. This approach, built upon surface soil moisture data retrieved from GNSS-R signal inversion, integrates soil–water characteristics and soil moisture values at a depth of 1 m. By employing a deep soil moisture content prediction model, it provides predictions of soil moisture at depths from 0 to 1 m, thus realizing the large-scale, real-time dynamic monitoring of deep soil moisture. The proposed approach was validated in a study area in Goodwell, Texas County, Oklahoma, USA. Predicted values of soil moisture at a randomly selected location in the study area at depths of 0.1 m, 0.2 m, 0.5 m, and 1 m were compared with ground truth values for the period from 25 October to 19 November 2023. The results indicated that the relative error (δ) was controlled within the range of ±14%. The mean square error (MSE) ranged from 2.90 × 10 − 5 to 1.88 × 10 − 4 , and the coefficient of determination ( R 2 ) ranged from 82.45% to 89.88%, indicating an overall high level of fitting between the predicted values and ground truth data. This validates the feasibility of the proposed approach, which has the potential to play a crucial role in agricultural production, geological disaster management, engineering construction, and heritage site preservation. [ABSTRACT FROM AUTHOR]

Wind turbines are one of the leading renewable sources of electricity. They are located in areas where the energy potential of the wind is high and more or less permanent. Their efficient operation depends on certain technical characteristics of the entire wind system (wind turbines, generator, automation system, regulation, and control). This paper analyses experimental data from wind turbines, WT, in the Dobrogea area: wind speed, v, velocity, n, and power, PEG, at the electric generator, EG. These are used to identify the local maxima of wind turbine power at different wind speeds. Based on this, a mathematical model for wind turbines and the power losses caused by inefficient control are determined. The mathematical model is used to visualize the maximum energy zones. At the end of this study, an algorithm is given that allows for the visualization of the optimal energy zone. The algorithm resulting from the analyzed case studies can be implemented by the control system in order to maximize the produced electricity with any variation in wind speed. [ABSTRACT FROM AUTHOR]

The market for smart greenhouses has been valued at USD 1.77 billion in 2022 and is expected to grow to 3.39 billion by 2030. In order to make this more efficient, with the help of Internet of Things (IoT) technology, it is desired to eliminate the problem of traditional agriculture, which has poor monitoring and accuracy control of the parameters of a culture. Climate control decisions in a greenhouse are made based on parameter monitoring systems, which can be remotely controlled. Instead of this adjustment of the measured parameters, it would be preferable from the point of view of energy consumption that they should be calculated at optimal values from the design phase of the greenhouse. For this reason, it would be better to perform an energy simulation of the greenhouse first. For the study carried out in this work, a small greenhouse (mini-greenhouse) was built. It was equipped with an IoT sensor system, which measured indoor climate parameters and could send data to the cloud for future recording and processing. A simplified mathematical model of the heat balance was established, and the measured internal parameters of the mini-greenhouse were compared with those obtained from the simulation. After validating the mathematical model of the mini-greenhouse, this paper aimed to find the optimal position for placing a normal-sized greenhouse. For this, several possible locations and orientations of the greenhouse were compared by running the mathematical model, with which the most unfavorable positions could be eliminated. Then, some considerably cheaper "mini-greenhouses" were made and placed in the locations with the desired orientations. Using sensor systems and technologies similar to those presented in this work, the parameters from all mini-greenhouses can be monitored in real time. This real-time monitoring allows for the simultaneous analysis of all greenhouses, without the disadvantages of data collection directly in the field, with all data being recorded in the cloud and other IoT-specific advantages being made use of. In the end, we can choose the optimal solution for the location of a real-size greenhouse. [ABSTRACT FROM AUTHOR]

This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease. [ABSTRACT FROM AUTHOR]

Back pain is regularly associated with biomechanical changes in the spine. The traditional methods to assess spine biomechanics use ionising radiation. Vertebral Metrics (VM) is a non-invasive instrument developed by the authors in previous research that assesses the spinous processes' position. However, the spine model used by VM is not accurate. To overcome it, the present paper proposes a pioneering and simple articulated model of the spine built through the data collected by VM. The model is based on the spring–mass system and uses the Levenberg–Marquardt algorithm to find the arrangement of vertebral bodies. It represents the spine as rigid geometric transformations from one vertebra to the other when the extremity vertebrae are stationary. The validation process used the Bland–Altman method to compare the Cobb and the intervertebral angles computed by the model with the radiographic exams of eight patients diagnosed with Ankylosing Spondylitis. The results suggest that the model is valid; however, previous clinical information would improve outcomes by customising the lower and upper vertebrae positions, since the study revealed that the C6 rotation slightly influences the computed angles. Applying VM with the new model could make a difference in preventing, monitoring, and early diagnosing spinal disorders. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for obtaining energy consumption of IMC architectures is constructed. This model provides energy estimation based on the distribution of a specific dataset. In addition, the estimation reduces the required simulation time to create an energy consumption model of SRAM-based IMC architectures. To validate our model with realistic data, the energy consumption of IMC is compared by using NeuroSim V3.0 for the CIFAR-10 and MNIST-like datasets. Furthermore, an application is created with our model to select highest performing quantization mapping based upon the parameters of energy consumption and accuracy. [ABSTRACT FROM AUTHOR]

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling. [ABSTRACT FROM AUTHOR]

Reducing energy consumption and increasing energy efficiency have been especially topical issues recently, affecting all areas of energy consumption, including industrial sectors. Continuous annealing lines, as important industrial production facilities, operate with high energy consumption, which can be analyzed and optimized using predictive mathematical models. For the purpose of this paper, a mathematical model was developed to compare five variants of different excess combustion air operating with the same heat input and fuel consumption. The reference variant had an excess combustion air with a value of 1.279 and the steel strip temperature at the outlet of the heating chamber was 609.5 °C. In terms of energy savings, variant 1 can be considered as the optimal variant, which had an excess combustion air value of 1.15 and a steel strip temperature at the outlet of the heating chamber of 637.3 °C. [ABSTRACT FROM AUTHOR]

Insulated plastic greenhouses (IPG) were a new type of facility emerging in production in China. The mechanism of construct parameters on the indoor solar radiation deserves further study. A mathematical model that can well describe the spatial and temporal distribution of solar radiation in the greenhouse was established. Based on this model, the effects of multiple construct parameters, such as insulation blanket shading, height–span ratio, greenhouse azimuth, and geographical latitude, on the indoor solar radiation of IPG were quantitatively specified. The results showed that the spatial and temporal distribution of inside solar radiation was highly variable along the span direction of IPG. And by analyzing the simulation data, it was found that for different heights of greenhouses, the corresponding optimal span is different. Therefore, in the construction of greenhouses, the appropriate height–span ratio should be selected according to the planting demand. And by simulating the inside solar radiation under different greenhouse azimuth angles, it was found that accumulated daily solar radiation in the greenhouse reaches the optimum value when the greenhouse azimuth angle is in the range of 0–20°. This paper can provide theoretical guidance for the design and optimization of structure parameters of IPG in China. [ABSTRACT FROM AUTHOR]

The World Health Organization (WHO) recommends the consideration of introducing routine hepatitis A vaccination into national immunization schedules for children ≥ 1 years old in countries with intermediate HAV endemicity. Recent data suggest that South Africa is transitioning from high to intermediate HAV endemicity, thus it is important to consider the impact and cost of potential routine hepatitis A vaccination strategies in the country. An age-structured compartmental model of hepatitis A transmission was calibrated with available data from South Africa, incorporating direct costs of hepatitis A treatment and vaccination. We used the calibrated model to evaluate the impact and costs of several childhood hepatitis A vaccination scenarios from 2023 to 2030. We assessed how each scenario impacted the burden of hepatitis A (symptomatic hepatitis A cases and mortality) as well as calculated the incremental cost per DALY averted as compared to the South African cost-effectiveness threshold. All costs and outcomes were discounted at 5%. For the modelled scenarios, the median estimated cost of the different vaccination strategies ranged from USD 1.71 billion to USD 2.85 billion over the period of 2023 to 2030, with the cost increasing for each successive scenario and approximately 39–52% of costs being due to vaccination. Scenario 1, which represented the administration of one dose of the hepatitis A vaccine in children < 2 years old, requires approximately 5.3 million vaccine doses over 2023–2030 and is projected to avert a total of 136,042 symptomatic cases [IQR: 88,842–221,483] and 31,106 [IQR: 22,975–36,742] deaths due to hepatitis A over the period of 2023 to 2030. The model projects that Scenario 1 would avert 8741 DALYs over the period of 2023 to 2030; however, it is not cost-effective against the South African cost-effectiveness threshold with an ICER per DALY averted of USD 21,006. While Scenario 3 and 4 included the administration of more vaccine doses and averted more symptomatic cases of hepatitis A, these scenarios were absolutely dominated owing to the population being infected before vaccination through the mass campaigns at older ages. The model was highly sensitive to variation of access to liver transplant in South Africa. When increasing the access to liver transplant to 100% for the baseline and Scenario 1, the ICER for Scenario 1 becomes cost-effective against the CET (ICER = USD 2425). Given these findings, we recommend further research is conducted to understand the access to liver transplants in South Africa and better estimate the cost of liver transplant care for hepatitis A patients. The modelling presented in this paper has been used to develop a user-friendly application for vaccine policy makers to further interrogate the model outcomes and consider the costs and benefits of introducing routine hepatitis A vaccination in South Africa. [ABSTRACT FROM AUTHOR]

The paper describes the design and manufacturing process of a fiber optic microphone based on a macro cavity at the end face of an optical fiber. The study explores the step-by-step fabrication of a droplet-shaped macro cavity on the optical fiber's end surface, derived from the formation of a quasi-periodic array of micro-cavities due to the fuse effect. Immersing the end face of an optical fiber with a macro cavity in liquid leads to the formation of a closed area of gas where interfacial surfaces act as Fabry–Perot mirrors. The study demonstrates that the macro cavity can act as a standard foundational element for diverse fiber optic sensors, using the droplet-shaped end-face cavity as a primary sensor element. An evaluation of the macro cavity interferometer's sensitivity to length alterations is presented, highlighting its substantial promise for use in precise fiber optic measurements. However, potential limitations and further research directions include investigating the influence of external factors on microphone sensitivity and long-term stability. This approach not only significantly contributes to optical measurement techniques but also underscores the necessity for the continued exploration of the parameters influencing device performance. [ABSTRACT FROM AUTHOR]

The objective of this research paper is to apply a mathematical model to estimate and predict the economic growth of the Caspian countries in the period from 1995 to 2022. We use multiple regression by applying the OLS method to estimate the impact of global oil price, energy resource production per capita, trade, and renewable energy on GDP per capita. The mathematical approach uses fixed and random effects models to assess the overall impact of the independent variables on economic growth in this region and over the period analysed. This study also aims to investigate whether the explanatory variables are cointegrated in the long run; as such, we carry out several mathematical cointegration tests, namely the Pedroni and Johansen tests. The mathematical analysis is completed by the estimation of short- and long-run parameters using the stochastic VAR/VEC models, the impulse response function, and the causality test to assess economic growth in this region. This study's main finding is that GDP per capita is increasingly influenced by its previous values, which is confirmed by considering lag 1 and lag 2. The results of the Granger causality tests identify several bidirectional relationships between GDP per capita and oil and gas production. These relationships are clearly positive evidence of the growth trend and progress of economic activity in the Caspian region. The practical implications of the study aim to promote and support the use of renewable energy sources. In this sense, policymakers in the Caspian countries should create favourable conditions for the transition to a green economy. An important aspect is the efforts of the government authorities to make their policies more environmentally friendly, as decarbonisation is a good practice in the current context of sustainability and related choices. As the Caspian countries are heavily dependent on conventional energy production, it is essential for them to increase their export earnings from energy resources via diversifying and strengthening new energy opportunities and partnerships. [ABSTRACT FROM AUTHOR]

Groundwater contamination by dense nonaqueous phase liquids (DNAPLs) poses a severe environmental threat due to their persistence and toxicity. Modeling DNAPL contamination is essential for understanding their distribution, predicting contaminant spread, and developing effective remediation strategies, but it is also challenging due to their complex multiphase behavior. Over the past few decades, researchers have developed various models, including multiphase flow, mass transfer, and solute transport models, to simulate the distribution of DNAPLs. To understand the research trends in DNAPL modeling in groundwater, a bibliometric analysis was conducted using CiteSpace based on 614 publications from the WoS Core Collection database (1993–2023). The publications were statistically analyzed, and the research hotspots and trends were summarized. The statistical analysis of the publications indicates that the United States is leading the international research on DNAPL models, followed by China and Canada; the collaboration between countries and disciplines in this field needs to be strengthened. Keyword clustering and burst detection reveal that the current research hotspots focus on multiphase flow models, mass transfer models, back diffusion, and practical applications of the models; the research trends are centered on back diffusion mechanisms, the characterization of contamination source zones, and prediction of the contaminant distribution at real-world sites, as well as optimization of the remediation strategies. [ABSTRACT FROM AUTHOR]

Flywheel energy storage systems (FESSs) are widely used for power regulation in wind farms as they can balance the wind farms' output power and improve the wind power grid connection rate. Due to the complex environment of wind farms, it is costly and time-consuming to repeatedly debug the system on-site. To save research costs and shorten research cycles, a hardware-in-the-loop (HIL) testing system was built to provide a convenient testing environment for the research of FESSs on wind farms. The focus of this study is the construction of mathematical models in the HIL testing system. Firstly, a mathematical model of the FESS main circuit is established using a hierarchical method. Secondly, the principle of the permanent magnet synchronous motor (PMSM) is analyzed, and a nonlinear dq mathematical model of the PMSM is established by referring to the relationship among d-axis inductance, q-axis inductance, and permanent magnet flux change with respect to the motor's current. Then, the power grid and wind farm test models are established. Finally, the established mathematical models are applied to the HIL testing system. The experimental results indicated that the HIL testing system can provide a convenient testing environment for the optimization of FESS control algorithms. [ABSTRACT FROM AUTHOR]

In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed. [ABSTRACT FROM AUTHOR]

In this research work, a new software tool concept and its application for the rapid and flexible development of mechanistic digital twin core models for bioprocesses in various reactor designs are presented. The newly developed software tool concept automatically combines user-selected submodels into an overall digital twin core model. The main part is a biokinetic submodel, of which three were designed for enzymatic, microbial and biocatalytic processes, which can be adapted to specific processes. Furthermore, the digital twin core model contains a physico-chemical submodel (e.g., calculating pH or oxygen transfer) and a reactor submodel. The basis of the reactor submodel is an ideally mixed stirred tank reactor. The biokinetic submodel is decoupled from the reactor submodels and enables an independent parameterisation of submodels. Connecting ideally mixed stirred tank reactor models allows for the simulation of different reactor designs. The implementation of an executable digital twin core model was accelerated, creating a new software tool concept. When the concept was applied, the development time and the computing time of digital twin core models for the cultivation of Saccharomyces cerevisiae in two coupled stirred tank reactors as well as for enzymatic hydrolysis processes in a packed-bed reactor were reduced by 90%. [ABSTRACT FROM AUTHOR]

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

The authors of this study focused on the energy and material assessment of processes for processing pellets from metal-bearing waste, specifically Fe concentrate. A mathematical model was created for process evaluation, with which thermotechnical calculations of parameters in the processing of metallized pellets were carried out. Thermodynamic calculations were performed to determine the enthalpy of the charge in individual devices (drying chamber, rotary kiln, cooler). For the reduction of Fe oxides, carbon from coke (with Fe oxide reductions of 50%, 61%, and 92%) and lignite (with Fe oxide reductions of 69% and 92%) were considered as part of the pellets. The degree of reduction of iron oxides was a determining parameter, and the consumption of the reducing agent corresponded to the direct reduction of Fe oxides by carbon with a coefficient of 1.5. Another determining parameter was the input and output temperature in individual devices. For a more precise description of the processes in individual devices, calculations were carried out zonally. The results of the calculations are analyses and recommendations for feasible alternatives for the reducing agent and associated processes. [ABSTRACT FROM AUTHOR]

The inaccurate positioning of a plat valve is a crucial factor affecting the efficiency and safety of drilling operations. Because of the complicated structure of vertical drilling, it is difficult to obtain the actual position of a plat valve during the working process. This work effectively addresses the challenge of accurately measuring the deflection angle of a plat valve in mechanical automatic vertical drilling. Initially, a comprehensive mathematical model was proposed for determining the angle range of the plat valve, which was founded on the thrust generated by vertical drilling. Furthermore, this work proposed a precise measurement methodology for acquiring the crucial parameters of the MVDT. The actual deviation angle range for the N-MVDT and O-MVDT vertical drilling was calculated using data obtained from measurements of the tools. At the same time, the influence of TID on the performance of the MVDT was determined. Then, a simulation was carried out to compare the calculation results. From this, it was determined that the deflection angle range of the O-MVDT at a higher rotational speed was [86°, 58°], and the deflection angle range of the N-MVDT was [−14°, 14°]. By comparing the two methods, the error in the angle range was derived. The error of the N-MVDT was less than 16.67%, and the error of O-MVDT was less than 9.43%, proving that the measurement method and the mathematical model can accurately estimate the deflection angle range of a plat valve for mechanical automatic vertical drilling. The experimental and mathematical model results consistently showed that the deflection angle  φ  of the N-MVDT was significantly smaller than that of the O-MVDT, so the TID significantly improved the stability of the MVDT. [ABSTRACT FROM AUTHOR]

This article concerns the problem of estimating the throughput and forecasting the operation of a coal transshipment complex that comprises a marine coal terminal and a railway station. Scenario modeling is employed to address this issue. The mathematical model of the transshipment complex has the form of a queuing network, which allows us to take into account the impact of random factors on the arrival of trains and departure of vessels from the system and their handling. In the model, we use the batch marked Markovian arrival process (BMMAP), which allows for the batch arrival of several types of requests, to describe the arrival of different categories of trains. Various queuing systems model particular structural elements of the complex to consider peculiarities of their work. We investigate the coal transshipment complex, which includes one of the largest and most modern coal export terminals in Russia. Based on the results of a numerical study, we estimate its current and maximum throughput, find bottlenecks in the system structure, and forecast its performance after the planned modernization. We also discuss the advantages and limitations of the model presented and its potential extension. [ABSTRACT FROM AUTHOR]

A trans-media vehicle is a new type of equipment that can adapt to two environments, water and air, to maintain optimal hydrodynamic and aerodynamic performance. However, no matter what kind of trans-media vehicle, its dynamics are much more complicated when traversing the interface of the medium, as the parameters are time-varying due to the change in ambient medium and vehicle attitudes. In order to improve the stability and performance of the trans-media vehicle in complex environments, an accurate mathematical model is established to characterize the dynamics of the trans-media vehicle in this process in this study. The time-varying hydrodynamic coefficients with different attitudes or depths are obtained using computational fluid dynamics software. The mathematical model is solved iteratively using a Runge–Kutta solver to calculate the dynamic response. A prototype of trans-media vehicle is fabricated, and motion experiments are performed in the pool. The experimental results confirm the effectiveness of the established model and lay the foundation for further controller design, providing a reference for the dynamic modeling of other similar equipment operating in complex environments. The primary novelty of this study lies in the fact that the established dynamic model considers the complex interaction between the attitude of the trans-media vehicle and the inherent different properties of water and air and utilizes computational fluid dynamics software to accurately obtain time-varying coefficients under different attitudes and depths. This approach not only recognizes the criticality of orientation-dependent hydrodynamic coefficients but also incorporates their temporal variations, which were often overlooked in previous studies. [ABSTRACT FROM AUTHOR]

The closed-loop control of pathological brain activity is a challenging task. In this study, we investigated the sensitivity of continuous epileptiform short discharge generation to electrical stimulation applied at different phases between the discharges using an in vitro 4-AP-based model of epilepsy in rat hippocampal slices. As a measure of stimulation effectiveness, we introduced a sensitivity function, which we then measured in experiments and analyzed with different biophysical and abstract mathematical models, namely, (i) the two-order subsystem of our previous Epileptor-2 model, describing short discharge generation governed by synaptic resource dynamics; (ii) a similar model governed by shunting conductance dynamics (Epileptor-2B); (iii) the stochastic leaky integrate-and-fire (LIF)-like model applied for the network; (iv) the LIF model with potassium M-channels (LIF+KM), belonging to Class II of excitability; and (v) the Epileptor-2B model with after-spike depolarization. A semi-analytic method was proposed for calculating the interspike interval (ISI) distribution and the sensitivity function in LIF and LIF+KM models, which provided parametric analysis. Sensitivity was found to increase with phase for all models except the last one. The Epileptor-2B model is favored over other models for subthreshold oscillations in the presence of large noise, based on the comparison of ISI statistics and sensitivity functions with experimental data. This study also emphasizes the stochastic nature of epileptiform discharge generation and the greater effectiveness of closed-loop stimulation in later phases of ISIs. [ABSTRACT FROM AUTHOR]

This research envisages a system composed of three subsystems connected in series. Each subsystem comprises three units connected in parallel. For the system to function, at least one unit per subsystem must remain operational. Unit failure is governed by an exponential distribution, while unit repair is governed by either a general distribution or a Gumbel–Hougaard family copula distribution. The primary goal of this research is to compare the overall performance of our system under these two different regimes for performing repairs. Laplace transforms and supplementary variable methods are employed in solving the system. Our metrics for evaluating system performance are the availability, reliability, mean time to failure, and cost. The second goal of this research is to showcase a strategy for reduction that enhances the overall efficiency and availability of our system. [ABSTRACT FROM AUTHOR]

Concrete is widely utilized across various industries as a containment material. One essential property related to its performance is permeability, which determines its ability to allow the passage of gases or liquids through its pores and capillaries and even the transmission of aggressive agents. This study focused on investigating the permeability of gases with varying atomic weights and molecular volumes, such as helium, nitrogen, oxygen, and argon, to pass through concrete. The primary objective was to determine the significance of variation in permeability and to evaluate and differentiate their behavior. To achieve this, concrete test specimens were employed, and factors such as cold joint impact, gas pressure, and specimen saturation levels were considered. Throughout the study, changes in weight, specimen humidity, resistivity, and ultrasonic pulse velocity were monitored. The findings suggested that within concrete, the variation in permeability for these gases is negligible. By utilizing the acquired data, the present study estimated the permeability of hydrogen through mathematical models based on gas pressure and concrete thickness. These insights contribute to a deeper comprehension of concrete gas permeability and its potential impact on improving hydrogen containment. [ABSTRACT FROM AUTHOR]

Measles is a highly contagious disease and remains a major cause of child mortality worldwide. While measles vaccine is highly effective, high levels of population immunity are needed to prevent outbreaks. Simple but accurate tools are needed to estimate the profile of population measles immunity by age to identify and fill immunity gaps caused by low levels of vaccination coverage. The measles immunity profile estimates and visualizes the percentage of each birth cohort immune or susceptible to measles based on measles vaccination coverage. Several tools that employed this approach have been developed in the past, including informal unpublished versions. However, these tools used varying assumptions and produced inconsistent results. We updated the measles population immunity profile methodology to standardize and better document the assumptions and methods; provide timely estimates of measles population immunity; and facilitate prompt actions to close immunity gaps and prevent outbreaks. We recommend assuming that the second dose of the measles-containing vaccine (MCV2) and doses given during supplementary immunization activities (SIAs) first reach children who have been previously vaccinated against measles, so that previously unvaccinated children are reached only when the coverage of MCV2 or SIA is higher than the coverage achieved by all previous measles vaccination opportunities. This updated method provides a conservative estimate of immunization program impact to assess measles outbreak risk and to facilitate early planning of timely preventive SIAs to close population immunity gaps. [ABSTRACT FROM AUTHOR]