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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]

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]

Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application of Burton and Kirk's fixed point theorem in extended Banach spaces. This paper aims to extend current results to a differential-inclusions scenario. The motivation of this paper for impulsive neutral differential equations is to investigate the existence of solutions for impulsive neutral differential equations with fractional Brownian motion and a Wiener process (topics that have not been considered and are the main focus of this paper). [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]

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]

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 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]

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]

In the evolving landscape of targeted marketing, integrating deep learning (DL) and explainable AI (XAI) offers a promising avenue for enhanced customer segmentation. This paper introduces a groundbreaking approach, DeepLimeSeg, which synergizes DL methodologies with Lime-based Explainability to segment customers effectively. The approach employs a comprehensive mathematical model to harness demographic data, behavioral patterns, and purchase histories, categorizing customers into distinct clusters aligned with their preferences and needs. A pivotal component of this research is the mathematical underpinning of the DeepLimeSeg approach. The Lime-based Explainability module ensures that the segmentation results are accurate and interpretable. The mathematical rigor facilitates businesses tailoring their marketing strategies with precision, optimizing sales outcomes. To validate the efficacy of DeepLimeSeg, we employed two real-world datasets: Mall-Customer Segmentation Data and an E-Commerce dataset. A comparative analysis between DeepLimeSeg and the traditional Recency, Frequency, and Monetary (RFM) analysis is presented. The RFM analysis, grounded in its mathematical modeling, segments customers based on purchase recency, frequency, and monetary value. Our preprocessing involved computing RFM scores for each customer, followed by K-means clustering to delineate customer segments. Empirical results underscored the superiority of DeepLimeSeg over other models in terms of MSE, MAE, and R 2 metrics. Specifically, the model registered an MSE of 0.9412, indicative of its robust predictive accuracy concerning the spending score. The MAE value stood at 0.9874, signifying minimal deviation from actual values. This paper accentuates the importance of mathematical modeling in enhancing customer segmentation. The DeepLimeSeg approach, with its mathematical foundation and explainable AI integration, paves the way for businesses to make informed, data-driven marketing decisions. [ABSTRACT FROM AUTHOR]

Simple Summary: The word "model" can be used with different meanings and different contexts, like a model student, clay models or a model railway. In some cases, the context can clarify exactly what is meant by "model", but sometimes several meanings of model can be present in one area. For instance, with reference to cancer research, there can be ambiguity for what is meant by model. This paper reviews the use of the word model as related to cancer research and within the specific area of the microenvironment that surrounds a cancer tumour. The review grouped different definitions of model into four categories (model organisms, in vitro models, mathematical models and computational models) and explored what is meant in each case, mentioning the advantages and disadvantages of the different models Next, a quantitative investigation of the scientific publications listed in the database of the United States National Library of Medicine was performed by counting the frequencies of use of these terms, as well as the components of the microenvironments and the organs modelled with these techniques. The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use. [ABSTRACT FROM AUTHOR]

Polyvinyl butyral (PVB) is a thermoplastic resin commonly used as an interlayer material in laminated glass. Combined with textile fibres from worn tyres, PVB can produce a composite material with unique properties. One such property is absorption. Absorption in textile fibre composite materials refers to the ability of the material to absorb or retain moisture or other fluids. The presence of moisture or liquids can affect the properties of composite materials, such as their strength, stiffness, and dimensional stability. As a result of the physical and chemical action of the environment, corrosion of plastics occurs and manifests itself in changes in appearance, surface quality, weight, dimensions, and also in changes in other properties. This paper investigates four composite materials with different fabrics content. The aim of this paper is to propose a generalized mathematical model for absorption values so that, with different ratios of textile fibre in the material, its quality indicators are at a sufficient level. Our study will proceed from the assumption that by changing the values of the individual coefficients of the selected model based on their analysis, we will achieve the required qualitative indicators. [ABSTRACT FROM AUTHOR]

Making sound trade-offs between the energy consumption and the makespan of workflow execution in cloud platforms remains a significant but challenging issue. So far, some works balance workflows' energy consumption and makespan by adopting multi-objective evolutionary algorithms, but they often regard this as a black-box problem, resulting in the low efficiency of the evolutionary search. To compensate for the shortcomings of existing works, this paper mathematically formulates the cloud workflow scheduling for an infrastructure-as-a-service (IaaS) platform as a multi-objective optimization problem. Then, this paper tailors a knowledge-driven energy- and makespan-aware workflow scheduling algorithm, namely EMWSA. Specifically, a critical task adjustment-based local search strategy is proposed to intelligently adjust some critical tasks to the same resource of their successor tasks, striving to simultaneously reduce workflows' energy consumption and makespan. Further, an idle gap reuse strategy is proposed to search the optimal energy consumption of each non-critical task without affecting the operation of other tasks, so as to further reduce energy consumption. Finally, in the context of real-world workflows and cloud platforms, we carry out comparative experiments to verify the superiority of the proposed EMWSA by significantly outperforming 4 representative baselines on 19 out of 20 workflow instances. [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]

A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain. [ABSTRACT FROM AUTHOR]

In an unstable economic climate, all market participants want to know is when is the timing to overcome a recession, and what measures and means to use for economic recovery. In this regard, the process through which the Eurozone economy has gained momentum since the summer of 2022 has been a volatile one. This was reflected in a sharp rise in the price level, followed by a sharp rise in the ECB interest rates. The purpose of this paper is to provide short-term forecasts of the main parameters of monetary and fiscal policy by the euro area monetary authorities, based on a model developed by the authors. The distinctive feature of the presented and proposed model lies in the particularly careful selection of the parameter values based on actual statistical data. The statistics used for the proposed model cover the period from 2015 to December 2022. The simulation results show that the European Central Bank (ECB) needs to maintain a policy of high interest rates for a period of 12 to 14 months, which will help to bring inflation down to 2–3 percent in the future and move to a stage and phase of sustainable economic growth. [ABSTRACT FROM AUTHOR]

This paper considers the equipment and power supply schemes for urban water supply, heat supply and sewerage pumping stations. Mathematical calculations of the impact of the static and full centrifugal pumps pressure ratio on the dynamic stability of synchronous electric motors were carried out. An analysis of the influence of pump parameters and engine load on the run-down parameters and drive stability during power shutdowns was carried out. It has been theoretically proven and practically confirmed that ensuring the stability of pumping station drives and the reduction in enterprise losses during various short-term disruptions in power supply networks can be provided by means of a high-speed backup source with a response time of less than 9 ms, dynamic voltage dip compensators with a response time of less than 3 ms and uninterruptible power supply sources. [ABSTRACT FROM AUTHOR]

Simple Summary: Neuroblastoma is a rare type of cancer that usually affects children. The high-risk patients' expected survival rate is less than 50%. One reason is the lack of precision in the standard treatment protocol: a one-size-fits-all multi-modal therapy. The study presented in this paper was designed to address this deficit by optimising the use of two chemotherapeutic agents—vincristine and cyclophosphamide—during induction chemotherapy—the part of the protocol that shrinks the primary tumour before surgical removal. We combined a mathematical model and an optimisation algorithm to identify the best chemotherapy schedules for a cohort of virtual patients with different initial tumour compositions. Our results reveal novel strategies to exploit a pair of drugs with different levels of efficacy, provide a platform on which to individualise induction chemotherapy, and lay the foundation for a personalised therapy that leverages targeted therapies, multi-region sequencing, liquid biopsies, and modern computational methods to improve today's multi-modal therapy. Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents' pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system. [ABSTRACT FROM AUTHOR]

Ensuring fire safety is an important condition for the successful operation of industrial enterprises. It is necessary to detect the threat of fire before the ignition. An indicator of danger is the appearance of gas, which occurs as a result of unauthorized heating of the equipment. Gas sensors make it possible to detect the appearance of gases characteristic for the decomposition of materials at the stage of smouldering and pyrolysis, which cause a change in the composition of the atmosphere. This paper presents a mathematical method for the rational placement of gas analyzers in the premises of potentially hazardous industries. The rational placement of gas sensors ensures safety, taking into account economic feasibility. For the first time, an analysis of the accumulation of gas flow from the source to the ceiling, and then to the location of the sensors, was used to select the location of gas sensors. Depending on the permissible values of the gas volume, the placement and number of gas sensors are selected. The calculation of the conditions for the rational placement of gas sensors is carried out according to the most common indicators, such as carbon monoxide and hydrogen at different sizes and heights of premises. [ABSTRACT FROM AUTHOR]

A new mathematical model of an aerosol fibrous filter, composed of a variety of nano- and microfibers, is developed. The combination of nano- and microfibers in a mixed-type filter provides a higher overall quality factor compared with filters with monodisperse fibers. In this paper, we propose a mathematical model of the flow of an incompressible fluid in a porous region consisting of a set of cylinders of various diameters in the range of nano- and micrometers to describe a mixed-type aerosol filter. The flow domain is a rectangular periodic cell with one microfiber and many nanofibers. The motion of the carrier medium is described by the boundary value problem in Stokes flow approximation with the no-slip boundary condition for microfibers and the slip condition for nanofibers. The boundary element method taking into account the slip and non-slip conditions is developed. The calculated velocity field, streamlines, vorticity distribution, and drag of separate fibers and the entire periodic cell are presented. Numerical results for the drag force of the porous medium of a mixed-type filter for the various ratios of mass proportion of nano- and microfibers, porosity, and filtration velocity are presented. The obtained results are compared with the analytical formulas based on the approximate theory of filtration of bimodal filters and with known experimental data. It is shown that with an increase in the mass fraction of nanofibers, the total drag force of the cell increases, while the relative contribution of nanofibers to the total drag force tends toward the value that is less than unity. An approximate analytical formula for the drag coefficient of a mixed aerosol filter is derived. The developed flow model and analytical formulas allow for estimating the aerodynamic drag of a mixed filter composed by nano- and microfibers. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical investigation of pultruded composite glass fibre-reinforced polymer (pGFRP) cross-arms subjected to flexural creep behaviour to assess their performance and sustainability in composite cross-arm structure applications. The primary objective of this study was to investigate the failure creep behaviour of pGFRP cross-arms with different stacking sequences. Specifically, the study aimed to understand the variations in strain rate exhibited during different stages of the creep process. Therefore, this study emphasizes a simplified approach within the experiment, numerical analysis, and mathematical modelling of three different pGFRP composites to estimate the stiffness reduction factors that determine the prediction of failure. The findings show that Findley's power law and the Burger model projected very different strains and diverged noticeably outside the testing period. Findley's model estimated a minimal increase in total strain over 50 years, while the Burger model anticipated PS-1 and PS-2 composites would fail within about 11 and 33 years, respectively. The Burger model's forecasts might be more reasonable due to the harsh environment the cross-arms are expected to withstand. The endurance and long-term performance of composite materials used in overhead power transmission lines may be predicted mathematically, and this insight into material property factors can help with design and maintenance. [ABSTRACT FROM AUTHOR]

Transformer-less connection schemes can provide a feasible solution for lowering the economic cost, occupied space, and device weight of modular multilevel converter (MMC) systems. However, due to the reduction in the converter transformer, the current flow loop is changed; as a result, the existing MMC model is not suitable. In this paper, the ac- and dc-side equivalent circuit models of the MMC system using a transformer-less connection scheme are established in both a–b–c stationary and d–q rotating coordinate systems. Then, a highly accurate mathematical analysis model is proposed, in which the interactions among the electrical quantities can be fully seen. The mathematical model is established in the time domain, and hence the amplitude and phase angle of every harmonic component in each quantity can be directly obtained. The proposed model is verified under various typical situations by comparing the calculated values with the actual waveforms. The comparison results prove that the calculation error is small enough to be negligible. The mathematical model in this paper can provide a powerful tool in terms of the performance analysis and the main circuit parameter design for MMCs in transformer-less applications. [ABSTRACT FROM AUTHOR]

NMDAR-dependent synaptic plasticity in the hippocampus consists of two opposing forces: long-term potentiation (LTP), which strengthens synapses and long-term depression (LTD), which weakens synapses. LTP and LTD are associated with memory formation and loss, respectively. Synaptic plasticity is controlled at a molecular level by Ca2+-mediated protein signaling. Here, Ca2+ binds the protein, calmodulin (CaM), which modulates synaptic plasticity in both directions. This is because Ca2+-bound CaM activates both LTD-and LTP-inducing proteins. Understanding how CaM responds to Ca2+ signaling and how this translates into synaptic plasticity is therefore important to understanding synaptic plasticity induction. In this paper, CaM activation by Ca2+ and calmodulin binding to downstream proteins was mathematically modeled using differential equations. Simulations were monitored with and without theoretical knockouts and, global sensitivity analyses were performed to determine how Ca2+/CaM signaling occurred at various Ca2+ signals when CaM levels were limiting. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM becoming redistributed from low-affinity to high-affinity binding targets. Specifically, CaM was redistributed away from LTD-inducing proteins to bind the high-affinity LTP-inducing protein, calmodulin-dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM-binding protein targets. The model thereby showed a novel form of CaM signaling by which the two opposing pathways crosstalk indirectly. The model also found that CaMKII can repress cAMP production by repressing CaM-regulated proteins, which catalyze cAMP production. The model also found that at low Ca2+ stimulation levels, typical of LTD induction, CaM signaling was unstable and is therefore unlikely to alone be enough to induce synaptic depression. Overall, this paper demonstrates how limiting levels of CaM may be a fundamental aspect of Ca2+ regulated signaling which allows crosstalk among proteins without requiring directly interaction. [ABSTRACT FROM AUTHOR]

This paper aims to analyse two energy storage methods—batteries and hydrogen storage technologies—that in some cases are treated as complementary technologies, but in other ones they are considered opposed technologies. A detailed technical description of each technology will allow to understand the evolution of batteries and hydrogen storage technologies: batteries looking for higher energy capacity and lower maintenance, while hydrogen storage technologies pursuing better volumetric and gravimetric densities. Additionally, as energy storage systems, a mathematical model is required to know the state of charge of the system. For this purpose, a mathematical model is proposed for conventional batteries, for compressed hydrogen tanks, for liquid hydrogen storage and for metal hydride tanks, which makes it possible to integrate energy storage systems into management strategies that aim to solve the energy balance in plants based on hybrid energy storage systems. From the technical point of view, most batteries are easier to operate and do not require special operating conditions, while hydrogen storage methods are currently functioning at the two extremes (high temperatures for metal and complex hydrides and low temperatures for liquid hydrogen or physisorption). Additionally, the technical comparison made in this paper also includes research trends and future possibilities in an attempt to help plan future policies. [ABSTRACT FROM AUTHOR]

The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when R 0 < 1 and R 0 > 1 , respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations. [ABSTRACT FROM AUTHOR]

Dynamic reconfiguration, the monitoring of power production, and the fault diagnosis of photovoltaic arrays, among other applications, require fast and accurate models of photovoltaic arrays. In the literature, some models use the Lambert-W function to represent each module of the array, which increases the calculation time. Other models that use implicit equations to avoid the Lambert-W function do not use the inflection voltages to simplify the system of nonlinear equations that represent the array, increasing the computational burden. Therefore, this paper proposes mathematical models for series-parallel (SP) and total-cross-tied (TCT) photovoltaic arrays based on the implicit equations of the single-diode model and the inflection points of the current–voltage curves. These models decrease the calculation time by reducing the complexity of the nonlinear equation systems that represent each string of SP arrays and the whole TCT. Consequently, the calculation process that solves the model speeds up in comparison with processes that solve traditional explicit models based on the Lambert-W function. The results of several simulation scenarios using the proposed SP model with different array sizes show a reduction in the computation time by 82.97 % in contrast with the traditional solution. Additionally, when the proposed TCT model for arrays larger than 2 × 2 is used, the reduction in the computation time is between 47.71 % and 92.28 % . In dynamic reconfiguration, the results demonstrate that the proposed SP model provides the same optimal configuration but 7 times faster than traditional solutions, and the TCT model is solved at least 4 times faster than classical solutions. [ABSTRACT FROM AUTHOR]

Infectious diseases continue to be a significant threat to human health and civilization, and finding effective methods to combat them is crucial. In this paper, we investigate the impact of awareness campaigns and optimal control techniques on infectious diseases without proper vaccines. Specifically, we develop an SIRS-type mathematical model that incorporates awareness campaigns through media and treatment for disease transmission dynamics and control. The model displays two equilibria, a disease-free equilibrium and an endemic equilibrium, and exhibits Hopf bifurcation when the bifurcation parameter exceeds its critical value, causing a switch in the stability of the system. We also propose an optimal control problem that minimizes the cost of control measures while achieving a desired level of disease control. By applying the minimum principle to the optimal control problem, we obtain analytical and numerical results that show how the infection rate of the disease affects the stability of the system and how awareness campaigns and treatment can maintain the stability of the system. This study highlights the importance of awareness campaigns in controlling infectious diseases and demonstrates the effectiveness of optimal control theory in achieving disease control with minimal cost. [ABSTRACT FROM AUTHOR]

The separation of Rare Earth Elements (REEs) is an important step in the valorization of REE ore and aims at producing individual rare earth compounds for the market. The separation is carried out industrially by solvent extraction (SX) using interconnected circuits consisting of cascades of mixer-settlers. The design of a REE separation circuit implies the selection of the operating conditions and of the number of mixer-settlers required to achieve a target degree of purity for the separated elements. This design work is either carried out by piloting a circuit or using a mathematical simulation. Independent of the method, the world expertise in this area is limited. This paper describes a simulation method requiring a minimum of calibration effort, which can be used to design a complete REE separation plant. The simulation enables assessment of the effect of the number of mixer-settlers per extraction, the scrubbing and stripping stage, as well as the pH of the aqueous solution and organic-phase contents of free and loaded extractant on the purity of the separated REEs. The simulation tool presented here has been developed from a fundamental analysis of the chemical reactions involved in the solvent extraction process. Unlike most of the simulation methods documented in the literature, the method requires no empirical calibration. The proposed method is validated using data from laboratory batch tests and with published data from continuous pilot and industrial REE separation circuits. The application of the simulation tool is illustrated with the planning of the test conditions for a forthcoming pilot test work and with the simulation of a 9-REE product SX separation plant. [ABSTRACT FROM AUTHOR]

Currently, the estimated range of an electric vehicle is a variable value. The assessment of this power reserve is possible by various methods, and the results of the assessment by these methods will be quite different. Thus, building a model based on these cycles is an extremely important task for manufacturers of electric vehicles. In this paper, a simulation model was developed to determine the range of an electric vehicle by cycles of movement. A mathematical model was created to study the power reserve of an electric vehicle, taking into account four driving cycles, in which the lengths of cycles and the forces acting on the electric vehicle are determined; the calculation of the forces of resistance to movement was carried out taking into account the efficiency of the electric motor; thus, the energy consumption of an electric vehicle is determined. The modeling of the study of motion cycles on the presented model was carried out. The mathematical evaluation of battery life was based on simulation results. Simulation modeling of an electric vehicle in the MATLAB Simulink software environment was performed. An assessment of the power reserve of the developed electric vehicle was completed. The power reserve was estimated using the four most common driving cycles—NEDC, WLTC, JC08, US06. Studies have shown that the highest speed of the presented US06 cycle provides the shortest range of an electric vehicle. The JC08 and NEDC cycles have similar developed speeds in urban conditions, while in NEDC there is a phase of out-of-town traffic; therefore, due to the higher speed, the electric vehicle covers a greater distance in equal time compared to JC08. At the same time, the NEDC cycle is the least dynamic and the acceleration values do not exceed 1 m/s2. Low dynamics allow for a longer range of an electric vehicle; however, the actual urban operation of an electric vehicle requires more dynamics. The cycles of movement presented in the article provide a sufficient variety and variability of the load of an electric vehicle and its battery over a wide range, which made it possible to conduct effective studies of the energy consumed, taking into account the recovery of electricity to the battery in a wide range of loads. It was determined that frequent braking, taking into account operation including in urban traffic, provides a significant return of electricity to the battery. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of a closed-cycle evaporation system for the desalination of seawater. The system couples the condensing end of a heat pump with a humidifier, where the air is dehumidified in the heat pump evaporator. First, the mechanism of action of the closed-cycle evaporation system was analyzed from the perspective of heat transfer, and the control equations for the heat and mass transfer of the system were investigated. In addition, a mathematical model of the system was developed and validated. The influence of several important parameters of the air and seawater entering the system on the system's performance under the design conditions was investigated numerically. The parametric analysis showed that the effect of the seawater mass flow rate on the system's productivity was not significant. As the air mass flow rate increases, the freshwater production rate increases and then decreases. The output ratio (GOR) of the system was estimated and found to be competitive with other reported HDH systems. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework that mathematically and optimally quantifies demand response (DR) provisions, considering the power availability of Internet of Things (IoT)-based house load management for the provision of flexibility in the smart grid. The proposed framework first models house loads using IoT windows and occupant behavior, and then integrates IoT-based house loads into DR programs based on a novel mathematical optimization model to provide the optimal power flexibility considering the penetration of IoT-based houses in distribution systems. Numerical results that consider a 33-bus distribution system are reported and discussed to demonstrate the effectiveness of flexibility provisions, from integrating IoT-based houses into DR programs, on peak load reduction and system capacity enhancement. [ABSTRACT FROM AUTHOR]

In the paper, a new method was presented using queueing theory models in order to ensure an optimal production department size, optimized production costs and optimal provision. Queueing/waiting mathematical models represent the development matrix for an experimental algorithm and implicitly numerical approach, both successfully applied (and confirmed in practice) in a production section design for a real industrial engineering unit with discussed method technological flow and equipment schemes compatibility. The total costs for a queueing system with S servers depend on the number of servers. The problem of minimizing cost in terms of S was the main aim of the paper. In order to solve it, we estimated all the variables of the system that influence the cost using the Monte Carlo method. For a Jackson queueing network, the involved linear system has good properties such that it can be solved by iterative methods such as Jacobi and Gauss–Seidel. [ABSTRACT FROM AUTHOR]

This paper presents a solution for the modelling, implementation and simulation of the fractional-order process of producing the enriched 13C isotope, through the chemical exchange between carbamate and carbon dioxide. To achieve the goal of implementation and simulation of the considered process, an original solution for the approximation of fractional-order systems at the variation of the system's differentiation order is proposed, based on artificial intelligence methods. The separation process has the property of being strongly non-linear and also having fractional-order behaviour. Consequently, in the implementation of the mathematical model of the process, the theory associated with the fractional-order system's domain has to be considered and applied. For learning the dynamics of the structure parameters of the fractional-order part of the model, neural networks, which are associated with the artificial intelligence domain, are used. Using these types of approximations, the simulation and the prediction of the produced 13C isotope concentration dynamics are made with high accuracy. In order to prove the efficiency of the proposed solutions, a comparation between the responses of the determined model and the experimental responses is made. The proposed model implementation is made based on using four trained neural networks. Moreover, in the final part of the paper, an original method for the online identification of the separation process model is proposed. This original method can identify the process of fractional differentiation order variation in relation to time, a phenomenon which is quite frequent in the operation of the real separation plant. In the last section of the paper, it is proven that artificial intelligence methods can successfully sustain the system model in all the scenarios, resulting in the feasible premise of designing an automatic control system for the 13C isotope concentration, a method which can be applied in the case of other industrial applications too. [ABSTRACT FROM AUTHOR]

Most biological processes take time to occur. In infectious diseases, such as malaria or chikungunya, there is a period of time between when a susceptible individual gets bitten by the vector, and when the individual develops the disease. These times are commonly modeled by introducing delays or by adding exposed as a new population class. Given a model based on differential equations, delays can be introduced in different forms. In this paper, we study different ways of introducing the delays and, alternatively, using exposed populations. We also analyze their steady solutions and stability, and establish the conditions under which the studied models predict an epidemic. Results and conclusions are presented. [ABSTRACT FROM AUTHOR]

The modular multilevel matrix converter (M3C) is the core component in low-frequency AC (LFAC) transmission, which is a competitive scheme for offshore wind power integration. In this paper, the M3C control strategy with the reduced switching frequency SM voltage balancing method is proposed. First, based on the conventional αβ0 and dq transformations, the M3C mathematical model is derived. Then, the dual-loop control structure with outer loop and inner loop controllers commonly used in voltage source converters is applied to the M3C. The inner loop controller consists of the current tracking controller in the dq reference frame and the circulating current suppressing controller in the αβ0 reference frame; the outer loop controller is proposed for the offshore wind farm LFAC integration scenario. Additionally, according to the operating characteristics of full-bridge sub-modules (FBSMs), three characteristic variables are defined and a reduced switching frequency SM voltage balancing method based on the nearest level control (NLC) is proposed. Finally, time-domain simulations in PSCAD/EMTDC demonstrate the feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and indirect mode of transmission), existence and uniqueness, as well as stability analysis of the solution of the model, are studied. The paper studies the effect of optimal control policy applied to shedding effect. The control is the observation of standard hygiene practices and chemical disinfectants in public spaces. Numerical simulations are carried out to support the analytic result and to show the significance of the fractional order from the biological viewpoint. [ABSTRACT FROM AUTHOR]

In light of the rapidly growing number of photovoltaic micro-grids, the modelling of their short-term power yields based on meteorological measurements is increasing in significance. This requires the knowledge of total and diffuse instantaneous solar radiation; however, most meteorological stations conduct actinometric measurements only with regard to total solar radiation, especially on a minute scale. This paper contains an analysis of the currently used PV cell mathematical model and suggests its modification aimed at calculating PV cell power with satisfactory accuracy, without the knowledge of diffuse solar radiation. Three function families were proposed to approximate the relationship between diffuse irradiance and the total and theoretical total irradiance variance for a cloudless sky. A program has been implemented to identify functions from the aforementioned function families. It leverages an evolution strategy algorithm and a fitness function based on the least-squares point method. It was employed to calculate the desired functions based on actual measurement data. The outcome was the sought-after dependence that enables predicting diffuse irradiance based on more frequently available measurement data. [ABSTRACT FROM AUTHOR]

Asymmetric thermal zones or even non-rectangular structures are common in residential buildings. These types of structures are not easy to model with specialized programs, and it is difficult to know the heat flows and the relationships between the different variables. This paper presents a methodology for modeling structures with multiple thermal zones using the graph theory arrangement. The methodology allows for generating a mathematical model using all the walls of each thermal zone. The modeling method uses the lumped parameter technique with a structure of two resistors and two capacitors for each thermal zone. The walls and internal surfaces of each zone define the thermal resistances, and the elements for the network structure are created by reducing resistances. The structure selected as a case study is similar to a residential apartment, which demonstrates the possibility of modeling complex and non-traditional structures. The accuracy of the generated mathematical model is verified by comparison with experimental data recorded in a scaled-down model. The reduced model is constructed using a 1:10 ratio with a real apartment. The proposed methodology is used to generate a graph arrangement adjusted to the case study, using the surfaces to build the mathematical model. The experimental data allowed to adjust the simulation results with errors in the range of 1.88% to 6.63% for different thermal zones. This methodology can be used to model different apartments, offices, or non-asymmetric structures and to analyze individual levels in buildings. [ABSTRACT FROM AUTHOR]

This paper presents a numerical model of a four-pass supercritical steam superheater with a complex flow system. The specific heat of steam is a function of temperature and pressure, and the specific heat of flue gas is a function of temperature. Pressure and temperature changes along the length of the tubes were also determined. The modified Churchill equation was used to calculate the steam-side friction factor of Darcy–Weisbach. The flue gas temperature variations behind the individual superheater tube rows were calculated. The steam and wall temperature distributions were determined in each tube row along its length. Knowing the temperature of the tube walls and the steam along the flow direction enables the selection of the correct steel grade for the tubes. Thanks to this advantage of the proposed method, the investment can be reduced in superheater construction without the danger of overheating the tube material. The results of the superheater simulation were compared with the results of measurements on the actual object. The proposed numerical method can find application in steam superheaters' design and performance calculations. It can also be used to monitor superheater operating parameters, which are difficult to measure due to the high flue gas temperature. [ABSTRACT FROM AUTHOR]

The generation of mathematical models for the analysis of buildings with multiple thermal zones is a large and complex task. Furthermore, the order and complexity of the dynamical model are increased by the number of included thermal zones. To overcome this problem, this paper presents an algorithm to define the mathematical model automatically, using the geometric and physics parameters as inputs. Additionally, the spatial position of each thermal zone must be recorded in an arrangement called a contact matrix. The algorithm for modeling systems with multiple thermal zones is the main contribution of this work. This algorithm is presented in pseudocode format and as an annex, an implementation in MATLAB software. One of the advantages of this methodology is that it allows us to work with parallelepipeds and not necessarily cubic thermal zones. The algorithm allows us to generate mathematical models with symbolic variables, starting from the knowledge of how many thermal zones compose the system and its geometric organization. This information must be organized in a matrix arrangement called a contact matrix. Different arrays of thermal zones were constructed with wooden boxes to verify the functionality of the models generated with the algorithm. Each case provided information that allowed us to adjust the mathematical models and their simulations, obtaining a range of errors between experimental and simulated temperatures from 2.08 to 5.6 , depending on the number of thermal zones studied. [ABSTRACT FROM AUTHOR]

It is well known that the one-dimensional cutting stock problem (1DCSP) is a combinatorial optimization problem with nondeterministic polynomial (NP-hard) characteristics. Heuristic and genetic algorithms are the two main algorithms used to solve the cutting stock problem (CSP), which has problems of small scale and low-efficiency solutions. To better improve the stability and versatility of the solution, a mathematical model is established, with the optimization objective of the minimum raw material consumption and the maximum remaining material length. Meanwhile, a novel algorithm based on deep reinforcement learning (DRL) is proposed in this paper. The algorithm consists of two modules, each designed for different functions. Firstly, the pointer network with encoder and decoder structure is used as the policy network to utilize the underlying mode shared by the 1DCSP. Secondly, the model-free reinforcement learning algorithm is used to train network parameters and optimize the cutting sequence. The experimental data show that the one-dimensional cutting stock algorithm model based on deep reinforcement learning (DRL-CSP) can obtain the approximate satisfactory solution on 82 instances of 3 data sets in a very short time, and shows good generalization performance and practical application potential. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical simulation model of an electric vehicle traction battery has been developed, in which the battery was studied during the dynamic modes of its charge and discharge for heavy electric vehicles in various driving conditions—the conditions of the urban cycle and movement outside the city. The state of a lithium-ion battery is modeled based on operational factors, including changes in battery temperature. The simulation results will be useful for the implementation of real-time systems that take into account the processes of changing the characteristics of traction batteries. The developed mathematical model can be used in battery management systems to monitor the state of charge and battery degradation using the assessment of the state of charge (SOC) and the state of health (SOH). This is especially important when designing and operating a smart battery management system (BMS) in virtually any application of lithium-ion batteries, providing information on how long the device will run before it needs to be charged (SOC value) and when the battery should be replaced due to loss of battery capacity (SOH value). Based on the battery equivalent circuit and the system of equations, a simulation model was created to calculate the electrical and thermal characteristics. The equivalent circuit includes active and reactive elements, each of which imitates the physicochemical parameter of the battery under study or the structural element of the electrochemical battery. The input signals of the mathematical model are the current and ambient temperatures obtained during the tests of the electric vehicle, and the output signals are voltage, electrolyte temperature and degree of charge. The resulting equations make it possible to assign values of internal resistance to a certain temperature value and a certain value of the degree of charge. As a result of simulation modeling, the dependence of battery heating at various ambient temperatures was determined. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution to the maximum power point tracking (MPPT) problem for photovoltaic (PV) applications in the form of an improved fractional method. The proposal makes use of a mathematical function that describes the relationship between power and voltage in a PV module in a neighborhood including the maximum power point (MPP). The function is generated by using only three points of the P–V curve. Next, by using geometrical relationships, an analytical value for the MPP can be obtained. The advantage of the proposed technique is that it provides an explicit mathematical expression for calculation of the voltage at the maximum power point ( v M P P ) with high accuracy. Even more, complex calculations, manufacturer data, the measurements of short circuit current ( i S C ) and open-circuit voltage ( v O C ) are not required, making the proposal less invasive than other solutions. The proposed method is validated using the P–V curve of one PV module. Experimental work demonstrates the speed in the calculation of v M P P and the feasibility of the proposed solution. In addition, this MPPT proposal requires only the typical and available measurements, namely, PV voltage and current. Consequently, the proposed method could be implemented in most PV applications. [ABSTRACT FROM AUTHOR]

Compared with the traditional lattice structure, the triply periodic minimal surface (TPMS) structure can avoid stress concentration effectively. Here, it is promising in the fields of lightweight and energy absorption. However, the number of structural parameters and mechanical properties of the TPMS structure is plentiful, and the relationship between them is unclassified. In this paper, for the first time, a unified mathematical model was proposed to establish the relationship between TPMS structural design parameters and mechanical properties. Fifteen primitive models were designed by changing the structural parameters (level-set value C and thickness T) and manufacturing by selective laser melting. The geometric defects and surface quality of the structures were explored by optical microscope and scanning electron microscopy (SEM). The mechanical properties were investigated by quasi-static compression test and finite element simulation. The influence of building direction on structural mechanical behavior (failure mode, stress-strain curve) was studied. The real mechanical properties (Young's modulus and plateau stress) of the structure could be predicted according to different C and T combinations. Finally, the energy absorption characteristics were explored. The results showed that when the C value is 0.6 in the range of 0–0.6, the energy absorption performance of the structure is at the maximum level. [ABSTRACT FROM AUTHOR]

Packing problems, also known as nesting problems or bin packing problems, are classic and popular NP-hard problems with high computational complexity. Inspired by classic reinforcement learning (RL), we established a mathematical model for two-dimensional (2D) irregular-piece packing combined with characteristics of 2D irregular pieces. An RL algorithm based on Monte Carlo learning (MC), Q-learning, and Sarsa-learning is proposed in this paper to solve a 2D irregular-piece packing problem. Additionally, mechanisms of reward–return and strategy-update based on piece packing were designed. Finally, the standard test case of irregular pieces was used for experimental testing to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can successfully realize packing of 2D irregular pieces. A similar or better optimization effect can be obtained compared to some classical heuristic algorithms. The proposed algorithm is an early attempt to use machine learning to solve 2D irregular packing problems. On the one hand, our hybrid RL algorithm can provide a basis for subsequent deep reinforcement learning (DRL) to solve packing problems, which has far-reaching theoretical significance. On the other hand, it has practical significance for improving the utilization rate of raw materials and broadening the application field of machine learning. [ABSTRACT FROM AUTHOR]

A battery-swapping station (BSS) can serve as a flexible source in distribution systems, since electric vehicle (EV) batteries can be charged at different time periods prior to their swapping at a BSS. This paper presents an EV battery service transformation from charging to swapping batteries for EVs for the capacity enhancement of a distribution system. A novel mathematical model is proposed to optimally quantify and maximize the flexibility of BSS loads in providing demand response for the utility operator while considering technical operations in the distribution grid. Case studies and numerical findings that consider data from the National Household Travel Survey and a 32-bus distribution system are reported and discussed to demonstrate the effectiveness of the proposed model. Offering battery-swapping services helps reduce not only the peak load, but also the station operation cost. [ABSTRACT FROM AUTHOR]

The optimization of a broach surface is of great significance to improve the cutting performance of the tool. However, the traditional optimization method (surface texture, coating, etc.) destroys the stress distribution of the tool and reduces the service life of the tool. To avoid these problems, four kinds of flocking surfaces (FB1, FB2, FB3, and FB4), imitating the biological structure of Daphniphyllum calycinum Benth (DCB), were fabricated on the rake face of the broach by electrostatic flocking. The broaching experiment, wettability, and spreading experiment were then conducted. Moreover, the mathematical model of the friction coefficient of the bionic broach was built. The effect of broaches with different flocking surfaces on the broaching force, chip morphology, and surface quality of workpieces was studied. The results indicate that the flocked broaches (FB) with good lubricity and capacity of microchips removal (CMR) present a smaller cutting force (Fc) and positive pressure (Ft) compared to the unflocked broach (NB), and reduce the friction coefficient (COF). The chip curl was decreased, and the shear angle was increased by FB, which were attributed to the function of absorbing lubricant, storing, and sweeping microchips. Its vibration suppression effect enhanced the stability in the broaching process and improved the surface quality of the workpiece. More importantly, the FB2 with the most reasonable fluff area and spacing exhibited the best cutting performance. The experimental conclusions and methods of this paper can provide a new research idea for functional structure tools. [ABSTRACT FROM AUTHOR]

In this study, the authors explored the issues of the Soderbergh electrolysis cell's increase in economic efficiency. This result was achieved by analyzing the temperature fields of the electrolysis cell in order to determine the overheating points. As a result, it led to the determination of the points of the hearth bottom's subsequent breakdown, causing the failure of the electrolysis cell. In this paper, the mathematical modeling of the temperature fields using a spatially distributed mathematical model and conducted experimental studies were carried out. The mathematical model also provides the opportunity to measure the temperature field in the hearth bottom (at the bottom) of the OA-300M electrolysis cell. The results of the given research can be used to solve the experimental determination of the hearth bottom internal defect problem. [ABSTRACT FROM AUTHOR]

CO2 is regarded as an effective and environmentally friendly refrigerant. Using a CO2 ejector is a proven method for enhancing the effectiveness of a transcritical CO2 refrigerant system. However, the complex internal flow of a CO2 ejector, involving supersonic effects, phase change effects, metastable effects, and so on, makes it difficult to understand. In order to summarize the current state of the technology and knowledge gaps, this work provides a comprehensive literature review on CO2 ejectors. In the first part, mathematical modelling and simulation calculations of CO2 ejectors are presented, and an overview and classification of ejector models are given. In the second part, the structural optimization part of the ejector is described in detail, and the nozzle structure, the mixing chamber length, improvements to multi-jet systems, and the impact of these factors on the system performance are analyzed. In the third part, flow visualization is used to study the complex flow phenomenon, and the effect of the shock wave on the entrained rate of the ejector is discussed. Finally, the paper outlines the relationship between all ejector technologies, working fluids, and ejector performance and makes valid recommendations for further research and development of CO2 ejectors. [ABSTRACT FROM AUTHOR]