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This study investigated the effect of compaction effort and soaking time on the shear strength properties of fine-grained gypsum-containing soils. The objective was to demonstrate that increasing compaction effort increases soil strength, specifically cohesion and the angle of shear strength, when subjected to soaking in freshwater. Unconsolidated undrained triaxial tests were carried out on CBR soil samples with different soaking times. The results showed a transition from brittle to ductile failure behaviour as the soaking time increased. Mohr–Coulomb failure envelopes showed reduced cohesion and angle of shear strength with increasing soak time. Regression models were developed to establish correlations between soaked and unsoaked strength parameters. Strong relationships were found between soil strength properties, compaction effort and soaking time. Empirical equations were proposed to estimate the cohesion and angle of shear strength from compaction effort and soaking time. This study highlighted the importance of considering gypsum-rich soils in civil engineering design. Gypsum dissolution during wetting significantly affected soil strength parameters. The regression models and empirical equations provide engineers with tools to assess the influence of compaction effort and soaking time on soil strength, thus aiding decision making when designing structures on gypsum-rich soils.

This study summarizes the most recent findings on osmotic dehydration, a crucial step in food preservation. The many benefits of osmotic dehydration are listed, including longer shelf life and preserved nutritional value. Mass transfer dynamics, which are critical to understanding osmotic dehydration, are explored alongside mathematical models essential for comprehending this process. The effect of osmotic agents and process parameters on efficacy, such as temperature, agitation and osmotic agent concentration, is closely examined. Pre-treatment techniques are emphasized in order to improve process effectiveness and product quality. The increasing demand for sustainability is a critical factor driving research into eco-friendly osmotic agents, waste valorization, and energy-efficient methods. The review also provides practical insights into process optimization and discusses the energy consumption and viability of osmotic dehydration compared to other drying methods. Future applications and improvements are highlighted, making it an invaluable tool for the food industry.

The studied solar pot is a recent invention, which is made for environmentally friendly cooking or heating (by utilizing solar energy) of foods and liquids. Its structure is similar to a double pipe heat exchanger, it has an outer mantle and an inner cooking tank. The goals of the paper are proposing a new physically-based mathematical model describing the solar pot and carrying out computer experiments with it, assembling an experimental system of the pot connected with a solar collector and performing measurements on it. Based on the results, the solar pot can successfully be used for cooking or sterilizing foods or liquids during the studied time period, in Hungary. In particular, based on measured data, the temperature level needed for heat treatment (75 °C) can be maintained in the cooking tank for several hours (~5 h, on the average) in a typical day in May.

Pruning residues, which occur every year in orchards and have many different utilization potentials, are an important issue for fruit producers. The shredding process is indispensable and critical for the utilization of these residues. The performance of the shredding process is affected by the operating parameters of the shredding machine as well as the moisture content of the residues to be shredded. In this study, olive pruning residues with three different moisture contents were shredded at three different rotor speeds in the developed shredding system. We determined how the power requirement of the shredder changed under different conditions, and empirical models were developed. The experiments showed that the average power requirement of the shredder ranged from 7.32 to 10.81 kW, and it was found that residues with low moisture content decreased the power values, while higher rotor speeds increased the power requirement. The developed final model has a mean absolute error (MAE) of 0.376, a root mean square error (RMSE) of 0.441, and a correlation coefficient (R2) of 0.859. The model serves as a reliable tool for estimating power requirements in the shredding of olive pruning residues, enabling the selection of the optimal rotor speed based on moisture content.

This paper proposes a mathematical model for the shading profiles of a PV module with thin, long linear elements. The model includes the brightness distribution over the entire shading region (umbra, penumbra, and antumbra). A corresponding calculation code in the form of m-files has been prepared for the MATLAB environment. The input data for the calculations are the coordinates of the Sun’s position in the sky, the dimensions and spatial orientation of the shading element, and the spatial orientation of the shaded PV module. The correctness of the model was verified by a measurement experiment carried out under actual outdoor weather conditions. Statistical analysis of the comparison between the measurement data from the experiment and the model showed its high accuracy. As part of this research work, it was also checked how shading with thin linear elements affects the current–voltage characteristics of the module. It turned out that even a small linear shading could reduce the power output of the module by more than 6%, with the distribution of this shading across the individual cells of the module being extremely important.

A device that transforms chemical energy into electrical energy is an electrochemical cell. The reaction type inside the cell determines whether it is exothermic or endothermic. This paper discusses the mathematical modelling of exothermic explosions in a slab. This model is based on a nonlinear equation containing a nonlinear term related to Arrhenius, bimolecular, and sensitised laws of reaction kinetics. The absolute temperature can be derived by solving the nonlinear equation using the Akbari–Ganji technique. The mathematical model also numerically solved and simulated in the MATLAB® v2016b software. The new simple theoretical result is validated with previously identified analytical and numerical findings. The influence of the parameters of Frank-Kamenetskii number, activation energy and the numerical exponent on temperature is discussed. The Frank-Kamenetskii number is observed to drop as the temperature is found to decrease, while the activation energy parameter is shown to increase. The numerical exponent has little or no effect on the temperature. An extension of this model to cylinder and sphere geometry is also provided.

The prediction of the terminal velocity of a single spherical particle is essential to realize mathematical modeling useful for the design and adjustment of separators used in wastewater treatment. For non-spherical and non-single particles, terminal velocity can be traced back to that of single spheres using coefficients and Kynch’s theory, respectively. Because separation processes can involve small or large particles and can be carried out using gravity, as with clarifiers/thickeners, or by centrifugation in centrifuges where the acceleration can exceed 10,000× g, the Reynolds number of the particle can be highly variable, ranging from 0.1 to 200,000. The terminal velocity depends on the drag coefficient, which depends, in turn, on the Reynolds number containing the terminal velocity. Because of this, to find the terminal velocity formula, it is preferable to look first for a relationship between the drag coefficient and the Archimedes number which does not contain the terminal velocity. Formulas already exist expressing the relationship between the drag coefficient and the Archimedes number, from which the relationship between the terminal velocity and the Archimedes number may be derived. To improve the accuracy obtained by these formulas, a new relationship was developed in this study, using dimensional analysis, which is valid for Reynolds number values between 0.1 and 200,000. The resulting mean relative difference, compared to the experimental standard drag curve, was only 1.44%. This formula was developed using the logarithms of dimensionless numbers, and the unprecedented accuracy obtained with this method suggested that an equally accurate formula for the drag coefficient could also be obtained with respect to the Reynolds number. Again, the resulting level of accuracy was unprecedentedly high, with a mean relative difference of 1.77% for Reynolds number values between 0.1 and 200,000.

This work explores the mathematical modelling capabilities of various iterations of ChatGPT, focusing on their performance across tasks of differing complexity and openness. The study examines the abilities of GPT-3.5, GPT-4.0, and a more instructed version, GPT-MM, in multiple scenarios. It is observed that all versions demonstrate basic mathematical problem-solving skills. However, their effectiveness varies with increasing task complexity. While GPT-4.0 and GPT-MM show marginal improvements in providing detailed solutions, significant challenges persist, especially in moderate to complex modelling contexts where comprehending the nuances of tasks becomes challenging. Additionally, the study suggests that the openness of modelling tasks has a limited impact on performance, highlighting that mathematical and contextual complexities play more critical roles. The implications of these observations are discussed in terms of potential enhancements to teaching methodologies and the integration of AI tools like GPT in educational settings. This reiterates the importance of further research to fully understand the capabilities and limitations of AI tools and ensure their effective use in education.

To investigate resistance change in the fire area of a roadway caused by roadway fires, a mathematical calculation model for thermal resistance is developed. Theoretical research is conducted to analyze the factors influencing resistance change through theoretical derivation, revealing that temperature is a key factor contributing to the change in thermal resistance. By leveraging the correlation between changes in CO concentration and temperature on the downwind side of the roadway within the fire zone, researchers developed mathematical models to predict temperature increases at various points downwind of the fire source. These models were then used to determine the mathematical relationship governing the change in thermal resistance. The accuracy of the numerical simulation software was validated using Fluent numerical simulation software and scaled-down model experiments. Full-scale numerical simulation experiments were conducted to investigate the fire characteristics of roadway fires and validate the thermal resistance mathematical model. The results indicate that the thermal resistance in the numerical simulation is 7.55 Pa at 20m from the fire source and 5.54 Pa at the end of the roadway. The decrease in resistance is linear. The minimum error between the thermal resistance calculated by the mathematical model and the gradient of the pressure drop in the numerical simulation is 0.03 Pa, approximately 2.3%. Furthermore, the fitting degree of the pressure drop in each section is as high as 97.7%. The calculation model demonstrates high accuracy and offers a theoretical foundation for investigating fire resistance in tunnel fire.

The work analyzes the performance assurance of mine hoisting machines, including the problem of the quality of performance of the functions. The quality of functioning allows evaluation of a set of properties of the process of lifting loads, designed to meet the given requirements in accordance with the purpose and evaluated performance indicators. In this case, the quality of the function depends not only on the elements that worked properly or failed during system functioning but also on the moments involving certain changes in the states of the system. The considered system of power supply of mine hoisting installations is rather complex with respect to reliability. The proposed approach allows this rather complex system to lead in terms of the form of a serial connection of elements, allowing for determining the influence of the functioning of its subsystems and electrical equipment on the technological process of cargo lifting in a coal mine. The presented mathematical concept of increasing the reliability and failure-free operation of mine hoisting plants with the help of the developed mathematical model of the mine hoisting plant allowed studying the reliability indicators of the hoisting plant operation and reserving the equipment most effectively to increase reliability. The determination of coupling coefficients in this study made it possible to analyze the impact of the reliability of electrical equipment and power supply systems on the operation of technological machines to improve the reliability of mining equipment and the efficiency of technical systems of mining equipment.

Syzygium aromaticum L. Myrtaceae is one of the plants rich in bioactive compounds that have beneficial effects on the skin. Fermented plant extracts (FPEs) obtained from this plant have recently been exploited as new cosmetic ingredients. The concept of our study was related to the use of clove buds in the fermentation process in order to obtain new cosmetic raw materials with high antioxidant potential. The focus was on evaluating antioxidant activity (AA), total polyphenol content (TPC), and lactic acid efficiency (LAe). For this purpose, the most favourable technological parameters of the fermentation process of clove buds were determined, including the type of microorganisms, initial sugar content, plant raw material content, and fermentation time. The most favourable parameters were correlated with the optimal parameters, which were determined based on response surface methodology (RSM). Based on DPPH and Folin–Ciocalteu assays and GC-MS analysis, optimal points of antioxidant activity against reactive oxygen species (analysed with RSM) were successfully selected, enabling quantitative mathematical representations. The optimisation revealed that using a strain of Lactobacillus rhamnosus MI-0272 in lactic fermentation and plant material (6.40%) and beet molasses (3.20%) results in the highest antioxidant potential of FPE (33.90 mmol Tx/L) and yielding LA with the highest efficiency (96%). The optimised FPE had higher polyphenol content (11.60 mmol GA/L ± 0.14), chelating and antioxidant activity (0.32 mmol Fe2+/L ± 0.01 and 11.60 mmol Tx/L ± 0.09), and Fe3+ ion reduction (49.09 mmol Fe3+/L ± 0.16) than the PE. In addition, the possibility of using the spent plant material remaining after the extraction process to prepare activated carbons capable of treating wastewater was investigated.

The issues of the evaluation and prediction of the reliability and testability of mining machinery and equipment are becoming particularly relevant, since the safety of technological processes and human life is reaching a new level of realisation due to changes in mining technology. The work is devoted to the development of a logical model for analysing the controllability of mining equipment. The paper presents a model of reliability of the operation of mining equipment on the example of a mine load and passenger hoist. This generalised model is made in the form of a graph of transitions and supplemented with a system of equations. The model allows for the estimation of the reliability of equipment elements and equipment as a whole. A mathematical and logical model for the calculation of the availability and downtime coefficients of various designs of mining equipment systems is proposed. This model became the basis for the methods to calculate the optimal values of diagnostic depth. At these calculated values, the maximum value of availability factor will be obtained. In this paper, an analytical study was carried out and dependences of the readiness factor of parameters of the investigated system such as the intensity of control of technical systems, intensity of failures, etc., were constructed. The paper proposes a mathematical model to assess the reliability of mine hoisting plants through its integration into the method of improving the reliability of mine hoisting plants.

The retreat of mountain glaciers inevitably leads to an increase in the number of outburst moraine lakes. One of the possible mechanisms of moraine dam outburst along with overflow over the crest is the formation of a filtration channel in the body of the moraine dam (piping). An algorithm for calculating the outburst flood hydrograph, describing the development of a filtration channel in the body of a moraine dam and the subsequent formation of water overflow when the soil above the channel collapses, is proposed in this paper. Verification of proposed methodology was carried out on the basis of experimental data and published data of real outbursts. Satisfactory results verifying this methodology made it possible to use the proposed methodology for the calculation of the hydrograph of the outburst of Lake Bashkara in the Elbrus region, which occurred on 1 September 2017. It is shown that the simulation results are quantitatively comparable with the estimates obtained from field data: the time of water discharge through the channel was 16 min, the period of the outburst wave passage was 40 min, and the maximum discharge was 636 m3/s. Thus, the possibility of applying the proposed methodology for calculating the destruction of natural moraine dams has been demonstrated.

In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion Dynamics (OD), Group Decision-Making (GDM) and Knowledge Dynamics (KD). In the OD case, we highlight special classes of social agents, such as informed agents, contrarians and extremists. As regards GDM, we present state-of-the-art models on various kinds of decision-making processes. In the KD case, we discuss processes of knowledge diffusion and creation via the presence of self-innovating agents. The primary question we wish to address is: to what extent does Sociophysics correspond to social reality? For that purpose, for each social diffusion model category, we present notable Sociophysics applications for real-world socioeconomic phenomena and, additionally, we provide a much-needed critique of the existing Sociophysics literature, so as to raise awareness of certain issues that currently undermine the effective application of Sociophysics, mainly in terms of modelling assumptions and mathematical formulation, on the investigation of key social processes.

Concentrating solar power (CSP) is a high-potential renewable energy source that can leverage various thermal applications. CSP plant development has therefore become a global trend. However, the designing of a CSP plant for a given solar resource condition and financial situation is still a work in progress. This study aims to develop a mathematical model to analyze the levelized cost of electricity (LCOE) of Thermal Energy Storage (TES)-integrated CSP plants in such circumstances. The developed model presents an LCOE variation for 18 different CSP configurations with TES incorporated for Rankine, Brayton, and combined power generation cycles, under regular TES materials and nano-enhanced TES materials. The model then recommends the most economical CSP plant arrangement. Within the scope of this study, it was found that the best configuration for electricity generation is a solar power tower with nano-enhanced phase change materials as the latent heat thermal energy storage medium that runs on the combined cycle. This returns an LCOE of 7.63 ct/kWh with a 22.70% CSP plant efficiency. The most favorable option in 50 MW plants is the combined cycle with a regular TES medium, which has an LCOE of 7.72 ct/kWh with a 22.14% CSP plant efficiency.

Inquiry and modelling are relevant processes of mathematical activity, and both are considered as important competencies for problem solving, since their subprocesses have a family resemblance that makes them mutually complementary and enriched. In this line, we report an investigation focused on the study of the synergies and relationships established between the inquiry and modelling processes emerging in a learning situation, based on a realistic and authentic archaeological context. To this end, we considered one theoretical cycle to explain each process, and then designed a learning situation contextualised in a realistic and authentic archaeological context which promoted the development of inquiry and modelling skills for its solving. Methodologically, we conducted a case study with students in a secondary school of Badalona (Catalonia, Spain), who solved the learning situation grouped into working teams. Through a thematic analysis, we identified the steps of both processes followed by the students when solving the learning situation, and thus we delved into the synergies and relationships established between inquiry and modelling processes. Finally, we reflect on how both processes mutually enrich when dealing with a problem-situation and propose an integrative cycle for the development of inquiry and modelling skills in the classroom.

Background: Supply chain networks (SCNs) have been interrupted by the COVID-19 pandemic, leaving them open to financial losses. SCs have been impacted by the pandemic, necessitating the adoption of sustainable practices and dynamic capacities to ensure resilience and performance. Several studies have focused on this subject, offering insights into the importance of sustainable supply-chain management, corporate governance, big data management activities, and digital technology in minimising the consequences of the pandemic and fostering sustainability. Methods: This study suggests an analytical framework for assessing environmentally friendly procedures and dynamic capacities to assure performance in a disruptive environment. Results: The following are some of the important details and contributions in this article: (1) developed a conceptual framework for assessing dynamic capacities and sustainable behaviours considering COVID-19, (2) concentrates on financial ratios during COVID-19, and (3) established drivers for sustainable practices and competencies during disruption and unpredictable business settings. Conclusions: The suggested model can assist practitioners in creating and implementing sustainable supply chain (SC) activities and tracking and assessing their effects on the sustainability of businesses. So, the proposed model can assist managers in creating and implementing sustainable supply-chain activities and tracking and analysing their effects on the sustainability of businesses.

Hydrodynamic traffic models are crucial to optimizing transportation efficiency and urban planning. They usually comprise a set of coupled partial differential equations featuring an arbitrary number of terms that aim to describe the different nuances of traffic flow. Consequently, traffic models quickly become complicated to solve and difficult to interpret. In this article, we present a general traffic model that includes a relaxation term and an inflow of vehicles term and utilize the mathematical technique of nondimensionalisation to obtain universal solutions to the model. Thus, we are able to show extreme sensitivity to initial conditions and parameter changes, a classical signature of deterministic chaos. Moreover, we obtain simple relations among the different variables governing traffic, thus managing to efficiently describe the onset of traffic jams. We validate our model by comparing different scenarios and highlighting the model’s applicability regimes in traffic equations. We show that extreme speed values, or heavy traffic inflow, lead to divergences in the model, showing its limitations but also demonstrating how the problem of traffic jams can be alleviated. Our results pave the way to simulating and predicting traffic accurately on a real-time basis.

The human brain is arguably the most complex “machine” to ever exist. Its detailed functioning is yet to be fully understood, let alone modelled. Neurological processes have logical signal-processing and biophysical aspects, and both affect the brain’s structure, functioning and adaptation. Mathematical approaches based on both information and graph theory have been extensively used in an attempt to approximate its biological functioning, along with Artificial Intelligence frameworks inspired by its logical functioning. In this article, an approach to model some aspects of the brain learning and signal processing is presented, mimicking the metastability and backpropagation found in the real brain while also accounting for neuroplasticity. Several simulations are carried out with this model to demonstrate how dynamic neuroplasticity, neural inhibition and neuron migration can reshape the brain’s logical connectivity to synchronise signal processing and obtain certain target latencies. This work showcases the importance of dynamic logical and biophysical remodelling in brain plasticity. Combining mathematical (agents, graph theory, topology and backpropagation) and biomedical ingredients (metastability, neuroplasticity and migration), these preliminary results prove complex brain phenomena can be reproduced—under pertinent simplifications—via affordable computations, which can be construed as a starting point for more ambitiously accurate simulations.

Syngas fermentation can play an important role in implementing the concept of biorefinery as it can serve as a platform to convert high-lignin biomass to biofuels. For the utilization of this process in commercial scale, the generation of an experimental database supported by a deterministic mathematical model and optimization is necessary. In this study, a locally isolated clostridial consortium, UACJUChE1, was used to convert pyro-syngas to ethanol and acetic acid. Mathematical models were developed and validated for a 3 L stirred and gas-sparged bioreactor operated in both semi-batch and continuous modes. The volumetric productivity of ethanol was correlated with the dilution rate and the gas residence time. The performance of the bioreactor, run in both semi-batch and continuous modes, was optimized using response surface methodology. For the semi-batch operation, a maximum ethanol concentration of 13.122 g/L after 30 h operation was achieved at optimum values of pyrolysis temperature, ratio of gas to liquid volume (VG/VL), and volumetric gas flow rate of 648 °C, 0.46, and 6.7 L/h respectively. For continuous operation, a maximum ethanol concentration of 29.450 g/L after 300 h is obtained at optimum values of VG/VL and ratio of gas to liquid volumetric flow rate of 0.28 and 335.148, respectively.

This work is concerned with bone remodeling, an intriguing and efficient biological process that ensures the optimal compliance of the human skeleton by screening and replacing any single piece of it on a recursive basis. We propose here that a class of algorithms, which are simple enough to be implemented at an individual cell level, suffices to account for the two main features of such homeostatic process: thorough screening of the whole skeleton on the one hand and destruction and subsequent replacement of any single bone piece on the other. This last process is accomplished at a microscopic scale by special groups of cells, assembled for that purpose, called Bone Multicellular Units (BMUs). Moreover, it is shown that the algorithms proposed are robust, i.e, they remain functional in a wide range of biomechanical environments, thus allowing for different remodeling rates at different places.

In the current digital transformation to Industry 4.0, the demands on the ability of countries to react responsibly and effectively to threats in the field of cyber security (CS) are increasing. Cyber safety is one of the pillars and concepts of Industry 4.0, as digitization brings convergence and integration of information technologies (IT) and operational technologies (OT), IT/OT systems, and data. Collecting and connecting a large amount of data in smart factories and cities poses risks, in a broader context for the entire state. The authors focus attention on the issue of CS, where, despite all digitization, the human factor plays a key role—an actor of risk as well as strengthening the sustainability and resilience of CS. It is obvious that in accordance with how the individuals (decision-makers) perceive the risk, thus they subsequently evaluate the situation and countermeasures. Perceiving cyber threats/risks in their complexity as a part of hybrid threats (HT) helps decision-makers prevent and manage them. Due to the growing trend of HT, the need for research focused on the perception of threats by individuals and companies is increasing. Moreover, the literature review points out a lack of methodology and evaluation strategy. This study presents the results of the research aimed at the mathematical modelling of risk perception of threats to the state and industry through the disruption of CS. The authors provide the developed factor model of cyber security (FMCS), i.e., the model of CS threat risk perception. When creating the FMCS, the researchers applied SEM (structural equation modelling) and confirmatory factor analysis to the data obtained by the implementation of the research tool (a questionnaire designed by the authors). The pillars and sub-pillars of CS defined within the questionnaire enable quantification in the perception of the level of risk of CS as well as differentiation and comparison between the analyzed groups of respondents (students of considered universities in SK and CZ). The convergent and discriminant validity of the research instrument is verified, and its reliability is confirmed (Cronbach’s alpha = 0.95047). The influence of the individual pillars is demonstrated as significant at the significance level of α = 5%. For the entire research set N = 964, the highest share of risk perception of CS threats is achieved by the DISRIT pillar (disruption or reduction of the resistance of IT infrastructure).

Objective: To estimate the prevalence and incidence of TB before and during the COVID-19 pandemic in Tamil Nadu, south India. Methods: In the present study, the effect of COVID-19 epidemiology on the TB epidemic was assessed by the SEIR (Susceptible-Exposed-Infected-Recovered), a compartmental epidemiological model. The model input parameters on compartments of TB and incidence of COVID-19 were collected from the published literature. Based on the data collected, point prevalence and incidence of TB per 100,000 population is calculated with and without COVID-19. A prediction was conducted up to 2025, trend analysis was performed, and a trend chi-square test and chi-square test of independence were used to test the difference between the prevalence with and without COVID-19. R software 2000 (R 4.0.0) was used for analysis. Results: The TB prevalence without and with COVID-19 decreases from 289 in 2020 to 271 in 2025 and from 289 in 2020 to 269 in 2025, respectively. Similarly, the incidence of TB was decreasing from 144 in 2020 to 135 in 2025 without COVID-19 and 143 in 2020 to 134 in 2025 with COVID-19. Though the TB burden is decreasing over the years, the trend was not statistically significant (p > 0.05). With respect to the district level, the prevalence and incidence of TB with and without COVID-19 is also found to be decreasing over the years. It was also found that the difference in the prevalence and incidence of TB with and without COVID-19 was not statically significant. Conclusion: The results of our study shows that there was an annual decline of around 2% from 2020 to 2025 in the trend of the prevalence and incidence of TB with and without COVID-19. Overall, there is a reduction, but it was not significant, and there is no significant effect of COVID-19 on TB in Tamil Nadu.

Among all hydrocarbons, the methane molecule contains the highest amount of hydrogen with respect to carbon. Therefore, the catalytic decomposition of methane is considered as an efficient approach to produce hydrogen along with nanostructured carbon product. On the other hand, the presence of hydrogen in the composition of the initial gas mixture is required for the stable operation of the catalyst. In present work, the experiments on the catalytic decomposition of methane–hydrogen mixture were performed in a flow-through quartz reactor equipped with McBain balances under atmospheric pressure. The catalyst NiO-CuO/Al2O3 was prepared by the mechanochemical activation technique. The maximum carbon yield of 34.9 g/gcat was obtained after 2 h of experiment at 610 °C. An excess of hydrogen in the reaction mixture provided the long-term activity of the nickel–copper catalyst. The durability tests ongoing for 6 h within a temperature range of 525–600 °C showed no noticeable deactivation of the catalyst. Two kinetic models, D1a and M1a, were proposed for the studied decomposition of the methane–hydrogen mixture over the nickel–copper catalyst. The kinetic constants for these models were determined by means of mathematical modelling.

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation containing a nonlinear term with an exponential relationship between intrinsic reaction rate and temperature. The porous catalyst particle’s concentration is obtained by solving the nonlinear equation using Akbari-Ganji’s method. A simple and closed-form analytical expression of the effectiveness factor for slab, cylindrical, and spherical geometries was also reported for all values of Thiele modulus, activation energy, and heat reaction. The accordance with results of a reliable numerical method shows the good accuracy that their approximate solution yields.

This research is devoted to the microstructure evolution and deformation behavior of the Al-1.2Mg-0.7Si-1.0Cu-0.1Sc-0.2Zr alloy during the isothermal multidirectional forging (MDF) in a large cumulative strain and temperature range. The structure investigation of the studied alloy revealed several phases precipitated during solidification, among which θ(Al2Cu), Q(Al5Cu2Mg8Si6), Mg2Si, Sc-bearing W(AlScCu) and V(AlSi2Sc2) phases were observed. The MDF at 150–350 °C and a maximum cumulative strain of 14.4 significantly refined grain structure providing a mean grain size of 1.2–2.1 µm. The L12 structured Al3(Sc,Zr) dispersoids with a mean size of 10 ± 1 nm were formed during two-step homogenization annealing. Due to Zener pinning of the nanoscale dispersoids and fine-grained structure, the alloy exhibited near-superplastic behavior in a temperature range of 460–500 °C and strain rate range of 2 × 10−3–1 × 10−2 s−1 with the maximum elongation to failure of ~300%. After a strengthening heat treatment, the forged alloy exhibited the yield strength of 326 ± 5 MPa, ultimate tensile strength of 366 ± 5 MPa, and elongation of 10 ± 3%. The hot deformation behavior was described using the Arrhenius type model. The developed model demonstrated high predictability accuracy with a maximum average absolute relative error of 6.6%.

The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.

We believe that there is sufficient evidence from basic science, longitudinal cohort studies and randomised controlled trials which validates the low-density lipoprotein cholesterol (LDL-C) or lipid hypothesis. It is important that we can communicate details of the cardiovascular disease (CVD) risk reduction that the average patient could expect depending on the scale of LDL-C decrease following lipid lowering therapy. It is also essential that residual risk (ResR) of CVD be highlighted. To achieve this aim by using existing trial evidence, we developed mathematical models initially for relative risk reduction (RRR) and absolute risk (AR) reduction and then showed that despite optimising LDL-C levels, a considerable degree of ResR remains that is dependent on AR. Age is significantly associated with AR (odds ratio: 1.02, 95% confidence intervals: 1.01–1.04) as was previously demonstrated by analysing the Whickham study cohort using a logistic regression model (age remaining significant even when all the other significant risk factors such as sex, smoking, systolic blood pressure, diabetes and family history were included in the regression model). A discussion of a paper by Ference et al. provided detailed evidence of the relationship between age and AR, based on lifetime LDL-C exposure. Finally, we discussed non-traditional CVD risk factors that may contribute to ResR based on randomised controlled trials investigating drugs improving inflammation, thrombosis, metabolic and endothelial status.

This study aimed to improve the control system of the biological stage of wastewater treatment using the quality control information system to support the concept of environmental efficiency management. In this case, the object of the study was the treatment facilities of Sumy city (Ukraine). For automatic control of wastewater quality, pH, oxidation reduction potential (ORP), electrical conductivity, and temperature indicators were taken, as well as hydrobiological analysis of activated sludge and mathematical modelling. The pH of wastewater at the input system has systematically unacceptable values (above 8.5 were recorded). Unacceptable concentrations of sulphur-containing toxicants arrive at the entrance of treatment facilities (0.22–1.3 mg/L). The response of activated sludge biocenosis to increasing concentrations of hydrogen sulphide in wastewater was analysed. Furthermore, a mathematical model of monoculture population growth, with two factors that affect population growth (nutrient concentration and monoculture production concentration), was implemented for the initial assessment of possible negative effects on wastewater treatment. The differential equation of the population dynamics of the i-th species of microorganisms in activated sludge was described. The applied system of automated monitoring of wastewater parameters with expert assessment of activated sludge and a unified mathematical model of approaches allows for a complex system of decision-making support to be realised. However, this requires the construction of mathematical models that would take into account the cause–effect relations that operate under conditions of incomplete technological information and the potential presence of emergencies due to natural disasters and military activities.

Time-kill curves (TKCs) are more informative compared with the use of minimum inhibitory concentration (MIC) as they allow the capture of bacterial growth and the development of drug killing rates over time, which allows to compute key pharmacodynamic (PD) parameters. Our study aimed, using a semi-mechanistic mathematical model, to estimate the best pharmacokinetic/pharmacodynamic (PK/PD) indices (ƒAUC/MIC or %ƒT > MIC) for the prediction of clinical efficacy of veterinary FQs in Staphylococcus pseudintermedius, Staphylococcus aureus, and Escherichia coli collected from canine pyoderma cases with a focus on the comparison between marbofloxacin and pradofloxacin. Eight TCKs for each bacterial species (4 susceptible and 4 resistant) were analysed in duplicate. The best PK/PD index was ƒAUC24h/MIC in both staphylococci and E. coli. For staphylococci, values of 25–40 h were necessary to achieve a bactericidal effect, whereas the calculated values (25–35 h) for E. coli were lower than those predicting a positive clinical outcome (100–120 h) in murine models. Pradofloxacin showed a higher potency (lower EC50) in comparison with marbofloxacin. However, no difference in terms of a maximal possible pharmacological killing rate (Emax) was observed. Taking into account in vivo exposure at the recommended dosage regimen (3 and 2 mg/kg for pradofloxacin and marbofloxacin, respectively), the overall killing rates (Kdrug) computed were also similar in most instances.

A theoretical model of amperometric enzyme electrodes has been developed in which chemical amplification occurs in a single enzyme membrane via cyclic substrate conversion. The system is based on non-stationary diffusion equations with a nonlinear factor related to the Michaelis–Menten kinetics of the enzymatic reaction. By solving the nonlinear equations using the AGM technique, simple analytical expressions of concentration substrate, product, and amperometric current response are derived. Further, biosensor sensitivity, resistance, and gain are obtained from the current. MATLAB programming was used to carry out the digital simulation. The analytical results are validated with the numerical results. The effect of substrate concentration, maximum enzymatic rate, and membrane thickness on biosensor response was evaluated.

In this paper, the mechanical characteristics of a miniature optomechanical accelerometer, similar to those proposed for a wide range of applications, have been investigated. With the help of numerical modelling, characteristics such as eigenfrequencies, quality factor, displacement magnitude, normalized translations, normalized rotations versus eigenfrequencies, as well as spatial distributions of the azimuthal and axial displacements and stored energy density in a wide frequency range starting from the stationary case have been obtained. Dependencies of the main mechanical characteristics versus the minimal and maximal system dimensions have been plotted. Geometries of the optomechanical accelerometers with micron size parts providing the low and the high first eigenfrequencies are presented. It is shown that via the choice of the geometrical parameters, the minimal measured acceleration level can be raised substantially.

The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other.

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy’s law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard’s equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect.

The heat conduction problem for a cylindrical ring reactor of finite length, filled with biomass, which is transported at a constant speed by means of a rotating screw, is considered. The screw is assumed to be mounted on a circular shaft and is inductively heated by the Joule–Lenz effect. The surfaces of the channel and the shaft are thermally insulated. At the entrance and exit of the channel, boundary conditions of the third kind are formulated. The surface of the screw is replaced by uniformly distributed point heat sources. The problem is solved using the decomposition of the investigated temperature into Fourier–Bessel series over space variables and the integral Laplace transform over time. It is shown that the temperature has a quasi-stationary character with a short-term transient process. A numerical analysis of the spatio-temporal structure of temperature and its relationship with the thermophysical, kinematic and geometric parameters of the screw and biomass was carried out. In particular, it was found that the temperature along the reactor increases almost linearly starting from 400 K. It is shown that as in the case of an infinitely long channel, the condition of space–time resonance of the temperature field is fulfilled here.

This study examined the effect of beef fermentation with Lactiplantibacillus paraplantarum (L) PTCC 1965, Lactiplantibacillus (L) plantarum subsp. plantarum PTCC 1745, and Lactiplantibacillus (L) pentosus PTCC 1872 bacteria on the growth of pathogenic bacteria, including Salmonella (S) Typhi PTCC 1609 and Staphylococcus (S) aureus PTCC 1826. The growth of lactic acid bacteria (LAB) and the effect of fermentation on pathogenic bacteria were studied using Weibull: biphasic linear and competitive models. The results showed that the rate of pH reduction was lower in the early stages and increased as the microbial population grew. The α parameter was lower for L. plantarum subsp. plantarum compared to L. paraplantarum and L. pentosus. The comparison of the α parameter for bacterial growth and pH data showed that the time interval required to initiate the rapid growth phase of the bacteria was much shorter than that for the rapid pH reduction phase. The pH value had a 50% greater effect on the inactivation of S. Typhi when compared to the samples containing L. plantarum subsp. plantarum and L. pentosus. The same parameter was reported to be 72% for the inactivation of St. aureus. In general, during the fermentation process, LAB strains caused a decrease in pH, and as a result, reduced the growth of pathogens, which improves consumer health and increases the food safety of fermented meat.

Leprosy (Hansen’s disease) is an infectious, neglected tropical skin disease caused by the bacterium Mycobacterium leprae (M. leprae). It is crucial to note that the dynamic behavior of any living microorganism such as M. leprae not only depends on the conditions of its current state (e.g., substrate concentration, medium condition, etc.) but also on those of its previous states. In this article, we have developed a three-dimensional mathematical model involving concentrations of healthy Schwann cells, infected Schwann cells, and M. leprae bacteria in order to predict the dynamic changes in the cells during the disease dissemination process; additionally, we investigated the effect of memory on system cell populations, especially on the M. leprae bacterial population, by analyzing the Caputo–Fabrizio fractionalized version of the model. Most importantly, we developed and investigated a fractionalized optimal-control-induced system comprising the combined drug dose therapy of Ofloxacin and Dapsone intended to achieve a more realistic treatment regime for leprosy. The main goal of our research article is to compare this fractional-order system with the corresponding integer-order model and also to distinguish the rich dynamics exhibited by the optimal-control-induced system based on different values of the fractional order ζ∈(0,1). All of the analytical results are validated through proper numerical simulations and are compared with some real clinical data.

This article presents a two-grid approach for developing a black-box iterative solver for a large class of real-life problems in continuum mechanics (heat and mass transfer, fluid dynamics, elasticity, electromagnetism, and others). The main requirements on this (non-)linear black-box solver are: (1) robustness (the lowest number of problem-dependent components), (2) efficiency (close-to-optimal algorithmic complexity), and (3) parallelism (a parallel robust algorithm should be faster than the fastest sequential one). The basic idea is to use the auxiliary structured grid for more computational work, where (non-)linear problems are simpler to solve and to parallelize, i.e., to combine the advantages of unstructured and structured grids: simplicity of generation in complex domain geometry and opportunity to solve (non-)linear (initial-)boundary value problems by using the Robust Multigrid Technique. Topics covered include the description of the two-grid algorithm and estimation of their robustness, convergence, algorithmic complexity, and parallelism. Further development of modern software for solving real-life problems justifies relevance of the research. The proposed two-grid algorithm can be used in black-box parallel software for the reduction in the execution time in solving (initial-)boundary value problems.

Assessing the transport flow robustness is a significant aspect of a qualitative solution to traffic management problems. Therefore, management should be based on appropriate criteria, accounting for different factors characterizing traffic flow sustainability. That’s why it is crucial to establish the impact rate for each group of factors on the robustness criterion. Therefore, the current study aims to obtain the dependence of the criterion changes for traffic flow sustainability on the traffic jam occurrence when changing the gradients’ product of traffic flow density and its speed. The value of the robustness criterion allows for performing an impact rating for input factors on traffic flow sustainability. All factors affecting transport flow robustness are divided into three groups. Based on simulation results, factors rating that impact the robustness margin value of the traffic flow is presented. Length and weight of automobiles are at first place according to impact terms on the sustainability loss of the traffic flow. In second place of impact on sustainability loss are the temporary factors group and factors group that considers the roadway environment’s infrastructure. Hence, the results can be used to analyze sustainability traffic flows in controlled highway network stretches and develop measures to increase sustainability reserve.

The complex societal phenomena occurring in our daily lives and the ongoing curricula demands of mathematics education imply the responsibility of teachers to discuss societal issues with their students in mathematics classrooms. Yet, the ways in which teachers respond to these demands are neither given nor straightforward. In this case study, we aim to understand how pre-service teachers are introduced to addressing societal issues during mathematical modelling activities through the examples utilised by a teacher educator. Theoretical perspectives from socio-critical modelling are used to investigate examples from a mathematics teacher education course where socio-critical perspectives of modelling activities were addressed. We found that the teacher educator included multiple activities with contexts relevant to pre-service teachers, such as littering, body images, and oil spills, and focused on problem posing. Also, the complexity of socio-critical modelling activities was illustrated by bringing various perspectives and alternatives, and a need for commitment to action and assuming responsibility was discussed. Our findings conclude that mathematical modelling can be one way of incorporating socio-critical issues in teacher education to prepare pre-service teachers to be, and become, critical and responsible citizens, yet, doing so requires the engagement of a community of teacher educators.

This study summarizes the most recent findings on osmotic dehydration, a crucial step in food preservation. The many benefits of osmotic dehydration are listed, including longer shelf life and preserved nutritional value. Mass transfer dynamics, which are critical to understanding osmotic dehydration, are explored alongside mathematical models essential for comprehending this process. The effect of osmotic agents and process parameters on efficacy, such as temperature, agitation and osmotic agent concentration, is closely examined. Pre-treatment techniques are emphasized in order to improve process effectiveness and product quality. The increasing demand for sustainability is a critical factor driving research into eco-friendly osmotic agents, waste valorization, and energy-efficient methods. The review also provides practical insights into process optimization and discusses the energy consumption and viability of osmotic dehydration compared to other drying methods. Future applications and improvements are highlighted, making it an invaluable tool for the food industry.

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment.

Electrically conductive membranes are a class of stimuli-responsive materials, which allow the adjustment of selectivity for and the rejection of charged species by varying the surface potential. The electrical assistance provides a powerful tool for overcoming the selectivity–permeability trade-off due to its interaction with charged solutes, allowing the passage of neutral solvent molecules. In this work, a mathematical model for the nanofiltration of binary aqueous electrolytes by an electrically conductive membrane is proposed. The model takes into account the steric as well as Donnan exclusion of charged species due to the simultaneous presence of chemical and electronic surface charges. It is shown that the rejection reaches its minimum at the potential of zero charge (PZC), where the electronic and chemical charges compensate for each other. The rejection increases when the surface potential varies in positive and negative directions with respect to the PZC. The proposed model is successfully applied to a description of experimental data on the rejection of salts and anionic dyes by PANi–PSS/CNT and MXene/CNT nanofiltration membranes. The results provide new insights into the selectivity mechanisms of conductive membranes and can be employed to describe electrically enhanced nanofiltration processes.

Worldwide, fruit processing industries reject high volumes of fruit waste, which represent rich sources of phenolic compounds and can be valorised through extraction, and then be reused for food, nutraceutical or cosmetic applications. In the present work, the optimisation of the recovery of phenolic compounds from apricot kernels and pulp, as well as peach pulp, through the green method of ultrasound and microwave assisted extraction (UMAE) is performed. Prior to extraction, a drying step of the pulps is conducted using freeze, vacuum and hot air drying. Except for the conventional extraction solvents of water and ethanol:water, a deep eutectic solvent (DES) formed by choline chloride/urea, and a natural deep eutectic solvent (NaDES) from choline chloride with lactic acid, are used, something that presentsecological benefits. With the aim of discovering the optimum extraction conditions, different values of the parameters of extraction time, utrasonic power and solvent/dry solid ratio are examined, and a mathematical model is developed to correlate them to the extraction yield (EY). The phenolic compounds and the antioxidant activity are determined through UV-Vis spectroscopy and High-Performance Liquid Chromatography (HPLC). The results of the study demonstrated that the most effective solvent in the extraction of apricot kernels is ethanol: water; DES is more efficient in the extraction of apricot pulp and NaDES in the extraction of peach pulps, reaching EYs of 25.65, 26.83 and 17.13%, respectively. In conclusion, both types of fruit waste are proved to have a significant content of valuable compounds, and the use of DES in fruit by-product extraction is effective and seems to be a promising alternative. Thus, the unexploited amounts of waste can be valorised through simple techniques and innovative solvents.

Larval mosquito development is directly impacted by environmental water temperature. Shallow water less than 1 m deep is a common larval mosquito habitat. Existing mathematical models estimate water temperature using meteorological variables, and they range in complexity. We developed a modification of an existing one-layer heat balance model for estimating hourly water temperature and compared its performance with that of a model that uses only air temperature and water volume as inputs and that uses air temperature itself as an indicator of water temperature. These models were assessed against field measurements from a shallow tidal wetland—a known larval habitat—in southwest Western Australia. We also analysed publicly available measurements of air temperature and river height to determine whether they could be used in lieu of field measurements to allow cost-effective long-term monitoring. The average error of the modified version of the heat balance equation was −0.5 °C per hour. Air temperature was the second-best performing method (x¯ error = −2.82 °C). The public data sources accurately represented the onsite water temperature measurements. The original heat balance model, which incorporates a parameterisation of evaporative heat flux, performed poorly in hot, dry, windy conditions. The modified model can be used as an input to larval mosquito development models, assisting Local Government Environmental Health officers to determine optimal mosquito development periods and the timing of mosquito monitoring activities to enhance mosquito control.

Propellant gauging is crucial for a spacecraft approaching the end of its lifespan. Current gauging systems for satellites typically have an accuracy rate of a few months to a year at the end of their operational life. Therefore, it is essential to determine the appropriate gauging system for mission operations. This research focuses on modeling the propellant gauging system for PRISMA, an Earth Observation (EO) satellite of the Italian Space Agency. The analysis centers on implementing algorithms that calibrate the remaining propellant mass in the satellite tank using traditional methods such as bookkeeping (BKP) and pressure-volume-temperature (PVT). To enhance accuracy in quantification, an unconventional approach called thermal propellant gauging (TPG) has been considered. Preliminary computations were conducted using data obtained from the PRISMA thermal model to understand the calibration accuracy of the three methods. At the end of its operational life, the BKP and PVT methods exhibited error rates of 4.6% and 4.8%, respectively, in calculating the mass. In contrast, the TPG method demonstrated a significantly higher precision with an error rate of 1.86%. However, at the beginning of the satellite’s operational life, the PVT and TPG methods showed error rates of 1.0% and 1.3%, respectively, while the BKP technique reported an error rate of 0.1%. Based on these findings, it has been concluded that combining the BKP and TPG approaches yields superior results throughout the satellite’s lifespan. Furthermore, the researchers have determined the specific time duration for which each of these distinct approaches can be effectively utilized.

This article is devoted to a brief review of the modelling of liquid membrane separation methods, such as emulsion, supported liquid membranes, film pertraction, and three-phase and multi-phase extraction. Mathematical models and comparative analyses of liquid membrane separations with different flow modes of contacting liquid phases are presented. A comparison of the processes of conventional and liquid membrane separations is carried out under the following assumptions: mass transfer is described by the traditional mass transfer equation; the equilibrium distribution coefficients of a component passing from one of the phases to another are constant. It is shown that, from the point of view of mass transfer driving forces, emulsion and film pertraction liquid membrane methods have advantages over the conventional conjugated extraction stripping method, when the mass-transfer efficiency of the extraction stage is significantly higher than the efficiency of the stripping stage. The comparison of the supported liquid membrane with conjugated extraction stripping showed that when mass-transfer rates on the extraction and stripping sides are different, the liquid membrane method is more efficient, while when they are equal to each other, both processes demonstrate the same results. The advantages and disadvantages of liquid membrane methods are discussed. The main disadvantages of liquid membrane methods—low throughput and complexity—can be overcome by using modified solvent extraction equipment to carry out liquid membrane separations.

This research investigated an alternate method for establishing the complex coefficients used in an electric vehicle’s mathematical energy consumption model. While other methods for creating electric vehicle energy models exist, it would be beneficial to have a rapid and inexpensive technique that remains accurate. Producing a mathematical energy model for such a vehicle has the challenge of determining its aerodynamic drag and rolling resistance coefficients. Currently and most often, expensive and tedious (time-consuming) methods are used to find these coefficients. Computational fluid dynamics (CFD), wind tunnel testing, and extensive mathematics make this objective challenging. For this work, a solar-powered electric vehicle provided the source data to derive its coefficients cost-effectively and efficiently. Data were collected during a road test of the solar electric vehicle from South Africa to Namibia stretching over 2000 km, in which all required energy variables were recorded. The collected data were used in an optimisation routine to establish the two coefficients by minimising the actual and modelled energy consumption error and controlling the driving speed. The outcome of the optimisation routine produced accurate coefficients with a final error value of less than 5% when applied to a validation data set not used during optimisation. With minor modifications, this method may be integrated into any electric vehicle computer system to autonomously identify its two hard-to-find coefficients while driving, which can be used to provide an accurate and realistic driving range estimation to the driver.

The subject of the research is a model of a magnetic launcher, which is an innovative alternative to commercially occurring unmanned aircraft launchers (UAV). As the take-off is an energy-demanding phase of the flight; therefore, abandoning the power supply of the UAV during this phase significantly affects increasing the potential range and duration of UAV flight. The magnetic launcher offers the significant advantage of minimizing friction between the starting cart and the launcher, resulting in the higher energy efficiency of the system. Research conducted so far has shown that the possibility of accelerating the aircraft on the longer runway offered by the launcher reduces aircraft overloads occurring during take-off. As a result, the launcher, aircraft, and onboard equipment are much safer. This paper presents the system’s mathematical modeling and numerical simulation results for micro-class UAV take-off and landing using the analyzed magnetic launcher. The computer program for analyzing system dynamics was implemented in the MATLAB environment. Simulation results were visualized graphically and as animations in Virtual Reality. The VR application was implemented in Unity and ran on VR goggles Oculus Quest2. The simulations carried out show that—in the absence of control—an important factor reducing the takeoff distance and affecting the aircraft load is the adoption of a non-zero takeoff thrust of the UAV. The initial pitch angle also has a significant impact on the takeoff process. With an increase in this parameter, the length of the takeoff distance decreases and the lift-off speed decreases, but too much pitch angle may result in the aircraft descending in the first moments of flight, which could lead to a collision with the launch rails.

Vaccination rates against SARS-CoV-2 in children aged five to eleven years remain low in many countries. The current benefit of vaccination in this age group has been questioned given that the large majority of children have now experienced at least one SARS-CoV-2 infection. However, protection from infection, vaccination or both wanes over time. National decisions on offering vaccines to this age group have tended to be made without considering time since infection. There is an urgent need to evaluate the additional benefits of vaccination in previously infected children and under what circumstances those benefits accrue. We present a novel methodological framework for estimating the potential benefits of COVID-19 vaccination in previously infected children aged five to eleven, accounting for waning. We apply this framework to the UK context and for two adverse outcomes: hospitalisation related to SARS-CoV-2 infection and Long Covid. We show that the most important drivers of benefit are: the degree of protection provided by previous infection; the protection provided by vaccination; the time since previous infection; and future attack rates. Vaccination can be very beneficial for previously infected children if future attack rates are high and several months have elapsed since the previous major wave in this group. Benefits are generally larger for Long Covid than hospitalisation, because Long Covid is both more common than hospitalisation and previous infection offers less protection against it. Our framework provides a structure for policy makers to explore the additional benefit of vaccination across a range of adverse outcomes and different parameter assumptions. It can be easily updated as new evidence emerges.