Mathematical Model Research Articles

Effluent quality improvement in sequencing batch reactor-based wastewater treatment processes using advanced control strategies

ABSTRACT The treatment of wastewater is highly challenging due to large fluctuations in flowrates, pollutants, and variable influent water compositions. A sequencing batch reactor (SBR) and modified SBR cycle-step-feed process (SSBR) configuration are studied in this work to effectively treat municipal wastewater while simultaneously removing nitrogen and phosphorus. To control the amount of dissolved oxygen in an SBR, three axiomatic control strategies (proportional integral (PI), fractional proportional integral (FPI), and fuzzy logic controllers) are presented. A biological process and relevant control algorithm has been designed using real-time plant data with the models of SBR and SSBR using the ASM2d mathematical model. On comparison, FPI showed a significant reduction in nutrient levels and added an improvement in effluent quality. The overall effluent quality is improved by 0.86% in FPI in comparison with PI controller. The SSBR, which was improved by precisely optimizing nutrient supply and aeration, establishes a delicate equilibrium. This refined method reduces oxygen requirements while reliably sustaining important biological functions. Focusing solely on the FPI controller's performance in terms of total air volume consumption, the step-feed SBR mechanism achieves an excellent 11.04% reduction in consumption.

Drying kinetics and thermodynamic properties of jabuticaba peel

Jabuticaba is a fruit of high nutritional value, and the peel, which is usually discarded, contains nutrients in greater concentration. An alternative for the use of jabuticaba bark is the preparation of flour. The aim of this research was to analyze the drying kinetics of jabuticaba bark by adjusting mathematical models and determining the effective diffusion coefficient, activation energy, and thermodynamic properties at different drying temperatures. The jaboticaba residues were dried in a forced ventilation oven at different temperatures of 45, 55, 65, and 75°C. Among the various models analyzed, Page was employed to streamline the drying phenomenon. The research observed that effective diffusion coefficient decreased with increasing temperature, and the activation energy for the liquid diffusion on drying was 32.63 kJ mol-1. Furthermore, enthalpy and entropy decreased with increasing drying temperature, while Gibbs’ free energy increased with increasing drying temperature.

Power Flow Calculation for AC/DC Power Systems with Line-Commutated Converter–Modular Multilevel Converter (LCC-MMC) Hybrid High-Voltage Direct Current (HVDC) Based on the Holomorphic Embedding Method

To harness the strengths and mitigate the limitations of line-commutated converter (LCC) and modular multilevel converter (MMC) HVDC systems, the LCC-MMC hybrid HVDC system has been developed. This paper proposes a holomorphic embedding (HE)-based power flow calculation method for AC/DC power systems with the LCC-MMC hybrid HVDC system. Firstly, the methodology involves establishing the mathematical model of the LCC-MMC hybrid HVDC system and its control modes. Subsequently, the HE formulation for the constructed LCC-MMC model is derived using the HE method. The proposed method simplifies the HE formulation using substitute variables, making it adaptable to various control modes. The designed HE formulation facilitates the derivation of the germ solution and the calculation of high-order power series coefficients. A sequential solution flow chart compatible with AC power flow algorithms is constructed to enhance the practicality of the HE method for real-world large-scale systems. The accuracy and effectiveness of the proposed method are verified through numerical tests on the modified IEEE 14-bus, IEEE 57-bus, and large 2383-bus system. The proposed method provides a reliable and efficient solution for power flow analysis in hybrid HVDC systems.

Optimizing vehicle route, schedule, and platoon formation considering time-dependent traffic congestion

Vehicle platooning, a strategy where vehicles drive in close formations, has emerged as a promising approach to reduce fuel consumption. This study presents a comprehensive model of the time-dependent vehicle platooning problem, which synchronously considers routing, scheduling, and platoon formation to minimize total fuel costs in a network affected by time-dependent traffic congestion. We first propose a mixed integer linear programming model to address this problem. To solve the problem, we develop two solution methods: a tabu search method and a platoon clustering algorithm. Through numerical experiments, we demonstrate the effectiveness of our mathematical model and the efficiency of the proposed algorithms. Our findings provide insights into the operational aspects of platooning and reveal that time-dependent traffic congestion can reduce the fuel-saving effects of platooning. This study underscores the importance of considering time-dependent traffic congestion in route planning and scheduling to ensure the effectiveness of vehicle platooning.

A step towards 6D WAXD tensor tomography.

X-ray scattering/diffraction tensor tomography techniques are promising methods to acquire the 3D texture information of heterogeneous biological tissues at micrometre resolution. However, the methods suffer from a long overall acquisition time due to multi-dimensional scanning across real and reciprocal space. Here, a new approach is introduced to obtain 3D reciprocal information of each illuminated scanning volume using mathematic modeling, which is equivalent to a physical scanning procedure for collecting the full reciprocal information required for voxel reconstruction. The virtual reciprocal scanning scheme was validated by a simulated 6D wide-angle X-ray diffraction tomography experiment. The theoretical validation of the method represents an important technological advancement for 6D diffraction tensor tomography and a crucial step towards pervasive applications in the characterization of heterogeneous materials.

Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand

This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence of a unique solution, demonstrating stability in the model. To derive approximate solutions, the generalized Adams-Bashforth-Moulton method is employed, further enhancing the study's analytical depth. Through a numerical simulation based on Thailand's data, the research delves into the intricacies of COVID-19 transmission, encompassing thorough data analysis and parameter estimation. The study advocates for a holistic approach, recommending a combined strategy of precautionary measures and home remedies, showcasing their substantial impact on pandemic mitigation. This comprehensive investigation significantly contributes to the broader understanding and effective management of the COVID-19 crisis, providing valuable insights for shaping public health strategies and guiding individual actions.

Electric Susceptibility at Partial Coverage of a Circular One-Side Access Capacitive Sensor with Rigid Polyurethane Foams

The capability of dielectric measurements was significantly increased with the development of capacitive one-side access physical sensors. Complete samples give no opportunity to study electric susceptibility at a partial coverage of the one-side access sensor’s active area; therefore, partial samples are proposed. The electric susceptibility at the partial coverage of a circular one-side access sensor with cylinders and shells is investigated for polyurethane materials. The implementation of the relative partial susceptibility permitted us to transform the calculated susceptibility data to a common scale of 0.0–1.0 and to outline the main trends for PU materials. The partial susceptibility, relative partial susceptibility, and change rate of relative partial susceptibility exhibited dependence on the coverage coefficient of the sensor’s active area. The overall character of the curves for the change rate of the relative partial susceptibility, characterised by slopes of lines and the ratio of the change rate in the centre and near the gap, corresponds with the character of the surface charge density distribution curves, calculated from mathematical models. The elaborated methods may be useful in the design and optimization of capacitive OSA sensors of other configurations of electrodes, independent of the particular technical solution.

Effect of Phase Shifting on Real-Time Detection and Classification of Power Quality Disturbances

Power quality improvement and Power quality disturbance (PQD) detection are two significant concerns that must be addressed to ensure an efficient power distribution within the utility grid. When the process to analyze PQD is migrated to real-time platforms, the possible occurrence of a phase mismatch can affect the algorithm’s accuracy; this paper evaluates phase shifting as an additional stage in signal acquisition for detecting and classifying eight types of single power quality disturbances. According to their mathematical models, a set of disturbances was generated using an arbitrary waveform generator BK Precision 4064. The acquisition, detection, and classification stages were embedded into a BeagleBone Black. The detection stage was performed using multiresolution analysis. The feature vectors of the acquired signals were obtained from the combination of Shannon entropy and log-energy entropy. For classification purposes, four types of classifiers were trained: multilayer perceptron, K-nearest neighbors, probabilistic neural network, and decision tree. The results show that incorporating a phase-shifting stage as a preprocessing stage significantly improves the classification accuracy in all cases.

Physical Analysis and Mathematical Modeling of the Hydrogen Storage Process in the MmNi4.2Mn0.8 Compound

The results of an experimental and mathematical study into the MmNi4.2Mn0.8 compound’s hydrogen storage properties are presented in the present research. Plotting and discussion of the experimental isotherms (P-C-T) for different starting temperatures (288 K, 298 K, 308 K, and 318 K) were carried out first. Then, the enthalpy and entropy of formation (ΔH0, ΔS0) were deduced from the plot of van’t Hoff. Following that, the P-C-T were contrasted with a mathematical model developed via statistical physics modeling. The steric and energetic parameters, such as the number of the receiving sites (n1, n2), their densities (Nm1, Nm2), and the energy parameters (P1, P2) of the system, were calculated thanks to the excellent agreement between the numerical and experimental results. Therefore, plotting and discussing these parameters in relation to temperature preceded their application in determining the amount of hydrogen in each type of site per unit of metal ([H/M]1, [H/M]2) as well as for the entire system [H/M] versus temperature and pressure besides the absorption energies associated with each kind of site (ΔE1, ΔE2) and the thermodynamic functions (free energy, Gibbs energy, and entropy) that control the absorption reaction.

Efficient pulse sequence design framework for high-dimensional MR fingerprinting scans using systematic error index.

For effective optimization of MR fingerprinting (MRF) pulse sequences, estimating and minimizing errors from actual scan conditions are crucial. Although virtual-scan simulations offer an approximation to these errors, their computational demands become expensive for high-dimensional MRF frameworks, where interactions between more than two tissue properties are considered. This complexity makes sequence optimization impractical. We introduce a new mathematical model, the systematic error index (SEI), to address the scalability challenges for high-dimensional MRF sequence design. By eliminating the need to perform dictionary matching, the SEI model approximates quantification errors with low computational costs. The SEI model was validated in comparison with virtual-scan simulations. The SEI model was further applied to optimize three high-dimensional MRF sequences that quantify two to four tissue properties. The optimized scans were examined in simulations and healthy subjects. The proposed SEI model closely approximated the virtual-scan simulation outcomes while achieving hundred- to thousand-times acceleration in the computational speed. In both simulation and in vivo experiments, the optimized MRF sequences yield higher measurement accuracy with fewer undersampling artifacts at shorter scan times than the heuristically designed sequences. We developed an efficient method for estimating real-world errors in MRF scans with high computational efficiency. Our results illustrate that the SEI model could approximate errors both qualitatively and quantitatively. We also proved the practicality of the SEI model of optimizing sequences for high-dimensional MRF frameworks with manageable computational power. The optimized high-dimensional MRF scans exhibited enhanced robustness against undersampling and system imperfections with faster scan times.

Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis

Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to <I>R</I><sub>0</sub>. Finally, the numerical results with Matlab are in conformity with theoretical results.

Limits of coefficient of performance of adsorption cooling cycle based on refrigerant’s type

This research work discusses how the thermodynamic properties of refrigerant constrain the upper limit of the coefficient of performance (COP) of adsorption cooling (AC) cycle. A mathematical model is developed based on the mass and energy balance across the adsorption bed and used to estimate the maximum COP. Langmuir model is used to derive the ideal COP. Besides, Carnot COP and exergy efficiency are derived to evaluate the adsorption cooling cycle further. These new parameters are applied to the available cycles in the open literature to assess how much room for improvement is still left in the adsorption technology based on the refrigerant type. Water, ammonia, methanol, ethanol, Butane, R134a, R32, CO2 and R1234ze are used in this study. The maximum cooling COP cannot exceed 1.0 for cooling applications and is always less than 2.0 for heat pumps. Results show that AC cycles using water or ethanol as refrigerants achieve the highest exergy efficiency. The AC cycle using water as an adsorbate and silica gel as an adsorbent has the highest relative COP, about 80 % at 85 °C regeneration temperature. In turn, CO2 exhibits the lowest one. This work is merely an attempt to save experimental effort and time by identifying the most suitable refrigerant based on its physical and thermal properties and the cycle operating conditions.

Prompt the problem – investigating the mathematics educational quality of AI-supported problem solving by comparing prompt techniques

The use of and research on the large language model (LLM) Generative Pretrained Transformer (GPT) is growing steadily, especially in mathematics education. As students and teachers worldwide increasingly use this AI model for teaching and learning mathematics, the question of the quality of the generated output becomes important. Consequently, this study evaluates AI-supported mathematical problem solving with different GPT versions when the LLM is subjected to prompt techniques. To assess the mathematics educational quality (content related and process related) of the LLM’s output, we facilitated four prompt techniques and investigated their effects in model validations (N = 1,080) using three mathematical problem-based tasks. Subsequently, human raters scored the mathematics educational quality of AI output. The results showed that the content-related quality of AI-supported problem solving was not significantly affected by using various prompt techniques across GPT versions. However, certain prompt techniques, particular Chain-of-Thought and Ask-me-Anything, notably improved process-related quality.

Water Pricing and Quotas: A Quantitative Analysis from a Private and Social Perspective

AbstractThe current situation of structural water scarcity due to the rise in demand, the reduction in supply as a consequence of climate change, increasingly frequent drought periods, and overall quantitative pressure on water resources creates a need for economic instruments to reduce the amount of water used, especially in the agricultural sector. Thus, water pricing and allocation quotas (proportional reduction of allocations) may be suitable tools to reduce demand or allocate scarce water resources. For a comparative analysis of the performance of these two measures, a Positive Mathematical Programming model has been developed, using the Guadalquivir River Basin as a case study. Additionally, the analysis takes into account the revenue generated from water pricing and the marginal cost of public funds. The results indicate that, from the farmer’s perspective, quotas result in smaller losses than water pricing. However, when considering water pricing along with the revenue generated from this measure, this mechanism would be more beneficial for society as a whole, since the taxes collected could be used for other purposes, albeit with efficiency losses measured by the marginal cost of public funds and the excess burden of taxation.

INNOVATIVE TECHNOLOGY FOR THE CONSTRUCTION OF A PYLON STATION OF THE METRO BASED ON THE EXPERIENCE OF USING NATM

Purpose. For quite a long time, the metro station of the pylon type of deep contour interval was considered an underground structure that no longer has development potential. However, after the introduction of innovative technologies during the construction of the Dnipro metro, in particular the New Austrian Tunneling Method (NATM), this design is being used again and has developed further use. The purpose of the scientific article is to analyze innovations in the technology of construction of a three-vaulted pylon metro station from precast reinforced concrete using NATM, which require scientific justification. Methodology. In order to achieve the goal, the traditional technology of constructing a deep contour interval pylon station was revised. An analysis of the features of NATM, which allow it to be used during the construction of a pylon station in strong rock, has been carried out. A step-by-step analysis of the construction of the station was implemented with the involvement of mathematical modeling based on the finite element method. For this purpose, a number of finite-element models of each stage of construction of a pylon-type station have been created. After the numerical analysis, the indicated models were adjusted in accordance with the changes associated with the new construction technology. Findings. The value of the stress-strain state of the pylon station was obtained during the numerical analysis of each stage of construction. Stress analysis proves the possibility of applying innovative construction technology in the case of a pylon station. Originality. On the basis of the performed numerical analysis of the phased construction of a pylon station based on NATM, dependencies were obtained that allow revising the existing concept of the construction of this type of station in strong rocks. The obtained data justify the application of NATM and release the potential of the analyzed underground structure. Practical value. The substantiation of the innovative technology based on NATM allows expanding the scope of its application and successfully carrying out the construction of such complex underground facilities.

Experimental study and numerical simulation on porosity dependent direct reducibility of high-grade iron oxide pellets in hydrogen

The transition to more environmentally friendly steel production methods has intensified research into hydrogen-based direct reduction (HyDR) of iron oxide pellets. The aim of this study is to systematically investigate the kinetics of the reduction process, the evolution of porosity and the resulting microstructural changes on the reduction behavior of high-quality pellets during HyDR of iron ore at different temperatures. A modified mathematical model is developed based on the shrinkage kernel model, taking into account both mass and heat transport in a hydrogen atmosphere. The effects of temperature, particle size and time on the reduction behavior of the pellets are investigated. The simulated results are validated and discussed by the results of a batch of iron oxide pellets consisting of ten almost spherical pellets subjected to the direct reduction process with pure hydrogen. The results show that the total energy input to the HyDR process is a complex balance of factors, including chemical reaction rates, diffusion dynamics and entropy generation. The increase in free volume and simultaneous decrease in pore diameter reflect the dynamic nature of the microstructure, which includes additional free volume and defects due to the volume discrepancies and associated stresses between the reactant and product phases. Furthermore, the data show that higher temperatures accelerate the reduction reactions, especially the transformation of wustite into metallic iron. This phase transition is characterized by a significant volume change that cannot be accommodated by elastic deformation alone, leading to the development of lattice defects such as cracks, creep pores and dislocations that serve as stress relief mechanisms. The trends for porosity change at 950 °C and 1000 °C observed in the experimental results are correct and in good agreement with the numerical and simulated results.

Preclinical assessment of a mathematical model for ablation zone prediction in thyroid laser ablation.

To develop and validate a 3D simulation model to calculate laser ablation (LA) zone size and estimate the volume of treated tissue for thyroid applications, a model was developed, taking into account dynamic optical and thermal properties of tissue change. For validation, ten Yorkshire swines were equally divided into two cohorts and underwent thyroid LA at 3W/1,400J and 3W/1,800J respectively with a 1064-nm multi-source laser (Echolaser X4 with Orblaze™ technology; ElEn SpA, Calenzano, Italy). The dataset was analyzed employing key statistical measures such as mean and standard deviation(SD). Model simulation data were compared with animal gross histology. Experimental data for longitudinal length, width (transverse length), ablation volume and sphericity were 11.0mm, 10.0mm, 0.6 mL and 0.91, respectively at 1,400J and 14.6mm, 12.4mm, 1.12 mL and 0.83, respectively at 1,800J. Gross histology data showed excellent reproducibility of the ablation zone among same laser settings; for both 1,400J and 1,800J, the SD of the in vivo parameters was ≤ 0.7mm, except for width at 1,800J, for which the SD was 1.1mm. Simulated data for longitudinal length, width, ablation volume and sphericity were 11.6mm, 10.0mm, 0.62 mL and 0.88, respectively at 1,400J and 14.2mm, 12.0mm, 1.06 mL and 0.84, respectively at 1,800J. Experimental data for ablation volume, sphericity coefficient, and longitudinal and transverse lengths of thermal damaged area showed good agreement with the simulation data. Simulation datasets were successfully incorporated into proprietary planning software (Echolaser Smart Interface, Elesta SpA, Calenzano, Italy) to provide guidance for LA of papillary thyroid microcarcinomas. Our mathematical model showed good predictability of coagulative necrosis when compared with data from in vivo animal experiments.

Drying kinetic, thermodynamic and quality analyses of infrared drying of truffle slices.

Kinetic and thermodynamic parameters are the most important part for making a suitable tool for drying agricultural products. Moreover, calculation of the energy required for the drying of product, the properties of the rehydration ratio, the food appearance changes, and the evaluation of the microstructure of food are crucial. Since the thermodynamic properties of truffle slices have not yet been reported, this study aims to establish a mathematical model to describe drying process of agriculture product, evaluate the effective moisture diffusion coefficient (Deff), determining the activation energy (Ea) to elucidate the thermodynamic characteristics, measure color characteristics, and rehydration ratio (RR) during the drying process of truffle slices. Truffle slices were dried in an infrared (IR) dryer at four temperatures of 50-80°C and two thicknesses of 0.5 and 1cm. The best model to describe the drying process of truffle slices was Midilli etal.'s model. The value of Deff, SEC, and RR were in the range of 3.06 × 10-8 to 2.48 × 10-7 m2/s, 79.68-191.271kWh/kg, and 5.99-7.49, respectively. The Deff of truffle slices increased with the above-mentioned parameters of the samples. The Ea obtained was 26.62-27.43kJ/mol. The results indicated that enthalpy and entropy decreased with increasing drying temperature, while Gibbs free energy improved. The enthalpy, entropy, and Gibbs free energy values changed between 24.48-25.28kJ/mol, -130.47 to -122.63 J/mol °K, and 63.97-70.17kJ/mol, respectively. In addition, the results of color attributes decreased with increasing temperature, while chroma oppositely increased.

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend

BackgroundSeveral models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves.MethodsWe used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the “rising trend line”; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave.ResultsUp to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy.ConclusionOur newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Application and Quality of Model-Based Meta-Analysis in Pharmaceutical Research: A Systematic Cross-Sectional Analysis and Practical Considerations.

Model-based meta-analysis (MBMA) can be used in assisting drug development and optimizing treatment in clinical practice, potentially reducing costs and accelerating drug approval. We aimed to assess the application and quality of MBMA studies. We searched multiple databases to identify MBMA in pharmaceutical research. Eligible MBMA should incorporate pharmacological concepts to construct mathematical models and quantitatively examine and/or predict drug effects. Relevant information was summarized to provide an overview of the application of MBMA. We used AMSTAR-2 and PRISMA 2020 checklists to evaluate the methodological and reporting quality of included MBMA, respectively. A total of 143 MBMA studies were identified. MBMA was increasingly used over time for one or more areas: drug discovery and translational research (n = 8, 5.6%), drug development decision making (n = 42, 29.4%), optimization of clinical trial design (n = 46, 32.2%), medication in special populations (n = 15, 10.5%), and rationality and safety of drug use (n = 71, 49.7%). The included MBMA covered 17 disease areas, with the top three being nervous system diseases (n = 19, 13.2%), endocrine/nutritional/metabolic diseases (n = 17, 11.8%), and neoplasms (n = 16, 11.1%). Of these MBMA studies, 138 (96.5%) were rated as very low quality. The average rate of compliance with PRISMA was only 51.4%. Our findings suggested that MBMA was mainly used to evaluate the efficacy and safety of drugs, with a focus on chronic diseases. The methodological and reporting quality of MBMA should be further improved. Given AMSTAR-2 and PRISMA checklists were not specifically designed for MBMA, adapted assessment checklists for MBMA should be warranted.