Mathematical Modeling Techniques Research Articles

ENHANCED DIAGNOSTIC TECHNIQUES FOR MARINE DIESEL ENGINES: ACHIEVING IMO DECARBONIZATION COMPLIANCE

This paper discusses hardware-based methods for monitoring the operational parameters of marine diesel engines and online mathematical modeling techniques (digital twins) for calculating the emissions of CO2, NOx, soot, and other harmful pollutants. It is demonstrated that measuring and analyzing the engine's vibrational diagrams in parallel with gas pressure diagrams in the cylinders allows the evaluation of the actual fuel injection and gas distribution timings. The obtained data is used to refine the mathematical model of the engine's working process, which determines the engine's indicator parameters and power, as well as the emission of harmful substances that need to be monitored in compliance with current IMO requirements. The authors have accumulated experience in using the discussed hardware-based methods for diagnosing marine engines during operation. The hardware and software methods discussed have been implemented into a real-time system for in-service diagnostics of marine engines. The system is designed based on a modern dual-core controller with high performance and low power consumption, incorporating a high-speed ADC with sufficient capability to monitor the working process with a 0.1-degree crankshaft rotation resolution for all types of marine main and auxiliary engines. The system also utilizes wireless data transmission technology. A contemporary Android/iOS smartphone or tablet serves as the computational and graphical component of the system. This real-time system enables the utilization of all the advantages of parallel pressure and vibroacoustic analysis, including real-time determination of key operating parameters, identification of top dead center position, and evaluation of fuel delivery and gas distribution phases. Additionally, it harnesses the benefits of employing a digital twin—an online mathematical model of the engine cylinder's working process. These solutions will enhance diagnostic quality and, ultimately, improve the operational efficiency of marine engines by reducing operational costs and extending the period of reliable, trouble-free operation.

Mechanical modelling of viscoelastic hierarchical suture joints and their optimisation and auxeticity

It has been widely recognised that suture joints play a fundamental role in the exceptional mechanical properties of many biological structures like the cranium and ammonite fossil shells. Up to date, many efforts have been devoted to investigate suture interfaces to predict the relations between the characteristics of its two phases, the teeth and the interface layer, and the structure effective properties. However, in very few works the viscoelasticity of the suture components has been taken into account. To provide a contribution in this limitedly explored research area, this paper describes the mathematical formulation and modelling technique leading to explicit expressions for the effective properties of viscoelastic suture joints with a general trapezoidal waveform. It emerges a strong influence of the suture geometric and mechanical characteristics on the effective properties and a parametric analysis reveals that an auxetic behavior can be obtained simply by tailoring the suture parameters. The effects of adding hierarchy into the above system are also explored and closed-form relations for the effective moduli are derived. Optimal levels of hierarchy can be identified and, similarly to the non-hierarchical case, an auxetic behavior emerges for particular values of the suture parameters. Finally, an extension of the theory to the sinusoidal sutures in biology is reported. By considering the examples of the cranium and the woodpecker beak, it emerges that the first is optimised to obtain high stiffness, while the second to obtain high energy dissipation levels.

Scheduling trucks and drones for cooperative deliveries

Truck and drone based cooperative delivery system is an emerging instant delivery mode for transporting packages in a more timely and efficient way than traditional delivery mode. This paper studies the scheduling of a fleet of truck groups, each of which can carry multiple drones. We formulate a mixed integer programming model for truck groups routes, and for the timing of the drones’ launching and return to their dedicated truck. The model objective is to minimize the total operational cost, including truck travel cost, drone travel cost, using truck groups fixed cost, and potential penalty for late delivery at customer locations. Column generation-based heuristic algorithm and some acceleration techniques are designed for solving the model efficiently. We carry out numerical experiments for validating the effectiveness of the mathematical model, algorithm, and acceleration techniques. In addition, sensitivity analyses are performed to derive some managerial implications.

Estimating the Population Growth Curve of Sea Turtle Eggs Production in Terengganu, Malaysia: Mathematical Modelling Approach

A growth curve is a growth pattern that is unique to each organism, species, or population. In general, the growth pattern is regulated by genetic and environmental factors, resulting in unique growth curves for each subpopulation of the same species. This research was written to identify the growth curve of the Terengganu’s sea turtle eggs population. This work was aided by a mathematical modelling technique, specifically the exponential and logistic growth models. The aim of this research is to select the most realistic model to describe sea turtle eggs production in Terengganu. Furthermore, this work is also intended to forecast the future population growth of sea turtles in Terengganu. Error analysis is used to compare the error produced by both models in comparison with the real data of sea turtle eggs. As a result, the logistic model is better suited to describing the growth of sea turtle eggs production in Terengganu. The logistic model indicated that the sea turtle population would steadily increase until it reached it carrying capacity. Thus, this research is critical for ensuring the sustainability of sea turtles by understanding the mechanism of logistic growth.

Assessing the joint prevalence of dementia and hearing loss in Scotland: a growth model for public health planning

Abstract Aim Data in Public Health studies often comes in mismatched age groups. This study investigated how mathematical modelling techniques could be used to estimate the number of individuals with dementia and hearing loss in Scotland given heterogeneous age group data. Subject and Methods Using established criteria for modelling hearing loss, current population level estimates from the Scottish National Records office were employed to calculate general estimates of the number of individuals with hearing loss in Scotland. Additionally, age group models developed by the European Collaboration on Dementia were used to generate estimates of the number of people with dementia in Scotland. To estimate the number of individuals with both conditions, the two models were combined in a single formula. Parameter optimization was performed on various growth models to determine the best fit to the data. Results The Stannard growth model was found to be the best fit to the data. Conclusion The prevalence of hearing loss, dementia and their co-occurrence exhibit a sigmoidal pattern, which is well-captured by the Stannard growth model, a logistic, sigmoidal type model. This study demonstrates the potential of mathematical modelling to provide nuanced and robust estimates of the prevalence of hearing loss, dementia and their co-occurrence given heterogeneous data sources. A lookup table is provided.

Non‐contact vacuum pumps

SummaryAn overview of the main methods for mathematical modeling of the working process of non‐contact vacuum pumps is given. The specifics and the main stages of mathematical model development for screw, scroll, claw and Roots vacuum pumps are considered. The results of mathematical modeling of pump characteristics are presented and compared with experimental data. The mathematical modeling technique presented here can be recommended for analyzing the influence of pump geometry and operating conditions on the pump characteristics of non‐contact oil‐free vacuum pumps.

Mathematical modeling techniques to predict the compressive strength of pervious concrete modified with waste glass powders

Mathematical modeling techniques to predict the compressive strength of pervious concrete modified with waste glass powders

Accurate simulation of THz generation with finite-element time domain methods.

We investigate the accurate full broadband simulation of complex nonlinear optical processes. A mathematical model and numerical simulation techniques in the time domain are developed to simulate complex nonlinear optical processes without the usual used slowly varying envelope approximation. We illustrate the accuracy by numerical simulations. Furthermore, they are used to elucidate THz generation in periodically poled Lithium Niobate (PPLN) including optical harmonic generation.

Parameters of TNF receptor co-expression in allergic and autoimmune processes: Differences and diagnostic significance

The authors used a method quantitative estimation density of TNFR1/TNFR2 on cells by flow cytometry with calibration particles, which allowed them to estimate the absolute number of receptors on cells regardless of the type of flow cytometer. The TNF receptor expression parameters were used to determine their association with the fact of disease and to build diagnostic models. The proposed methodological approach using a combination of flow cytometry and mathematical modeling techniques represents a promising direction for testing the diagnostic and prognostic significance of the studied biomarkers. The multifactorial regression analysis constructed on the basis of this approach made it possible to refine and supplement diagnostic schemes for determining the probability of rheumatoid arthritis and bronchial asthma in patients.

SLOW AND FAST SUBSYSTEMS FOR COMPLEX UNCOMPETITIVE INHIBITOR MECHANISMS

To fully understand intricate enzyme reaction models, one must explore beyond the confines of chemical and biological tools and look toward mathematical modeling and model reduction techniques. Mathematical modeling and model reduction techniques have the potential to provide a vast array of analysis tools for such models. This piece of work entails a review and discussion of a complex noncompetitive inhibitor model. This model is composed of seven non-linear differential equations with constant rates. We propose two efficient model reduction techniques: quasi- steady-state approximation (QSSA) and quasi-equilibrium approximation (QEA). By utilizing the suggested methods, the model equations are segregated into slow and fast subsystems, leading to the attainment of reduced models and slow manifolds with fewer variables and parameters. The outcomes manifest some analytical approximate solutions for the proposed model and establish a profound agreement between model dynamics for both the original and the reduced models. Observing that the reduced models can accurately identify certain critical model parameters is intriguing.

МЕТОДИЧЕСКИЕ ОСОБЕННОСТИ ПОСТРОЕНИЯ КУРСА ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ С ЦЕЛЬЮ ФОРМИРОВАНИЯ ЦЕЛОСТНОЙ КАРТИНЫ МИРА ШКОЛЬНИКА

The article proposes a methodological construction of a course of differential equations aimed at forming a holistic picture of the student’s world. Its features and differences in comparison with the classical university course are revealed. The questions about the selection of the content, the choice of methods and means of solving differential equations, the construction of a diagnostic apparatus aresolved The provisions of the system-activity approach, theoretical statements of practice-oriented learning, methods and techniques of mathematical modeling are implemented.

A Systematic Review of Machine Learning Techniques and Applications in Soil Improvement Using Green Materials

According to an extensive evaluation of published studies, there is a shortage of research on systematic literature reviews related to machine learning prediction techniques and methodologies in soil improvement using green materials. A literature review suggests that machine learning algorithms are effective at predicting various soil characteristics, including compressive strength, deformations, bearing capacity, California bearing ratio, compaction performance, stress–strain behavior, geotextile pullout strength behavior, and soil classification. The current study aims to comprehensively evaluate recent breakthroughs in machine learning algorithms for soil improvement using a systematic procedure known as PRISMA and meta-analysis. Relevant databases, including Web of Science, ScienceDirect, IEEE, and SCOPUS, were utilized, and the chosen papers were categorized based on: the approach and method employed, year of publication, authors, journals and conferences, research goals, findings and results, and solution and modeling. The review results will advance the understanding of civil and geotechnical designers and practitioners in integrating data for most geotechnical engineering problems. Additionally, the approaches covered in this research will assist geotechnical practitioners in understanding the strengths and weaknesses of artificial intelligence algorithms compared to other traditional mathematical modeling techniques.

Application of Machine Learning and Neural Networks to Predict the Yield of Cereals, Legumes, Oilseeds and Forage Crops in Kazakhstan

The article provides an overview of the accuracy of various yield forecasting algorithms and offers a detailed explanation of the models and machine learning algorithms that are required for crop yield forecasting. A unified crop yield forecasting methodology is developed, which can be adjusted by adding new indicators and extensions. The proposed methodology is based on remote sensing data taken from free sources. Experiments were carried out on crops of cereals, legumes, oilseeds and forage crops in eastern Kazakhstan. Data on agricultural lands of the experimental farms were obtained using processed images from Sentinel-2 and Landsat-8 satellites (EO Browser) for the period of 2017–2022. In total, a dataset of 1600 indicators was collected with NDVI and MSAVI indices recorded at a frequency of once a week. Based on the results of this work, it is found that yields can be predicted from NDVI vegetation index data and meteorological data on average temperature, surface soil moisture and wind speed. A machine learning programming language can calculate the relationship between these indicators and build a neural network that predicts yield. The neural network produces predictions based on the constructed data weights, which are corrected using activation function algorithms. As a result of the research, the functions with the highest prediction accuracy during vegetative development for all crops presented in this paper are multi-layer perceptron, with a prediction accuracy of 66% to 99% (85% on average), and polynomial regression, with a prediction accuracy of 63% to 98% (82% on average). Thus, it is shown that the use of machine learning and neural networks for crop yield prediction has advantages over other mathematical modelling techniques. The use of machine learning (neural network) technologies makes it possible to predict crop yields on the basis of relevant data. The individual approach of machine learning to each crop allows for the determination of the optimal learning algorithms to obtain accurate predictions.

A novel hybrid approach GREG-fuzzy-GA for minimizing work piece temperature during 2.5D milling of Inconel625 super alloy

PurposeMilling is a flexible creation process for the manufacturing of dies and aeronautical parts. While machining thin-walled parts, heat generation during machining essentially affects the accuracy. The workpiece temperature (WT), as well as the responses like material removal rate (MRR) and surface roughness (SR) for input parameters like cutting speed (CS), feed rate (F), depth-of-cut (DOC), step over (SO) and tool diameter (TD), becomes critical for sustaining the accuracy of the thin walls.Design/methodology/approachResponse surface methodology was used to make 46 tests. To convert the multi-character problem into a single-character problem, the weightage was assessed using the entropy approach and the grey relational coefficient (GRC) was determined. To investigate the connection among input parameters and single-objective (GRC), a fuzzy mathematical modelling technique was used. The optimal performance of process parameters was estimated by grey relational entropy grade (GREG)-fuzzy and genetic algorithm (GA) optimization.FindingsSR was found to be a significant process parameter, with CS, feed and DOC, respectively. Similarly, F, DOC and TD were found to be significant process parameters with MRR, respectively, and F, DOC, SO and TD were found to be significant process parameters with WT, respectively. GREG-fuzzy-GA found more suitable for minimizing the WT with the constraint s of SR and MRR and provide maximum desirability of 0.665. The projected and experimental values have a good agreement, with a standard error of 5.85%, and so the responses predicted by the suggested method are better optimized.Originality/valueThe GREG-fuzzy-GA is a new hybrid technique for analysing Inconel625 behaviour during machining in a 2.5D milling process.

Significance of Linear Programming for Optimization

Linear programming (LP) is a powerful mathematical technique that has revolutionized optimization problems across various fields. This abstract highlights the significance of linear programming in optimization and its profound impact on decision-making, resource allocation, and efficiency enhancement. The primary objective of linear programming is to maximize or minimize a linear objective function, subject to a set of linear constraints. LP provides a systematic framework for modeling and solving complex optimization problems, enabling decision-makers to make informed choices and allocate resources optimally. The significance of linear programming lies in its ability to address a wide range of real-world challenges efficiently and effectively. In the realm of operations research, linear programming has found extensive applications in supply chain management, production planning, scheduling, and logistics optimization. By formulating decision problems into mathematical models, LP allows organizations to streamline their processes, minimize costs, optimize resource utilization, and maximize overall productivity. Linear programming has also made significant contributions in the field of economics. It has enabled economists to analyze and optimize economic systems, such as determining the optimal production levels for different goods, optimizing resource allocation in a market, and solving complex pricing problems. LP provides a quantitative framework for economic decision-making, facilitating the identification of optimal solutions and supporting policy development. Furthermore, linear programming plays a crucial role in the field of transportation and network optimization. It aids in solving problems related to route optimization, facility location, network design, and capacity planning. By efficiently allocating resources and optimizing transportation networks, LP helps reduce costs, improve service levels, and enhance overall efficiency in the transportation sector. In summary, the significance of linear programming for optimization is evident in its wide-ranging applications and its ability to tackle complex decision problems in various domains. By employing mathematical modeling and optimization techniques, LP allows decision-makers to make informed choices, allocate resources optimally, and achieve desired objectives. The ongoing advancements in LP algorithms and computing technologies further enhance its applicability and make it an indispensable tool for optimization in today's dynamic and competitive world.

Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method

Biological tissue has a multidimensional and non-homogeneous inner structure by nature. The temperature distribution and freezing front locations in biological tissue are crucial to optimizing the damage to tissue during cryosurgery. There is a need for a good mathematical model and effective simulation techniques to predict the effectiveness of the therapy. The present study concerns the numerical study of phase change phenomena during cryosurgery using the three-phase lag (TPL) bioheat model in arbitrary soft tissue domains, i.e., circular (Γ1), ameba-like (Γ2), and multiconnected (Γ3). We employ the effective heat capacity formulation to solve the nonlinear governing equation. The Gaussian radial basis function and Crank–Nicolson finite difference approximation are applied for spatial and time derivatives, respectively. Using the present algorithm, we study the impact of phase lag (τv) due to thermal displacement involved in the TPL model on phase change interface position and thermal distribution in all three domains. The obtained results may be beneficial in the field of oncology.

Modified distance optimization method for the asymmetric bioreduction conditions of phenyl(thiophen-2-yl)methanone by Weissella paramesenteroides N7

Chirality plays a significant part in life since it is closely linked to carrying out the many metabolic processes that make up a living being. Chiral secondary alcohols such as diaryl-, aryl heteroaryl-, and diheteroaryl are employed in pharmaceuticals as drug intermediates. Although biocatalytic asymmetric reduction of prochiral ketones containing aromatic and heteroaromatic groups is widely known, biocatalytic reduction of heteroaromatic prochiral ketones containing sulfur heteroatoms is rarely known. Very few studies exist in the literature, including the biocatalytic reduction of phenyl(thiophen-2-yl)methanone (1). Moreover, the biocatalytic reduction of 1 with a mathematical modelling and optimization technique is unknown until now. In this study, Weissella paramesenteroides N7 biocatalyst for the asymmetric bioreduction of 1 using a novel modified distance optimization method. Optimization conditions were found as pH = 6.46, temperature = 26 °C, incubation period = 71 h, agitation speed = 200 rpm by the modified distance optimization method, and it was determined that the conversion and enantiomeric excess (ee) under these conditions could be 98.7% and 98%, respectively. Under these proposed optimization conditions, (S)-phenyl(thiophen-2-yl)methanol ((S)-2) was obtained with >99% ee, >99% conversion, and 97% yield. In addition, 11.29 g of 1 was completely converted into (S)-2 (11.07 g, 97% isolated yield) under optimized conditions. This is the first report about the fabrication of enantiopure (S)-2 in high gram scale using a biocatalyst and a novel modified distance optimization technique. In this study, the successful applicability of the new modified distance optimization method in biocatalytic asymmetric reduction reactions has been successfully demonstrated.

A mathematical modeling technique to understand the role of decoy receptors in ligand-receptor interaction

The ligand-receptor interaction is fundamental to many cellular processes in eukaryotic cells such as cell migration, proliferation, adhesion, signaling and so on. Cell migration is a central process in the development of organisms. Receptor induced chemo-tactic sensitivity plays an important role in cell migration. However, recently some receptors identified as decoy receptors, obstruct some mechanisms of certain regular receptors. DcR3 is one such important decoy receptor, generally found in glioma cell, RCC cell and many various malignant cells which obstruct some mechanism including apoptosis cell-signaling, cell inflammation, cell migration. The goal of our work is to mathematically formulate ligand-receptor interaction induced cell migration in the presence of decoy receptors. We develop here a novel mathematical model, consisting of four coupled partial differential equations which predict the movement of glioma cells due to the reaction-kinetic mechanism between regular receptors CD95, its ligand CD95L and decoy receptors DcR3 as obtained in experimental results. The aim is to measure the number of cells in the chamber’s filter for different concentrations of ligand in presence of decoy receptors and compute the distance travelled by the cells inside filter due to cell migration. Using experimental results, we validate our model which suggests that the concentration of ligands plays an important role in cell migration.

MATHEMATICAL MODELLING OF THE PROCESS OF QUALITY CONTROL OF CONSTRUCTION PRODUCTS

The study's abstract summarizes the findings of years of research in the area of quality management of industrial production and construction production, which were based on mathematical modeling techniques, process, and outcomes of implementing the developed program of monitoring and quality control in the enterprise's production process. The objective of this work is to show to the scientific community the useful outcomes of mathematical modeling in software applications. Quality control and safety represent increasingly important concerns for project managers. Defects or failures in constructed facilities can result in very large costs. Even with minor defects, re-construction may be required and facility operations impaired. Increased costs and delays are the result. In the worst case, failures may cause personal injuries or fatalities. Accidents during the construction process can similarly result in personal injuries and large costs. Indirect costs of insurance, inspection and regulation are increasing rapidly due to these increased direct costs. Good project managers try to ensure that the job is done right the first time and that no major accidents occur on the project. The research focused on describing applicable mathematical models, viewpoints, and practical outcomes of their use in the applied sector to evaluate quality control. This mathematical model was applied by the authors. The outcomes of using this approach are presented in the article. By utilizing mathematical modeling techniques, the authors created an experimental software management and quality assessment system. The authors continue their study in this area to enhance prognostic and diagnostic processes based on mathematical modeling methodologies for diagnostic systems and quality management systems.. The independent quality control, which was based on some traditional inspection techniques and used mathematical modeling techniques, revealed a negligible partial discrepancy in the results of the estimation, proving both the efficacy of the product and the suitability of the mathematical modeling concept. Keywords: Quality control, mathematical modeling, construction quality.

Analysis Model of Molten Crystallization of Mold Flux based on Image Segmentation Recognition

In this paper, through the research and analysis of the melting and crystallization process of mold flux, the characteristics of steel are improved. In the process of casting billet, the solidification characteristics of continuous casting billet are closely related to the physical and chemical properties of mold flux. The hot wire recognition image caused a great waste of manpower and material resources. Therefore, it is particularly important to develop automatic feature extraction and mathematical modeling techniques for sequence images. In this paper, correlation analysis, image segmentation and extraction technology, time series, discrete wavelet and other related models are used to study the images in the melting and crystallization process of mold flux, and analyze the differences of mold flux in the melting and crystallization process, so as to solve the kinetic relationship between the melting and crystallization process of mold flux.