Papers by Keyword: Mathematical Modeling

Abstract: This study analyzes the global experience with trolley-assist haul trucks in mining, substantiates their feasibility for Ukrainian open-pit mines, and develops a mathematical model describing the dependence of economic effect on the electrification coefficient (k_e) of haul roads. The methodology involves analyzing technical and operational data from Canada, Finland, Zambia, and South Africa, adapting it to Ukrainian conditions, and modeling the integral economic effect. The dependence is described by a saturating Hill function, with parameters determined via the least squares’ method using empirical and calculated data. Results show that a combined diesel–trolley system offers an optimal balance between economic efficiency, productivity, and capital costs. The model identifies an optimal k_e range of 0.20–0.40 for Ukraine, achieving 70–80% of the full electrification benefits. The analysis confirms nonlinear growth of the effect and saturation beyond k_e≈0.40. For the first time, global operational data have been integrated with modeling for Ukrainian open pits, producing a tool adaptable to various mining and geological conditions. The methodology supports phased electrification, fuel savings of 25–30%, CO₂ reduction by 20–25%, and substantial productivity gains.

Abstract: This study investigates the calco-carbonic balance of drinking water in Taza, Morocco, a critical parameter for ensuring water quality and preserving distribution infrastructure. Using Principal Component Analysis (PCA) and Multiple Linear Regression (MLR) with Statistica 12, we examine the interactions between the physicochemical parameters and the Langelier Saturation Index (LSI). The study highlights the difficulty of factors influencing this balance, which is crucial for preventing scaling. Scaling can lead to reduced water flow, decreased energy efficiency, increased maintenance costs, premature equipment wear, and deterioration of water quality. The results identify the parameters impacting this balance, including temperature, total hardness, dissolved oxygen, and pH. PCA enabled us to extract valuable insights from physicochemical analyses, revealing significant correlations between these parameters and suggesting optimization strategies.The predictive model for the Langelier Saturation Index, with a determination coefficient (R² = 0.925) and a standard error (σerr = 0.07), provides a valuable tool for expecting and correcting imbalances, therefore ensuring better management of drinking water quality in Taza.

Abstract: The article investigates the process of liquid penetration into porous building materials, including concrete, brick, drywall, plaster, aerated concrete, and others. The influence of moisture on the durability, thermal insulation properties, and structural integrity of materials is examined. The relevance of developing mathematical models for predicting moisture ingress in constructions is highlighted, as this enables the minimization of operational costs and enhancement of building energy efficiency. A nonlinear diffusion model is proposed, taking into account the dependence of the diffusion coefficient on moisture concentration. Experimental data were approximated, and model parameters for specific materials were determined. Both stationary and nonstationary moisture transport problems are considered, with analytical solutions and a methodology for their application in predicting the depth of moisture penetration presented. The results can be integrated into BIM systems, opening new perspectives for use in digital construction.

Abstract: This paper deals with the problem of visualization of the widely known and of considerable practical value problem of sound wave propagation in a liquid medium containing gas bubbles. The study was carried out using modern methods of computer simulation in the COMSOL Multiphysics software environment, which provides extensive opportunities for numerical analysis of complex physical processes. In the course of the study, a set of calculations was performed, which made it possible to obtain a series of illustrative images reflecting the distribution of acoustic and sound pressure both in the volume of the water medium and on the boundary surfaces at different sound frequencies. The constructed model demonstrated its efficiency, allowing to identify areas with increased and decreased acoustic pressure formed on the surface of air bubbles under the influence of sound waves. Visualization of these processes opens up opportunities for analysis and optimization of acoustic systems operating in the presence of gas inclusions in the liquid.

Abstract: In this paper, a new method for solving Maxwell's equations associated with electrostatic separators is presented. The boundary value problem is transformed into an optimization problem by using the finite element method. Numerical simulations were carried out using Matlab software that performs equation-based multiphysics modeling for different physical processes by applying the finite element method and modified method of characteristics to a system of partial differential equations. The finite-element method is used to solve Poisson's equation, and a modified method of characteristics is used to satisfy the current continuity condition. The two methods are repeated to obtain a consistent solution to the described equations. The simulation model has been developed to determine the influence of the electrical conductor, semiconductor, and dielectric particles on the important parameters of the corona mechanism, namely the distribution of electric potential, electric field, current density, space charge density, and collection efficiency.

Abstract: The application of abstract discrete automatons in automated production control systems represents a significant stride towards achieving enhanced precision, flexibility, and efficiency in manufacturing processes. One of the standout advantages of using abstract discrete automatons is the ability to achieve precise control over production processes. These systems excel in modeling complex discrete event systems, allowing for real-time adaptation to changing conditions. This adaptability is invaluable in industries where production requirements and parameters can shift rapidly. Through the careful design and deployment of difference equations, automated production control systems can optimize the utilization of resources. The integration of abstract discrete automatons enables a high degree of quality assurance. Complex system design, integration issues, and the need for skilled personnel are among the hurdles that must be addressed. The synergy between mathematical models and automation technologies holds immense potential for optimizing production processes across various sector. The implementation of difference equations and abstract discrete automatons in automated production control systems marks a significant step towards advancing manufacturing efficiency. These mathematical and computational tools provide a robust framework for optimizing processes, reducing waste, and enhancing overall productivity. Abstract discrete automatons excel in handling complex, real-time changes, making them well-suited for industries where adaptability to shifting demands and conditions is paramount. By leveraging mathematical models and automation, production processes can achieve a level of precision and consistency that is challenging to attain through manual control.

Abstract: The importance of fossil fuel in our day-to-day life cannot be described in words. Worldwide fossil fuel usage amounted to around 128,550 terawatts per hour. Keeping all the necessity of fossil fuel in our daily life, we cannot deny the fact that the vast usage of fossil fuel is one of the most vital reasons behind global warming and climate change. Many reports claim that the global temperature has increased by 1°C dues to excessive usage of fossil fuels. Moreover, the resources of fossil fuel are limited and humanity may run out of these limited resources in the future. In order to reduce global warming, in this study, we are proposing to increase the usage of solar energy instead of fossil fuel using mathematical modeling techniques. We have formulated a three-compartmental model with the compartments Global Temperature, Fossil Fuel Consumption and Solar Energy Consumption with interactions between the compartments. We have conducted both qualitative and numerical analysis of the model. The qualitative analysis includes the study of equilibrium, stability, nature of the stability at the equilibrium points. From the results of the numerical analysis, we can conclude that increasing the usage of solar systems can effectively reduce global warming. In countries like Bangladesh, the vast implementation of solar energy can be more effective than in other countries as the average temperature remains quite higher than in other countries, also for the availability of enough sunlight.

Abstract: The prototype of the compressed air foam system was improved based on the evaluation of the numerical parameters obtained with the help of the developed mathematical model of the foam generation process and the pneumatic-hydraulic scheme. The prototype provides the possibility of foam generation both in autonomous mode, due to the installation of cylinders with compressed gas, and in stationary mode, due to the supply of compressed air from an external source. This allows the use of an improved model of the compressed air foam system both in stationary mode (dry pipes, gas stations, etc.) and for use on heavy and light fire trucks, which is important for large cities. Testing of the improved prototype of the system for extinguishing model fires was carried out. The system provides extinguishing of model fires of class 183 B and 144 B when using both a general-purpose foaming agent and a special film-forming foaming agent. When using a film-forming foaming agent, the extinguishing time was reduced by 1.75 times, the consumption of fire extinguishing solution by 1.47 times. But at the same time, it should be taken into account that the cost of the film-forming foaming agent Sofir (sofirafff 6 %) is more than 3.2 times the cost of the general-purpose foaming agent Sofir. The effectiveness of the improved model in extinguishing class A fires was also confirmed. The autonomous compressed air foam system ensures extinguishing of a class 4 A model fire in 90 seconds. Dry foam with a factor of 14 is noted to be more effective in extinguishing solid combustible substances.

Abstract: Anaerobic digestion is a promising technology due to its significant economic and environmental potential. Nevertheless, its development is a substantial challenge for researchers since this biochemical process is difficult to predict due to the many reactions involved. Thus, mathematical modeling becomes necessary to analyze the fermentation process and determine the complex kinetic parameters to identify and predict the system's performance under the most varied conditions. This research aims to apply the AM2 model to simulate the anaerobic digestion process of municipal solid waste. The experimental results obtained from our previous research work were used for identifying the parameters of the AM2 model and for its validation by the cross-validation method. Simulations showed that the model could effectively reproduce the dynamics of the evolution of the anaerobic digestion process with reasonable accuracy.

Abstract: Rice is one of the most consumed cereals in the world, and the cultivation of this crop has significant relevance in the southern region of Brazil. When subjected to inadequate conditions of temperature and humidity, rice becomes susceptible to attacks from pests and fungi and, therefore, care in the storage process is of paramount importance, since this is largely responsible for the quality of the harvest. Such care allows the food to arrive without harm to the consumer. In this sense, the mathematical modeling, among numerous possibilities, allows for evaluating the internal temperature of a silo and, through this, taking preventive measures so that the grains maintain their quality. The objective of this work is to model the heat transfer process in a silo prototype containing rice in husk through the explicit finite difference method for a one-dimensional and transient model considering two approaches centered on the spatial derivative: error of order 2 and 4. In addition, the thermal diffusivity of the grain with average value was analyzed. The results obtained by the solutions were analyzed through graphs and statistical indexes comparing with the experimental data of the literature, and the computer simulation was performed through the Google Colab platform. The chosen methodology proved effective for the work, and the predicted temperatures for the approximations of order 2 and 4 denote similarities both graphically and in the precision of the statistical indexes.