The developed method of optimal design of flexible optical networks takes into account various factors and goals to ensure efficient use of resources, high performance, scalability, and adaptability. A mathematical model is developed to determine the key parameters of the fiber optic linear network route. The topology of the route of a fiber-optic linear network based on the proposed matrix model is proposed. An algorithm for using the matrix model of parameters based on the proposed variant of the fiber-optic linear network route is developed. The application of a systematic approach using the proposed method will allow network designers to achieve optimal design of flexible optical networks that efficiently use resources, provide high performance, as well as scalability and adaptability necessary for future growth and technological progress.

This article discusses the process of copper smelting in a Vanyukov furnace, with special attention paid to maintaining the optimal melt temperature, which is a key factor in the stable operation of the furnace. The article presents the results of experimental studies conducted at the Balkhash Copper Smelter, as well as experimental statistical data on the input and output parameters of the automated process control system (APCS). To build a mathematical model of the process, the System Identification Toolbox package in the MATLAB environment was used. As part of the work, modeling was carried out using a PID controller, its parameters were optimized to minimize the mean square error of regulation. In addition, the effectiveness of a fuzzy controller was considered, which showed a decrease in the dynamic error and a smoother process.

A comprehensive study was conducted to develop a two-dimensional mathematical model for a thermal storage tank containing internal disk-shaped obstacles. This model, incorporating appropriate initial and boundary conditions, was solved using the built-in solvers of the licensed COMSOL Multiphysics 5.6 software. The COMSOL model demonstrated a maximum deviation of 2.2% from experimental results and even smaller discrepancies compared to ANSYS Fluent, validating its accuracy in describing the charging and discharging processes of a sensible heat storage tank with internal obstacles. Using this validated algorithm, numerical studies were performed to analyse temperature distribution and performance indicators for three distinct tank configurations. Among these configurations, the storage tank with a middle disk consistently exhibited superior performance. This tank achieved the highest mixing efficiency, as evidenced by smoother variations in the Richardson number and a more uniform temperature distribution. It also attained the highest capacity ratio (90.12%) and exergy efficiency (81.67%), indicating its effectiveness in heat retention and the quality of stored thermal energy. Furthermore, it demonstrated the highest charging efficiency at 67.51%, highlighting its ability to store incoming heat more effectively. These findings establish the tank with a middle disk as the most efficient configuration for thermal energy storage and uniform temperature distribution. © 2024 Al-Farabi Kazakh National University.

Abstract In this paper, a digital twin of the network of heating systems for smart cities is developed using the example of the city of Almaty. The study used machine learning algorithms to estimate future thermal energy consumption and develop thermodynamic formulas. This work offers a thorough and in-depth analysis of thermal energy consumption. In addition, the paper identifies the relationship between thermal energy consumption and ambient temperature, and wind uncertainty in certain urban areas using machine learning methods to predict thermal energy consumption. Using both training and regression models, this interdependence is revealed. The obtained forecasts provide useful information for studying the structure of heat consumption in Almaty and reducing heat losses by reducing overheating in the zones of heating networks. In addition, the study analyzes high-resolution spatial data collected from 385 homes and 62 heat transfer circuits located throughout the city during the heating season. The study examines the degree of relationship between the ambient temperature and the amount of heat energy used in the areas of Astana. A minor impact of wind speed is also estimated. These discoveries allow us to use machine learning algorithms to find the location of hot spots and inefficient zones with high losses.

The paper introduces a mathematical model that describes the cavitation process occurring during the passage of a water steam flow in various geometric configurations of a hydrodynamic device. The flow experiences a localized constriction (convergent nozzle) followed by expansion (divergent nozzle), exemplified by a Venturi tube or a Laval nozzle. A narrow flow channel connecting the convergent and divergent sections is equipped with a narrow-section nozzle for injecting methane molecules into the high-speed steam flow. As the steam-gas mixture passes through this zone, it is irradiated with an electron beam and sprayed into a cylindrical chamber at atmospheric pressure, where the distribution of methane molecules in water vapor forms an aerosol. Key geometric parameters of the constriction and expansion zones of the hydraulic system (cavitation-jet chamber) are determined to ensure the uniform distribution of dispersed-phase particles (methane) in the dispersion medium (water vapor). Velocity and pressure distributions of the mixed steam-gas flow are calculated using a turbulent mathematical model, specifically the k-ω model, while the motion of methane particles is simulated using a particle tracing method. The uniformity of methane molecule distribution in water vapor is assessed using Ripley’s K-function. The best performance of the hydrogen-producing chamber was observed when the cavitation-inducing nozzle’s convergence angle exceeded 50 degrees. The divergence angle of the nozzle within the range of 30–40 degrees provided the best distribution in terms of uniformity of the methane particles in the chamber. © 2023 by the authors.

This study investigates the enhancement of the ETRO-02 ozonator's efficiency for surface water purification using a voltage inverter. The main objective is to reduce energy consumption while increasing ozone output through the application of high-frequency electrical corona discharge. The research addresses the growing demand for sustainable water purification technologies amid rising pollution levels. Traditional ozonators often suffer from high energy use and unstable ozone generation, limiting their practical deployment.In this study, a multilevel voltage inverter was introduced to stabilize power delivery and improve ozone production efficiency. Experimental testing was conducted using an ETRO-02 ozonator, standard filtration systems, and a custom-built inverter unit. Key operational parameters, including input/output voltage, inverter frequency, and water properties (temperature, pH, hardness), were evaluated. The results showed ozone output increased by 20–30%, with disinfection efficiency reaching up to 97% at optimal conditions.The findings suggest that integrating a voltage inverter significantly improves energy efficiency and operational stability of ozonator-based systems. This approach offers a cost-effective, environmentally friendly solution for water treatment. Further research is recommended to optimize long-term performance and explore real-time control through automation systems. © 2025, Zibeline International Publishing Sdn. Bhd.. All rights reserved.

From the middle of XX century, natural gas is an important mineral, widely used in the energy sector. Transportation of natural gas is carried out via gas pipeline networks and compression stations. One of the key features which need to be implemented for any centrifugal gas compressor is a surge protection. This article describes the method and develops software application intended for simulation and study of surge protection system of a centrifugal compressor used in modern gas compression stations. Within the article research method, modelling environment’s block diagram, proposed algorithms and results are described. For surge cases control and prediction, Anti-surge control block implemented which based on practical experience and centrifugal compressor theory. To avoid complicated energy balancing differential equations the volumetric flow calculation algorithm proposed which is used in combination with Redlich-Kwong equation of state. Developed software’s adequacy test performed through modeling of one-stage gas compression scheme at rated speed with comparison of parameters with reference commercial software and verification of the anti-surge control system.

Аннотация. В этой статье рассматривается значимость адаптивного управления параллельного манипулятора для оптимизации ветряной электростанции. Работа представляет анализ современных технологий и методов прогнозирования, включая Simulink пакет Simscape, которые применяются для предсказания изменений ветровых условий и оптимизации работы ветроустановок. Основываясь на данных о погоде, исторических тенденциях и других важных факторах, предиктивное управление позволяет принимать решения заблаговременно, учитывая потенциальные изменения в работе ветроэнергетических систем. Дальнейшее исследование и разработка предиктивных моделей и алгоритмов являются ключевыми направлениями для повышения эффективности и устойчивости ветроэнергетики.

In the article the model of light reflection based on the combination of two cubic bidirectional reflectance distribution functions is developed. The main components of color and the main requirements for reproducing the object`s glares are analyzed. The usage characteristics of Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong model are considered. The necessity of approximating the Blinn-Phong model by a function of low degree is justified. The characteristics of the cubic polynomial approximation of the Blinn-Phong model are determined. It was established that the main drawback of this approximation is a significant deviation of the function from the reference function in the glare’s attenuation zone. The combined function that combines two cubic functions is proposed. The first cubic function reproduces the glare’s epicenter, and the second replaces the specified function in the attenuation zone. A system of equations for calculating the coefficients of the second function was created. The formula for the connection point of two cubic functions is obtained. A graph of the developed combined model based on cubic functions is obtained. For the combined and original cubic functions a comparison of the maximum relative errors in the glare’s epicenter zone, the maximum absolute errors, and the relative errors at the inflection point was made. A three-dimensional plot of the absolute error of the combined cubic model from the Blinn-Phong model depending on the shininess and the angle value is built. Visualization results based on the combined and the original cubic functions are compared. It is confirmed that the proposed reflection model increases the realism of glare formation in the attenuation zone. The resulting combined reflection model provides a highly accurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used.

Different types of transport involved in the performance of intercity cargo multimodal transportation are characterized by mutual advantages and disadvantages. The main reason why multimodal transportation is gaining more and more use and development is to avoid the use of transportation that burns hydrocarbons and is not environmentally friendly. New prospects also concern increased transportation safety, the possibility of ensuring the working conditions of delivery workers, and reducing logistics costs. However, the successful interaction of different types of transport in the logistics chain can be ensured when the organizational and technological parameters of individual links of the overall transport process are mutually agreed upon. This article is devoted to the coordination of individual stages of the multimodal delivery process, taking into account that the process is discrete in its content. The tact, which has the content of a time window for performing the operation is used for discrete processes. Due to the fact that multimodal transportation of goods is carried out on a large network, time is one of the most important criteria for their perfection. Two time criterias are applied in the article, which take into account the fact that the multimodal process must be synchronized and that the transportation of a large group of goods can be carried out in separate parts. An estimation criterion was also applied, which takes into account constant, variable, contingent costs, which are carried out depending on the structure of the process.