Search Results (780)

This paper presents research and theoretical development of a mathematical model that, first, allows us to understand how the positional exactitude of the output link of a four-bar mechanism depends on the manufacturing dimensional tolerances. To find this dependence, the total differentials of the kinematic constraint functions that govern the field of positions must be determined for each kinematic cycle of the mechanism under consideration. These total differentials lead to a system of equations whose solution gives the positional errors of the movable output links as a function of the manufacturing dimensional errors and an incidence matrix that varies with each one of the positions of the input element. On the other hand, the theoretical transmission ratio between the output velocities with respect to the input velocity of the articulated kinematic chain is defined, and for determining the total errors in each ratio, the total differential of each one of them is calculated, showing a clear dependence with respect to the positional errors of the output links (previously defined) of the mechanism. The sum of the theoretical transmission ratio and its respective error provides the real transmission ratio. Furthermore, the described methodology allows for determining the sensitivity (influence coefficients) in the transmission ratios due to errors inherent in the link lengths. Finally, the presented analytical approach is numerically implemented through an example of articulated parallelogram design, principally characterizing in graphic form the transmission ratios in their regions of permitted movements and blocking positions, for a specific IT degree of precision of the bilateral dimensional tolerances of their functional geometric parameters, with the objective of analyzing every aspect related to the performance of the mechanisms. This formalism is validated through three particular design cases using a CAD model in a simulation module of kinematic motion analysis; additionally, the evolution of the transmission angle is discussed. The methods and conclusions proposed in this document also leave open the way as future work to study separately the magnitudes and signs of the positional errors and the transmission ratio, or even the influence coefficients themselves, in order to assign the most convenient degree of IT precision for each link in the mechanism with the purpose of reducing errors in the designs and obtain better efficiency in the transmission ratio. Full article

To ensure the transition to electric transport in order to reduce CO₂ emissions, a number of projects have been initiated to develop and introduce new types of locally produced vehicles. The Russian Federation market is quite conservative and has its own specifics and a special consumer model. In addition, the component base of localized components for electric vehicles is relatively small, which is justified by relatively low demand and market volumes. To create the concept of a Class C passenger vehicle with electric traction, marketing research was conducted in a group of people who are potentially ready to abandon traditional vehicles and choose electric vehicles or hybrids. The purpose of the study is to evaluate the opinion of consumers and to form the technical characteristics of a Class C hybrid car based on localized components. Methods: To obtain the results, various components of the power unit were modeled, and a balanced solution was found that meets the requirements of consumers in the region. Mathematical modeling was carried out and analytical studies of the power reserve of various configurations of power units within the WLTC cycle were carried out in the digital environment of Siemens Amesim. Analytical work on the study of the composition of cars for calculating the masses of modern components and aggregates was carried out using Autodatas. Consumer opinions were assessed through a survey using the Yandex. Forms service. The relevance of the study is confirmed by the lack of domestic models of sequential hybrids on the market and the lack of similar studies, based on the opinion of a potential consumer. The result is the technical parameters of the main components and assemblies, which should ensure the optimal cost of the final product and meet the requirements of the consumer. Conclusion: As a result of the study, a concept of a combined sequential-type power unit was developed based on available components, meeting the main consumer properties, and the technical characteristics of the components were presented. Full article

Mathematical modeling competency is essential for engineering students, yet significant cognitive obstacles impede their ability to apply theoretical concepts like derivatives to real-world optimization problems. This study investigates the cognitive processes and obstacles encountered by Industrial Engineering and Management students when solving applied derivative problems, utilizing the Mathematical Modeling Cycle (MMC) and Duval’s theory of semiotic registers as analytical frameworks. A qualitative case study design was employed, analyzing students’ written exam responses to an applied optimization task involving tour organization with variable pricing structures. Three representative cases were examined in detail, revealing distinct patterns of cognitive engagement. Results identified specific cognitive obstacles including misunderstanding of variables and domains, weak connections between mathematical and economic contexts, difficulties in graphical representation of constraints, and deficits in validation and critical thinking. While students demonstrated procedural fluency in symbolic manipulation and mathematical work, they struggled to coordinate between different semiotic registers (verbal, algebraic, graphical, and contextual) and failed to complete the full modeling cycle, particularly in the crucial validation stages. These findings suggest that cognitive obstacles stem from representational gaps rather than general learning difficulties, indicating the need for targeted pedagogical interventions that explicitly address transitions between semiotic registers and emphasize the iterative nature of mathematical modeling in engineering contexts. Full article

The labyrinth weir is an effective hydraulic structure, offering high discharge efficiency and economic advantages, making it a suitable option for dam construction or rehabilitation projects. Owing to its complex geometry, significant research efforts have been dedicated to enhancing its hydraulic performance. Since the beginning of this century, Computational Fluid Dynamics (CFD) has emerged as a vital approach, complementing traditional methods in the design of hydraulic structures. This study employs CFD ANSYS FLUENT to examine the discharge coefficient of a semicircular labyrinth weir, featuring a cyclic arrangement and a half-round crest profile. The numerical models and simulations address two-phase flow (air and water) under incompressible and free-surface conditions. The CFD ANSYS FLUENT approach used is multiphase flow modeling using the Volume of Fluid method to track the free water surface. For turbulence effects, it is complemented with the standard k-ε model and the Semi-Implicit Method for Pressure Linked Equations algorithm for pressure–velocity coupling. In addition, for boundary conditions, the flow velocity was defined as the inlet to the channel and atmospheric pressure as the outlet, and the walls of the channel and weir are considered solid, stationary, and non-sliding walls. The model was validated with experimental data reported in the literature. The results indicate that the semicircular labyrinth weir achieves greater discharge capacity when the headwater ratio H_T/P increases for H_T/P ≤ 0.25. A regression analysis mathematical model was also developed, using the H_T/P ratio, to predict the discharge coefficient for 0.05 ≤ H_T/P ≤ 1. Relative to other geometrical configurations, the semicircular labyrinth weir demonstrated a discharge capacity that was up to 88% higher than that of the trapezoidal labyrinth weir. Both weir and cycle efficiency were assessed, and maximum weir efficiency was observed when H_T/P ≤ 0.1, while cycle efficiency peaked at H_T/P ≤ 0.25. The geometric configuration under analysis demonstrated greater economic efficiency by providing a reduced total length and enhanced discharge capacity relative to trapezoidal designs, especially when the sidewall angle α is considered as α ≤ 12°. The study concludes by presenting a design sequence detailing the required concrete volume for construction, which is subsequently compared to the specifications of a trapezoidal labyrinth weir. Full article

Fuel cells are highly efficient electrochemical devices that convert the chemical energy of fuel directly into electrical energy, while generating minimal pollutant emissions. In recent decades, they have established themselves as a key technology for sustainable energy supply in the transport sector, stationary systems, and portable applications. In order to assess their real contribution to environmental protection and energy efficiency, a comprehensive analysis of their life cycle, Life Cycle Assessment (LCA) is necessary, covering all stages, from the extraction of raw materials and the production of components, through operation and maintenance, to decommissioning and recycling. Particular attention is paid to the environmental challenges associated with the extraction of platinum catalysts, the production of membranes, and waste management. Economic aspects, such as capital costs, the price of hydrogen, and maintenance costs, also have a significant impact on their widespread implementation. This manuscript presents detailed mathematical models that describe the electrochemical characteristics, energy and mass balances, degradation dynamics, and cost structures over the life cycle of fuel cells. The models focus on proton exchange membrane fuel cells (PEMFCs), with possible extensions to other types. LCA is applied to quantify environmental impacts, such as global warming potential (GWP), while the levelized cost of electricity (LCOE) is used to assess economic viability. Particular attention is paid to the sustainability challenges of platinum catalyst extraction, membrane production, and end-of-life material recovery. By integrating technical, environmental, and economic modeling, the paper provides a systematic perspective for optimizing fuel cell deployment within a circular economy. Full article

The article examines the use of hydrogen fuel as an alternative to traditional diesel fuel for internal combustion engines (ICE) in railway applications. The main objective of the study is to analyze the operational consumption of hydrogen fuel based on the mathematical modeling of the working cycle of the EMD 12-645E3C engine installed on CIE 071 locomotives used in freight and passenger service. The article provides information on the design features of the EMD 12-645E3C engine, its technical parameters, and the results of bench tests. The indicator parameters of the engine at various controller positions are determined and analyzed, and the results of mathematical modeling of its operation on hydrogen fuel are presented. Particular attention is paid to changes in indicator parameters, including the maximum combustion pressure and the peak gas temperature in the cylinder, as well as comparing the mass consumption of diesel and hydrogen fuel. The study results demonstrate that the use of hydrogen allows the engine to maintain effective power across all operational modes while simultaneously reducing energy costs up to 8%. In this case, the pressure and temperature of the gases in the cylinder increased by 3–6% and 5–8%. Recommendations are also provided regarding technical challenges associated with transitioning to hydrogen fuel, including the modernization of the combustion chamber, fuel system, and safety system. Full article

This paper analyzes the behavior of a three-phase induction motor (IM) during voltage sags in the supply network and its subsequent re-acceleration following voltage recovery. A dynamic mathematical model based on the two-axis (d,q) representation of the IM is developed, taking into account variations in supply voltage, electromagnetic torque, and stator currents over time. The model enables a detailed assessment of motor stability and transient behavior when the supply voltage falls below nominal levels. The analysis covers sag depths of 0.9–0.5 ${\mathrm{U}}_{\mathrm{N}}$ and interruption durations of 0.14 s and 1.14 s, quantifying stator currents and electromagnetic torque both at the instant of the dip and within the first cycles after recovery. Particular attention is given to identifying the conditions under which the IM may fail to re-accelerate or transition into generator mode, depending on the depth and duration of the voltage sag and the type of mechanical load. The study includes simulations for a 0.75 kW IM under both constant and variable torque conditions, as well as different types and durations of short-circuit faults in the supply system. Results show that sag duration has little effect at sag onset but strongly influences recovery inrush and torque oscillations; shorter interruptions yield lower recovery currents. The findings provide practical insights for the design of more robust power supply infrastructures and the refinement of motor control and protection strategies. Full article

Polycystic Ovary Syndrome (PCOS) is a widespread hormonal disorder affecting women of reproductive age, often leading to infertility and associated complications. This study presents a comprehensive stochastic mathematical framework to analyze the dynamics of PCOS with a particular focus on infertility and treatment outcomes. Here, the transitions between compartments represent progression of women through clinical states of PCOS (risk, diagnosis, treatment, recovery) rather than infection or transmission, since PCOS is a non-communicable disorder. The model incorporates probabilistic elements to break the symmetric and predictable assumptions inherent in deterministic approaches. This allows it to reflect the randomness and asymmetry in hormonal regulation and ovulation cycles, enabling a more realistic representation of disease progression. By utilizing stochastic differential equations, the study evaluates the impact of treatment adherence on fertility restoration. We establish the conditions for disease extinction versus the existence of an ergodic stationary distribution, which represents a form of long-term statistical symmetry. The results emphasize the importance of early diagnosis and consistent treatment. Furthermore, the proposed approach provides a valuable tool for clinicians to predict patient-specific trajectories and optimize individualized treatment plans, accounting for the asymmetric nature of patient responses. Full article

This study introduces MIRANDA, a computer vision system, and RELAPP, a complementary force measurement system, developed for characterizing viscoelastic materials. Our aim was to evaluate their combined ability to predict key rheological parameters and demonstrate their utility in material analysis, offering an alternative to traditional methods. We analyzed five distinct flour dough samples, correlating MIRANDA and RELAPP variables with established rheological reference values. Support Vector Machine (SVM) regression models were trained using MIRANDA’s stable TR and elasticity data to predict industrially relevant parameters: baking strength (W), tenacity (P), extensibility (L), and final viscosity (RVU) from Chopin alveograph and viscosimeter. The predictive models showed promising results, with R² values of 0.594 (p = 0) for W, 0.575 (p = 0) for P, and 0.612 (p = 0.03763) for viscosity, all statistically significant. While these findings are promising, it is important to note that the small sample size may limit the generalizability of these models. The synergy between the systems was evident, exemplified by strong positive correlations, such as between MIRANDA’s Elasticity and RELAPP’s c_exp (parameter ‘c’ of its mathematical model m1, r = 0.858) and final resistive force (r = 0.839). Despite the limited sample size, these findings highlight MIRANDA’s versatility and speed for efficient material characterization. MIRANDA and RELAPP offer significant industrial implications for viscoelastic materials, including accelerating development cycles and enhancing continuous quality control. This approach has strong potential to reduce reliance on slower, traditional methods, warranting further validation with larger datasets. Full article

The peculiarity of the functioning of modern electric power systems, caused by the presence of renewable energy sources, flexible control devices based on power electronics, and the reduction of the reserve of the transmission capacity of the electric network, increases the relevance of identifying and damping low-frequency oscillations (LFOs) of the electrical mode. This paper presents a comparative analysis of methods for estimating the parameters of low-frequency oscillations. Their applicability limits are shown as well as their peculiarity associated with low adaptability, and time costs in assessing the parameters of the electrical mode with low-frequency oscillations are revealed. A method for the accelerated evaluation of low-frequency oscillation parameters is proposed, the delay of which is ¼ of the oscillation cycle. The method was tested on both synthetic and physical signals. In the first case, the source of data was a four-machine mathematical model of a power system. In the second case, signals of transient processes occurring in a real power system were used as physical data. The accuracy of the proposed method was obtained by calculating the difference between the original and reconstructed signals. As a result, calculated error values were obtained, describing the accuracy and efficiency of the proposed method. The proposed algorithm for estimating LFO parameters displayed an error value not exceeding 0.8% for both synthetic and physical data. Full article

As a core device in the natural gas supply chain, the compressor unit of the gas storage reservoir is crucial to the improvement of storage and transportation efficiency through its operation optimization. Based on the basic structure, working principle, and layout mode of the compressor unit of the gas-storage reservoir, this paper establishes a mathematical model for the operation optimization of the compressor unit, proposes an optimization method for the series-parallel operation of the compressor unit, and develops optimization software for the matching operation of the compressor unit. Aiming at the compressor unit used in the gas-storage reservoir with the largest gas injection and production capacity in China, this paper analyzes the variation laws of the compressor inlet temperature and the inlet and outlet pressures during the gas injection cycle, conducts research on the operation-matching optimization of the compressor unit within a one-month long cycle, and obtains the optimization scheme of the series-operation of the compressor unit and the energy-consumption results. Compared with the actual operation data, the monthly power consumption is reduced by 5.12%. The operation optimization situation of the compressor unit on typical days is analyzed to obtain the operation optimization law of the series-connected compressor unit. This research provides a theoretical basis and practical guidance for the operation-scheme optimization of the compressor unit of the gas-storage reservoir and has important practical application value. Full article

Efficient control of HIV-1 infection relies on highly active antiretroviral therapy (HAART). However, this therapy is not curative and requires continuous drug administration. Application of HIV-1 defective interfering particles (DIPs), engineered with ablations in key viral protein expressions (e.g., Tat, Rev, Vpu, and Env), suggests a therapeutic potential transforming them into Therapeutic Interfering Particles (TIPs). A recent animal HIV model study in non-human primates reports a substantial reduction in viral load after a single intravenous injection of TIPs. In contrast, human clinical trials demonstrate no beneficial effect of defective interfering particles (DIPs) in people living with HIV-1. This discrepancy highlights the importance of further investigation of HIV-TIP interactions. A quantitative view of intracellular replication for HIV-1 in the presence of TIPs is still missing. Here, we develop a high-resolution mathematical model to study various aspects of the interference of a specific engineered TIP-2 particle characterized by a 2.5-kb deletion in the HIV pol-vpr region with HIV-1 replication within infected CD4+ T cells. We define the conditions in terms of the number of homozygous HIV-1 virions and TIP-2 particles that enable the reduction of the wild-type virus replication number to the value of about one. The deterministic model predicts that at a ratio of 1 HIV-1 to 10 TIP-2 particles, the infected cell still produces some viruses, although in a minor quantity, i.e., about two virions per cycle. Pre-activation of the interferon type I (IFN-I) system results in a complete block of HIV-1 production by TIP-2 co-infected cells. Overall, the modelling results suggest that to improve the effectiveness of TIPs in reducing HIV infection, their combination with other types of antiviral protection should be considered. Our results can be used in the development of combination therapy aimed at treating HIV-1 infection. Full article

This paper presents a modular hybrid mathematical model of bacterial fermentation developed by integrating a detailed kinetic model for the central carbon metabolism of Escherichia coli with a simplified four-compartment model of a large stirred bioreactor. The model describes the growth dynamics of E. coli, taking into account the hydrodynamic characteristics of the cultivation environment and spatial concentration gradients. The first module simulates liquid exchange flows between neighboring reactor zones and tracks the spatial distribution of substrate, acetate, dissolved oxygen, and biomass, while the second one, which is a kinetic model, includes main metabolic pathways such as glycolysis, the tricarboxylic acid cycle, and oxidative phosphorylation. Compared to most previous hybrid approaches relying on simplified kinetics, the present model integrates a detailed kinetic representation of E. coli central metabolism and is openly implemented on the BioUML platform, which ensures its reproducibility and extensibility. Numerical simulations reveal how mixing intensity affects concentration gradients and metabolic regimes across the reactor. Additionally, the model was used to identify an optimal mixing regime corresponding to the state where the system first enters the regime of complete aerobic substrate oxidation. The proposed model is applicable for numerical analysis of industrial-scale bioreactors and for predicting metabolic dynamics under various hydrodynamic conditions. Full article

Forests play a pivotal role in the global carbon cycle, yet accurately simulating forest soil carbon dynamics remains a significant challenge for process-based models. This review systematically compares the mechanistic foundations of traditional models (e.g., Century, CLM5) with emerging microbial-explicit models (e.g., MEND), highlighting key differences in mathematical formulation (first-order kinetics vs. Michaelis–Menten kinetics), carbon pools partitioning (measurable vs. non-measurable experimentally), and the representation of soil carbon stabilization mechanisms (inherent recalcitrance, physical protection, and chemical protection). Despite advances in process-based models in predicting forest soil organic carbon (SOC), improving prediction accuracy, and assessing SOC response to climate change, current research still faces several challenges. These include difficulties in capturing depth-dependent variations in critical microbial parameters such as microbial carbon use efficiency (CUE), limited capacity to distinguish the relative contributions of aboveground and belowground litter inputs to SOC formation, and a general lack of long-term observational data across soil profiles. To address these limitations, this study emphasizes the importance of integrating remote sensing data and refining cross-scale simulation approaches. Such improvements are essential for enhancing model predictive accuracy and establishing a more robust theoretical basis for forest carbon management and climate change mitigation. Full article

Agile satellites leverage rapid and flexible maneuvering to image more targets per orbital cycle, which is essential for time-sensitive emergency operations, particularly disaster assessment. Correspondingly, the increasing observation data volumes necessitate the use of on-orbit computing to bypass storage and transmission limitations. However, coordinating precedence-dependent observation, computation, and downlink operations within limited time windows presents key challenges for agile satellite service optimization. Therefore, this paper proposes a deep reinforcement learning (DRL) approach to solve the joint observation and on-orbit computation scheduling (JOOCS) problem for agile satellite constellations. First, the infrastructure under study consists of observation satellites, a GEO satellite (dedicated to computing), ground stations, and communication links interconnecting them. Next, the JOOCS problem is described using mathematical formulations, and then a partially observable Markov decision process model is established with the objective of maximizing task completion profits. Finally, we design a joint scheduling decision algorithm based on multiagent proximal policy optimization (JS-MAPPO). Concerning the policy network of agents, a problem-specific encoder–decoder architecture is developed to improve the learning efficiency of JS-MAPPO. Simulation results show that JS-MAPPO surpasses the genetic algorithm and state-of-the-art DRL methods across various problem scales while incurring lower computational costs. Compared to random scheduling, JOOCS achieves up to 82.67% higher average task profit, demonstrating enhanced operational performance in agile satellite constellations. Full article