Comprehensive Mathematical Model Research Articles

Analysis of a fractional-order model for dengue transmission dynamics with quarantine and vaccination measures

A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals.

Optimization of dual-function suspension structures using particle swarm optimization approaches

The suspension system integrating both vibration control and energy harvesting capabilities is denoted as Dual-function Suspension (DFS). The principal objectives for DFS encompass lightweight structure, high output force, extensive adjustability in damping, and minimized energy consumption. In pursuit of optimizing the linear motor and magnetorheological damper (MRD) amalgamated into the DFS, a multi-objective Particle Swarm Optimization (PSO) algorithm is conceived, emphasizing primary and secondary objectives to enhance the holistic performance of the DFS. A comprehensive mathematical model of the DFS is established, and subsequent to this modeling, the structural parameters of DFS are meticulously analyzed. Drawing upon the insights from this analysis, primary and supplementary optimization objectives are delineated, employing PSO for the refinement of the DFS structure. Following this, the Pareto solution set, derived from the optimization process, is judiciously selected utilizing fuzzy theorem principles. The outcomes reveal that, under the constraints of unaltered suspension packaging dimensions and overall energy consumption, the optimized suspension system manifests a 50% augmentation in output force, a 30% expansion in adjustable damping range, and a 39% reduction in thrust ripple compared to its pre-optimized state.

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.

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.

Comprehensive mathematical model for efficient and robust control of irrigation canals

Linear control-oriented models are important to represent canal dynamics for designing controllers. This study focuses on hydraulic control structure (gate) modelling to address the complex interdependent behavior inherent in irrigation canals. A comprehensive mathematical model that incorporates the water level with gate-opening to model discharge is introduced for single and multiple canal pool scenarios. The proposed model captures the hydraulic coupling within and among canal pools, a key finding. The model is evaluated extensively under uniform and non-uniform flows across three distinct canals, highlighting the model’s applicability to various systems. The uncertainty inherent within the nominal model is also assessed for varying operating conditions and hydraulic parameters. The proposed model is compared with the existing and the Saint-Venant (SV) model, showing improved accuracy in water-level predictions. This advancement in hydraulic modelling contributes to adaptable canal models essential in developing robust controllers to enhance water management in irrigation canals.

Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics

A comprehensive mathematical model of the multiphysics flow of blood and Cerebrospinal Fluid (CSF) in the brain can be expressed as the coupling of a poromechanics system and Stokes' equations: the first describes fluids filtration through the cerebral tissue and the tissue's elastic response, while the latter models the flow of the CSF in the brain ventricles. This model describes the functioning of the brain's waste clearance mechanism, which has been recently discovered to play an essential role in the progress of neurodegenerative diseases. To model the interactions between different scales in the porous medium, we propose a physically consistent coupling between Multi-compartment Poroelasticity (MPE) equations and Stokes' equations. In this work, we introduce a numerical scheme for the discretization of such coupled MPE-Stokes system, employing a high-order discontinuous Galerkin method on polytopal grids to efficiently account for the geometric complexity of the domain. We analyze the stability and convergence of the space semidiscretized formulation, we prove a-priori error estimates, and we present a temporal discretization based on a combination of Newmark's β-method for the elastic wave equation and the θ-method for the other equations of the model. Numerical simulations carried out on test cases with manufactured solutions validate the theoretical error estimates. We also present numerical results on a two-dimensional slice of a patient-specific brain geometry reconstructed from diagnostic images, to test in practice the advantages of the proposed approach.

Analyzing the effects of polymeric dielectric materials on micro capacitive pressure sensors: A model incorporating displacement-dependent porosity

Recently, the extensive utilization of porous polymeric materials to amplify the sensitivity of capacitive devices is noticeable. The absence of an effective mathematical model for studying these devices has spurred the development of a comprehensive mathematical model in the current work. This model is formulated to analyze the static and dynamic behavior of systems incorporating a porous polymer dielectric material within the gap between flexible and fixed microplates. The derived nonlinear governing equations encompass the effects of electrostatic force, von-Karman nonlinear strains, and displacement-dependent porosity. Employing spatial decomposition, the resulting nonlinear algebraic equations and ordinary differential equations are leveraged to study the static and transient dynamic behavior, as well as the frequency response of the sensor using a learning approach. Two scenarios are investigated to assess the impact of various geometrical and physical parameters on sensor sensitivity one with a polymeric material and another without, each with distinct parameter values. The results reveal that the inclusion of a polymeric dielectric material increases electrostatic force but concurrently elevates the equivalent stiffness of the structure. The effectiveness of using a polymeric dielectric material is contingent upon the specific geometrical and physical properties of the sensor. Moreover, the obtained results in simplified cases are compared to existing numerical and experimental data, demonstrating a high degree of agreement. This work significantly contributes to advancing the understanding of sensors incorporating porous polymer dielectric materials and underscores their potential for enhanced sensitivity across diverse applications.

Effect of geothermal heat transfer on performance of the adiabatic compressed air energy storage systems with the salt cavern gas storage

The temperature and pressure of compressed air influence the output performance of the adiabatic compressed air energy storage system with salt cavern gas storage. However, current studies often overlook the impact of geothermal heat transfer on system performance. In this paper, a mathematical model of the energy storage system with salt cavern gas storage is developed, considering the geothermal heat transfer in wellbore and salt carven. The model is used to illustrate the effects of geothermal heat transfer on the system performance through a sensitivity analysis of some key parameters. The results show that geothermal heat transfer will significantly reduce the gas and energy storage capacity, with a maximum reduction of 15.3 % and 11.1 % at a depth of 2000 m, respectively. Furthermore, this reduction would increase with the depth of the salt cavern. The geothermal energy reduces the round-trip efficiency from 68.7 % to 66.26 % and the energy storage density from 5.18 kWh·m−3 to 4.32 kWh·m−3. For common salt cavern gas storage at a depth of about 600 m ∼ 1200 m, the negative impacts of geothermal heat transfer on round-trip efficiency and energy storage density are less than 2.2 % and 0.5 kWh·m−3, respectively. Sensitivity analysis also demonstrates that the primary factors influencing the system’s performance are the thermal conductivity of the surrounding rock, the volume of the salt cavern, and the length of the wellbores. The secondary factors include the heat transfer coefficient on the inner wall of the salt cavern, the inner pipe radius, and the roughness of the inner pipe. Irrelevant factors include the thermal conductivity of the protective fluid and the thermal conductivity of the cement layer. The proposed comprehensive mathematical model of the system and simulation findings aid in forecasting the performance of storage systems and offer theoretical guidance for the design of large-scale compressed air energy storage systems.

Resource Scheduling Optimization of Fresh Food Delivery Porters Considering Ambient Temperature Variations

In the context of an evolving socio-economic landscape and rising living standards, the online market for fresh products, encompassing fruits, vegetables, meats, dairy, and eggs, has seen substantial growth, necessitating sophisticated logistics for e-commerce home delivery. This study tackles the distinct challenges of fresh product delivery, which demand rigorous adherence to climate conditions and product mix during transport, significantly influencing the operational strategies and scheduling of delivery platforms. To address these challenges, a comprehensive mathematical model was developed to optimize fresh food home delivery scheduling, focusing on reducing spoilage rates and accommodating the dynamic impact of environmental temperature changes. The model posits assumptions of a consistent and ample supply of fresh goods, standard initial quality loss, and efficient porter assignment for multi-category order combinations. It introduces three objective functions, targeting the minimization of fresh food loss, maximization of customer satisfaction, and reduction of distributor costs. The efficacy of the model and its genetic-algorithm-based solution method was assessed through numerical analysis and case studies, illustrating that the model enhances delivery efficiency and service quality across varying temperature conditions. This substantiates the critical role of environmental temperature management in optimizing fresh food delivery, offering a robust framework for advancing logistical operations in the perishable goods sector and ensuring quality and efficiency in fresh food e-commerce delivery.

Backstepping Control of an AC/DC/AC Converter in a Grid Connected Wind Power System

The contribution of this paper is to study a nonlinear control approach known as the backstepping control method to manage reactive and active power using new parametric values for the grid connected wind power generation system. Specifically, the research focuses on a system containing a wind turbine system, a permanent magnet synchronous generator (PMSG), and a grid connected via AC/DC/AC converter. A comprehensive mathematical model for both the wind turbine system, PMSG, and the grid connected via AC/DC/AC converter was developed for this purpose. The Simulation results of the grid-connected wind power generation system are presented and analyzed to show the performance of the nonlinear backstepping control method. The characteristics of the response to variations in generator speed and the power injected into the grid show the highlight of the performance of the backstepping method, under varying wind conditions.

Dynamic Demand Modeling Incorporating Renewable Energy Sources Using a Population-Based Optimization Method

Due to the inclusion of distributed generation (DG) in microgrids (MGs), the accelerated growth in demand, and environmental concerns, suitable management and operational strategies are imperative. The utilization of wind and solar energy has rapidly increased in MGs. However, due to the uncertainties these systems present, accurately predicting energy generation remains challenging. This necessitates modeling the system’s random variables (such as renewable resource output and possibly load demand) using appropriate and feasible methods. The primary objective of this article is to determine the optimal setpoints for renewable energy sources (RES) and all elements involved in the MG, minimizing the total operation cost. The system comprises wind turbines (WT), photovoltaic panels (PV), energy storage systems (ESS), and electric vehicles (EVs). Weibull distribution and the Hottel and Liu Jordan equations are employed to determine the potential available capacity of wind and solar energy generation, respectively. ESS is utilized to enhance MG performance. For optimal management, a comprehensive mathematical model with practical constraints for each MG element is extracted. An efficient Population-Based Incremental Learning (PBIL) metaheuristic method is proposed to solve the optimization objective in an MG, demonstrating that this energy management system optimizes and effectively coordinates DG and ESS energy generation considering economic considerations. Finally, PBIL is compared with a commonly used model, Particle Swarm Optimization (PSO), across various scenarios, analyzing and evaluating their outcomes, showcasing a reduction in operation costs.

Heat transfer simulation of reline flowing in an elliptic shaped duct: A deep eutectic solvent

Deep Eutectic solvents have emerged as promising alternatives to conventional solvents due to their unique properties and applications. The flow of deep eutectic solvents in various industrial processes has garnered significant attention due to their versatile applications in fields ranging from chemical engineering to energy storage. This study presents a comprehensive mathematical model aimed at elucidating the intricate behavior of eutectic solvent flow within an elliptic duct, a geometric configuration relevant to many real-world systems. In this article, the deep eutectic solvent is composed of choline chloride–urea and is also called Reline. The proposed mathematical model accounts for the complex interplay of fluid dynamics, thermodynamics, and elliptic duct geometry. Key components of the model include the Navier-Stokes equations, which describe the fluid flow, coupled with heat transfer equations to account for temperature variations within the system. The model also considers the phase change behavior of the eutectic solvent, which may exhibit solidification or crystallization phenomena under certain conditions. Numerical simulations and analytical solutions are employed to investigate various aspects of eutectic solvent flow within elliptic ducts, such as velocity profiles, pressure distributions, temperature gradients, and phase transition phenomena. The study explores the influence of key parameters, including the Reynolds number, the aspect ratio of the duct, and the thermophysical properties of the eutectic solvent, on the system’s behavior. From the results, it was clearly observed that the velocity at the narrow region decreased as the pressure raised and the Reynold’s number profile indicated the presence of turbulent flow behavior.

Research on the Optimization of Pricing and the Replenishment Decision-Making Problem Based on LightGBM and Dynamic Programming

Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the “small production and big market” setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical model of replenishment plans and pricing strategies for each category of vegetables and individual products. In this paper, we analyze the following three questions: Question One: What is the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two: What is the relationship between total sales volume and cost-plus pricing of vegetable categories? And is it possible to provide the daily total replenishment and pricing strategy of each vegetable category for the following week to maximize supermarket profit? Question Three: How can we incorporate the market demand for single vegetable products into a profit-maximizing program for supermarkets? Is it possible to further formulate the replenishment plan requirements for single products? To answer the first question, we created pivot tables to analyze occupancy. We found that mosaic leaves, peppers, and edible mushrooms accounted for a larger proportion of occupacy, while cauliflowers, aquatic rhizomes, and eggplants accounted for a smaller proportion. For the single items, lettuce, cabbage, green pepper, screw pepper, enoki mushroom, and shiitake mushroom accounted for a large proportion of their respective categories. We used the Pearson correlation coefficient and the Mfuzz package based on fuzzy c-means (FCM) algorithm to analyze the correlation between vegetable categories and single products. We found that there was a strong correlation between vegetable categories. Moreover, the sale of vegetable items belonging to the same category exhibited the same patterns of change over time. In order to address the second question, we established the LightGBM sales forecasting model. Combined with previous sales data, we forecasted and planned an efficient daily replenishment volume for each vegetable category in the coming week. In addition, we developed a pricing strategy for vegetable categories to maximize supermarket profits. For the third question, we built a dynamic programming model combining an optimal replenishment volume with a product pricing strategy for single items, which let the supermarket maximize its expected profits.

Mathematical modeling of an electrostatic MEMS with tilted elastomeric micro-pillars

The aim of this study is to develop a comprehensive mathematical model for an electrostatic MEMS (Micro-Electro-Mechanical Systems) with gap-filling tilted micro-pillars. Elastomeric pillars are used due to their high dielectric constant, resulting in a higher equivalent permittivity of the gap medium. This leads to increased sensitivity and decreased required voltage. Although this system has gained popularity in recent years, a thorough understanding and accurate predictions of its behavior require a detailed mathematical model. Regrettably, the existing literature does not offer adequate information. The present model incorporates three coupled set of nonlinear differential equations that govern the longitudinal and transverse vibrations of the PDMS (Polydimethylsiloxane) pillars, as well as the transverse vibrations of the moving electrode. It demonstrates how the device's behavior is affected by varying tilt angles and numbers of micro-pillars. The viscoelastic properties of the PDMS pillars are also taken into account, following the Kelvin-Voigt model with non-linear strains. Numerical methods are used to solve the governing equations, enabling investigation of static deformation and vibrational responses under different DC (Direct Current) and DC+AC (Alternating Current) actuations. The nonlinear equations proposed in this study provide a valuable tool for accurately predicting the behavior of capacitive MEMS devices that use microstructured gaps with tilted micro-pillar arrays.

A comprehensive optimization mathematical model for wind solar energy storage complementary distribution network based on multi-regulatory devices under the background of renewable energy integration

In the context of global energy transformation and sustainable development, integrating and utilizing renewable energy effectively have become the key to the power system advancement. However, the integration of wind and photovoltaic power generation equipment also leads to power fluctuations in the distribution network. The research focuses on the multifaceted challenges of optimizing the operation of distribution networks. It explores the operation and control methods of active distribution networks based on energy storage and reactive power compensation equipment. The stable operation of the distribution network is analyzed under the conditions of wind and photovoltaic integration, with a particular focus on precise regulation to address the limitations of existing methods. Afterwards, the study proposes an improvement plan that combines on load tap changer transformers and reactive power compensation equipment to solve complex power balance problems through second-order cone programming relaxation method. The results of numerical analysis show that the constructed mathematical model maintains a stable voltage of 1 to 1.1 pu at distribution network nodes within 24 h. Especially during peak hours from 15:00 to 24:00, it remains normal without any abnormal fluctuations when the control equipment is not added. These results confirm that precise regulation of multiple devices ensures voltage stability and avoids low or high voltage issues.

A nutritional modelling framework for inclusion in a Norwegian food system model

The aim of this study was to apply a comprehensive mathematical model designed to assess the current and future availability of food, as well as the resulting nutrient availability and intake, in the context of the Norwegian population. The model explores various scenarios, including self-sufficiency levels for food supply and impacts on nutrition recommendations. A food mass balance charting production, import, export, feed, seed, and consumer allocation in the Norwegian food system provided insights into the nutrients available to the population. The analysis included a comparison with two versions of the Nordic Nutrient Recommendations (NNR)1, with the latest version recommending substantial changes in food consumption compared to current dietary patterns in Norway. The nutrient analysis compared the food mass to Matvaretabellen2 and was supplemented with data from the United Nations World Population Prospects3 and the Food and Agriculture Organisation/World Health Organisation/United Nations4 report to ensure comprehensive nutrient analysis. Micronutrient gaps were observed in Iodine (94% of the target intake) and Vitamin D (46% of the target intake), while saturated-fatty acids slightly exceeded the recommended requirements (107% of the upper limit) based on the current baseline scenario. The updated NNR4 recommends changes to specific food categories, namely fruits, vegetables, nuts, and seeds. A secondary scenario testing compared against the updated NNR found that increasing the availability of the supply of these groups does not result in any new nutrient gaps, demonstrating the feasibility of addressing the issue on a national supply basis. These approach offers a mathematical-modelling based tool that can be used to provide information for a national food system. Leveraging the model’s capacity to simulate various scenarios, informed decisions to optimise self-sufficiency levels and align food supply with recommended nutritional guidelines can be made. To improve the model, higher data resolution and clearer categorisation of food groups are required which can then be linked into a more complete national food system. The mathematical model presented in this study provides a framework for understanding of food and nutrient availability in Norway. By identifying critical nutrient gaps and potential solutions, this research contributes knowledge for a healthier and sustainable food future for the nation.

Enhanced ship engine vibration reduction using magnetorheological dampers and Adaptive Neuro-Fuzzy Control System

ABSTRACT In this paper, an innovative approach is proposed to mitigate ship engine vibrations by integrating a semi-active control system with magnetorheological (MR) dampers and an Adaptive Neuro-Fuzzy Control System (ANFIS). The ANFIS controller adjusts MR damper damping force to effectively adapt to engine vibrations. A comprehensive mathematical model simulates the complex dynamics of the ship engine vibration system, validated with real-world data. The model incorporates engine vibration measurements and MR damper properties to train the ANFIS controller. Compared to passive control systems, the proposed semi-active system reduces torsional vibrations by 22.606% and longitudinal vibrations by 29.840%. The ANFIS controller dynamically adjusts damping force in response to engine conditions, ensuring optimal performance. This system effectively mitigates ship engine vibrations, improving overall ship performance and passenger comfort. Consistency between modeling and experimental results confirms the system's viability and efficacy.

Syncretic project management in the era of artificial intelligence explosion

As the technological landscape rapidly evolves, the convergence of innovation and artificial intelligence (AI) presents unprecedented opportunities and challenges for project management. This paper introduces a comprehensive mathematical model for the syncretic management of innovative projects in the age of the AI explosion. Syncretism in this context refers to the seamless integration of diverse elements, including interdisciplinary collaboration, AI technologies, and adaptive methodologies, to optimize project outcomes. The proposed model encompasses various facets of project management, innovation, and AI integration. It delineates stages of project lifecycle management, emphasizing resource allocation, risk assessment, and adaptive strategies. In the innovation management domain, the model incorporates methodologies for idea generation, technology scouting, and open innovation, recognizing AI's role in shaping the innovative landscape. A crucial aspect of the model lies in the integration of AI technologies throughout the project. This includes identifying relevant use cases, managing data effectively, selecting appropriate AI models, and establishing decision support systems. The syncretic approach emphasizes cross-functional collaboration, fostering an environment where different disciplines seamlessly contribute to project success. Resource optimization is a key focus, leveraging AI to allocate resources efficiently, predict maintenance needs, and enhance overall project performance. Ethical and legal considerations are embedded within the model to ensure responsible AI usage, and the paper outlines mechanisms for ongoing training and development to equip teams with the necessary skills. The model's effectiveness is evaluated through the lens of monitoring and evaluation, with defined key performance indicators, continuous monitoring, and feedback loops for iterative improvements. Communication and collaboration are underscored, utilizing modern tools to facilitate stakeholder engagement and effective teamwork. This paper contributes to the evolving discourse on project management by providing a robust framework that adapts to the dynamic nature of AI and innovation. It serves as a guide for project managers, interdisciplinary teams, and decision-makers navigating the challenges and opportunities presented by the syncretic management of innovative projects in the era of the AI explosion.

Syncretic management of innovative projects in the age of ai explosion

As the technological landscape rapidly evolves, the convergence of innovation and artificial intelligence (AI) presents unprecedented opportunities and challenges for project management. This paper introduces a comprehensive mathematical model for the syncretic management of innovative projects in the age of the AI explosion. Syncretism in this context refers to the seamless integration of diverse elements, including interdisciplinary collaboration, AI technologies, and adaptive methodologies, to optimize project outcomes. The proposed model encompasses various facets of project management, innovation, and AI integration. It delineates stages of project lifecycle management, emphasizing resource allocation, risk assessment, and adaptive strategies. In the innovation management domain, the model incorporates methodologies for idea generation, technology scouting, and open innovation, recognizing AI's role in shaping the innovative landscape. A crucial aspect of the model lies in the integration of AI technologies throughout the project. This includes identifying relevant use cases, managing data effectively, selecting appropriate AI models, and establishing decision support systems. The syncretic approach emphasizes cross-functional collaboration, fostering an environment where different disciplines seamlessly contribute to project success. Resource optimization is a key focus, leveraging AI to allocate resources efficiently, predict maintenance needs, and enhance overall project performance. Ethical and legal considerations are embedded within the model to ensure responsible AI usage, and the paper outlines mechanisms for ongoing training and development to equip teams with the necessary skills. The model's effectiveness is evaluated through the lens of monitoring and evaluation, with defined key performance indicators, continuous monitoring, and feedback loops for iterative improvements. Communication and collaboration are underscored, utilizing modern tools to facilitate stakeholder engagement and effective teamwork. This paper contributes to the evolving discourse on project management by providing a robust framework that adapts to the dynamic nature of AI and innovation. It serves as a guide for project managers, interdisciplinary teams, and decision-makers navigating the challenges and opportunities presented by the syncretic management of innovative projects in the era of the AI explosion.

Hydrodynamic Analysis Of Water Hammer Phenomena In Hydropower Stations Under Turbine Extreme Operating Conditions

This research article investigates transient hydraulic effects, particularly water hammer phenomena, in a hydropower plant (HEPP) through a comprehensive mathematical model and simulation analysis. Utilizing methods of characteristics and FORTRAN programming, the study develops a model that incorporates water hammer considerations, including friction, in the water conveyance system of the HEPP. The system layout encompasses an upstream reservoir, penstock, turbine unit, and downstream reservoir. The research explores the influence of guide vane closure and pressure regulating valve (PRV) opening and closing laws on pressure variations, mass oscillations, and water level fluctuations within the system. Numerical results indicate that PRV failure may not significantly impact turbine speed, but it results in excessive pressure oscillations in the spiral casing head, exceeding allowable pressure control values. The study identifies a critical PRV diameter of 0.6m, causing a maximum pressure in the spiral case of 370m, surpassing the acceptable limit of 250m, with a speed rise rate exceeding 50%. Conversely, a PRV diameter greater than or equal to 0.9m leads to unnecessary water energy loss. The findings emphasize the importance of carefully selecting PRV parameters to optimize system stability and efficiency. The study's comprehensive analysis provides valuable insights into the interplay of various parameters, contributing to a scientific basis for optimizing operational parameters and ensuring reliable and efficient hydropower plant performance.