Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (16,092)

Search Parameters:
Keywords = discretization

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
22 pages, 2259 KB  
Article
Experimental and Numerical Investigation of a Novel Low-Cost Solar Air Heater with Large-Scale V-Shaped Fins to Enhance Heat Transfer
by Omayma Elakrout, Ons Ghriss, Abdallah Bouabidi and Maarten Vanierschot
Energies 2025, 18(20), 5503; https://doi.org/10.3390/en18205503 (registering DOI) - 18 Oct 2025
Abstract
This study investigates the performance of a novel, low-cost solar air heater equipped with large V-shaped fins using experiments and numerical simulations. The solar air heater consists of an absorber plate, a glass cover and airflow ducts. Its performance is evaluated under varying [...] Read more.
This study investigates the performance of a novel, low-cost solar air heater equipped with large V-shaped fins using experiments and numerical simulations. The solar air heater consists of an absorber plate, a glass cover and airflow ducts. Its performance is evaluated under varying fin configurations: finless and (a)symmetric V-shaped fins with four, six, and eight fins. Computational fluid dynamics simulations using the RNG k-epsilon and discrete ordinate models were validated by experimental findings, showing good agreement with minimal discrepancies between both. The experimental setup recorded a maximum air temperature of 55 °C, corresponding to a temperature rise of 33 °C from an inlet temperature of 22 °C, under an inlet air velocity of 2.7 m/s. Results demonstrate that increasing the number of fins significantly enhances heat transfer efficiency, with heat transfer rising from 134.35 W (finless) to 233.29 W (8 fins). The large-scale fins improved thermal performance significantly while still maintaining a low-pressure drop. Moreover, the fins are very low-cost to implement, in contrast to most heat transfer enhancements in solar air heaters, making this design a very budget-friendly solution. This study provides valuable insights into optimizing solar air heater systems, contributing to the advancement of solar heating solutions for a wide range of energy-efficient applications. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
Show Figures

Figure 1

18 pages, 10816 KB  
Article
From Continuous Integer-Order to Fractional Discrete-Time: A New Computer Virus Model with Chaotic Dynamics
by Imane Zouak, Ahmad Alshanty, Adel Ouannas, Antonio Mongelli, Giovanni Ciccarese and Giuseppe Grassi
Technologies 2025, 13(10), 471; https://doi.org/10.3390/technologies13100471 - 17 Oct 2025
Abstract
Computer viruses remain a persistent technological challenge in information security. They require mathematical frameworks that realistically capture their propagation in digital networks. Classical continuous-time, integer-order models often overlook two key aspects of cyber environments: their inherently discrete nature and the memory-dependent effects of [...] Read more.
Computer viruses remain a persistent technological challenge in information security. They require mathematical frameworks that realistically capture their propagation in digital networks. Classical continuous-time, integer-order models often overlook two key aspects of cyber environments: their inherently discrete nature and the memory-dependent effects of networked interactions. In this work, we introduce a fractional-order discrete computer virus (FDCV) model, derived from a three-dimensional continuous integer-order formulation and reformulated into a two-dimensional fractional discrete framework. We analyze its rich dynamical behaviors under both commensurate and incommensurate fractional orders. Leveraging a comprehensive toolbox including bifurcation diagrams, Lyapunov spectra, phase portraits, the 0–1 test for chaos, spectral entropy, and C0 complexity measures, we demonstrate that the FDCV system exhibits persistent chaos and high dynamical complexity across broad parameter regimes. Our findings reveal that fractional-order discrete models not only enhance the dynamical richness compared to integer-order counterparts but also provide a more realistic representation of malware propagation. These insights advance the theoretical study of fractional discrete systems, supporting the development of potential technologies for cybersecurity modeling, detection, and prevention strategies. Full article
Show Figures

Figure 1

17 pages, 2445 KB  
Article
Establishment and Parameter Calibration of a DEM-Based Contact Model for Leymus chinensis Seed–Straw Mixtures
by Qihao Wan, Anbin Zhang, Wenxue Dong, Fei Liu, Yingsi Wu, Yin Qi and Yuxing Ren
Appl. Sci. 2025, 15(20), 11163; https://doi.org/10.3390/app152011163 - 17 Oct 2025
Abstract
The study of Leymus chinensis seed cleaning has been hindered by the lack of accurate discrete-element contact parameters for seed–straw interactions, thereby limiting, to some extent, the optimization of cleaning equipment. To address this issue, the present study analyzed a mixture of L. [...] Read more.
The study of Leymus chinensis seed cleaning has been hindered by the lack of accurate discrete-element contact parameters for seed–straw interactions, thereby limiting, to some extent, the optimization of cleaning equipment. To address this issue, the present study analyzed a mixture of L. chinensis seeds and straw, and determined their fundamental physical and contact parameters via laboratory experiments. The Hertz–Mindlin (no slip) discrete element simulation model was employed to calibrate the parameters of the seed–straw mixture. A Plackett–Burman test was used to identify key factors significantly affecting the repose angle, including the seed–seed static friction coefficient and the seed–straw static and dynamic friction coefficients. These factors’ optimal ranges were further refined using steepest ascent experiments. A Box–Behnken design was used to optimize contact parameters, resulting in the following values: a seed–seed static friction coefficient of 0.709, a seed–straw static friction coefficient of 0.281, and a seed–straw dynamic friction coefficient of 0.085. Validation experiments demonstrated an error of less than 2.14%, confirming the reliability of the calibrated parameters. This study offers a theoretical foundation for discrete element simulations in L. chinensis seed cleaning applications. Full article
(This article belongs to the Section Agricultural Science and Technology)
25 pages, 2343 KB  
Article
A Multi-Objective Simulation–Optimization Framework for Emergency Department Efficiency Using RSM and Goal Programming
by Felipe Baesler, Oscar Cornejo, Carlos Obreque, Eric Forcael and Rudy Carrasco
Systems 2025, 13(10), 912; https://doi.org/10.3390/systems13100912 - 17 Oct 2025
Abstract
This study presents a novel approach that integrates Discrete Event Simulation (DES) with Design of Experiments (DOE) techniques, framed within a stochastic optimization context and guided by a multi-objective goal programming methodology. The focus is on enhancing the operational efficiency of an emergency [...] Read more.
This study presents a novel approach that integrates Discrete Event Simulation (DES) with Design of Experiments (DOE) techniques, framed within a stochastic optimization context and guided by a multi-objective goal programming methodology. The focus is on enhancing the operational efficiency of an emergency department (ED), illustrated through a real-world case study conducted in a Chilean hospital. The methodology employs Response Surface Methodology (RSM) to explore and optimize the impact of four critical resources: physicians, nurses, rooms, and radiologists. The response variable, formulated as a goal programming function, captures the aggregated patient flow time across four representative care tracks. The optimization process proceeded iteratively: early stages relied on linear approximations to identify promising improvement directions, while later phases applied a central composite design to model nonlinear interactions through a quadratic response surface. This progression revealed complex interdependencies among resources, ultimately leading to a local optimum. The proposed approach achieved a 50% reduction in the aggregated objective function and improved individual patient flow times by 7% to 26%. Compared to traditional metaheuristic methods, this simulation–optimization framework offers a computationally efficient alternative, particularly valuable when the simulation model is complex and resource-intensive. These findings underscore the value of combining simulation, RSM, and multi-objective optimization to support data-driven decision-making in complex healthcare settings. The methodology not only improves ED performance but also offers a flexible and scalable framework adaptable to other clinical environments seeking resource optimization and operational improvement. Full article
(This article belongs to the Section Systems Engineering)
Show Figures

Figure 1

21 pages, 2221 KB  
Article
Staying Competitive in Clean Manufacturing: Insights on Barriers from Industry Interviews
by Paulomi Nandy, Thomas Wenning, Alex Botts and Harshal J. Kansara
Sustainability 2025, 17(20), 9233; https://doi.org/10.3390/su17209233 - 17 Oct 2025
Abstract
While industrial emissions research has historically focused on energy-intensive sectors like steel, cement, and chemicals, this study addresses a critical gap by examining barriers across all the manufacturing industry in the U.S. Sectors like food processing, retail, plastics, and transportation face unique challenges [...] Read more.
While industrial emissions research has historically focused on energy-intensive sectors like steel, cement, and chemicals, this study addresses a critical gap by examining barriers across all the manufacturing industry in the U.S. Sectors like food processing, retail, plastics, and transportation face unique challenges distinct from heavy industry, operating on thin margins with limited bargaining power while experiencing heightened consumer and stakeholder pressure for improved environmental responsibility. Through structured interview data collection process and using quantitative ratings and qualitative analysis, this research identifies and categorizes emission reduction barriers across four key themes: financial, technical, organizational, and regulatory. Unlike energy-intensive industries that may pursue hydrogen or carbon capture technologies, discrete manufacturing industry like automotive, electrical and electronics, and machine manufacturers typically focus on energy efficiency, electrification of thermal processes, and alternate fuel switching, solutions better aligned with their lower-temperature processes and distributed facility profiles. The study’s primary contribution lies in documenting specific barrier manifestations within organizations and identifying proven mitigation strategies that companies have successfully implemented or observed among peers. Full article
(This article belongs to the Topic Energy Economics and Sustainable Development)
Show Figures

Figure 1

24 pages, 375 KB  
Article
Existence and Uniqueness of Positive Solutions to Fractional Problems of Brézis–Oswald-Type with Unbalanced Growths and Hardy Potentials
by Yun-Ho Kim
Fractal Fract. 2025, 9(10), 672; https://doi.org/10.3390/fractalfract9100672 - 17 Oct 2025
Abstract
The aim of this paper is to establish the existence and uniqueness of positive solutions to the non-local Brézis–Oswald-type fractional problems that involve fractional (r,q)-Laplace operators and Hardy potentials. In particular, we observe an eigenvalue problem associated with [...] Read more.
The aim of this paper is to establish the existence and uniqueness of positive solutions to the non-local Brézis–Oswald-type fractional problems that involve fractional (r,q)-Laplace operators and Hardy potentials. In particular, we observe an eigenvalue problem associated with the fractional (r,q)-Laplacian to determine the existence of at least one positive weak solution for our problem. The main features of this paper are the lack of the semicontinuity property of an energy functional related to our problem and the presence of a singular coefficient. The decisive tool for overcoming this technical difficulty is the concentration–compactness principle in fractional, critical and Hardy terms. Moreover, we establish the uniqueness results of Brézis–Oswald–type by exploiting a generalization of the discrete Picone inequality. Full article
(This article belongs to the Special Issue Variational Problems and Fractional Differential Equations)
17 pages, 4607 KB  
Article
A Discrete Element Simulation Method for Self-Healing of Salt Rock Damage
by Zhuangzhuang He, Yan Qin, Shuangxi Feng, Jiayu Qin, Nengxiong Xu and Yuxi Guo
Appl. Sci. 2025, 15(20), 11156; https://doi.org/10.3390/app152011156 - 17 Oct 2025
Abstract
Salt rock, owing to its excellent rheological and self-healing properties, has been widely applied in underground gas storage. However, a numerical method capable of systematically simulating the entire damage–healing process of salt rock is still lacking, which limits the in-depth understanding of fracture [...] Read more.
Salt rock, owing to its excellent rheological and self-healing properties, has been widely applied in underground gas storage. However, a numerical method capable of systematically simulating the entire damage–healing process of salt rock is still lacking, which limits the in-depth understanding of fracture evolution mechanisms and the long-term stability of storage caverns. To overcome this limitation, this study improves the parallel bond model within the framework of the Discrete Element Method (DEM) by incorporating a stress-driven healing criterion and a healing-equivalent stress coupling algorithm, thereby enabling the complete simulation of crack initiation, propagation, and closure in salt rock. The results show that the proposed method effectively captures healing effects: under uniaxial compression and tension, the number of cracks decreased by approximately 27% and 23%, with strength recovery of 110.7% and 7%, respectively. Moreover, the reconstruction of particle contact chains closely corresponds to the crystal-bridge phenomena observed in experiments, verifying the model’s reliability in reproducing macroscopic mechanical responses. In addition, the healing process exhibits a temporal characteristic in which crack closure occurs earlier than volumetric strain reduction, indicating an evolution pattern of “structural closure first, macroscopic densification later.” This study not only fills the gap in DEM-based simulation of salt rock damage–healing processes but also provides theoretical support for long-term stability evaluation and operational optimization of underground salt cavern storage. Full article
21 pages, 2160 KB  
Review
Review of Advances in the Robotization of Timber Construction
by Fang-Che Cheng, Henriette Bier, Ningzhu Wang and Alisa Andrasek
Buildings 2025, 15(20), 3747; https://doi.org/10.3390/buildings15203747 - 17 Oct 2025
Abstract
The construction industry faces persistent productivity shortfalls and rising carbon dioxide emissions, which drives a shift toward the use of low-carbon materials and higher degrees of automation. Timber, a renewable and carbon-sequestering material, becomes especially compelling when combined with robotic fabrication. Although rapid [...] Read more.
The construction industry faces persistent productivity shortfalls and rising carbon dioxide emissions, which drives a shift toward the use of low-carbon materials and higher degrees of automation. Timber, a renewable and carbon-sequestering material, becomes especially compelling when combined with robotic fabrication. Although rapid advances have been implemented in the last decade, research and practice remain fragmented, and systematic evaluations of technological readiness are scarce. This gap is addressed in this review through critical literature synthesis of robotic timber construction, combining bibliometric analysis with a comparative evaluation of twelve representative case studies from 2020 to 2025. Computational and robotic tools are mapped across the design to fabrication pipeline, and emerging advancements are identified such as digital twins, real-time adaptive workflows, and machine learning driven fabrication, alongside discrete and circular strategies. Barriers to scale up are also assessed, including mid-level technology readiness, regulatory and safety obligations for human–robot interaction, evidence on cost and productivity, and workforce training needs. By clarifying the current level of robotization and specifying both research gaps and industrial prerequisites, this study provides a structured foundation for the next phase of development. It helps scholars by consolidating methods and metrics for rigorous evaluation, and it helps practitioners by highlighting pathways to scalable, certifiable, and circular deployment that align cost, safety, and training requirements. Full article
(This article belongs to the Special Issue AI in Construction: Automation, Optimization, and Safety)
Show Figures

Figure 1

20 pages, 2883 KB  
Article
Systematic Evaluation of Sea Stars of the Genus Heliaster from the Southeastern Pacific and Redescription of Heliaster helianthus
by Jennifer Catalán, Christian M. Ibáñez, Sergio A. Carrasco, Javier Sellanes, Angie Díaz and M. Cecilia Pardo-Gandarillas
Taxonomy 2025, 5(4), 59; https://doi.org/10.3390/taxonomy5040059 - 17 Oct 2025
Abstract
Heliaster has long been considered to comprise seven nominal species of starfish distributed across the Eastern Pacific, from Baja California (Mexico) southward to central Chile. Along the southeastern Pacific coast, three taxa have been traditionally recognized: H. helianthus (Paita, northern Peru, to Concepción, [...] Read more.
Heliaster has long been considered to comprise seven nominal species of starfish distributed across the Eastern Pacific, from Baja California (Mexico) southward to central Chile. Along the southeastern Pacific coast, three taxa have been traditionally recognized: H. helianthus (Paita, northern Peru, to Concepción, central-southern Chile), H. polybrachius (Mexico to Perú), and H. canopus (Juan Fernández Archipelago and Desventuradas Islands). However, extensive morphological overlap among these forms has cast doubt on the validity of H. canopus, with some authors treating it as a synonym for H. helianthus. To clarify this ambiguity, we applied an integrative framework combining detailed morphometrics, phylogenetic inference from mitochondrial (COI) and nuclear (H3) markers, and two species delimitation approaches (bPTP and ASAP). Our sampling spanned Peru, continental Chile, and the oceanic islands of Juan Fernández and Desventuradas. Variation in ray number and relative arm length among H. helianthus, H. canopus, and H. polybrachius proved allometric, scaling strongly with body diameter rather than indicating discrete species boundaries. Molecular data show >95% sequence similarity across all nominal taxa and recover a single, well-supported clade; bPTP and ASAP likewise support one Heliaster lineage throughout the southeastern Pacific, corresponding to H. helianthus. Accordingly, we redescribe H. helianthus, designate a neotype from Quintay, Chile, and formally synonymize H. canopus and H. polybrachius under H. helianthus. Our results indicate that a single species spans the Eastern Pacific from Ecuador and Peru to central-southern Chile, including offshore islands, underscoring the value of integrative taxonomy for robust delimitation and accurate biodiversity assessments in marine invertebrates. Full article
(This article belongs to the Collection Taxonomy on Aquatic Life (TAL))
Show Figures

Figure 1

21 pages, 8538 KB  
Article
The Critical Role of Small-Scale Dissipation in Deriving Subgrid Forcing Within an Ocean Quasi-Geostrophic Model
by Honggen Sun and Qiang Deng
Mathematics 2025, 13(20), 3317; https://doi.org/10.3390/math13203317 - 17 Oct 2025
Abstract
Due to computational constraints, ocean numerical models are often executed on low-resolution (LR) grids. To maintain consistency between LR simulations and coarsened high-resolution (HR) solutions, a subgrid forcing term is commonly integrated into the LR model as a parameterization scheme. Although numerous data-driven [...] Read more.
Due to computational constraints, ocean numerical models are often executed on low-resolution (LR) grids. To maintain consistency between LR simulations and coarsened high-resolution (HR) solutions, a subgrid forcing term is commonly integrated into the LR model as a parameterization scheme. Although numerous data-driven parameterizations have been developed to establish the relationship between resolved LR variables and corresponding subgrid forcing, the accurate extraction of target subgrid forcing remains an open challenge that significantly impacts the performance of such parameterizations. Small-scale dissipation (ssd) operators are widely used to enhance numerical stability while introducing minimal energy dissipation; however, this study demonstrates that these operators critically influence the accurate representation of subgrid forcing: an aspect that has not been adequately addressed. Within a quasi-geostrophic ocean modeling framework, new formulations have been rigorously derived for subgrid forcing that explicitly accounts for ssd effects. Numerical experiments confirm that the proposed forcing enables LR simulations to reproduce coarsened HR results with high fidelity. This work demonstrates that greater attention to the specific numerical discretization scheme is required for the accurate extraction of subgrid forcing from HR simulations. Although these newly developed extraction algorithms are diagnostic in nature, they could provide accurate target data that facilitate the subsequent development of data-driven parameterization schemes. Full article
Show Figures

Figure 1

20 pages, 1847 KB  
Article
A Novel Two-Stage Gas-Excitation Sampling and Sample Delivery Device: Simulation and Experiments
by Xu Yang, Dewei Tang, Qiquan Quan and Zongquan Deng
Machines 2025, 13(10), 958; https://doi.org/10.3390/machines13100958 - 17 Oct 2025
Abstract
Asteroids are remnants of primordial material from the early stages of solar system formation, approximately 4.6 billion years ago, and they preserve invaluable records of the processes underlying planetary evolution. Investigating asteroids provides critical insights into the mechanisms of planetary development and the [...] Read more.
Asteroids are remnants of primordial material from the early stages of solar system formation, approximately 4.6 billion years ago, and they preserve invaluable records of the processes underlying planetary evolution. Investigating asteroids provides critical insights into the mechanisms of planetary development and the potential origins of life. To enable efficient sample acquisition under vacuum and microgravity conditions, this study introduces a two-stage gas-driven asteroid sampling strategy. This approach mitigates the challenges posed by low-gravity environments and irregular asteroid topography. A coupled computational fluid dynamics–discrete element method (CFD–DEM) framework was employed to simulate the gas–solid two-phase flow during the sampling process. First, a model of the first-stage gas-driven sampling device was developed to establish the relationship between the inlet angle of the gas nozzle and the sampling efficiency, leading to the optimization of the nozzle’s structural parameters. Subsequently, a model of the integrated two-stage gas-driven sampling and sample-delivery system was constructed, through which the influence of the second-stage nozzle inlet angle on the total collected sample mass was investigated, and its design parameters were further refined. Simulation outcomes were validated against experimental data, confirming the reliability of the CFD–DEM coupling approach for predicting gas–solid two-phase interactions. The results demonstrate the feasibility of collecting asteroid regolith with the proposed two-stage gas-driven sampling and delivery system, thereby providing a practical pathway for extraterrestrial material acquisition. Full article
(This article belongs to the Section Machine Design and Theory)
Show Figures

Figure 1

19 pages, 5686 KB  
Article
RipenessGAN: Growth Day Embedding-Enhanced GAN for Stage-Wise Jujube Ripeness Data Generation
by Jeon-Seong Kang, Junwon Yoon, Beom-Joon Park, Junyoung Kim, Sung Chul Jee, Ha-Yoon Song and Hyun-Joon Chung
Agronomy 2025, 15(10), 2409; https://doi.org/10.3390/agronomy15102409 - 17 Oct 2025
Abstract
RipenessGAN is a novel Generative Adversarial Network (GAN) designed to generate synthetic images across different ripeness stages of jujubes (green fruit, white ripe fruit, semi-red fruit, and fully red fruit), aiming to provide balanced training data for diverse applications beyond classification accuracy. This [...] Read more.
RipenessGAN is a novel Generative Adversarial Network (GAN) designed to generate synthetic images across different ripeness stages of jujubes (green fruit, white ripe fruit, semi-red fruit, and fully red fruit), aiming to provide balanced training data for diverse applications beyond classification accuracy. This study addresses the problem of data imbalance by augmenting each ripeness stage using our proposed Growth Day Embedding mechanism, thereby enhancing the performance of downstream classification models. The core innovation of RipenessGAN lies in its ability to capture continuous temporal transitions among discrete ripeness classes by incorporating fine-grained growth day information (0–56 days) in addition to traditional class labels. The experimental results show that RipenessGAN produces synthetic data with higher visual quality and greater diversity compared to CycleGAN. Furthermore, the classification models trained on the enriched dataset exhibit more consistent and accurate performance. We also conducted comprehensive comparisons of RipenessGAN against CycleGAN and class-conditional diffusion models (DDPM) under strictly controlled and fair experimental settings, carefully matching model architectures, computational resources, training conditions, and evaluation metrics. The results indicate that although diffusion models yield highly realistic images and CycleGAN ensures stable cycle-consistent generation, RipenessGAN provides superior practical benefits in training efficiency, temporal controllability, and adaptability for agricultural applications. This research demonstrates the potential of RipenessGAN to mitigate data imbalance in agriculture and highlights its scalability to other crops. Full article
(This article belongs to the Section Precision and Digital Agriculture)
Show Figures

Figure 1

21 pages, 1158 KB  
Article
Day-Ahead Coordinated Reactive Power Optimization Dispatching Based on Semidefinite Programming
by Binbin Xu, Mengqi Liu, Yilin Zhong, Peijie Cong, Bo Zhu, Tao Liu, Yujun Li and Zhengchun Du
Energies 2025, 18(20), 5469; https://doi.org/10.3390/en18205469 - 17 Oct 2025
Abstract
With access to new energy sources, the problem of reactive power optimization and dispatching has become increasingly important for research. However, the reactive power optimization problem is a mixed integer nonlinear optimization problem. In order to solve the integer variables and nonlinear conditions [...] Read more.
With access to new energy sources, the problem of reactive power optimization and dispatching has become increasingly important for research. However, the reactive power optimization problem is a mixed integer nonlinear optimization problem. In order to solve the integer variables and nonlinear conditions existing therein, a method for coordinated reactive power optimization and dispatching based on semidefinite programming is proposed. Firstly, a reactive power optimization model considering discrete variables and continuous variables is established with the minimization of total operating cost as the objective function; secondly, the discrete variables are transformed into equality constraints by quadratic equations, and then a solvable semi-definite programming problem is obtained; thirdly, the rank-one constraint is restored by the Iterative Optimization based Gaussian Randomization Method (IOGRM), and the optimal solution equivalent to the original problem is obtained. Finally, the correctness and effectiveness of the proposed model and solution method are verified by analyzing and comparing with the second-order cone programming (SOCP) through the modified IEEE standard example. Full article
Show Figures

Figure 1

22 pages, 6448 KB  
Article
The Design and Application of a Digital Portable Acoustic Teaching System
by Xiuquan Li, Guochao Tu, Qingzhao Kong, Lin Chen, Xin Zhang and Ruiyan Wang
Buildings 2025, 15(20), 3736; https://doi.org/10.3390/buildings15203736 - 17 Oct 2025
Abstract
To address the limitations of traditional acoustic experimental equipment, such as large volume, discrete modules, and complex operation, this paper proposes and implements a set of digital portable acoustic teaching systems. The hardware component is based on an FPGA, enabling a highly integrated [...] Read more.
To address the limitations of traditional acoustic experimental equipment, such as large volume, discrete modules, and complex operation, this paper proposes and implements a set of digital portable acoustic teaching systems. The hardware component is based on an FPGA, enabling a highly integrated design for signal source excitation and multi-channel synchronous acquisition. It supports the output of various signals, including pulses, sine waves, chirps, and arbitrary waveforms. The software component is developed based on the Qt framework, offering cross-platform compatibility and excellent graphical interaction capabilities. It supports signal configuration, data acquisition, real-time processing, result visualization, and historical playback, establishing a closed-loop experimental workflow of signal excitation–synchronous acquisition–real-time processing–data storage–result visualization. The system supports both local USB connection and remote TCP operation modes, accommodating scenarios such as real-time classroom experiments and cross-regional collaborative teaching. The verification results of three typical experiments, namely, multi-media sound velocity measurement, TDOA hydrophone positioning, and remote acoustic detection, demonstrate that the system performs well in terms of measurement accuracy, positioning stability, and the feasibility of remote detection. This study demonstrates the technical advantages and engineering adaptability of a digital teaching platform in acoustic experimental education. It provides a scalable system solution for cross-regional hybrid teaching models and practice-oriented education under the framework of emerging engineering disciplines. Future work will focus on expanding experimental scenarios, enhancing system intelligence, and improving multi-user collaboration capabilities, aiming to develop a more comprehensive and efficient platform to support acoustic teaching. Full article
Show Figures

Figure 1

20 pages, 436 KB  
Article
Numerical Solutions for Fractional Bagley–Torvik Equation with Integral Boundary Conditions
by Xueling Liu, Jing Huang, Junlin Li and Yufeng Zhang
Symmetry 2025, 17(10), 1755; https://doi.org/10.3390/sym17101755 - 17 Oct 2025
Abstract
The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE poses additional difficulties, and efficient approaches for handling nonlinear terms [...] Read more.
The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE poses additional difficulties, and efficient approaches for handling nonlinear terms are still lacking in the literature. This study proposes an improved numerical method for the fractional BTE with integral boundary conditions. By employing an integration technique, the original problem is transformed into a weakly singular Fredholm–Hammerstein (F–H) integral equation of the second kind. To address the nonlinear terms, an enhanced piecewise Taylor expansion scheme is developed to construct the discrete form, while the uniqueness of the solution is proven using the contraction mapping theorem in Banach spaces. The convergence and error analyses are rigorously carried out, and numerical experiments confirm the accuracy and efficiency of the proposed approach. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

Back to TopTop