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15 pages, 4353 KB  
Article
Simulation Study on the Effect of Molecular Structure Characteristics of Lubricant Base Oils on Lubrication Performance
by Boxi Tian, Yixi Shao, Feng Zhu, Chengzhi Hu, Tiedong Zhang, Jiaxin Liu, Honglin Xu, Chengyuan Cao, Hongliang Yu and Weiwei Wang
Lubricants 2025, 13(9), 398; https://doi.org/10.3390/lubricants13090398 (registering DOI) - 8 Sep 2025
Abstract
The complex composition of lubricating base oils makes it difficult to analyze the influence of specific molecular structure on lubricating performance. To achieve this target, nine kinds of poly α-olefin molecules with different structure characteristics were designed, which prepared the lubricant models. Molecular [...] Read more.
The complex composition of lubricating base oils makes it difficult to analyze the influence of specific molecular structure on lubricating performance. To achieve this target, nine kinds of poly α-olefin molecules with different structure characteristics were designed, which prepared the lubricant models. Molecular dynamic simulation was used to analyze the tribological performance under pressure of 500 MPa, temperature 353 K, and shear velocity of 20 m/s; the volume compression and shear stress of lubricant films were obtained. Molecular volume, adsorption energies, radius of gyration, and mean square displacement were used to analyze the relationship between molecular structure and lubricant performance. Results show that the characteristic of the Iso and Mid type have the best friction reduction performance. The molecules of the Iso structure have the highest oil film thickness and the best load-bearing performance. The radius of gyration increases with the shear simulation for most of the molecules. The adsorption energy of End is the highest, and the Mid is the smallest. Among the nine molecules, C20Iso shows excellent performance both in load-bearing and friction reduction, which provides a reference for the molecular design of high-performance lubricant base oils. Full article
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27 pages, 10443 KB  
Article
Bifacial Solar Modules Under Real Operating Conditions: Insights into Rear Irradiance, Installation Type and Model Accuracy
by Nairo Leon-Rodriguez, Aaron Sanchez-Juarez, Jose Ortega-Cruz, Camilo A. Arancibia Bulnes and Hernando Leon-Rodriguez
Eng 2025, 6(9), 233; https://doi.org/10.3390/eng6090233 (registering DOI) - 8 Sep 2025
Abstract
Bifacial Photovoltaic (bPV) technology is rapidly becoming the standard in the solar photovoltaic (PV) industry due to its ability to capture reflected radiation and generate additional energy. This experimental study analyses the electrical performance of bPV modules under specific installation conditions, including varying [...] Read more.
Bifacial Photovoltaic (bPV) technology is rapidly becoming the standard in the solar photovoltaic (PV) industry due to its ability to capture reflected radiation and generate additional energy. This experimental study analyses the electrical performance of bPV modules under specific installation conditions, including varying heights, module tilt angles (MTA), and surface reflectivity. The methodology combines controlled indoor testing with outdoor experiments that replicate real-world operating environments. The outdoor test setup was carefully designed and included dual data acquisition systems: one with independent sensors and another with wireless telemetry for data transfer from the inverter. A thermal performance model was used to estimate energy output and was benchmarked against experimental measurements. All electrical parameters were obtained in accordance with international standards, including current-voltage characteristic (I–V curve) corrections, using calibrated instruments to monitor irradiance and temperature. Indoor measurements under Standard Test Conditions yielded at bifaciality coefficient φ=0.732, a rear bifacial power gain BiFi=0.285, and a relative bifacial gain BiFirel=9.4%. The outdoor configuration employed volcanic red stone (Tezontle) as a reflective surface, simulating a typical mid-latitude installation with modules mounted 1.5 m above ground, tilted from 0° to 90° regarding floor and oriented true south. The study was conducted at a site located at 18.8° N latitude during the early summer season. Results revealed significant non-uniformity in rear-side irradiance, with a 32% variation between the lower edge and the centre of the bPV module. The thermal model used to determine electrical performance provides power values higher than those measured in the time interval between 10 a.m. and 3 p.m. Maximum energy output was observed at a MTA of 0°, which closely aligns with the optimal summer tilt angle for the site’s latitude. Bifacial energy gain decreased as the MTA increased from 0° to 90°. These findings offer practical, data-driven insights for optimizing bPV installations, particularly in regions between 15° and 30° north latitude, and emphasize the importance of tailored surface designs to maximize performance. Full article
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31 pages, 3665 KB  
Article
Collaborative Mechanism of Soil and Water Ecological Governance Under Public–Private Partnership Model Considering Carbon Trading
by Junhua Zhang, Xiaodan Yun, Yaohong Yang, Ran Jing and Wenchao Jin
Sustainability 2025, 17(17), 8064; https://doi.org/10.3390/su17178064 (registering DOI) - 7 Sep 2025
Abstract
In the current soil erosion control efforts, the lack of collaboration among multiple stakeholders is a major problem that restricts governance performance. Based on carbon trading and the Public–Private Partnership model, this paper constructs a tripartite differential game model involving the government, enterprises, [...] Read more.
In the current soil erosion control efforts, the lack of collaboration among multiple stakeholders is a major problem that restricts governance performance. Based on carbon trading and the Public–Private Partnership model, this paper constructs a tripartite differential game model involving the government, enterprises, and farmers, focusing on the government subsidy and the enterprise–farmer benefit-sharing mechanism. It systematically analyzes the dynamic evolution process of multi-stakeholder collaborative governance behavior under the collaborative mechanism. Through numerical simulation, the impacts of key variables such as benefit-sharing ratio, synergy effect of measures, and unit carbon sequestration on the optimization of enterprise governance measures, effort level, government fiscal expenditure, and tripartite benefits were analyzed. The results indicate that (1) the benefit-sharing ratio has a significant bidirectional regulatory effect on the system, with both excessively high and excessively low ratios weakening the collaborative governance effect; (2) the synergistic effect between governance measures significantly enhances the enthusiasm of enterprise governance and promotes the allocation of resources towards measure with better carbon sequestration benefits; and (3) the unit carbon sequestration significantly affects governance structure and government subsidy strategies, with the government being more sensitive to carbon sink responses of afforestation measures. The research results provide a theoretical basis for optimizing the ecological governance system under the “dual carbon” goal and also provide policy references for promoting the transformation of governance model from “government-led” to “multi-stakeholder collaboration”. Full article
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16 pages, 3953 KB  
Article
3D-Printed Prosthetic Solutions for Dogs: Integrating Computational Design and Additive Manufacturing
by Jeremy Sarpong, Khalil Khanafer and Mohammad Sheikh
Designs 2025, 9(5), 107; https://doi.org/10.3390/designs9050107 (registering DOI) - 7 Sep 2025
Abstract
This study investigates the mechanical performance of two prosthetic forelimb designs for dogs—one with a solid structure and the other with a perforated structure—using Finite Element Analysis (FEA). Both models were analyzed under static loading conditions representing approximately 60% of a dog’s body [...] Read more.
This study investigates the mechanical performance of two prosthetic forelimb designs for dogs—one with a solid structure and the other with a perforated structure—using Finite Element Analysis (FEA). Both models were analyzed under static loading conditions representing approximately 60% of a dog’s body weight, the typical load borne by the forelimbs. The prosthetics were modeled with ABS plastic, a widely used 3D printing material, and evaluated for Von Mises stress, total deformation, elastic strain, and factor of safety. The analysis showed that both models remained within the elastic limit of the material, indicating that no permanent deformation would occur under the applied loads. The Solid Model demonstrated a significantly higher factor of safety (14) and lower deformation, confirming its structural strength but also highlighting excessive rigidity, increased material use, and higher cost. In contrast, the Perforated Model exhibited slightly higher localized stresses and a lower factor of safety (3.01), yet it still met essential safety requirements while providing greater compliance, flexibility, and material efficiency. These attributes are desirable for comfort, adaptability, and practicality in veterinary applications. Although its long-term durability requires further evaluation, the Perforated Model strikes a more effective balance between safety, comfort, and sustainability. Based on these findings, the perforated design is considered the more suitable option for canine prosthetic development. Future work will extend the analysis to dynamic loading scenarios, such as walking and running, to better simulate real-world performance. Full article
(This article belongs to the Special Issue Design Process for Additive Manufacturing)
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23 pages, 5769 KB  
Article
Impact of Climate Change on the Climatic Suitability of Oilseed Rape (Brassica apus L.) Planting in Jiangsu Province, China
by Yuqing Shi, Qichun Zhu, Mengquan Zhu, Nan Jiang, Lixuan Ren and Yunsheng Lou
Agriculture 2025, 15(17), 1900; https://doi.org/10.3390/agriculture15171900 (registering DOI) - 7 Sep 2025
Abstract
Climate change has caused considerable uncertainty to oilseed rape production. However, the climatic suitability for oilseed rape cultivation and its future changing trend remain unclear, specifically in Jiangsu Province—a major oilseed rape producing-region in China. Based on the past 50 years (1969–2018) of [...] Read more.
Climate change has caused considerable uncertainty to oilseed rape production. However, the climatic suitability for oilseed rape cultivation and its future changing trend remain unclear, specifically in Jiangsu Province—a major oilseed rape producing-region in China. Based on the past 50 years (1969–2018) of daily meteorological data from 13 meteorological stations in the province, this study established a climate suitability assessment model for oilseed rape cultivation. Temperature, precipitation, and sunlight were comprehensively analyzed, with suitable zones delineated through GIS spatial analysis and the natural break method. With the incorporation of SSP2-4.5 climatic scenario simulation data, the study projected the evolving trends of oilseed rape cultivation climatic suitability zones from 2024 to 2050 in the province. The findings reveal that over the past five decades, the climatic suitability for oilseed rape planting in the province has demonstrated the following patterns: temperature suitability increased by 0.02 per decade, precipitation suitability declined by −0.01 per decade, sunlight suitability decreased by −0.01 per decade, and comprehensive suitability rose by 0.01 per decade. High climatic suitability with the index of 0.80–1.00 was predominantly clustered in the central region, while moderate suitability zones with the index of 0.50–0.80 were mainly found in its northern and southern regions. Unsuitable zones with the index of 0.00–0.50 were mainly confined to the northern and southern extremities of the province. Under future climate scenarios, oilseed rape planting suitability is projected to improve significantly, with highly suitable zones expanding, particularly into the central and parts of the northern Jiangsu. Moderately suitable zones also will be extended, including potential areas such as the parts of Lianyungang and Wuxi. Unsuitable zones will be reduced, with only limited areas like southern Wuxi retaining lower suitability. Future temperature increases in Lianyungang are expected to be in favor of oilseed rape production. However, excessive precipitation in the southern region will require enhanced drainage measures. Improved temperature and precipitation conditions in Xuzhou are anticipated to boost the climatic suitability. Overall, oilseed rape planting climatic factors in the central and northern regions are projected to improve, enabling production expansion, while the southern region will face the challenge of excessive precipitation in Jiangsu Province. Full article
(This article belongs to the Section Ecosystem, Environment and Climate Change in Agriculture)
23 pages, 6875 KB  
Article
Precision-Controlled Bionic Lung Simulator for Dynamic Respiration Simulation
by Rong-Heng Zhao, Shuai Ren, Yan Shi, Mao-Lin Cai, Tao Wang and Zu-Jin Luo
Bioengineering 2025, 12(9), 963; https://doi.org/10.3390/bioengineering12090963 (registering DOI) - 7 Sep 2025
Abstract
Mechanical ventilation is indispensable for patients with severe respiratory conditions, and high-fidelity lung simulators play a pivotal role in ventilator testing, clinical training, and respiratory research. However, most existing simulators are passive, single-lung models with limited and discrete control over respiratory mechanics, which [...] Read more.
Mechanical ventilation is indispensable for patients with severe respiratory conditions, and high-fidelity lung simulators play a pivotal role in ventilator testing, clinical training, and respiratory research. However, most existing simulators are passive, single-lung models with limited and discrete control over respiratory mechanics, which constrains their ability to reproduce realistic breathing dynamics. To overcome these limitations, this study presents a dual-chamber lung simulator that can operate in both active and passive modes. The system integrates a sliding mode controller enhanced by a linear extended state observer, enabling the accurate replication of complex respiratory patterns. In active mode, the simulator allows for the precise tuning of respiratory muscle force profiles, lung compliance, and airway resistance to generate physiologically accurate flow and pressure waveforms. Notably, it can effectively simulate pathological conditions such as acute respiratory distress syndrome (ARDS) and chronic obstructive pulmonary disease (COPD) by adjusting key parameters to mimic the characteristic respiratory mechanics of these disorders. Experimental results show that the absolute flow error remains within ±3L/min, and the response time is under 200ms, ensuring rapid and reliable performance. In passive mode, the simulator emulates ventilator-dependent conditions, providing continuous adjustability of lung compliance from 30 to 100mL/cmH2O and airway resistance from 2.01 to 14.67cmH2O/(L/s), with compliance deviations limited to ±5%. This design facilitates fine, continuous modulation of key respiratory parameters, making the system well-suited for evaluating ventilator performance, conducting human–machine interaction studies, and simulating pathological respiratory states. Full article
(This article belongs to the Section Biomedical Engineering and Biomaterials)
22 pages, 2118 KB  
Article
Two-Stage Robust Optimization for Bi-Level Game-Based Scheduling of CCHP Microgrid Integrated with Hydrogen Refueling Station
by Ji Li, Weiqing Wang, Zhi Yuan and Xiaoqiang Ding
Electronics 2025, 14(17), 3560; https://doi.org/10.3390/electronics14173560 (registering DOI) - 7 Sep 2025
Abstract
Current technical approaches find it challenging to reduce hydrogen production costs in combined cooling, heating, and power (CCHP) microgrids integrated with hydrogen refueling stations (HRS). Furthermore, the stability of such systems is significantly impacted by multiple uncertainties inherent on both the source and [...] Read more.
Current technical approaches find it challenging to reduce hydrogen production costs in combined cooling, heating, and power (CCHP) microgrids integrated with hydrogen refueling stations (HRS). Furthermore, the stability of such systems is significantly impacted by multiple uncertainties inherent on both the source and load sides. Therefore, this paper proposes a two-stage robust optimization for bi-level game-based scheduling of a CCHP microgrid integrated with an HRS. Initially, a bi-level game structure comprising a CCHP microgrid and an HRS is established. The upper layer microgrid can coordinate scheduling and the step carbon trading mechanism, thereby ensuring low-carbon economic operation. In addition, the lower layer hydrogenation station can adjust the hydrogen production plan according to dynamic electricity price information. Subsequently, a two-stage robust optimization model addresses the uncertainty issues associated with wind turbine (WT) power, photovoltaic (PV) power, and multi-load scenarios. Finally, the model’s duality problem and linearization problem are solved by the Karush–Kuhn–Tucker (KKT) condition, Big-M method, strong duality theory, and column and constraint generation (C&CG) algorithm. The simulation results demonstrate that the strategy reduces the cost of both CCHP microgrid and HRS, exhibits strong robustness, reduces carbon emissions, and can provide a useful reference for the coordinated operation of the microgrid. Full article
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27 pages, 8247 KB  
Article
Experimental–Numerical Investigation of the Ductile Damage of TRIP 780 Steel
by Rafael Oliveira Santos, Patrick de Paula Coelho, Gabriela Vincze, Fabiane Roberta Freitas da Silva, Rogério Albergaria de Azevedo Junior, Saulo Brinco Diniz and Luciano Pessanha Moreira
Metals 2025, 15(9), 991; https://doi.org/10.3390/met15090991 (registering DOI) - 7 Sep 2025
Abstract
This study presents a combined experimental–numerical methodology to calibrate the mechanical behavior of an advanced high-strength steel (AHSS) with transformation-induced plasticity (TRIP) effects, incorporating both initial plastic anisotropy and ductile damage. The investigated TRIP 780 grade, widely used in the automotive industry for [...] Read more.
This study presents a combined experimental–numerical methodology to calibrate the mechanical behavior of an advanced high-strength steel (AHSS) with transformation-induced plasticity (TRIP) effects, incorporating both initial plastic anisotropy and ductile damage. The investigated TRIP 780 grade, widely used in the automotive industry for its exceptional strength–ductility balance, exhibits a complex deformation response that demands accurate constitutive modeling for reliable sheet metal forming simulations. The methodology minimizes the number of required specimen geometries without compromising accuracy. Three flat-sheet specimens were employed: standard uniaxial tension (UT) and two double-notched designs reproducing intermediate (ID) and plane strain (PS) modes. Experiments combined digital image correlation with finite element analysis. Hill’s 48 quadratic yield criterion captured the initial anisotropy of the TRIP 780 sheet, while the parameters of a phenomenological ductile damage model were calibrated from the experimental data. The TRIP effect under UT was quantified by X-ray diffraction, showing a decrease in retained austenite from 9.9% (as-received) to 3.2% at 21% equivalent plastic strain. Fractography revealed damage initiation dominated by void nucleation at phase boundaries. The proposed approach yielded stress–strain predictions with R2 values exceeding 0.99. This simplified approach offers a cost-effective and experimentally feasible framework for constitutive modeling of AHSS grades, enabling practical applications in advanced sheet forming simulations. Full article
(This article belongs to the Special Issue Advances in Metal Forming and Plasticity)
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27 pages, 5772 KB  
Article
Prediction of Ecological Zoning and Optimization Strategies Based on Ecosystem Service Value and Ecological Risk
by Qing Liu, Yaoyao Zhao, Shuhai Zhuo, Yixian Mo and Peng Zhou
Land 2025, 14(9), 1824; https://doi.org/10.3390/land14091824 (registering DOI) - 7 Sep 2025
Abstract
As a typical coastal tourist city, Sanya has experienced large-scale urbanization driven by tourism development, leading to landscape fragmentation, disorderly urban sprawl, and irrational resource utilization. These factors have intensified regional ecological risks and caused the degradation of ecosystem service functions, thereby constraining [...] Read more.
As a typical coastal tourist city, Sanya has experienced large-scale urbanization driven by tourism development, leading to landscape fragmentation, disorderly urban sprawl, and irrational resource utilization. These factors have intensified regional ecological risks and caused the degradation of ecosystem service functions, thereby constraining sustainable urban development. Therefore, establishing urban ecological zoning can identify the dynamic relationship between ecological conditions and urban growth, ease human-land conflicts, and promote high-quality urban development. This study employed the value equivalency method and the landscape ecological risk index method to calculate the ecosystem service value (ESV) and the ecological risk index (ERI) of Sanya City from 2000 to 2020 and to delineate ecological zones. The PLUS model was used to predict the changes in ecological zoning of Sanya City under a natural development scenario in 2030. The results demonstrate the following: (1) The ecological risk in the study area shows a distribution pattern of “high in the south and low in the north,” with low-risk areas being the dominant type, accounting for about 80% of the total area. Over time, the area of high-risk zones has shown an increasing trend, while that of low-risk zones has decreased year by year. (2) The ecosystem service value in the study area shows a distribution pattern of “high in the north and low in the south,” with a decreasing trend over time, with a cumulative reduction of 2.11 × 108 ten thousand yuan from 2000 to 2020. (3) Among the four ecological zones, the ecological protection zone is the dominant type, accounting for about 50%. The increase in the ecological early warning zone is the most significant. In contrast, the ecological optimization and improvement zones show a marked decrease. The prediction results show that by 2030, the ecological early warning and ecological protection zones will increase, while the other zones will decrease. This study adopts a temporal-dynamic approach by constructing a framework that integrates historical evolution with future simulation, providing scientific evidence for building Sanya’s ecological security pattern and spatial governance. It offers practical significance for coordinating regional ecological conservation with urban development. Full article
18 pages, 3483 KB  
Article
Research on the Optimization of Healthy Living Environments in Liyuan Block Empowered by CFD Technology: A Case Study of the Liyuan Block in Dabaodao, Qingdao
by Huiying Zhang, Hui Feng, Xiaolin Zang and Ang Sha
Buildings 2025, 15(17), 3223; https://doi.org/10.3390/buildings15173223 (registering DOI) - 7 Sep 2025
Abstract
In the process of revitalizing historic districts, creating a healthy living environment requires a focus on the microclimate comfort of historic districts. Microclimate comfort refers to the comprehensive physiological perception and psychological satisfaction of climate elements such as heat, wind, and humidity under [...] Read more.
In the process of revitalizing historic districts, creating a healthy living environment requires a focus on the microclimate comfort of historic districts. Microclimate comfort refers to the comprehensive physiological perception and psychological satisfaction of climate elements such as heat, wind, and humidity under specific local environmental conditions, typically within a spatial range of horizontal scale < 100 m and vertical scale < 10 m. Among these, wind environment quality, as a key factor influencing pedestrian health experiences and cultural tourism appeal, holds particular research value. This study takes the Dabao Island Courtyard District in Qingdao as its subject, employing computational fluid dynamics (CFD) simulation methods from the artificial intelligence (AI) technology framework for modeling. CFD is a numerical method based on computer simulation, which solves fluid control equations (such as the Navier–Stokes equations) through iterative optimization to achieve high-fidelity simulation of physical environments such as airflow, turbulence, and heat transfer. A three-dimensional geometric model of the Dabao Island courtyard district was established, and boundary conditions were set based on local meteorological data. Numerical simulations were conducted to analyze the wind environment before and after the renovation of different layouts, functional spaces, and spatial scales (individual courtyards, clustered courtyards, and surrounding neighborhoods) of the courtyard district. The results indicate that factors such as building layout, street orientation, and renovation strategies significantly influence the wind environment of the Dabao Island neighborhood courtyards, thereby affecting residents’ perceptions of wind comfort. For example, unreasonable building layouts can lead to excessive local wind speeds or vortex phenomena, reducing wind comfort, whereas reasonable renovation and update strategies can facilitate the introduction of wind corridors into the historical courtyard buildings, improving wind environment quality. This study contributes to better protection and utilization of traditional neighborhoods during urban renewal processes, creating a more comfortable wind environment for residents, providing scientific decision-making support for the renovation of historical neighborhoods under the Healthy China strategy, and offering methodological references for wind environment research in other similar traditional neighborhoods. Full article
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22 pages, 10808 KB  
Article
MART: Ship Trajectory Prediction Model Based on Multi-Dimensional Attribute Association of Trajectory Points
by Senyang Zhao, Wei Guo and Yi Liu
ISPRS Int. J. Geo-Inf. 2025, 14(9), 345; https://doi.org/10.3390/ijgi14090345 (registering DOI) - 7 Sep 2025
Abstract
Ship trajectory prediction plays an important role in numerous maritime applications and services. With the development of deep learning technology, the deep learning prediction method based on Automatic Identification System (AIS) data has become one of the hot topics in current maritime traffic [...] Read more.
Ship trajectory prediction plays an important role in numerous maritime applications and services. With the development of deep learning technology, the deep learning prediction method based on Automatic Identification System (AIS) data has become one of the hot topics in current maritime traffic research. However, as current models always concatenate dynamic information with distinct meanings (such as position, ship speed, and heading) into a single integrated input when processing trajectory point information as input, it becomes difficult for the models to grasp the correlations between different types of dynamic information of trajectory points and the specific information contained in each type of dynamic information itself. Aiming at the problem of insufficient modeling of the relationships among dynamic information in ship trajectory prediction, we propose the Multi-dimensional Attribute Relationship Transformer (MART) model. This model introduces a simulated trajectory training strategy to obtain the Association Loss (AssLoss) for learning the associations among different types of dynamic information; and it uses the Distance Loss (DisLoss) to integrate the relative distance information of the attribute embedding encoding to assist the model in understanding the relationships among different values in the dynamic information. We test the model on two AIS datasets, and the experiments show this model outperforms existing models. In the 15 h long-term prediction task, compared with other models, the MART model improves the prediction accuracy by 9.5% on the Danish Waters Dataset and by 15.4% on the Northern European Dataset. This study reveals the importance of the relationship between attributes and the relative distance of attribute values in spatiotemporal sequence modeling. Full article
(This article belongs to the Topic Artificial Intelligence Models, Tools and Applications)
15 pages, 841 KB  
Article
Extended von Bertalanffy Equation in Solow Growth Modelling
by Antonio E. Bargellini, Daniele Ritelli and Giulia Spaletta
Algorithms 2025, 18(9), 565; https://doi.org/10.3390/a18090565 (registering DOI) - 7 Sep 2025
Abstract
The aim of this work is to model the growth of an economic system and, in particular, the evolution of capital accumulation over time, analysing the feasibility of a closed-form solution to the initial value problem that governs the capital-per-capita dynamics. The latter [...] Read more.
The aim of this work is to model the growth of an economic system and, in particular, the evolution of capital accumulation over time, analysing the feasibility of a closed-form solution to the initial value problem that governs the capital-per-capita dynamics. The latter are related to the labour-force dynamics, which are assumed to follow a von Bertalanffy model, studied in the literature in its simplest form and for which the existence of an exact solution, in terms of hypergeometric functions, is known. Here, we consider an extended form of the von Bertalanffy equation, which we make dependent on two parameters, rather than the single-parameter model known in the literature, to better capture the features that a reliable economic growth model should possess. Furthermore, we allow one of the two parameters to vary over time, making it dependent on a periodic function to account for seasonality. We prove that the two-parameter model admits an exact solution, in terms of hypergeometric functions, when both parameters are constant. In the time-varying case, although it is not possible to obtain a closed-form solution, we are able to find two exact solutions that closely bound, from below and from above, the desired one, as well as its numerical approximation. The presented models are implemented in the Mathematica environment, where simulations, parameter sensitivity analyses and comparisons with the known single-parameter model are also performed, validating our findings. Full article
(This article belongs to the Section Analysis of Algorithms and Complexity Theory)
16 pages, 3154 KB  
Article
Finite Element Simulation of Crystal Plasticity in the Tensile Fracture Behavior of PBF-LB/M CoCrFeNiMn High Entropy Alloy
by Liangliang Wu, Wei Duan, Shuaifeng Zhang, Xiao Yang, Wen Li, Xu Shen, Yan Zhang and Jianxin Zhou
Metals 2025, 15(9), 990; https://doi.org/10.3390/met15090990 (registering DOI) - 7 Sep 2025
Abstract
CoCrFeNiMn high entropy alloy (HEA) fabricated via laser-based powder bed fusion (PBF-LB/M) exhibits exceptional mechanical properties, including high strength, better ductility than titanium alloy, and superior corrosion resistance. This study simulates the intergranular fracture behavior of PBF-LB/M CoCrFeNiMn HEA under tensile loading by [...] Read more.
CoCrFeNiMn high entropy alloy (HEA) fabricated via laser-based powder bed fusion (PBF-LB/M) exhibits exceptional mechanical properties, including high strength, better ductility than titanium alloy, and superior corrosion resistance. This study simulates the intergranular fracture behavior of PBF-LB/M CoCrFeNiMn HEA under tensile loading by embedding cohesive elements with damage mechanisms into polycrystalline representative volume elements based on the crystal plasticity finite element method. The simulation results show good agreement with reported experimental stress–strain curves, demonstrating that the crystal plastic constitutive model combined with the cohesive constitutive model can accurately describe both the macroscopic response behavior and fracture failure behavior of the CoCrFeNiMn HEA. Furthermore, this work investigates the mechanical properties of the HEA in different tensile directions, the improvement of anisotropy through columnar-to-equiaxed grain transition, and the effect of texture strength on crack initiation and propagation. The results show that the polycrystalline CoCrFeNiMn HEA exhibits anisotropic mechanical properties: simulated yield strengths (YSs) are 436.9 MPa (in the scanning direction) and 484.7 MPa (in the building direction), tensile strengths (TSs) reach 639 MPa and 702.5 MPa, and elongations (ELs) are 10.6% and 21.8%, respectively. After equiaxed grain formation, the EL in the scanning direction increased from 10.6% to 17.2%, while the EL in the building direction decreased from 21.8% to 20.3%. Concurrently, the anisotropy coefficients of YS, TS, and EL decreased by 1.8%, 2.2%, and 36.1%, respectively. The cracks initiate at stress concentrations and subsequently propagate along grain boundaries until final fracture. Variations in texture strength significantly influence the crack initiation location and propagation path in the CoCrFeNiMn HEA. Full article
22 pages, 29763 KB  
Article
Numerical Modelling of Rock Fragmentation in Landslide Propagation: A Test Case
by Claudia Zito, Massimo Mangifesta, Mirko Francioni, Luigi Guerriero, Diego Di Martire, Domenico Calcaterra, Corrado Cencetti, Antonio Pasculli and Nicola Sciarra
Geosciences 2025, 15(9), 354; https://doi.org/10.3390/geosciences15090354 (registering DOI) - 7 Sep 2025
Abstract
Landslides and rockfalls can negatively impact human activities and cause radical changes to the surrounding environment. For example, they can destroy entire buildings and roadway infrastructure, block waterways and create sudden dams, resulting in upstream flooding and increased flood risk downstream. In extreme [...] Read more.
Landslides and rockfalls can negatively impact human activities and cause radical changes to the surrounding environment. For example, they can destroy entire buildings and roadway infrastructure, block waterways and create sudden dams, resulting in upstream flooding and increased flood risk downstream. In extreme cases, they can even cause loss of life. External factors such as weathering, vegetation and mechanical stress alterations play a decisive role in their evolution. These actions can reduce strength, which can have an adverse impact on the slope’s ability to withstand failure. For rockfalls, this process also affects fragmentation, creating variations in the size, shape and volume of detached blocks, which influences propagation and impact on the slope. In this context, the Morino-Rendinara landslide is a clear example of rockfall propagation influenced by fragmentation. In this case, fragmentation results from tectonic stresses acting on the materials as well as specific climatic conditions affecting rock mass properties. This study explores how different fragmentation scales influence both velocity and landslide propagation along the slope. Using numerical models, based on lumped mass approach and stochastic analyses, various scenarios of rock material fracturing were examined and their impact on runout was assessed. Different scenarios were defined, varying only the fragmentation degree and different random seed sets at the beginning of simulations, carried out using the Rock-GIS tool. he results suggest that rock masses with high fracturing show reduced cohesion along joints and cracks, which significantly lowers their shear strength and makes them more prone to failure. Increased fragmentation further decreases the bonding between rock blocks, thereby accelerating landslide propagation. Conversely, less fragmented rocks retain higher resistance, which limits the extent of movement. These processes are influenced by uncertainties related to the distribution and impact of different alteration grades, resulting from variable tectonic stresses and/or atmospheric weathering. Therefore, a stochastic distribution model was developed to integrate the results of all simulations and to reconstruct both the landslide propagation and the evolution of its deposits. This study emphasizes the critical role of fragmentation and the volume involved in rockfalls and their runout behaviour. Furthermore, the method provides a framework for enhancing risk assessment in complex geological environments and for developing mitigation strategies, particularly regarding runout distance and block size. Full article
(This article belongs to the Section Natural Hazards)
22 pages, 3412 KB  
Article
Fault Identification Method for Photovoltaic Power Grids Based on an Improved GABP Neural Network and Fuzzy System
by Xiaofeng Dong, Houtao Sun, Zhongxiu Han, Yuanchen Xia, Hongjun Wang and Qingwen Mou
Symmetry 2025, 17(9), 1476; https://doi.org/10.3390/sym17091476 (registering DOI) - 7 Sep 2025
Abstract
Fault detection and classification localization in photovoltaic power grids is a key challenge in photovoltaic power systems. Due to the greater fluctuation of power data in photovoltaic power grids, traditional grid fault detection methods suffer from inefficiency, low accuracy, and inaccurate fault localization [...] Read more.
Fault detection and classification localization in photovoltaic power grids is a key challenge in photovoltaic power systems. Due to the greater fluctuation of power data in photovoltaic power grids, traditional grid fault detection methods suffer from inefficiency, low accuracy, and inaccurate fault localization in photovoltaic scenarios. In this paper, a fuzzy control technique combined with an improved GABP neural network is used to identify potential fault nodes in the photovoltaic distribution network. The symmetric crossover operator of the genetic algorithm and the symmetry constraints of the neural network weight matrix are used to improve the model’s ability to capture the symmetric fluctuation characteristics of photovoltaic data, while a classification module consisting of three fuzzy controllers is used for fault identification. The simulation results show that the recognition method proposed in this paper has good performance and the fault classification accuracy reaches 92.75%, which provides a practical reference value for the management of photovoltaic distribution network. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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