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Keywords = line distribution generalization

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15 pages, 3978 KiB  
Article
Buoyancy Characteristics of Synchronous Grouting Slurry in Shield Tunnels
by Wangjing Yao, Jianchao Sheng, Junhao Tian, Binpin Wei, Jiuchun Sun and Zhe Wang
Appl. Sci. 2025, 15(16), 8994; https://doi.org/10.3390/app15168994 - 14 Aug 2025
Abstract
Synchronous grouting slurry is widely used in shield tunnel construction to fill the gaps between stratum and shield tail segments. However, as grout is nearly liquid in the initial stages, the tunnel lining segments recently separated from the shield tail are easily affected [...] Read more.
Synchronous grouting slurry is widely used in shield tunnel construction to fill the gaps between stratum and shield tail segments. However, as grout is nearly liquid in the initial stages, the tunnel lining segments recently separated from the shield tail are easily affected by the upward buoyancy generated by grout, causing issues such as longitudinal misalignment and opening of ring joints. Therefore, studying the upward buoyancy characteristics of synchronous grout is crucial. In this study, floating characterisation parameters of grout were investigated using buoyancy model tests, orthogonal tests, and comprehensive tests. The floating characterisation parameters are affected by distribution ratio and types of each grout component. The relationship between the floating characterisation parameters of grout and buoyancy was established. The results show that density, flow index, and shear strength can be used as the floating characterisation parameters. Binder–sand and water–binder ratios have the largest impact on the density. The bentonite–water ratio exerts a primary influence on the flow index, while the water–binder ratio contributes a secondary effect. In addition, bentonite–water and binder–sand ratios have the greatest effect on the shear strength. Furthermore, the particle size of sand and type of bentonite considerably influence the flow index and shear strength. A high-shear grout using well-graded fine sand and a high mesh of sodium bentonite was considered in this study. When the content of bentonite exceeds 7% (P2.2), Archimedes’ law is not applicable for calculating the upward buoyancy of grout. Buoyancy supply rate exhibits gradual enhancement with flow index elevation, yet with diminishing growth rates. Full article
(This article belongs to the Section Civil Engineering)
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17 pages, 4999 KiB  
Article
Simulating the Phylogenetic Diversity Metrics of Plant Communities in Alpine Grasslands of Xizang, China
by Mingxue Xiang, Tao Ma, Wei Sun, Shaowei Li and Gang Fu
Diversity 2025, 17(8), 569; https://doi.org/10.3390/d17080569 - 14 Aug 2025
Viewed by 46
Abstract
Phylogenetic diversity serves as a critical complement to traditional species diversity metrics. However, the performance variations among different computational models in simulating phylogenetic diversity within plant communities in the alpine grasslands of the Qinghai-Xizang Plateau remain insufficiently characterized. Here, we evaluated nine modeling [...] Read more.
Phylogenetic diversity serves as a critical complement to traditional species diversity metrics. However, the performance variations among different computational models in simulating phylogenetic diversity within plant communities in the alpine grasslands of the Qinghai-Xizang Plateau remain insufficiently characterized. Here, we evaluated nine modeling approaches—random forest (RF), generalized boosting regression (GBR), multiple linear regression (MLR), artificial neural network (ANN), generalized linear regression (GLR), conditional inference tree (CIT), extreme gradient boosting (eXGB), support vector machine (SVM), and recursive regression tree (RRT)—for predicting three key phylogenetic diversity metrics [Faith’s phylogenetic diversity (PD), mean pairwise distance (MPD), mean nearest taxon distance (MNTD)] using climate variables and NDVImax. Our comprehensive analysis revealed distinct model performance patterns under grazing vs. fencing regimes. The eXGB algorithm demonstrated superior accuracy for fencing conditions, achieving the lowest relative bias (−0.08%) and RMSE (9.54) for MPD, along with optimal performance for MNTD (bias = 2.95%, RMSE = 44.86). Conversely, RF emerged as the most robust model for grazing scenarios, delivering the lowest bias (−1.63%) and RMSE (16.89) for MPD while maintaining strong predictive capability for MNTD (bias = −1.09%, RMSE = 27.59). Notably, scatterplot analysis revealed that only RF, GBR, and eXGB maintained symmetrical distributions along the 1:1 line, while other models showed problematic one-to-many value mappings or asymmetric patterns. These findings show that machine learning (especially RF and eXGB) enhances phylogenetic diversity predictions by integrating climate and NDVI data, though model performance varies by metric and management context. This study offers a framework for ecological forecasting, emphasizing multi-metric validation in biodiversity modeling. Full article
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15 pages, 2755 KiB  
Article
Comparative Analysis of the Substitution Effect of Smart Inverter-Based Energy Storage Systems on the Improvement of Distribution System Hosting Capacity Using Vertical Photovoltaic Systems
by Seungmin Lee, Garam Kim, Seungwoo Son and Junghun Lee
Energies 2025, 18(16), 4307; https://doi.org/10.3390/en18164307 - 13 Aug 2025
Viewed by 184
Abstract
Renewable energy sources, particularly solar photovoltaics (PVs), are rapidly expanding to achieve carbon neutrality. Integrated photovoltaic (IPV) solutions in underutilized spaces offer a viable option for countries with land constraints and public opposition. Vertical PV (VPV) systems, featuring bifacial solar modules installed vertically, [...] Read more.
Renewable energy sources, particularly solar photovoltaics (PVs), are rapidly expanding to achieve carbon neutrality. Integrated photovoltaic (IPV) solutions in underutilized spaces offer a viable option for countries with land constraints and public opposition. Vertical PV (VPV) systems, featuring bifacial solar modules installed vertically, facing east and west, present a promising alternative. In contrast to conventional tilted PV (CPV) systems, which peak around midday, VPV systems generate more power in the morning and afternoon. This mitigates issues such as the duck curve and curtailment caused by midday overgeneration. Moreover, combining VPV and CPV systems can increase the solar hosting capacity of a distribution line (DL) for PV-system interconnections, driving research interest. This study assessed the hosting-capacity improvements from VPV systems by analyzing voltage fluctuations and thermal constraints using OpenDSS software (Version 9.1.1.1). The potential substitution effect of a smart inverter-based energy-storage system (ESS) was also explored. The analysis, based on real-grid conditions in South Korea, incorporated actual DL data, generation and demand profiles, and operational data from both VPV and CPV systems. Worst-case scenarios were simulated to evaluate their impact on grid stability. The results demonstrate that VPV systems can increase hosting capacity by up to 23% and ensure stable grid operation by reducing power-generation uncertainties. Full article
(This article belongs to the Section F2: Distributed Energy System)
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17 pages, 2641 KiB  
Article
Pilot Protection for Transmission Line of Grid-Forming Photovoltaic Systems Based on Jensen–Shannon Distance
by Kuan Li, Qiang Huang and Rongqi Fan
Appl. Sci. 2025, 15(15), 8697; https://doi.org/10.3390/app15158697 - 6 Aug 2025
Viewed by 171
Abstract
When faults occur in transmission lines of grid-forming PV systems, the LVRT control and virtual impedance function cause the fault characteristics of grid-forming inverters to differ significantly from those of synchronous generators, which deteriorates the performance of existing protection schemes. To address this [...] Read more.
When faults occur in transmission lines of grid-forming PV systems, the LVRT control and virtual impedance function cause the fault characteristics of grid-forming inverters to differ significantly from those of synchronous generators, which deteriorates the performance of existing protection schemes. To address this issue, this paper analyzes the fault characteristics of PV transmission lines under grid-forming control objectives and the adaptability of traditional current differential protection. Subsequently, a novel pilot protection based on the Jensen–Shannon distance is proposed for transmission line of grid-forming PV systems. Initially, the post-fault current samples are modeled as discrete probability distributions. The Jensen–Shannon distance algorithm quantifies the similarity between the distributions on both line ends. Based on the calculated distance results, internal and external faults are distinguished, optimizing the performance of traditional waveform-similarity-based pilot protection. Simulation results verify that the proposed protection reliably identifies internal and external faults on the protected line. It demonstrates satisfactory performance across different fault resistances and fault types, and exhibits strong noise immunity and synchronization error tolerance. In addition, the proposed pilot protection is compared with the existing waveform-similarity-based protection schemes. Full article
(This article belongs to the Special Issue Power System Protection: Current and Future Prospectives)
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15 pages, 997 KiB  
Article
Reactive Power Optimization Control Method for Distribution Network with Hydropower Based on Improved Discrete Particle Swarm Optimization Algorithm
by Tao Liu, Bin Jia, Shuangxiang Luo, Xiangcong Kong, Yong Zhou and Hongbo Zou
Processes 2025, 13(8), 2455; https://doi.org/10.3390/pr13082455 - 3 Aug 2025
Viewed by 304
Abstract
With the rapid development of renewable energy, the proportion of small hydropower as a clean energy in the distribution network (DN) is increasing. However, the randomness and intermittence of small hydropower has brought new challenges to the operation of DN; especially, the problems [...] Read more.
With the rapid development of renewable energy, the proportion of small hydropower as a clean energy in the distribution network (DN) is increasing. However, the randomness and intermittence of small hydropower has brought new challenges to the operation of DN; especially, the problems of increasing network loss and reactive voltage exceeding the limit have become increasingly prominent. Aiming at the above problems, this paper proposes a reactive power optimization control method for DN with hydropower based on an improved discrete particle swarm optimization (PSO) algorithm. Firstly, this paper analyzes the specific characteristics of small hydropower and establishes its mathematical model. Secondly, considering the constraints of bus voltage and generator RP output, an extended minimum objective function for system power loss is established, with bus voltage violation serving as the penalty function. Then, in order to solve the following problems: that the traditional discrete PSO algorithm is easy to fall into local optimization and slow convergence, this paper proposes an improved discrete PSO algorithm, which improves the global search ability and convergence speed by introducing adaptive inertia weight. Finally, based on the IEEE-33 buses distribution system as an example, the simulation analysis shows that compared with GA optimization, the line loss can be reduced by 3.4% in the wet season and 13.6% in the dry season. Therefore, the proposed method can effectively reduce the network loss and improve the voltage quality, which verifies the effectiveness and superiority of the proposed method. Full article
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17 pages, 3817 KiB  
Article
The Distribution Characteristics of Frost Heaving Forces on Tunnels in Cold Regions Based on Thermo-Mechanical Coupling
by Yujia Sun, Lei Peng and Qionglin Li
Appl. Sci. 2025, 15(15), 8537; https://doi.org/10.3390/app15158537 - 31 Jul 2025
Viewed by 198
Abstract
To address the freezing damage to tunnel lining caused by frost heaving of the surrounding rock in water-rich tunnels in cold regions, a numerical thermo-mechanical coupling model for tunnel-surrounding rock that considers the anisotropy of frost heave deformation was established by examining overall [...] Read more.
To address the freezing damage to tunnel lining caused by frost heaving of the surrounding rock in water-rich tunnels in cold regions, a numerical thermo-mechanical coupling model for tunnel-surrounding rock that considers the anisotropy of frost heave deformation was established by examining overall frost heaves in a freeze–thaw cycle. Using a COMSOL Multiphysics 6.0 platform and the sequential coupling method, the temperature field evolution of tunnel-surrounding rock, freezing cycle development, and distribution characteristics of the frost heaving force of a tunnel lining under different minimum temperatures, numbers of negative temperature days, frost heave ratios, and anisotropy coefficients of frost heave deformation were systematically simulated. The results revealed that the response of the temperature field of tunnel-surrounding rock to the external temperature varies spatially with time lags, the shallow surface temperatures and the area around the lining fluctuate with the climate, and the temperature of the deep surrounding rock is dominated by the geothermal gradient. The extent of the freezing cycle and the frost heaving force increase significantly when lowering the minimum temperature. The maximum frost heaving force usually occurs in the region of the side wall and the spring line, and tensile stress is prone to be generated at the spring line; the influence of slight fluctuations in the minimum temperature or the short shift in the coldest day on the frost heaving force is limited. A substantial increase in frost heaving force is observed with higher frost heave ratios; for example, an increase from 0.25% to 2.0% results in a 116% rise at the sidewall. Although the increase in the anisotropy coefficient of frost heave deformation does not change the overall distribution pattern of frost heaving force, it can exacerbate the directional concentration of frost heave strain, which can increase the frost heaving force at the periphery of the top arch of the lining. This study revealed the distribution pattern and key influencing factors of the freezing cycle and frost heaving force for tunnels, providing a theoretical basis and data reference for the frost resistance design of tunnels in cold regions. Full article
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22 pages, 8473 KiB  
Article
Designing a Power Supply System for an Amphibious Robot Based on Wave Energy Generation
by Lishan Ma, Fang Huang, Lingxiao Li, Qiang Fu, Chunjie Wang and Xinpeng Wang
J. Mar. Sci. Eng. 2025, 13(8), 1466; https://doi.org/10.3390/jmse13081466 - 30 Jul 2025
Viewed by 308
Abstract
As the range of applications for amphibious robots expands, higher demands are being placed on their working time and working range. This paper proposed a power supply system for an amphibious robot based on wave energy generation, which can convert wave energy into [...] Read more.
As the range of applications for amphibious robots expands, higher demands are being placed on their working time and working range. This paper proposed a power supply system for an amphibious robot based on wave energy generation, which can convert wave energy into electric energy to enhance endurance. First, the no-load induced electromotive force, magnetic line distribution vector diagrams, and magnetic density cloud diagrams of the cylindrical and flat generators were compared by finite element simulation, which determined that the cylindrical structure has better power generation performance. Then, the electromagnetic parameters of the cylindrical generator were analyzed using Ansys Maxwell, and the final dimensions were determined. Finally, the wave motion was simulated using a swing motor, and the effects of different cutting speeds for the actuator before and after rectification, as well as series-parallel capacitance on the power generation performance of the designed generator, were experimentally analyzed. This provides a potential solution to enhance the working time and working range of amphibious robots. Full article
(This article belongs to the Section Ocean Engineering)
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18 pages, 2954 KiB  
Article
A Multi-Objective Decision-Making Method for Optimal Scheduling Operating Points in Integrated Main-Distribution Networks with Static Security Region Constraints
by Kang Xu, Zhaopeng Liu and Shuaihu Li
Energies 2025, 18(15), 4018; https://doi.org/10.3390/en18154018 - 28 Jul 2025
Viewed by 306
Abstract
With the increasing penetration of distributed generation (DG), integrated main-distribution networks (IMDNs) face challenges in rapidly and effectively performing comprehensive operational risk assessments under multiple uncertainties. Thereby, using the traditional hierarchical economic scheduling method makes it difficult to accurately find the optimal scheduling [...] Read more.
With the increasing penetration of distributed generation (DG), integrated main-distribution networks (IMDNs) face challenges in rapidly and effectively performing comprehensive operational risk assessments under multiple uncertainties. Thereby, using the traditional hierarchical economic scheduling method makes it difficult to accurately find the optimal scheduling operating point. To address this problem, this paper proposes a multi-objective dispatch decision-making optimization model for the IMDN with static security region (SSR) constraints. Firstly, the non-sequential Monte Carlo sampling is employed to generate diverse operational scenarios, and then the key risk characteristics are extracted to construct the risk assessment index system for the transmission and distribution grid, respectively. Secondly, a hyperplane model of the SSR is developed for the IMDN based on alternating current power flow equations and line current constraints. Thirdly, a risk assessment matrix is constructed through optimal power flow calculations across multiple load levels, with the index weights determined via principal component analysis (PCA). Subsequently, a scheduling optimization model is formulated to minimize both the system generation costs and the comprehensive risk, where the adaptive grid density-improved multi-objective particle swarm optimization (AG-MOPSO) algorithm is employed to efficiently generate Pareto-optimal operating point solutions. A membership matrix of the solution set is then established using fuzzy comprehensive evaluation to identify the optimal compromised operating point for dispatch decision support. Finally, the effectiveness and superiority of the proposed method are validated using an integrated IEEE 9-bus and IEEE 33-bus test system. Full article
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11 pages, 2348 KiB  
Article
Study on Smoke Flow and Temperature Distribution Patterns in Fires at Deeply Buried Subway Stations
by Huailin Yan, Heng Liu, Yongchang Zhao and Zirui Bian
Fire 2025, 8(8), 296; https://doi.org/10.3390/fire8080296 - 28 Jul 2025
Viewed by 436
Abstract
To enhance the fire safety protection level of deeply buried metro stations, this study conducted full-scale fire experiments based on Wulichong Station of Guiyang Metro Line 3. It systematically investigated the laws of smoke movement and temperature distribution under the coupled effects of [...] Read more.
To enhance the fire safety protection level of deeply buried metro stations, this study conducted full-scale fire experiments based on Wulichong Station of Guiyang Metro Line 3. It systematically investigated the laws of smoke movement and temperature distribution under the coupled effects of different fire source powers and smoke extraction system states. Through the set up of multiple sets of comparative test conditions, the study focused on analyzing the influence mechanism of the operation (on/off) of the smoke extraction system on smoke spread characteristics and temperature field distribution. The results indicate that under the condition where the smoke extraction system is turned off, the smoke exhibits typical stratified spread characteristics driven by thermal buoyancy, with the temperature rising significantly as the vertical height increases. When the smoke extraction system is activated, the horizontal airflow generated by mechanical smoke extraction significantly alters the flame morphology (with an inclination angle exceeding 45°), effectively extracting and discharging the hot smoke and leading to a more uniform temperature distribution within the space. Full article
(This article belongs to the Special Issue Advances in Fire Science and Fire Protection Engineering)
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27 pages, 3280 KiB  
Article
Design and Implementation of a Robust Hierarchical Control for Sustainable Operation of Hybrid Shipboard Microgrid
by Arsalan Rehmat, Farooq Alam, Mohammad Taufiqul Arif and Syed Sajjad Haider Zaidi
Sustainability 2025, 17(15), 6724; https://doi.org/10.3390/su17156724 - 24 Jul 2025
Viewed by 471
Abstract
The growing demand for low-emission maritime transport and efficient onboard energy management has intensified research into advanced control strategies for hybrid shipboard microgrids. These systems integrate both AC and DC power domains, incorporating renewable energy sources and battery storage to enhance fuel efficiency, [...] Read more.
The growing demand for low-emission maritime transport and efficient onboard energy management has intensified research into advanced control strategies for hybrid shipboard microgrids. These systems integrate both AC and DC power domains, incorporating renewable energy sources and battery storage to enhance fuel efficiency, reduce greenhouse gas emissions, and support operational flexibility. However, integrating renewable energy into shipboard microgrids introduces challenges, such as power fluctuations, varying line impedances, and disturbances caused by AC/DC load transitions, harmonics, and mismatches in demand and supply. These issues impact system stability and the seamless coordination of multiple distributed generators. To address these challenges, we proposed a hierarchical control strategy that supports sustainable operation by improving the voltage and frequency regulation under dynamic conditions, as demonstrated through both MATLAB/Simulink simulations and real-time hardware validation. Simulation results show that the proposed controller reduces the frequency deviation by up to 25.5% and power variation improved by 20.1% compared with conventional PI-based secondary control during load transition scenarios. Hardware implementation on the NVIDIA Jetson Nano confirms real-time feasibility, maintaining power and frequency tracking errors below 5% under dynamic loading. A comparative analysis of the classical PI and sliding mode control-based designs is conducted under various grid conditions, such as cold ironing mode of the shipboard microgrid, and load variations, considering both the AC and DC loads. The system stability and control law formulation are verified through simulations in MATLAB/SIMULINK and practical implementation. The experimental results demonstrate that the proposed secondary control architecture enhances the system robustness and ensures sustainable operation, making it a viable solution for modern shipboard microgrids transitioning towards green energy. Full article
(This article belongs to the Special Issue Smart Grid Technologies and Energy Sustainability)
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17 pages, 7385 KiB  
Article
Time-Division Subbands Beta Distribution Random Space Vector Pulse Width Modulation Method for the High-Frequency Harmonic Dispersion
by Jian Wen and Xiaobin Cheng
Electronics 2025, 14(14), 2852; https://doi.org/10.3390/electronics14142852 - 16 Jul 2025
Viewed by 250
Abstract
Conventional space vector pulse width modulation (CSVPWM) with the fixed switching frequency generates significant sideband harmonics in the three-phase voltage. Discrete random switching frequency SVPWM (DRSF-SVPWM) methods have been widely applied in motor control systems for the suppression of tone harmonic energy. To [...] Read more.
Conventional space vector pulse width modulation (CSVPWM) with the fixed switching frequency generates significant sideband harmonics in the three-phase voltage. Discrete random switching frequency SVPWM (DRSF-SVPWM) methods have been widely applied in motor control systems for the suppression of tone harmonic energy. To further reduce the amplitude of the high-frequency harmonic with a limited switching frequency variation range, this paper proposes a time-division subbands beta distribution random SVPWM (TSBDR-SVPWM) method. The overall frequency band of the switching frequency is equally divided into N subbands, and each fundamental cycle of the line voltage is segmented into 2*(N-1) equal time intervals. Additionally, within each time segment, the switching frequency is randomly selected from the corresponding subband and follows the optimal discrete beta distribution. The switching frequency harmonic energy in the line voltage spectrum spreads across multiple frequency subbands and discrete frequency components, thereby forming a more uniform power spectrum of the line voltage. Both simulation and experimental results validate that, compared with CSVPWM, the sideband harmonic amplitude is reduced by more than 8.5 dB across the entire range of speed and torque conditions in the TSBDR-SVPWM. Furthermore, with the same variation range of the switching frequency, the proposed method achieves the lowest switching frequency harmonic amplitude and flattest line voltage spectrum compared with several state-of-the-art random modulation methods. Full article
(This article belongs to the Section Power Electronics)
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22 pages, 1328 KiB  
Article
Genetic Analysis of Main Gene + Polygenic Gene of Nutritional Traits of Land Cotton Cottonseed
by Yage Li, Weifeng Guo, Liangrong He and Xinchuan Cao
Agronomy 2025, 15(7), 1713; https://doi.org/10.3390/agronomy15071713 - 16 Jul 2025
Viewed by 223
Abstract
Background: The regulation of oil and protein contents in cottonseed is governed by a complex genetic network. Gaining insight into the mechanisms controlling these traits is necessary for dissecting the formation patterns of cottonseed quality. Method: In this study, Xinluzhong 37 (P1 [...] Read more.
Background: The regulation of oil and protein contents in cottonseed is governed by a complex genetic network. Gaining insight into the mechanisms controlling these traits is necessary for dissecting the formation patterns of cottonseed quality. Method: In this study, Xinluzhong 37 (P1) and Xinluzhong 51 (P2) were selected as parental lines for two reciprocal crosses: P1 × P2 (F1) and its reciprocal P2 × P1 (F1′). Each F1 was selfed and backcrossed to both parents to generate the F2 (F2′), B1 (B1′), and B2 (B2′) generations. To assess nutritional traits in hairy (non-delinted) and lint-free (delinted) seeds, two indicators, oil content and protein content, were measured in both seed types. Joint segregation analysis was employed to analyze the inheritance of these traits, based on a major gene plus polygene model. Results: In the orthogonal crosses, the CVs for the four nutritional traits ranged at 2.710–7.879%, 4.086–11.070%, 2.724–6.727%, and 3.717–9.602%. In the reciprocal crosses, CVs ranged at 2.710–8.053%, 4.086–9.572%, 2.724–6.376%, and 3.717–8.845%. All traits exhibited normal or skewed-normal distributions. For oil content in undelinted/delinted seeds, polygenic heritabilities in the orthogonal cross were 0.64/0.52, and 0.40/0.36 in the reciprocal cross. For protein content, major-gene heritabilities in the orthogonal cross were 0.79 (undelinted) and 0.78 (delinted), while those in the reciprocal cross were both 0.62. Conclusions: Oil and protein contents in cottonseeds are quantitative traits. In both orthogonal and reciprocal crosses, oil content is controlled by multiple genes and is shaped by additive, dominance, and epistatic effects. Protein content, in contrast, is largely controlled by two major genes along with minor genes. In the P1 × P2 combination, major genes act through additive, dominance, and epistatic effects, while in the P2 × P1 combination, their effects are additive only. In both combinations, minor genes contribute through additive and dominance effects. In summary, the oil content in cottonseed is mainly regulated by polygenes, whereas the protein content is primarily determined by major genes. These genetic features in both linted, and lint-free seeds may offer a theoretical foundation for molecular breeding aimed at improving cottonseed oil and protein quality. Full article
(This article belongs to the Section Crop Breeding and Genetics)
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13 pages, 1294 KiB  
Article
From Complex to Quaternions: Proof of the Riemann Hypothesis and Applications to Bose–Einstein Condensates
by Jau Tang
Symmetry 2025, 17(7), 1134; https://doi.org/10.3390/sym17071134 - 15 Jul 2025
Viewed by 836
Abstract
We present novel proofs of the Riemann hypothesis by extending the standard complex Riemann zeta function into a quaternionic algebraic framework. Utilizing λ-regularization, we construct a symmetrized form that ensures analytic continuation and restores critical-line reflection symmetry, a key structural property of the [...] Read more.
We present novel proofs of the Riemann hypothesis by extending the standard complex Riemann zeta function into a quaternionic algebraic framework. Utilizing λ-regularization, we construct a symmetrized form that ensures analytic continuation and restores critical-line reflection symmetry, a key structural property of the Riemann ξ(s) function. This formulation reveals that all nontrivial zeros of the zeta function must lie along the critical line Re(s) = 1/2, offering a constructive and algebraic resolution to this fundamental conjecture. Our method is built on convexity and symmetrical principles that generalize naturally to higher-dimensional hypercomplex spaces. We also explore the broader implications of this framework in quantum statistical physics. In particular, the λ-regularized quaternionic zeta function governs thermodynamic properties and phase transitions in Bose–Einstein condensates. This quaternionic extension of the zeta function encodes oscillatory behavior and introduces critical hypersurfaces that serve as higher-dimensional analogues of the classical critical line. By linking the spectral features of the zeta function to measurable physical phenomena, our work uncovers a profound connection between analytic number theory, hypercomplex geometry, and quantum field theory, suggesting a unified structure underlying prime distributions and quantum coherence. Full article
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21 pages, 3570 KiB  
Article
Fatigue Life Analysis of Cylindrical Roller Bearings Considering Elastohydrodynamic Lubrications
by Ke Zhang, Zhitao Huang, Qingsong Li and Ruiyu Zhang
Appl. Sci. 2025, 15(14), 7867; https://doi.org/10.3390/app15147867 - 14 Jul 2025
Viewed by 281
Abstract
Cylindrical roller bearings are widely used in industrial machinery, automotive systems, and aerospace applications, where their reliability directly affects the performance and safety of mechanical systems. The fatigue life of cylindrical roller bearings is significantly affected by their elastohydrodynamic lubrication condition, with variations [...] Read more.
Cylindrical roller bearings are widely used in industrial machinery, automotive systems, and aerospace applications, where their reliability directly affects the performance and safety of mechanical systems. The fatigue life of cylindrical roller bearings is significantly affected by their elastohydrodynamic lubrication condition, with variations potentially reaching multiple times. However, conventional quasi-static models often neglect lubrication effects. This study establishes a quasi-static analysis model for cylindrical roller bearings that incorporates the effects of elastohydrodynamic lubrication by integrating elastohydrodynamic lubrication theory with the Lundberg–Palmgren life model. The isothermal line contact elastohydrodynamic lubrication equations are solved using the multigrid method, and the contact load distribution is determined through nonlinear iterative techniques to calculate bearing fatigue life. Taking the N324 support bearing on the main shaft of an SFW250-8/850 horizontal hydro-generator as an example, the influences of radial load, inner race speed, and lubricant viscosity on fatigue life are comparatively analyzed. Experimental validation is conducted under both light-load and heavy-load operating conditions. The results demonstrate that elastohydrodynamic lubrication markedly increases contact loads, leading to a reduced predicted fatigue life compared with that of the De Mul model (which ignores lubrication). The proposed lubrication-integrated model achieves an average deviation of 5.3% from the experimental data, representing a 16.1% improvement in prediction accuracy over the De Mul model. Additionally, increased rotational speed and lubricant viscosity accelerate fatigue life degradation. Full article
(This article belongs to the Special Issue Advances and Applications in Mechanical Fatigue and Life Assessment)
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18 pages, 1184 KiB  
Article
A Confidential Transmission Method for High-Speed Power Line Carrier Communications Based on Generalized Two-Dimensional Polynomial Chaotic Mapping
by Zihan Nie, Zhitao Guo and Jinli Yuan
Appl. Sci. 2025, 15(14), 7813; https://doi.org/10.3390/app15147813 - 11 Jul 2025
Viewed by 323
Abstract
The deep integration of smart grid and Internet of Things technologies has made high-speed power line carrier communication a key communication technology in energy management, industrial monitoring, and smart home applications, owing to its advantages of requiring no additional wiring and offering wide [...] Read more.
The deep integration of smart grid and Internet of Things technologies has made high-speed power line carrier communication a key communication technology in energy management, industrial monitoring, and smart home applications, owing to its advantages of requiring no additional wiring and offering wide coverage. However, the inherent characteristics of power line channels, such as strong noise, multipath fading, and time-varying properties, pose challenges to traditional encryption algorithms, including low key distribution efficiency and weak anti-interference capabilities. These issues become particularly pronounced in high-speed transmission scenarios, where the conflict between data security and communication reliability is more acute. To address this problem, a secure transmission method for high-speed power line carrier communication based on generalized two-dimensional polynomial chaotic mapping is proposed. A high-speed power line carrier communication network is established using a power line carrier routing algorithm based on the minimal connected dominating set. The autoregressive moving average model is employed to determine the degree of transmission fluctuation deviation in the high-speed power line carrier communication network. Leveraging the complex dynamic behavior and anti-decoding capability of generalized two-dimensional polynomial chaotic mapping, combined with the deviation, the communication key is generated. This process yields encrypted high-speed power line carrier communication ciphertext that can resist power line noise interference and signal attenuation, thereby enhancing communication confidentiality and stability. By applying reference modulation differential chaotic shift keying and integrating the ciphertext of high-speed power line carrier communication, a secure transmission scheme is designed to achieve secure transmission in high-speed power line carrier communication. The experimental results demonstrate that this method can effectively establish a high-speed power line carrier communication network and encrypt information. The maximum error rate obtained by this method is 0.051, and the minimum error rate is 0.010, confirming its ability to ensure secure transmission in high-speed power line carrier communication while improving communication confidentiality. Full article
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