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Search Results (626)

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12 pages, 736 KiB  
Article
Hybrid Framework of Fermi–Dirac Spin Hydrodynamics
by Zbigniew Drogosz
Physics 2025, 7(3), 31; https://doi.org/10.3390/physics7030031 (registering DOI) - 1 Aug 2025
Abstract
The paper outlines the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel–Stewart method of introducing dissipation. The local equilibrium expressions for the baryon current, the energy–momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi–Dirac [...] Read more.
The paper outlines the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel–Stewart method of introducing dissipation. The local equilibrium expressions for the baryon current, the energy–momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi–Dirac statistics are obtained and compared with the earlier derived versions where the Boltzmann approximation was used. The expressions in the two cases are found to have the same form, but the coefficients are shown to be governed by different functions. The relative differences between the tensor coefficients in the Fermi–Dirac and Boltzmann cases are found to grow exponentially with the baryon chemical potential. In the proposed formalism, nonequilibrium processes are studied including mathematically possible dissipative corrections. Standard conservation laws are applied, and the condition of positive entropy production is shown to allow for the transfer between the spin and orbital parts of angular momentum. Full article
(This article belongs to the Special Issue High Energy Heavy Ion Physics—Zimányi School 2024)
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20 pages, 2854 KiB  
Article
Trait-Based Modeling of Surface Cooling Dynamics in Olive Fruit Using Thermal Imaging and Mixed-Effects Analysis
by Eddy Plasquy, José M. Garcia, Maria C. Florido and Anneleen Verhasselt
Agriculture 2025, 15(15), 1647; https://doi.org/10.3390/agriculture15151647 - 30 Jul 2025
Abstract
Effective postharvest cooling of olive fruit is increasingly critical under rising harvest temperatures driven by climate change. This study models passive cooling dynamics using a trait-based, mixed-effects statistical framework. Ten olive groups—representing seven cultivars and different ripening or size stages—were subjected to controlled [...] Read more.
Effective postharvest cooling of olive fruit is increasingly critical under rising harvest temperatures driven by climate change. This study models passive cooling dynamics using a trait-based, mixed-effects statistical framework. Ten olive groups—representing seven cultivars and different ripening or size stages—were subjected to controlled cooling conditions. Surface temperature was recorded using infrared thermal imaging, and morphological and compositional traits were quantified. Temperature decay was modeled using Newton’s Law of Cooling, extended with a quadratic time term to capture nonlinear trajse thectories. A linear mixed-effects model was fitted to log-transformed, normalized temperature data, incorporating trait-by-time interactions and hierarchical random effects. The results confirmed that fruit weight, specific surface area (SSA), and specific heat capacity (SHC) are key drivers of cooling rate variability, consistent with theoretical expectations, but quantified here using a trait-based statistical model applied to olive fruit. The quadratic model consistently outperformed standard exponential models, revealing dynamic effects of traits on temperature decline. Residual variation at the group level pointed to additional unmeasured structural influences. This study demonstrates that olive fruit cooling behavior can be effectively predicted using interpretable, trait-dependent models. The findings offer a quantitative basis for optimizing postharvest cooling protocols and are particularly relevant for maintaining quality under high-temperature harvest conditions. Full article
(This article belongs to the Section Agricultural Product Quality and Safety)
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18 pages, 3379 KiB  
Article
Research on Electric Vehicle Differential System Based on Vehicle State Parameter Estimation
by Huiqin Sun and Honghui Wang
Vehicles 2025, 7(3), 80; https://doi.org/10.3390/vehicles7030080 - 30 Jul 2025
Abstract
To improve the stability and safety of electric vehicles during medium-to-high-speed cornering, this paper investigates torque differential control for dual rear-wheel hub motor drive systems, extending beyond traditional speed control based on the Ackermann steering model. A nonlinear three-degree-of-freedom vehicle dynamics model incorporating [...] Read more.
To improve the stability and safety of electric vehicles during medium-to-high-speed cornering, this paper investigates torque differential control for dual rear-wheel hub motor drive systems, extending beyond traditional speed control based on the Ackermann steering model. A nonlinear three-degree-of-freedom vehicle dynamics model incorporating the Dugoff tire model was established. By introducing the maximum correntropy criterion, an unscented Kalman filter was developed to estimate longitudinal velocity, sideslip angle at the center of mass, and yaw rate. Building upon the speed differential control achieved through Ackermann steering model-based rear-wheel speed calculation, improvements were made to the conventional exponential reaching law, while a novel switching function was proposed to formulate a new sliding mode controller for computing an additional yaw moment to realize torque differential control. Finally, simulations conducted on the Carsim/Simulink platform demonstrated that the maximum correntropy criterion unscented Kalman filter effectively improves estimation accuracy, achieving at least a 22.00% reduction in RMSE metrics compared to conventional unscented Kalman filter. With torque control exhibiting higher vehicle stability than speed control, the RMSE values of yaw rate and sideslip angle at the center of mass are reduced by at least 20.00% and 4.55%, respectively, enabling stable operation during medium-to-high-speed cornering conditions. Full article
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21 pages, 1210 KiB  
Article
Fixed-Time Bearing-Only Formation Control Without a Global Coordinate Frame
by Hanqiao Huang, Mengwen Lu, Bo Zhang and Qian Wang
Electronics 2025, 14(15), 3021; https://doi.org/10.3390/electronics14153021 - 29 Jul 2025
Viewed by 102
Abstract
This work addresses distributed fixed-time bearing-only formation stabilization for multi-agent systems lacking shared orientation knowledge. Addressing the challenge of missing global coordinate alignment in multi-agent systems, this work introduces a novel distributed estimator ensuring almost globally fixed-time convergence of orientation estimates. Leveraging this [...] Read more.
This work addresses distributed fixed-time bearing-only formation stabilization for multi-agent systems lacking shared orientation knowledge. Addressing the challenge of missing global coordinate alignment in multi-agent systems, this work introduces a novel distributed estimator ensuring almost globally fixed-time convergence of orientation estimates. Leveraging this estimator, we develop a distributed bearing-only formation control law specifically designed for agents governed by double-integrator dynamics, guaranteeing fixed-time convergence. Comprehensive stability analysis proves the almost global fixed-time stability of the overall closed-loop system. Crucially, the proposed control strategy drives actual formation to achieve the desired geometric pattern with almost global exponential convergence within a fixed time bound. Rigorous numerical experiments corroborate the theoretical framework. Full article
(This article belongs to the Special Issue Research on Cooperative Control of Multi-agent Unmanned Systems)
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27 pages, 1332 KiB  
Article
Generalizing Coherent States with the Fox H Function
by Filippo Giraldi
Quantum Rep. 2025, 7(3), 33; https://doi.org/10.3390/quantum7030033 - 28 Jul 2025
Viewed by 319
Abstract
In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized coherent states, as particular cases, and resolve the identity operator, [...] Read more.
In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized coherent states, as particular cases, and resolve the identity operator, over the Fock space, with a weight function that is the product of a Fox H function and a Wright generalized hypergeometric function. The novel generalized coherent states, or the corresponding truncated generalized coherent states, are characterized by anomalous statistics for large values of the number of excitations: the corresponding decay laws exhibit, for determined values of the involved parameters, various behaviors that depart from exponential and inverse-power-law decays, or their product. The analysis of the Mandel Q factor shows that, for small values of the label, the statistics of the number of excitations becomes super-Poissonian, or sub-Poissonian, by simply choosing sufficiently large values of one of the involved parameters. The time evolution of a generalized coherent state interacting with a thermal reservoir and the purity are analyzed. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
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23 pages, 1593 KiB  
Article
Natural Ventilation Technique of uNVeF in Urban Residential Unit Through a Case Study
by Ming-Lun Alan Fong and Wai-Kit Chan
Urban Sci. 2025, 9(8), 291; https://doi.org/10.3390/urbansci9080291 - 25 Jul 2025
Viewed by 665
Abstract
The present study was motivated by the need to enhance indoor air quality and reduce airborne disease transmission in dense urban environments where high-rise residential buildings face challenges in achieving effective natural ventilation. The problem lies in the lack of scalable and convenient [...] Read more.
The present study was motivated by the need to enhance indoor air quality and reduce airborne disease transmission in dense urban environments where high-rise residential buildings face challenges in achieving effective natural ventilation. The problem lies in the lack of scalable and convenient tools to optimize natural ventilation rate, particularly in urban settings with varying building heights. To address this, the scientific technique developed with an innovative metric, the urbanized natural ventilation effectiveness factor (uNVeF), integrates regression analysis of wind direction, velocity, air change rate per hour (ACH), window configurations, and building height to quantify ventilation efficiency. By employing a field measurement methodology, the measurements were conducted across 25 window-opening scenarios in a 13.9 m2 residential unit on the 35/F of a Hong Kong public housing building, supplemented by the Hellman Exponential Law with a site-specific friction coefficient (0.2907, R2 = 0.9232) to estimate the lower floor natural ventilation rate. The results confirm compliance with Hong Kong’s statutory 1.5 ACH requirement (Practice Note for Authorized Persons, Registered Structural Engineers, and Registered Geotechnical Engineers) and achieving a peak ACH at a uNVeF of 0.953 with 75% window opening. The results also revealed that lower floors can maintain 1.5 ACH with adjusted window configurations. Using the Wells–Riley model, the estimation results indicated significant airborne disease infection risk reductions of 96.1% at 35/F and 93.4% at 1/F compared to the 1.5 ACH baseline which demonstrates a strong correlation between ACH, uNVeF and infection risks. The uNVeF framework offers a practical approach to optimize natural ventilation and provides actionable guidelines, together with future research on the scope of validity to refine this technique for residents and developers. The implications in the building industry include setting up sustainable design standards, enhancing public health resilience, supporting policy frameworks for energy-efficient urban planning, and potentially driving innovation in high-rise residential construction and retrofitting globally. Full article
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15 pages, 2733 KiB  
Article
Dynamic Analysis of an Offshore Knuckle-Boom Crane Under Different Load Applications Laws
by Ivan Tomasi and Luigi Solazzi
Appl. Sci. 2025, 15(14), 8100; https://doi.org/10.3390/app15148100 - 21 Jul 2025
Viewed by 307
Abstract
This study investigates the dynamic behavior of an articulated boom offshore crane under various load application laws. The following steps were taken to perform numerical simulations using the finite-element method (FEM): Definition of the model’s geometry, materials, and boundary conditions. The modal analyses [...] Read more.
This study investigates the dynamic behavior of an articulated boom offshore crane under various load application laws. The following steps were taken to perform numerical simulations using the finite-element method (FEM): Definition of the model’s geometry, materials, and boundary conditions. The modal analyses reveal significant resonance frequencies in the direction of load application (payload). The crane’s displacement, velocity, and acceleration responses are closely related to load application laws, specifically the time required to reach the structure’s full payload (epsilon). It is highly correlated with the dynamic factor (maximum acceleration multiplied by payload), which has a wide range of effects on the structure, including the effects of overstress, overturning, buckling, and so on. The main findings reveal a very strong exponential correlation, allowing the dynamic effect to be estimated as a function of epsilon time. This is a useful tool for increasing the safety and reliability of offshore lifting operations. Full article
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19 pages, 1682 KiB  
Article
The Use of Video Games in Language Learning: A Bibliometric Analysis
by Alain Presentación-Muñoz, Alberto González-Fernández, Miguel Rodal and Jesús Acevedo-Borrega
Metrics 2025, 2(3), 12; https://doi.org/10.3390/metrics2030012 - 21 Jul 2025
Viewed by 212
Abstract
Advances in technology and changes in the way people entertain themselves have made video games a cultural agent on a par with more traditional games, including language learning. In addition, the use of video games in education is becoming increasingly common and numerous [...] Read more.
Advances in technology and changes in the way people entertain themselves have made video games a cultural agent on a par with more traditional games, including language learning. In addition, the use of video games in education is becoming increasingly common and numerous benefits associated with their use have been discovered. The aim of this article is to analyze the search trends in studies dealing with the use of video games in language learning. To this end, a bibliometric analysis was carried out by applying the traditional laws of bibliometrics (Price’s law, Bradford’s law of concentration, Lotka’s law, Zipf’s law and h-index) to documents published in journals indexed in the Core Collection of the Web of Science (WoS). Annual publications between 2009 and 2022 show an exponential growth R2 = 86%. The journals with the most publications are Computer assisted language learning (Taylor & Francis) and Computers and Education (Elsevier). Jie Chi-Yang and Gwo Jen-Hwan were the most cited authors. The United States and Taiwan were the countries with the highest scientific output. The use of video games in language learning has been of particular interest in recent years, with benefits found for students who use them in their classes, although more research is needed to establish criteria and requirements for each video game for its intended purpose. Full article
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25 pages, 4626 KiB  
Article
Study on Evolution Mechanism of Agricultural Trade Network of RCEP Countries—Complex System Analysis Based on the TERGM Model
by Shasha Ding, Li Wang and Qianchen Zhou
Systems 2025, 13(7), 593; https://doi.org/10.3390/systems13070593 - 16 Jul 2025
Viewed by 300
Abstract
The agricultural products trade network is essentially a complex adaptive system formed by nonlinear interactions between countries. Based on the complex system theory, this study reveals the dynamic self-organization law of the RCEP regional agricultural products trade network by using the panel data [...] Read more.
The agricultural products trade network is essentially a complex adaptive system formed by nonlinear interactions between countries. Based on the complex system theory, this study reveals the dynamic self-organization law of the RCEP regional agricultural products trade network by using the panel data of RCEP agricultural products export trade from 2000 to 2023, combining social network analysis (SNA) and the temporal exponential random graph model (TERGM). The results show the following: (1) The RCEP agricultural products trade network presents a “core-edge” hierarchical structure, with China as the core hub to drive regional resource integration and ASEAN countries developing into secondary core nodes to deepen collaborative dependence. (2) The “China-ASEAN-Japan-Korea “riangle trade structure is formed under the RCEP framework, and the network has the characteristics of a “small world”. The leading mode of South–South trade promotes the regional economic order to shift from the traditional vertical division of labor to multiple coordination. (3) The evolution of trade network system is driven by multiple factors: endogenous reciprocity and network expansion are the core structural driving forces; synergistic optimization of supply and demand matching between economic and financial development to promote system upgrading; geographical proximity and cultural convergence effectively reduce transaction costs and enhance system connectivity, but geographical distance is still the key system constraint that restricts the integration of marginal countries. This study provides a systematic and scientific analytical framework for understanding the resilience mechanism and structural evolution of regional agricultural trade networks under global shocks. Full article
(This article belongs to the Section Systems Practice in Social Science)
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21 pages, 10296 KiB  
Article
Spatiotemporal Mechanical Effects of Framework–Slope Systems Under Frost Heave Conditions
by Wendong Li, Xiaoqiang Hou, Jixian Ren and Chaoyang Wu
Appl. Sci. 2025, 15(14), 7877; https://doi.org/10.3390/app15147877 - 15 Jul 2025
Viewed by 261
Abstract
To investigate the slope instability caused by differential frost heaving mechanisms from the slope crest to the toe during frost heave processes, this study takes a typical silty clay slope in Xinjiang, China, as the research object. Through indoor triaxial consolidated undrained shear [...] Read more.
To investigate the slope instability caused by differential frost heaving mechanisms from the slope crest to the toe during frost heave processes, this study takes a typical silty clay slope in Xinjiang, China, as the research object. Through indoor triaxial consolidated undrained shear tests, eight sets of natural and frost-heaved specimens were prepared under confining pressure conditions ranging from 100 to 400 kPa. The geotechnical parameters of the soil in both natural and frost-heaved states were obtained, and a spatiotemporal thermo-hydro-mechanical coupled numerical model was established to reveal the dynamic evolution law of anchor rod axial forces and the frost heave response mechanism between the frame and slope soil. The analytical results indicate that (1) the frost heave process is influenced by slope boundaries, resulting in distinct spatial variations in the temperature field response across the slope surface—namely pronounced responses at the crest and toe but a weaker response in the mid-slope. (2) Under the coupled drive of the water potential gradient and gravitational potential gradient, the ice content in the toe area increases significantly, and the horizontal frost heave force exhibits exponential growth, reaching its peak value of 92 kPa at the toe in February. (3) During soil freezing, the reverse stress field generated by soil arching shows consistent temporal variation trends with the temperature field. Along the height of the soil arch, the intensity of the reverse frost heave force field displays a nonlinear distribution characteristic of initial strengthening followed by attenuation. (4) By analyzing the changes in anchor rod axial forces during frost heaving, it was found that axial forces during the frost heave period are approximately 1.3 times those under natural conditions, confirming the frost heave period as the most critical condition for frame anchor design. Furthermore, through comparative analysis with 12 months of on-site anchor rod axial force monitoring data, the reliability and accuracy of the numerical simulation model were validated. These research outcomes provide a theoretical basis for the design of frame anchor support systems in seasonally frozen regions. Full article
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20 pages, 5292 KiB  
Article
Study on the Complexity Evolution of the Aviation Network in China
by Shuolei Zhou, Cheng Li and Shiguo Deng
Systems 2025, 13(7), 563; https://doi.org/10.3390/systems13070563 - 9 Jul 2025
Viewed by 281
Abstract
As China’s economy grows and travel demand increases, its aviation market has evolved to become the second-largest in the world. This study presents a pioneering analysis of China’s aviation network evolution (1990–2024) by integrating temporal dynamics into a network density matrix theory, addressing [...] Read more.
As China’s economy grows and travel demand increases, its aviation market has evolved to become the second-largest in the world. This study presents a pioneering analysis of China’s aviation network evolution (1990–2024) by integrating temporal dynamics into a network density matrix theory, addressing critical gaps in prior static network analyses. Unlike conventional studies focusing on isolated topological metrics, we introduce a triangulated methodology: ① a network sequence analysis capturing structural shifts in degree distribution, clustering coefficient, and path length; ② novel redundancy–entropy coupling quantifying complexity evolution beyond traditional efficiency metrics; and ③ economic-network coordination modeling with spatial autocorrelation validation. Key innovations reveal previously unrecognized dynamics: ① Time-embedded density matrices (ρ) demonstrate how sparsity balances information propagation efficiency (η) and response diversity, resolving the paradox of functional yet sparse connectivity. ② Redundancy–entropy synergy exposes adaptive trade-offs. Entropy (H) rises 18% (2000–2024), while redundancy (R) rebounds post-2010 (0.25→0.33), reflecting the strategic resilience enhancement after early efficiency-focused phases. ③ Economic-network coupling exhibits strong spatial autocorrelation (Morans I>0.16, p<0.05), with eastern China achieving “primary coordination”, while western regions lag due to geographical constraints. The empirical results confirm structural self-organization. Power-law strengthening, route growth exponentially outpacing cities, and clustering (C) rising 16% as the path length (L) increases, validating the hierarchical hub formation. These findings establish aviation networks as dynamically optimized systems where economic policies and topological laws interactively drive evolution, offering a paradigm shift from descriptive to predictive network management. Full article
(This article belongs to the Section Systems Practice in Social Science)
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14 pages, 3542 KiB  
Article
Study on Angular Velocity Measurement for Characterizing Viscous Resistance in a Ball Bearing
by Kyungmok Kim
Machines 2025, 13(7), 578; https://doi.org/10.3390/machines13070578 - 3 Jul 2025
Viewed by 266
Abstract
This article describes a machine vision-based method for measuring the angular velocity of a rotating disk to characterize the viscous resistance of a ball bearing. A bright marker was attached to a disk connected to a shaft supported by two ball bearings. Rotation [...] Read more.
This article describes a machine vision-based method for measuring the angular velocity of a rotating disk to characterize the viscous resistance of a ball bearing. A bright marker was attached to a disk connected to a shaft supported by two ball bearings. Rotation of the marker was recorded with a digital camera. A simple algorithm was developed to track the trajectory of the marker and calculate angular displacement of the disk. For accurate detection of the rotating marker, the algorithm employed Multi-Otsu thresholding and the Least Squares Method (LSM). Verification of the proposed method was carried out through a direct comparison between the predicted rotational speeds and measured ones by a commercial tachometer. It was demonstrated that the percentage error of the proposed method was less than 1.75 percent. The evolution of angular velocity after motor power-off was measured and found to follow an exponential decay law. The exponent was found to remain consistent regardless of the induced rotational speed. This proposed measurement method will offer a simple and accurate non-contact solution for monitoring angular velocity and characterizing the resistance of a bearing. Full article
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18 pages, 3139 KiB  
Article
Sliding Mode Thrust Control Strategy for Electromagnetic Energy-Feeding Shock Absorbers Based on an Improved Gray Wolf Optimizer
by Wenqiang Zhang, Jiayu Lu, Wenqing Ge, Xiaoxuan Xie, Cao Tan and Huichao Zhang
World Electr. Veh. J. 2025, 16(7), 366; https://doi.org/10.3390/wevj16070366 - 2 Jul 2025
Viewed by 189
Abstract
Owing to its high energy efficiency, regenerative capability, and fast dynamic response, the Electromagnetic Energy-Feeding Shock Absorber has found widespread application in automotive suspension control systems. To further improve thrust control precision, this study presents a sliding mode thrust controller designed using an [...] Read more.
Owing to its high energy efficiency, regenerative capability, and fast dynamic response, the Electromagnetic Energy-Feeding Shock Absorber has found widespread application in automotive suspension control systems. To further improve thrust control precision, this study presents a sliding mode thrust controller designed using an improved Gray Wolf Optimization algorithm. Firstly, an improved exponential reaching law is adopted, where a saturation function replaces the traditional sign function to enhance system tracking accuracy and stability. Meanwhile, a position update strategy from the particle swarm optimization (PSO) algorithm is integrated into the gray wolf optimizer (GWO) to improve the global search ability and the balance of local exploitation. Secondly, the improved GWO is combined with sliding mode control to achieve online optimization of controller parameters, ensuring system robustness while suppressing chattering. Finally, comparative analyses and simulation validations are conducted to verify the effectiveness of the proposed controller. Simulation results show that, under step input conditions, the improved GWO reduces the rise time from 0.0034 s to 0.002 s and the steady-state error from 0.4 N to 0.12 N. Under sinusoidal input, the average error is reduced from 0.26 N to 0.12 N. Under noise disturbance, the average deviation is reduced from 2.77 N to 2.14 N. These results demonstrate that the improved GWO not only provides excellent trajectory tracking and control accuracy but also exhibits strong robustness under varying operating conditions and random white noise disturbances. Full article
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18 pages, 1451 KiB  
Article
Sustainable Trajectory Tracking Control for Underactuated Ships Using Non-Singular Fast Terminal Sliding Mode Control
by Minjie Zheng, Qianqiang Chen, Yulai Su and Guoquan Chen
Sustainability 2025, 17(13), 5866; https://doi.org/10.3390/su17135866 - 26 Jun 2025
Viewed by 272
Abstract
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To [...] Read more.
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To address these challenges, this paper proposes a novel non-singular fast terminal sliding mode control (NFTSMC) strategy for sustainable trajectory tracking of underactuated ships. The proposed approach first designs a virtual control law based on surge and sway position errors, and then develops a non-singular fast terminal sliding mode control law using an exponential reaching strategy, guaranteeing finite-time convergence and eliminating singularities. The Lyapunov-based stability analysis proves the boundedness and convergence of tracking errors under external disturbances. The simulation results demonstrate that the proposed non-singular fast terminal sliding mode control outperforms traditional sliding mode control in terms of convergence speed, tracking accuracy, and control smoothness, especially under wind, wave, and current disturbances. Full article
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10 pages, 761 KiB  
Article
Football Games Consist of a Self-Similar Sequence of Ball-Keeping Durations
by Keiko Yokoyama, Hiroyuki Shima, Akifumi Kijima and Yuji Yamamoto
Fractal Fract. 2025, 9(7), 406; https://doi.org/10.3390/fractalfract9070406 - 24 Jun 2025
Viewed by 428
Abstract
In football, local interactions between players generate long-term game trends at the global scale, and vice versa—the global trends also influence individual decisions and actions. The harmonization of local and global scales often creates self-organizing spatiotemporal patterns in the movements of players and [...] Read more.
In football, local interactions between players generate long-term game trends at the global scale, and vice versa—the global trends also influence individual decisions and actions. The harmonization of local and global scales often creates self-organizing spatiotemporal patterns in the movements of players and the ball. In this study, we confirmed that, in real football games, the probability distribution of the ball-keeping duration tends to obey negative power-law behavior, exhibiting hierarchical fractal self-similarity at both the local scale (i.e., individual-player level) and at the global scale (i.e., whole-game level). Furthermore, we found that the probability distribution functions transitioned from an exponential distribution to a power-law distribution at a certain characteristic time and that the characteristic time was equal to the upper limit of the time during which the trend of the game was maintained. Full article
(This article belongs to the Section Life Science, Biophysics)
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