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28 pages, 4910 KB  
Article
Monitoring the Integrity and Vulnerability of Linear Urban Infrastructure in a Reclaimed Coastal City Using SAR Interferometry
by WoonSeong Jeong, Moon-Soo Song, Manik Das Adhikari and Sang-Guk Yum
Buildings 2025, 15(21), 3865; https://doi.org/10.3390/buildings15213865 (registering DOI) - 26 Oct 2025
Abstract
Reclaimed coastal areas are highly susceptible to uneven subsidence caused by the consolidation of soft marine deposits, which can induce differential settlement, structural deterioration, and systemic risks to urban infrastructure. Further, engineering activities, such as construction and loadings, exacerbate subsidence, impacting infrastructure stability. [...] Read more.
Reclaimed coastal areas are highly susceptible to uneven subsidence caused by the consolidation of soft marine deposits, which can induce differential settlement, structural deterioration, and systemic risks to urban infrastructure. Further, engineering activities, such as construction and loadings, exacerbate subsidence, impacting infrastructure stability. Therefore, monitoring the integrity and vulnerability of linear urban infrastructure after construction on reclaimed land is critical for understanding settlement dynamics, ensuring safe and reliable operation and minimizing cascading hazards. Subsequently, in the present study, to monitor deformation of the linear infrastructure constructed over decades-old reclaimed land in Mokpo city, South Korea (where 70% of urban and port infrastructure is built on reclaimed land), we analyzed 79 Sentinel-1A SLC ascending-orbit datasets (2017–2023) using the Persistent Scatterer Interferometry (PSInSAR) technique to quantify vertical land motion (VLM). Results reveal settlement rates ranging from −12.36 to 4.44 mm/year, with an average of −1.50 mm/year across 1869 persistent scatterers located along major roads and railways. To interpret the underlying causes of this deformation, Casagrande plasticity analysis of subsurface materials revealed that deep marine clays beneath the reclaimed zones have low permeability and high compressibility, leading to slow pore-pressure dissipation and prolonged consolidation under sustained loading. This geotechnical behavior accounts for the persistent and spatially variable subsidence observed through PSInSAR. Spatial pattern analysis using Anselin Local Moran’s I further identified statistically significant clusters and outliers of VLM, delineating critical infrastructure segments where concentrated settlement poses heightened risks to transportation stability. A hyperbolic settlement model was also applied to anticipate nonlinear consolidation trends at vulnerable sites, predicting persistent subsidence through 2030. Proxy-based validation, integrating long-term groundwater variations, lithostratigraphy, effective shear-wave velocity (Vs30), and geomorphological conditions, exhibited the reliability of the InSAR-derived deformation fields. The findings highlight that Mokpo’s decades-old reclamation fills remain geotechnically unstable, highlighting the urgent need for proactive monitoring, targeted soil improvement, structural reinforcement, and integrated InSAR-GNSS monitoring frameworks to ensure the structural integrity of road and railway infrastructure and to support sustainable urban development in reclaimed coastal cities worldwide. Full article
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25 pages, 48579 KB  
Article
Parametric Surfaces for Elliptic and Hyperbolic Geometries
by László Szirmay-Kalos, András Fridvalszky, László Szécsi and Márton Vaitkus
Mathematics 2025, 13(21), 3403; https://doi.org/10.3390/math13213403 (registering DOI) - 25 Oct 2025
Abstract
Background/Objectives: In computer graphics, virtual worlds are constructed and visualized through algorithmic processes. These environments are typically populated with objects defined by mathematical models, traditionally based on Euclidean geometry. However, there is increasing interest in exploring non-Euclidean geometries, which require adaptations of [...] Read more.
Background/Objectives: In computer graphics, virtual worlds are constructed and visualized through algorithmic processes. These environments are typically populated with objects defined by mathematical models, traditionally based on Euclidean geometry. However, there is increasing interest in exploring non-Euclidean geometries, which require adaptations of the modeling techniques used in Euclidean spaces. Methods: This paper focuses on defining parametric curves and surfaces within elliptic and hyperbolic geometries. We explore free-form splines interpreted as hierarchical motions along geodesics. Translation, rotation, and ruling are managed through supplementary curves to generate surfaces. We also discuss how to compute normal vectors, which are essential for animation and lighting. The rendering approach we adopt aligns with physical principles, assuming that light follows geodesic paths. Results: We extend the Kochanek–Bartels spline to both elliptic and hyperbolic geometries using a sequence of geodesic-based interpolations. Simple recursive formulas are introduced for derivative calculations. With well-defined translation and rotation in these curved spaces, we demonstrate the creation of ruled, extruded, and rotational surfaces. These results are showcased through a virtual reality application designed to navigate and visualize non-Euclidean spaces. Full article
23 pages, 2406 KB  
Article
Dynamic Hyperbolic Tangent PSO-Optimized VMD for Pressure Signal Denoising and Prediction in Water Supply Networks
by Yujie Shang and Zheng Zhang
Entropy 2025, 27(11), 1099; https://doi.org/10.3390/e27111099 (registering DOI) - 24 Oct 2025
Abstract
Urban water supply networks are prone to complex noise interference, which significantly degrades the performance of data-driven forecasting models. Conventional denoising techniques, such as standard Variational Mode Decomposition (VMD), often rely on empirical parameter selection or optimize only a subset of parameters, lacking [...] Read more.
Urban water supply networks are prone to complex noise interference, which significantly degrades the performance of data-driven forecasting models. Conventional denoising techniques, such as standard Variational Mode Decomposition (VMD), often rely on empirical parameter selection or optimize only a subset of parameters, lacking a robust mechanism for identifying noise-dominant components post-decomposition. To address these issues, this paper proposed a novel denoising framework termed Dynamic Hyperbolic Tangent PSO-optimized VMD (DHTPSO-VMD). The DHTPSO algorithm adaptively adjusts inertia weights and cognitive/social learning factors during iteration, mitigating the local optima convergence typical of traditional PSO and enabling automated VMD parameter selection. Furthermore, a dual-criteria screening strategy based on Variance Contribution Rate (VCR) and Correlation Coefficient Metric (CCM) is employed to accurately identify and eliminate noise-related Intrinsic Mode Functions (IMFs). Validation using pressure data from District A in Zhejiang Province, China, demonstrated that the proposed DHTPSO-VMD method significantly outperforms benchmark approaches (PSO-VMD, EMD, SABO-VMD, GWO-VMD) in terms of Signal-to-Noise Ratio (SNR), Mean Absolute Error (MAE), and Mean Square Error (MSE). Subsequent forecasting experiments using an Informer model showed that signals preprocessed with DHTPSO-VMD achieved superior prediction accuracy (R2 = 0.948924), underscoring its practical utility for smart water supply management. Full article
(This article belongs to the Section Signal and Data Analysis)
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32 pages, 1525 KB  
Article
Analysis of Acoustic Wave Propagation in Defective Concrete: Evolutionary Modeling, Energetic Coercivity, and Defect Classification
by Mario Versaci, Matteo Cacciola, Filippo Laganà and Giovanni Angiulli
Appl. Sci. 2025, 15(21), 11378; https://doi.org/10.3390/app152111378 - 23 Oct 2025
Viewed by 131
Abstract
This study introduces a theoretical and computational framework for modeling acoustic wave propagation in defective concrete, with applications to non-destructive testing and structural health monitoring. The formulation is based on a coupled system of evolutionary hyperbolic equations, where internal defects are explicitly represented [...] Read more.
This study introduces a theoretical and computational framework for modeling acoustic wave propagation in defective concrete, with applications to non-destructive testing and structural health monitoring. The formulation is based on a coupled system of evolutionary hyperbolic equations, where internal defects are explicitly represented as localized energetic sources or sinks. A key contribution is the definition of a coercivity coefficient, which quantifies the energetic effect of defects and enables their classification as stabilizing, neutral, or dissipative. The model establishes a rigorous relationship between defect morphology, spatial distribution, and the global energetic stability of the material. Numerical simulations performed with an explicit finite-difference time-domain scheme confirm the theoretical predictions: the normalized total energy remains above 95% for stabilizing defects (μi>0), decreases by about 10% for quasi-neutral cases (μi0), and drops below 50% within 200μs for dissipative defects (μi<0). The proposed approach reproduces the attenuation and phase behavior of classical Biot-type and Kelvin–Voigt models with deviations below 5% while providing a richer energetic interpretation of local defect dynamics. Although primarily theoretical, this study establishes a physically consistent and quantitatively validated framework that supports the development of predictive ultrasonic indicators for the energetic classification of defects in concrete structures. Full article
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18 pages, 3257 KB  
Article
Influence of Motive Nozzle Supersonic Part Profiling on the Effectiveness of the Vaporization Process: Experimental Results
by Serhii Sharapov, Danylo Husiev, Anton Verbytskiy, Roman Vaskin, Ivan Kozii, Leonid Plyatsuk, Iryna Vaskina, Dmytro Hopkalo and Yuliia Denysenko
Thermo 2025, 5(4), 44; https://doi.org/10.3390/thermo5040044 - 23 Oct 2025
Viewed by 121
Abstract
This article presents experimental results for motive nozzles with profiled supersonic parts of parabolic, hyperbolic, and elliptical shapes, compared to conical nozzles with unprofiled supersonic parts. This study examined the effect of nozzle geometry and profile on thermodynamic and flow parameters of the [...] Read more.
This article presents experimental results for motive nozzles with profiled supersonic parts of parabolic, hyperbolic, and elliptical shapes, compared to conical nozzles with unprofiled supersonic parts. This study examined the effect of nozzle geometry and profile on thermodynamic and flow parameters of the vaporization process. The measured parameters included outlet pressure, flow velocity, and mass vapor content, along with dimensionless efficiency indicators, such as relative outflow velocity and the velocity coefficient. Graphical dependencies of these parameters on the relative initial underheating, (1 − εs0), were obtained. This parameter represents the ratio of the pressure difference between inlet and saturation conditions (at inlet temperature) to the inlet pressure. The results show that profiled nozzles operate effectively over a wider range of (1 − εs0) = 0.20–0.45, compared to conical unprofiled nozzles. The vaporization constant for profiled nozzles remained at bn ≈ (2/3)0.5 along their length. The velocity coefficients for profiled designs were 4–6% higher, and the volumetric vapor content at the outlet was also greater, indicating a more efficient vaporization process. Overall, the findings demonstrate that profiling the supersonic section of a motive nozzle improves the operating range, flow characteristics, and vaporization quality compared to conventional conical designs. Full article
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25 pages, 5190 KB  
Article
An Automated System for Underground Pipeline Parameter Estimation from GPR Recordings
by Daniel Štifanić, Jelena Štifanić, Nikola Anđelić and Zlatan Car
Remote Sens. 2025, 17(20), 3493; https://doi.org/10.3390/rs17203493 - 21 Oct 2025
Viewed by 208
Abstract
Underground pipelines form a critical part of urban infrastructure, yet their complex configurations and fragmented documentation hinder efficient maintenance and risk management. Ground-penetrating radar provides a non-invasive method for subsurface inspection; however, traditional interpretation of B-scan data relies heavily on manual analysis, which [...] Read more.
Underground pipelines form a critical part of urban infrastructure, yet their complex configurations and fragmented documentation hinder efficient maintenance and risk management. Ground-penetrating radar provides a non-invasive method for subsurface inspection; however, traditional interpretation of B-scan data relies heavily on manual analysis, which is time-consuming and prone to error. This research proposes a two-step automated system for the detection and quantitative characterization of underground pipelines from GPR B-scans. In the first step, hyperbolic reflections are automatically detected and localized using state-of-the-art object detection algorithms, where YOLOv11x achieved superior stability compared to RT-DETR-X. In the second step, detected hyperbolic reflections are processed in order to estimate key parameters, including two-way travel time, burial depth, pipeline diameter, and the angle between GPR survey line and pipeline. Experimental results from 5-fold cross-validation demonstrate that TWTT and burial depth can be estimated with high performance, while pipeline diameter and angle exhibit moderate performance, reflecting their higher complexity and sensitivity to noise. According to the experimental results, EfficientNetV2L consistently produced the best overall performance. The proposed automated system reduces reliance on manual inspection, improves efficiency, and establishes a foundation for real-time, autonomous GPR-based underground infrastructure assessment. Full article
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22 pages, 9604 KB  
Article
Elliptic Functions and Advanced Analysis of Soliton Solutions for the Dullin–Gottwald–Holm Dynamical Equation with Applications of Mathematical Methods
by Syed T. R. Rizvi, Ibtehal Alazman, Nimra and Aly R. Seadawy
Symmetry 2025, 17(10), 1773; https://doi.org/10.3390/sym17101773 - 21 Oct 2025
Viewed by 102
Abstract
We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic (sech/tanh), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons [...] Read more.
We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic (sech/tanh), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons (bright and dark) arose as limiting cases of the elliptic solutions. We specified the parameter regimes that produced each profile and illustrated representative solutions with 2D/3D plots to highlight symmetry. The results provide a unified, reproducible procedure for generating solitary and periodic DGH waves and expand the catalog of exact solutions for this model. Full article
(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)
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25 pages, 9844 KB  
Article
Deep Learning and Geometric Modeling for 3D Reconstruction of Subsurface Utilities from GPR Data
by Peyman Jafary, Davood Shojaei and Krista A. Ehinger
Sensors 2025, 25(20), 6414; https://doi.org/10.3390/s25206414 - 17 Oct 2025
Viewed by 277
Abstract
Accurate underground utility mapping remains a critical yet complex task in Ground Penetrating Radar (GPR) interpretation, essential to avoiding costly and dangerous excavation errors. This study presents a novel deep learning-based pipeline for 3D reconstruction of buried linear utilities from high-resolution GPR B-scan [...] Read more.
Accurate underground utility mapping remains a critical yet complex task in Ground Penetrating Radar (GPR) interpretation, essential to avoiding costly and dangerous excavation errors. This study presents a novel deep learning-based pipeline for 3D reconstruction of buried linear utilities from high-resolution GPR B-scan data. Three state-of-the-art models—YOLOv8, YOLOv11, and Mask R-CNN—were employed for both bounding box and keypoint detection of hyperbolic reflections, using a real-world GPR dataset. On the test set, Mask R-CNN achieved the highest keypoint F1-score (0.822) and bounding box F1-score (0.867), outperforming the YOLO models. Detected summit points were clustered using a 3D DBSCAN algorithm to approximate the spatial trajectories of buried utilities. RANSAC-based line fitting was then applied to each cluster, yielding an average RMSE of 0.06 across all fitted 3D paths. The key innovation of this hybrid model lies in its use of real-world data (avoiding synthetic augmentation), direct summit point detection (beyond bounding box analysis), and a geometric 3D reconstruction pipeline. This approach addresses key limitations in prior studies, including poor generalizability to complex real-world scenarios and the reliance on full 3D data volumes. Our method offers a more practical and scalable solution for subsurface utility mapping in real-world settings. Full article
(This article belongs to the Section Radar Sensors)
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17 pages, 2475 KB  
Article
YOLO-LMTB: A Lightweight Detection Model for Multi-Scale Tea Buds in Agriculture
by Guofeng Xia, Yanchuan Guo, Qihang Wei, Yiwen Cen, Loujing Feng and Yang Yu
Sensors 2025, 25(20), 6400; https://doi.org/10.3390/s25206400 - 16 Oct 2025
Viewed by 380
Abstract
Tea bud targets are typically located in complex environments characterized by multi-scale variations, high density, and strong color resemblance to the background, which pose significant challenges for rapid and accurate detection. To address these issues, this study presents YOLO-LMTB, a lightweight multi-scale detection [...] Read more.
Tea bud targets are typically located in complex environments characterized by multi-scale variations, high density, and strong color resemblance to the background, which pose significant challenges for rapid and accurate detection. To address these issues, this study presents YOLO-LMTB, a lightweight multi-scale detection model based on the YOLOv11n architecture. First, a Multi-scale Edge-Refinement Context Aggregator (MERCA) module is proposed to replace the original C3k2 block in the backbone. MERCA captures multi-scale contextual features through hierarchical receptive field collaboration and refines edge details, thereby significantly improving the perception of fine structures in tea buds. Furthermore, a Dynamic Hyperbolic Token Statistics Transformer (DHTST) module is developed to replace the original PSA block. This module dynamically adjusts feature responses and statistical measures through attention weighting using learnable threshold parameters, effectively enhancing discriminative features while suppressing background interference. Additionally, a Bidirectional Feature Pyramid Network (BiFPN) is introduced to replace the original network structure, enabling the adaptive fusion of semantically rich and spatially precise features via bidirectional cross-scale connections while reducing computational complexity. In the self-built tea bud dataset, experimental results demonstrate that compared to the original model, the YO-LO-LMTB model achieves a 2.9% improvement in precision (P), along with increases of 1.6% and 2.0% in mAP50 and mAP50-95, respectively. Simultaneously, the number of parameters decreased by 28.3%, and the model size reduced by 22.6%. To further validate the effectiveness of the improvement scheme, experiments were also conducted using public datasets. The results demonstrate that each enhancement module can boost the model’s detection performance and exhibits strong generalization capabilities. The model not only excels in multi-scale tea bud detection but also offers a valuable reference for reducing computational complexity, thereby providing a technical foundation for the practical application of intelligent tea-picking systems. Full article
(This article belongs to the Section Smart Agriculture)
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25 pages, 23378 KB  
Article
Dispersive Soliton Solutions and Dynamical Analyses of a Nonlinear Model in Plasma Physics
by Alwaleed Kamel, Ali H. Tedjani, Shafqat Ur Rehman, Muhammad Bilal, Alawia Adam, Khaled Aldwoah and Mohammed Messaoudi
Axioms 2025, 14(10), 763; https://doi.org/10.3390/axioms14100763 - 14 Oct 2025
Viewed by 188
Abstract
In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research [...] Read more.
In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research aims to achieve three main objectives. First, we uncover soliton solutions of the coupled system in hyperbolic, trigonometric, and rational forms, both in single and combined expressions. These results are obtained using the extended rational sinh-Gordon expansion method and the GG,1G-expansion method. Second, we analyze the dynamic characteristics of the model by performing bifurcation and sensitivity analyses and identifying the corresponding Hamiltonian function. To understand the mechanisms of intricate physical phenomena and dynamical processes, we plot 2D, 3D, and contour diagrams for appropriate parameter values. We also analyze the bifurcation of phase portraits of the ordinary differential equations corresponding to the investigated partial differential equation. The novelty of this study lies in the fact that the proposed model has not been previously explored using these advanced methods and comprehensive dynamical analyses. Full article
(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)
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19 pages, 493 KB  
Article
Hyperbolic Discounting and Its Influence on Loss Tolerance: Evidence from Japanese Investors
by Yu Kuramoto, Aliyu Ali Bawalle, Mostafa Saidur Rahim Khan and Yoshihiko Kadoya
Risks 2025, 13(10), 202; https://doi.org/10.3390/risks13100202 - 14 Oct 2025
Viewed by 317
Abstract
Hyperbolic discounting, a key determinant of intertemporal behavior, captures individuals’ preferences for smaller immediate rewards over larger delayed ones. This study examined how hyperbolic discounting influences investment loss tolerance using a large-scale dataset of Japanese investors. Loss tolerance is defined as the extent [...] Read more.
Hyperbolic discounting, a key determinant of intertemporal behavior, captures individuals’ preferences for smaller immediate rewards over larger delayed ones. This study examined how hyperbolic discounting influences investment loss tolerance using a large-scale dataset of Japanese investors. Loss tolerance is defined as the extent of financial loss that an investor is willing to endure before changing their investment strategy. Although hyperbolic discounting shapes intertemporal investment decisions, its role in explaining loss tolerance remains largely unknown. Using a large dataset from the “Survey on Life and Money” comprising 107,294 observations and employing ordered probit regression, we found a significant negative relationship between hyperbolic discounting and investment loss tolerance: investors exhibiting stronger hyperbolic discounting are more likely to exit positions prematurely during market downturns, despite potential long-term recovery. The estimated marginal effect (−0.070 ***) underscores the economic significance of the association between hyperbolic discounting and loss tolerance. These results provide evidence that time-inconsistent preferences not only shape intertemporal choices but also reduce resilience to financial losses. The findings carry important implications for investors, highlighting the value of commitment mechanisms and education programs to counteract short-termism, and for policymakers seeking to design behavioral interventions that promote stable, long-term participation in financial markets. Full article
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15 pages, 3266 KB  
Article
Experimental and Numerical Research on p-y Curve of Offshore Photovoltaic Pile Foundations on Sandy Soil Foundation
by Sai Fu, Hongxin Chen, Guo-er Lv, Xianlin Jia and Xibin Li
J. Mar. Sci. Eng. 2025, 13(10), 1959; https://doi.org/10.3390/jmse13101959 - 13 Oct 2025
Viewed by 227
Abstract
While methods like cyclic triaxial testing and p-y model updating theory exist in geotechnical and offshore wind engineering, they have not been systematically applied to solve the specific deformation problems of offshore PV piles. This study investigates a specific offshore photovoltaic (PV) project [...] Read more.
While methods like cyclic triaxial testing and p-y model updating theory exist in geotechnical and offshore wind engineering, they have not been systematically applied to solve the specific deformation problems of offshore PV piles. This study investigates a specific offshore photovoltaic (PV) project in Qinhuangdao City, Hebei Province. Initially, field tests of horizontal static load on steel pipe pile foundations were conducted. A finite element model (FEM) of single piles was subsequently developed and validated. Further analysis examined the failure modes, initial stiffness, and ultimate resistance of offshore PV single piles in sandy soil foundations under varying pile diameters and embedment depths. The hyperbolic p-y curve model was modified by incorporating pile diameter size effects and embedment depth considerations. Key findings reveal the following: (1) The predominant failure mechanism of fixed offshore PV monopiles manifests as wedge-shaped failure in shallow soil layers. (2) Conventional API specifications and standard hyperbolic models demonstrate significant deviations in predicting p-y (horizontal soil resistance-pile displacement) curves, whereas the modified hyperbolic model shows good agreement with field measurements and numerical simulations. This research provides critical data support and methodological references for calculating the horizontal bearing capacity of offshore PV steel pipe pile foundations. Full article
(This article belongs to the Special Issue Advances in Offshore Foundations and Anchoring Systems)
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33 pages, 4092 KB  
Article
Lie Symmetry Analysis, Rogue Waves, and Lump Waves of Nonlinear Integral Jimbo–Miwa Equation
by Ejaz Hussain, Aljethi Reem Abdullah, Khizar Farooq and Syed Asif Ali Shah
Symmetry 2025, 17(10), 1717; https://doi.org/10.3390/sym17101717 - 13 Oct 2025
Viewed by 217
Abstract
In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wave structures. Additionally, precise solitary wave solutions [...] Read more.
In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wave structures. Additionally, precise solitary wave solutions of the extended (3 + 1)-dimensional Jimbo–Miwa equation using the multivariate generalized exponential rational integral function technique (MGERIF) are studied. The extended (3 + 1)-dimensional Jimbo–Miwa equation is crucial for studying nonlinear processes in optical communication, fluid dynamics, materials science, geophysics, and quantum mechanics. The multivariate generalized exponential rational integral function approach offers advantages in addressing challenges involving exponential, hyperbolic, and trigonometric functions formulated based on the generalized exponential rational function method. The solutions provided by MGERIF have numerous applications in various fields, including mathematical physics, condensed matter physics, nonlinear optics, plasma physics, and other nonlinear physical equations. The graphical features of the generated solutions are examined using 3D surface graphs and contour plots, with theoretical derivations. This visual technique enhances our understanding of the identified answers and facilitates a more profound discussion of their practical applications in real-world scenarios. We employ the MGERIF approach to develop a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study’s outcomes enhance both nonlinear dynamical processes and solitary wave theory. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Partial Differential Equations)
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28 pages, 6660 KB  
Article
Self-Regulating Fuzzy-LQR Control of an Inverted Pendulum System via Adaptive Hyperbolic Error Modulation
by Omer Saleem, Jamshed Iqbal and Soltan Alharbi
Machines 2025, 13(10), 939; https://doi.org/10.3390/machines13100939 - 12 Oct 2025
Viewed by 326
Abstract
This study introduces an innovative self-regulating intelligent optimal balancing control framework for inverted pendulum-type mechatronic platforms, designed to enhance reference tracking accuracy and improve disturbance rejection capability. The control procedure is synthesized by synergistically integrating a baseline Linear Quadratic Regulator (LQR) with a [...] Read more.
This study introduces an innovative self-regulating intelligent optimal balancing control framework for inverted pendulum-type mechatronic platforms, designed to enhance reference tracking accuracy and improve disturbance rejection capability. The control procedure is synthesized by synergistically integrating a baseline Linear Quadratic Regulator (LQR) with a fuzzy controller via a customized linear decomposition function (LDF). The LDF dissociates and transforms the LQR control law into compounded state tracking error and tracking error derivative variables that are eventually used to drive the fuzzy controller. The principal contribution of this study lies in the adaptive modulation of these compounded variables using reconfigurable tangent hyperbolic functions driven by the cubic power of the error signals. This nonlinear preprocessing of the input variables selectively amplifies large errors while attenuating small ones, thereby improving robustness and reducing oscillations. Moreover, a model-free online self-tuning law dynamically adjusts the variation rates of the hyperbolic functions through dissipative and anti-dissipative terms of the state errors, enabling autonomous reconfiguration of the nonlinear preprocessing layer. This dual-level adaptation enhances the flexibility and resilience of the controller under perturbations. The robustness of the designed controller is substantiated via tailored experimental trials conducted on the Quanser rotary pendulum platform. Comparative results show that the prescribed scheme reduces pendulum angle variance by 41.8%, arm position variance by 34.6%, and average control energy by 28.3% relative to the baseline LQR, while outperforming conventional fuzzy-LQR by similar margins. These results show that the prescribed controller significantly enhances disturbance rejection and tracking accuracy, thereby offering a numerically superior control of inverted pendulum systems. Full article
(This article belongs to the Special Issue Mechatronic Systems: Developments and Applications)
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26 pages, 4342 KB  
Article
Investigation into Anchorage Performance and Bearing Capacity Calculation Models of Underreamed Anchor Bolts
by Bin Zheng, Tugen Feng, Jian Zhang and Haibo Wang
Appl. Sci. 2025, 15(20), 10929; https://doi.org/10.3390/app152010929 - 11 Oct 2025
Viewed by 145
Abstract
Underreamed anchor bolts, as an emerging anchoring element in geotechnical engineering, operate via a fundamentally distinct load transfer mechanism compared with conventional friction type anchors. The accurate and reliable prediction of their ultimate bearing capacity constitutes a pivotal technological impediment to their broader [...] Read more.
Underreamed anchor bolts, as an emerging anchoring element in geotechnical engineering, operate via a fundamentally distinct load transfer mechanism compared with conventional friction type anchors. The accurate and reliable prediction of their ultimate bearing capacity constitutes a pivotal technological impediment to their broader engineering adoption. Firstly, this paper systematically elucidates the constituent mechanisms of underreamed anchor resistance and their progressive load transfer trajectory. Subsequently, in situ full-scale pull-out experiments are leveraged to decompose the load–displacement response throughout its entire evolution. The multi-stage development law and the underlying mechanisms governing the evolution of anchorage characteristics are thereby elucidated. Based on the experimental dataset, a three-dimensional elasto-plastic numerical model is rigorously established. The model delineates, at high resolution, the failure mechanism of surrounding soil mass and the spatiotemporal evolution of its three-dimensional displacement field. A definitive critical displacement criterion for the attainment of the ultimate bearing capacity of underreamed anchors is established. Consequently, analytical models for the ultimate side frictional stress and end-bearing capacity at the limit state are advanced, effectively circumventing the parametric uncertainties inherent in extant empirical formulations. Ultimately, characteristic parameters of the elasto-plastic branch of the load–displacement curve are extracted. An ultimate bearing capacity prognostic framework, founded on an optimized hyperbolic model, is established. Its superior calibration fidelity to the evolving load–displacement response and its demonstrable engineering applicability are rigorously substantiated. Full article
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