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15 pages, 1857 KB  
Article
Determining Water Content in Waste Sludge Cake by Time-Domain NMR
by Cengiz Okay, Irfan Basturk, Selda Murat Hocaoglu, Recep Partal, Georgy Mozzhukhin, Pavel Kupriyanov and Bulat Rameev
Environments 2026, 13(5), 253; https://doi.org/10.3390/environments13050253 - 1 May 2026
Abstract
The application of low-field time-domain nuclear magnetic resonance (TD-NMR) to measure water content and assess moisture-related relaxation behavior in sludge samples has been investigated. The results of TD-NMR measurements on 26 dewatered sludge samples revealed a strong correlation between sludge water content and [...] Read more.
The application of low-field time-domain nuclear magnetic resonance (TD-NMR) to measure water content and assess moisture-related relaxation behavior in sludge samples has been investigated. The results of TD-NMR measurements on 26 dewatered sludge samples revealed a strong correlation between sludge water content and key features of the T2 distribution curves, including the maximum relaxation time and peak area, demonstrating the potential of the TD-NMR method for estimating sludge moisture content. No consistent relationship was observed between the peaks in T2 relaxation distribution curves obtained by Inverse Laplace Transform (ILT) and the expected water fraction ratios, apparently because the sludge structure is highly variable from sample to sample. Despite the complex and heterogeneous nature of sludge samples, the direct correspondence between key features of the T2 relaxation curves and moisture content demonstrates the high potential of TD-NMR as a tool for rapid and reliable moisture monitoring, even in an online device configuration. Full article
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26 pages, 1827 KB  
Article
Pilot Study on the Use of Rheology and Low Field Nmr to Characterize the Liver of Obese Patients Undergoing Metabolic and Bariatric Surgery
by Alice Biasin, Silvia Palmisano, Michela Abrami, Deborah Bonazza, Fabrizio Zanconati, Domenico Tierno, Federica Tonon, Nhung Hai Truong, Thanh Dang Minh, Ralf Weiskirchen, Fulvia Felluga, Bruna Scaggiante, Mario Grassi and Gabriele Grassi
Int. J. Mol. Sci. 2026, 27(9), 4040; https://doi.org/10.3390/ijms27094040 - 30 Apr 2026
Abstract
Background and aims. Liver mechanical properties’ (stiffness/viscoelasticity) evaluation is relevant for diagnosing/monitoring liver fibrosis. Due to limitations of the commonly used elastography, we propose the use of rheology and Low Field-Nuclear Magnetic Resonance (LF-NMR). Methods. In 30 liver samples from patients undergoing [...] Read more.
Background and aims. Liver mechanical properties’ (stiffness/viscoelasticity) evaluation is relevant for diagnosing/monitoring liver fibrosis. Due to limitations of the commonly used elastography, we propose the use of rheology and Low Field-Nuclear Magnetic Resonance (LF-NMR). Methods. In 30 liver samples from patients undergoing bariatric surgery and 18 control samples, we evaluated the shear modulus G/critical stress τc (elastic properties) and mean complex modulus Ga* (elastic/viscous properties) by rheology. LF-NMR was used to measure the spin–spin relaxation time (T2m), reflecting iron content. The expression of iron-related proteins and of pro-fibrotic proteins were evaluated by qRT-PCR. Tissue histology was also determined. Results. Ga*/Gc were higher in pathological samples, which also showed increased expression of pro-fibrotic proteins. Fibrosis determination displayed a correspondence of 4/30 samples for elastography/histology and 17/30 for rheology/histology. T2m was significantly lower in pathological livers, indicating iron accumulation as confirmed by increased expression of iron-related proteins. T2m was more effective than histology in detecting iron. An inverse correlation was observed between T2m and Ga*/G showing that iron accumulation is associated with increased liver elasticity/viscoelasticity, i.e., fibrosis. Additionally, an inverse correlation of Ga*/G with transferrin, was observed. Conclusion. As our patients mostly have mild liver fibrosis, the combined use of rheology/LF-NMR can effectively detect early changes in liver mechanical properties, aiding in staging and diagnosis of fibrosis. Full article
(This article belongs to the Special Issue Liver Fibrosis: Molecular Pathogenesis, Diagnosis and Treatment)
46 pages, 1265 KB  
Article
Deterministic Q-Learning with Relational Game Theory: Polynomial-Time Convergence to Minimal Winning Coalitions in Symmetric Influence Networks and Extension
by Duc Nghia Vu and Janos Demetrovics
Mathematics 2026, 14(9), 1526; https://doi.org/10.3390/math14091526 - 30 Apr 2026
Abstract
This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties [...] Read more.
This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties of relational dependencies and Armstrong’s axioms to transform the problem into one solvable in polynomial time. Our framework reduces the state space from exponential O(2n) to O(n2) through a sufficient statistic representation based on coalition size, follower reach, and terminal status, while achieving O(n4) time complexity under deterministic, static, and sufficiently symmetric influence structures. The QLRG framework introduces three critical innovations: (1) a principled agent selection mechanism derived directly from the Q-function that eliminates heuristic weight tuning; (2) a formal Boost action defined through temporal closure operators that captures influence spread dynamics; and (3) a constrained MDP formulation that enforces relational consistency through action elimination rather than penalty terms. We prove that the Bellman optimality operator forms a contraction mapping, guaranteeing deterministic convergence to optimal policies with established rates of O(1/√k) for decreasing learning rates or linear convergence up to bias for constant rates. To bridge the gap between this idealized model and the asymmetry inherent in real OSNs, we further develop a cluster-based sufficient statistics approach. By partitioning the network into communities with bounded internal variation, we relax the global symmetry requirement while preserving polynomial state space complexity, and obtaining a single within-community swap changes the optimal Q-value by at most ε_i/(1−γ), which is a local Lipschitz continuity result. The implications of this are both theoretical and practical, and they form the bedrock for relaxing the global symmetry assumption in the QLRG framework. Empirical validation on synthetic networks satisfying the symmetry assumption demonstrates that QLRG consistently identifies minimal winning coalitions matching the optimal solutions found by exhaustive search, while operating with polynomial-time complexity. Unlike conventional approaches, our framework simultaneously satisfies four critical properties: deterministic convergence, policy optimality, minimal coalition identification, and computational tractability. The work bridges computational social science and operations research, providing a mathematically rigorous foundation for strategic decision-making in influencer marketing and coalition formation. While the framework requires symmetry assumptions that may only hold approximately in real-world OSNs, it establishes an idealized baseline for future extensions addressing stochasticity, dynamics, and partial observability. This research represents a paradigm shift from empirical improvements to theoretically grounded convergence guarantees for coalition formation problems, demonstrating how structural mathematical insights can transform intractable problems into efficiently solvable ones without sacrificing solution quality. Full article
24 pages, 1871 KB  
Article
Design and Analysis of Minimum-Weighted Connected Capacitated Vertex Cover Algorithms for Link Monitoring in IoT-Enabled WSNs
by Miray Kol, Ege Erberk Uslu, Zuleyha Akusta Dagdeviren and Orhan Dagdeviren
Sensors 2026, 26(9), 2752; https://doi.org/10.3390/s26092752 - 29 Apr 2026
Viewed by 91
Abstract
Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach [...] Read more.
Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach to protect against attacks, but energy, connectivity, and capacity constraints should be considered while picking monitor nodes. In this paper, we tackle the Minimum-Weighted Connected Capacitated Vertex Cover (MWCCVC) problem, which minimizes monitoring costs, ensures backbone connectivity, and adheres to per-node capacity constraints. Unlike prior works that consider weighted vertex cover, connectivity constraints, or capacitated variants separately, the proposed MWCCVC model jointly integrates all three dimensions within a single vertex cover-based monitoring framework. We first provide a Branch-and-Bound (B&B) solver with linear programming relaxation bounds and constraint-based pruning strategies that produces optimum solutions. Three constructive greedy heuristics (GD, GR, GW) and two hybrid genetic algorithms (HGA, HGA-v2) that combine parameterized greedy decoders with evolutionary search are proposed; all methods guarantee full edge coverage, induced-subgraph connectivity, and max-flow-validated capacity feasibility. Tests on 130 small, 160 medium, and 19 large benchmark instances show that HGA matches B&B optima on every small instance, beats the time-limited B&B by 6.6% on medium instances, where the percentage is computed based on the relative difference in average total weight with respect to B&B, and stays the best on large graphs with up to 1000 nodes. The HGA-v2 tries to balance the quality and speed, with only a 3.1% difference at 10× faster execution. Full article
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28 pages, 9613 KB  
Article
High-Frequency Skywave Source Geolocation Using Deep Learning-Based TDOA Estimation and Bias-Regularized Semidefinite Programming with Field Evaluation
by Chen Xu, Houlong Ai, Le He, Chaoyu Hu, Siyi Chen, Zhaoyang Li and Xijun Liu
Sensors 2026, 26(9), 2755; https://doi.org/10.3390/s26092755 - 29 Apr 2026
Viewed by 86
Abstract
High-frequency (HF) skywave propagation exploits ionospheric reflection for beyond-line-of-sight transmission, making time-difference-of-arrival (TDOA)-based geolocation a primary technique for localizing non-cooperative HF emitters. However, reliable TDOA estimation remains challenging due to time-varying ionospheric conditions, wideband multipath dispersion, and low signal-to-noise ratio (SNR). This paper [...] Read more.
High-frequency (HF) skywave propagation exploits ionospheric reflection for beyond-line-of-sight transmission, making time-difference-of-arrival (TDOA)-based geolocation a primary technique for localizing non-cooperative HF emitters. However, reliable TDOA estimation remains challenging due to time-varying ionospheric conditions, wideband multipath dispersion, and low signal-to-noise ratio (SNR). This paper proposes an integrated framework coupling realistic channel synthesis, deep learning-based TDOA estimation, and convex optimization-based localization. Three contributions are made. First, an improved wideband ionospheric channel model is constructed by integrating the International Reference Ionosphere (IRI) with region-specific calibration and a stochastic perturbation module, yielding time-varying multipath responses for physics-consistent waveform generation. Second, a convolutional neural network (CNN)-based TDOA estimator is designed to jointly exploit time-domain complex-baseband in-phase/quadrature (I/Q) waveforms, multi-weight generalized cross-correlation (GCC) feature maps, and channel-state information (CSI) within a unified regression network, achieving robust delay estimation under severe noise and multipath conditions. Third, the geolocation problem is formulated as a bias-regularized constrained least-squares problem with unknown ionospheric excess-delay surrogates, and a semidefinite programming (SDP) relaxation is derived to yield a tractable solution without prescribing a fixed virtual reflection height. Simulations show that the proposed estimator consistently outperforms competing algorithms across a wide SNR range and narrows the gap to the Cramér–Rao lower bound (CRLB) at high SNR. On field-recorded signals, the estimator reduces the mean absolute TDOA deviation by 51% relative to GCC with phase transform (GCC-PHAT), and the end-to-end pipeline achieves a mean geolocation error of 19.67 km across 100 field segments, outperforming all compared baselines. Full article
(This article belongs to the Special Issue Smart Sensor Systems for Positioning and Navigation: 2nd Edition)
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17 pages, 337 KB  
Article
Support Size of ε-Capacity-Achieving Inputs for the Amplitude-Constrained AWGN Channel
by Luca Barletta and Alex Dytso
Entropy 2026, 28(5), 500; https://doi.org/10.3390/e28050500 - 28 Apr 2026
Viewed by 87
Abstract
We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling [...] Read more.
We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling of its support size as a function of the amplitude constraint remains an open problem. In this work, we instead consider the minimal support size required to achieve capacity up to an ε-gap. We introduce the quantity Kε(A), defined as the smallest support size among discrete inputs supported on [A,A] that achieves mutual information within ε of capacity. We show that this relaxed formulation is significantly more tractable and admits sharp characterizations in several vanishing-gap regimes. In particular, for polynomially decaying gaps, ε=Aβ with β1, we establish that Kε(A)=Θ(AlogA) as A. For exponentially small gaps, we obtain bounds of order between AlogA and A3/2. Our approach combines approximation-theoretic bounds for Gaussian mixtures with information-theoretic control of entropy via χ2-divergence, together with a wrapping argument that relates the problem to approximating the uniform distribution on a circle. Beyond the technical results, our framework provides a conceptual explanation for the variety of scaling laws observed in prior numerical studies, suggesting that these may correspond to different regimes of ε-optimality rather than intrinsic properties of the exact optimizer. Full article
30 pages, 1724 KB  
Article
Second-Order Cone Programming Algorithm for Collaborative Optimization of Load Restoration Integrated with Electric Vehicles
by Dexiang Li, Ling Li, Huijie Sun, Milu Zhou, Zhijian Du and Jiekang Wu
Energies 2026, 19(9), 2123; https://doi.org/10.3390/en19092123 - 28 Apr 2026
Viewed by 83
Abstract
In response to the influence of extreme disasters, damage to distribution lines and user outages, a parallel implementation strategy is proposed for emergency repair of disaster-damaged distribution networks and rapid restoration of power supply for users, considering the collaboration of “human–vehicle–road–pile” resources. This [...] Read more.
In response to the influence of extreme disasters, damage to distribution lines and user outages, a parallel implementation strategy is proposed for emergency repair of disaster-damaged distribution networks and rapid restoration of power supply for users, considering the collaboration of “human–vehicle–road–pile” resources. This strategy constructs a hierarchical optimization framework, with the upper-level model aiming to minimize the repair time for disaster damage. It adopts a collaborative optimization approach between repair resources and transportation routes to quickly repair the connection between the distribution network and the main power network. In the lower-level model, a model predictive control mechanism is adopted to schedule electric vehicles (EVs) in Real-time as mobile energy storage systems, and vehicle-to-grid (V2G) service technology is used to provide an emergency power supply for key loads during the repair period, achieving parallel optimization of “repair–restoration”. Considering constraints such as emergency repair resources, time-varying transportation, electric vehicle scheduling and power management, charging pile capacity, power flow safety of the distribution network, and topology of the distribution network, second-order cone relaxation technology is adopted to improve solving efficiency. The simulation results show that compared with the traditional serial restoration strategy, the proposed strategy delivers a dual benefit: it significantly eliminates the power supply vacuum period without compromising the efficiency of emergency repair operations. Specifically, it increases weighted load restoration by 57.2% compared with traditional sequential methods and reduces the average outage time for key loads from 3.22 h to 0.5 h, effectively enhancing the resilience and restoration ability of the power supply guarantee of the distribution network. Full article
(This article belongs to the Section E: Electric Vehicles)
21 pages, 3121 KB  
Article
Study of Viscoelastic Characteristics of Polyacrylamide Solutions in Polymer Flooding of Heterogeneous Reservoirs
by Inzir Ramilevich Raupov, Ahmed Kone and Alexey Feinberg
Gels 2026, 12(5), 367; https://doi.org/10.3390/gels12050367 - 28 Apr 2026
Viewed by 101
Abstract
This study addresses the need for enhanced oil recovery (EOR) in mature reservoirs, particularly in Russian oil fields that have undergone prolonged production and exhibit declining performance. Among EOR techniques, polymer flooding remains one of the most widely applied and effective methods following [...] Read more.
This study addresses the need for enhanced oil recovery (EOR) in mature reservoirs, particularly in Russian oil fields that have undergone prolonged production and exhibit declining performance. Among EOR techniques, polymer flooding remains one of the most widely applied and effective methods following conventional waterflooding. In this work, the rheological and viscoelastic behavior of partially hydrolyzed polyacrylamide (HPAM) solutions and their impact on oil displacement efficiency in heterogeneous reservoirs were investigated. Two polymers with different molecular weights were evaluated using steady shear, oscillatory rheology, and one-dimensional core flooding experiments. The results revealed pronounced shear-thinning behavior, with viscosity increasing with polymer concentration and molecular weight. Viscoelasticity was observed only for the high-molecular-weight polymer, characterized by a well-defined linear viscoelastic region and relaxation behavior sensitive to pore size, salinity, and temperature. Core flooding experiments showed that waterflooding recovered 30–31% OOIP, while high-molecular-weight polymer injection increased recovery to ~62% OOIP. In contrast, low-molecular-weight polymer yielded only ~40% OOIP, whereas a combined injection strategy achieved up to 74–76% OOIP. These findings highlight the critical role of polymer molecular weight and viscoelasticity in improving sweep efficiency and enhancing oil recovery in heterogeneous reservoirs. Full article
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13 pages, 2003 KB  
Article
Respiratory Cycle Influence on Lumbosacral Muscle Function: A Tensiomyographic Analysis
by Anthony B. Trombetta, William J. Hanney, Abigail W. Anderson and Morey J. Kolber
Muscles 2026, 5(2), 30; https://doi.org/10.3390/muscles5020030 - 28 Apr 2026
Viewed by 82
Abstract
Background: Tensiomyography (TMG) offers a noninvasive means of evaluating skeletal muscle contractile properties, including muscle displacement (Dm), delay time (Td), contraction time (Tc), half-relaxation time (Tr), and sustain time (Ts). When applied to lumbosacral musculature, interpretation may be influenced by changes in muscle [...] Read more.
Background: Tensiomyography (TMG) offers a noninvasive means of evaluating skeletal muscle contractile properties, including muscle displacement (Dm), delay time (Td), contraction time (Tc), half-relaxation time (Tr), and sustain time (Ts). When applied to lumbosacral musculature, interpretation may be influenced by changes in muscle stiffness that occur across the respiratory cycle. Understanding these fluctuations is essential for improving measurement consistency and data interpretation. Methods: Thirty healthy young adults (mean ± SD age = 21.07 ± 1.55 years) underwent TMG assessment of the erector spinae (ES) and latissimus dorsi (LD) at four distinct lung volumes: end-tidal inspiratory volume (ETIV), end-tidal expiratory volume (ETEV), total lung capacity (TLC), and residual volume (RV). Visual cues were used to guide participants’ respiratory phases. Paired-samples t-tests compared TMG parameters across respiratory conditions. Results: For the ES, significant differences were observed in Dm, Tr, and Ts between ETIV and ETEV (p ≤ 0.05), ETIV and TLC (p ≤ 0.05), and ETEV and RV (p ≤ 0.05). No statistically significant differences were identified for the LD (p ≥ 0.12). Conclusions: Some erector spinae contractile properties vary across the respiratory cycle, which may affect TMG outcomes. The findings of this research lend belief to the idea that a standardized respiratory phase during data collection may improve the reliability and comparability of TMG measurements involving trunk musculature. Future research could address the negative findings for latissimus dorsi and further determine which muscles require respiratory standardization. Full article
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17 pages, 563 KB  
Article
A Deployable Engineering Framework for Olfactory-Induced Relaxation Assessment: Modular Architecture and Signal Processing Pipeline for Wearable EEG
by Chien-Yu Lu, Wei-Zhen Su, Tzu-Hung Chien and Chin-Wen Liao
Eng 2026, 7(5), 198; https://doi.org/10.3390/eng7050198 - 27 Apr 2026
Viewed by 199
Abstract
This paper presents a modular system architecture and an automated signal processing pipeline designed to quantify neurophysiological relaxation responses to fragrance using consumer-grade wearable electroencephalography (EEG). By integrating real-time data streaming via Open Sound Control (OSC) with a high-performance backend, the platform enables [...] Read more.
This paper presents a modular system architecture and an automated signal processing pipeline designed to quantify neurophysiological relaxation responses to fragrance using consumer-grade wearable electroencephalography (EEG). By integrating real-time data streaming via Open Sound Control (OSC) with a high-performance backend, the platform enables objective assessment of olfactory stimuli through a reproducible Sleep Readiness Index (SRI) derived from spectral power shifts. To mitigate the signal quality constraints inherent in portable hardware, the framework utilizes a robust suite of engineering controls, including zero-phase filtering and automated artifact rejection, ensuring data integrity across short-window trials. Validation through construct-level analysis of public sleep datasets and synthetic sensitivity testing confirms the index’s directional reliability, while runtime benchmarking demonstrates sub-millisecond compute times suitable for interactive wellness applications. Ultimately, this framework provides a transparent, auditable engineering scaffold that replaces subjective self-reports with a standardized, within-session proxy metric for comparative fragrance evaluation. Full article
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39 pages, 4668 KB  
Article
Mathematical Modeling of Learnable Discrete Wavelet Transform for Adaptive Feature Extraction in Noisy Non-Stationary Signals
by Jiaxian Zhu, Chuanbin Zhang, Zhaoyin Shi, Hang Chen, Zhizhe Lin, Weihua Bai, Huibing Zhang and Teng Zhou
Mathematics 2026, 14(9), 1457; https://doi.org/10.3390/math14091457 - 26 Apr 2026
Viewed by 120
Abstract
The mathematical characterization of non-stationary signals remains a significant challenge, particularly when impulsive components are obscured by high-dimensional noise and structural coupling. This paper proposes an application-driven mathematical methodology for a learnable discrete wavelet transform (LDWT) that combines classical multi-resolution analysis with task-optimized [...] Read more.
The mathematical characterization of non-stationary signals remains a significant challenge, particularly when impulsive components are obscured by high-dimensional noise and structural coupling. This paper proposes an application-driven mathematical methodology for a learnable discrete wavelet transform (LDWT) that combines classical multi-resolution analysis with task-optimized data-driven adaptivity. Rather than introducing entirely new foundational theory, our approach strategically relaxes constraints from orthogonal wavelet theory within the non-perfect reconstruction filter bank framework, enabling controlled spectral decomposition optimized for supervised fault diagnosis. We introduce a specialized regularization term based on the half-band property to ensure spectral complementarity and minimize cross-band correlation, while a Jacobian-based stabilization approach is formulated to ensure the convergence of filter coefficients during optimization. The proposed algorithmic architecture, LDBRFnet, features a dual-branch encoder system designed to capture the mathematical synergy between sub-band-level global statistics and time-domain local morphology. This dual-view representation effectively mitigates feature leakage and overconfidence in classification. Theoretical analysis and numerical experiments demonstrate that the learned filters satisfy the frequency-shift property and maintain robust spectral partitioning even under low signal-to-noise ratios. Validation on complex vibration datasets confirms that the framework achieves superior diagnostic accuracy (over 95.5%) and computational efficiency, reducing model parameters by 96.7% compared to state-of-the-art baselines. This work provides a generalizable mathematical approach for adaptive signal decomposition and robust pattern recognition in interdisciplinary applications. Full article
(This article belongs to the Special Issue Mathematical Modeling of Fault Detection and Diagnosis)
27 pages, 9156 KB  
Article
Physics-Driven Hybrid Framework for Vehicle State Estimation Using Residual Learning and Adaptive UKF
by Peng Zhou, Yanbin Zhou, Xi Sun, Ziming Li, Mingpu Liu and Ping Han
Appl. Sci. 2026, 16(9), 4230; https://doi.org/10.3390/app16094230 - 26 Apr 2026
Viewed by 121
Abstract
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical [...] Read more.
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical interpretability. This paper proposes a Physics-Driven Hybrid Estimation Framework (PD-HEF) to bridge this gap. First, a nonlinear nominal model is constructed as a physical skeleton, and dynamic residual equations are derived to define learning targets. Second, a Spatio-Temporal Feature Coupled Residual Network is designed to capture time-domain phase lag and compensate for spatial nonlinear deviations. Furthermore, a hybrid unscented Kalman filter is developed to inject predicted residuals into the sigma-point evolution. A Dual-Layer Adaptive Mechanism is also introduced to regulate trust weights based on innovation statistics. Joint simulations demonstrate that the proposed framework reduces the root mean square error by over 60% compared to traditional observers while satisfying real-time constraints. Full article
(This article belongs to the Section Mechanical Engineering)
18 pages, 1266 KB  
Article
A Compact Closed-Form Dynamic Hysteresis Model for Energy-Loss Prediction in Power Magnetic Components
by Yingjie Tang, Chayma Guemri and Matthew Franchek
Energies 2026, 19(9), 2078; https://doi.org/10.3390/en19092078 - 24 Apr 2026
Viewed by 193
Abstract
Magnetic hysteresis strongly influences energy dissipation and efficiency in power magnetic components under time-varying excitation. This work proposes a compact dynamic hysteresis model using a Hammerstein structure, consisting of a closed-form arctangent static operator followed by a first-order relaxation dynamic stage. The formulation [...] Read more.
Magnetic hysteresis strongly influences energy dissipation and efficiency in power magnetic components under time-varying excitation. This work proposes a compact dynamic hysteresis model using a Hammerstein structure, consisting of a closed-form arctangent static operator followed by a first-order relaxation dynamic stage. The formulation enables direct datasheet-based parameterization and avoids iterative differential solvers or distributed hysteron representations, resulting in low calibration effort and computational cost. The static hysteresis behavior is characterized using four static parameters directly identified from manufacturer B-H datasheets, while dynamic effects are captured using two global calibration parameters derived from datasheet loss curves. This formulation enables accurate reconstruction of major and minor hysteresis loops, while introducing frequency-dependent phase lag and dynamic loop opening. Model performance is evaluated under diverse excitations, including sinusoidal, amplitude-modulated, FORC and chirp signals, showing waveform deviations below 7.2% peak-to-peak NRMSE relative to classical hysteresis models. Energy-loss predictions are validated against manufacturer datasheet curves for ferrite material 3C90 across multiple frequencies, yielding a root-mean-square relative error of 8.3% with 89% of operating points within ±20% deviation. The proposed model provides a datasheet-driven framework for hysteresis and energy-loss prediction in power magnetic components. Full article
30 pages, 1007 KB  
Article
Field-Theoretic Derivation of the Constructal Law from Non-Equilibrium Thermodynamics
by Antonio F. Miguel
Symmetry 2026, 18(5), 732; https://doi.org/10.3390/sym18050732 - 24 Apr 2026
Viewed by 213
Abstract
Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic [...] Read more.
Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic state variable, represented by a time-dependent conductivity tensor. Using a variational approach grounded in non-equilibrium thermodynamics, we derive a general tensor evolution equation. Within this framework, macroscopic flow architecture emerges deterministically from the continuous competition between non-linear flux-induced accretion, linear entropic relaxation, and spatial smoothing. Scaling analysis reduces this dynamic to a tri-parameter dimensionless phase space: a morphogenic number driving structural growth, a structural diffusion number governing spatial coherence, and a stochastic intensity number providing the microscopic seeds for symmetry breaking. Our principal result is the analytical prediction of a critical bifurcation. When the local morphogenic number strictly exceeds unity, the system escapes its stable, isotropic configuration and branches into highly conductive, anisotropic architectures. We demonstrate the predictive validity and trans-scalar applicability of this continuum theory by mapping it to highly diverse phase transitions, successfully capturing phenomena ranging from microscopic aerosol agglomeration and microbial resistance, to macroscopic coral plasticity and crystal growth instabilities, and finally to the astrophysical launching of relativistic jets from black holes. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2026)
32 pages, 2487 KB  
Article
Harmonic Resonance Mechanism and Suppression Strategies for High-Voltage Cables with Frequency-Dependent Parameters
by Zhaoyu Qin, Yan Zhang, Yuli Wang, Ge Wang and Xiaoyi Cheng
Appl. Sci. 2026, 16(9), 4202; https://doi.org/10.3390/app16094202 (registering DOI) - 24 Apr 2026
Viewed by 134
Abstract
The increasing integration of nonlinear loads in modern power systems has made harmonic pollution a critical challenge to the operational safety of power cables. This study develops a frequency-dependent high-voltage cable system model using the ATP-EMTP (Alternative Transients Program-Electro Magnetic Transient Program) electromagnetic [...] Read more.
The increasing integration of nonlinear loads in modern power systems has made harmonic pollution a critical challenge to the operational safety of power cables. This study develops a frequency-dependent high-voltage cable system model using the ATP-EMTP (Alternative Transients Program-Electro Magnetic Transient Program) electromagnetic transient simulation platform, systematically investigating the amplification mechanisms and propagation characteristics of grounding currents under multi-type harmonic disturbances. A frequency-dependent parameter correction model is established by integrating the conductor skin effect and the dielectric relaxation properties of the insulation layers. This model incorporates the multi-structure combination among conductors, insulation, and metallic screen. It effectively overcomes the limitations of conventional lumped-parameter models in higher frequency harmonic analysis. Key findings are as follows: (1) The combined influence of harmonic frequency and amplitude leads to a grounding current amplification of up to 445 times (at 1950 Hz with 30% distortion level). Notably, current-source excitation produces significantly greater amplification than voltage-source excitation. (2) The distributed capacitance of long-distance cables (>8 km) exacerbates resonance risks within specific frequency bands (750–1250 Hz), resulting in a maximum harmonic amplification factor of 34.73 (observed for the 17th harmonic in a 15 km cable). (3) The contribution of voltage-source harmonics diminishes to less than 5% of the total current at high frequencies (≥1250 Hz), indicating a pattern of current-dominated harmonic superposition. Full article
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