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Search Results (278)

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Keywords = one-dimensional analytical model

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8 pages, 1166 KB  
Proceeding Paper
Heat Pipe-Assisted Air Cooling for Fuel Cells in Aviation: Heat Transfer Modeling and Design Modifications
by Friedrich Franke, Fabian Kramer, Markus Kober and Stefan Kazula
Eng. Proc. 2026, 133(1), 53; https://doi.org/10.3390/engproc2026133053 - 29 Apr 2026
Abstract
Decarbonizing air travel poses a major technological challenge, driven by the substantial power requirements of the drivetrain and the demanding weight and volume constraints of airborne systems. One promising avenue involves leveraging the high specific energy of hydrogen by designing compact, high-power fuel [...] Read more.
Decarbonizing air travel poses a major technological challenge, driven by the substantial power requirements of the drivetrain and the demanding weight and volume constraints of airborne systems. One promising avenue involves leveraging the high specific energy of hydrogen by designing compact, high-power fuel cell stacks to supply power for electric drivetrains. However, a key drawback of such propulsion architectures is the substantial heat generated within the fuel cells, which necessitates bulky and heavy thermal management systems to ensure safe and continuous operation. This study investigates a proposed air-based thermal management system, which operates by introducing pulsating heat pipes into the bipolar plates of a High-Temperature Polymer Electrolyte Membrane Fuel Cell (HT-PEM FC) stack. If proven to be feasible, heat pipe assisted air cooling may provide the benefit of reducing overall system complexity by decreasing the number of components in the thermal management system. To evaluate the thermal performance of the proposed system, a one-dimensional thermal model was initially developed in a previous study to describe the temperature distribution along the length of a heat pipe. Building upon this foundation, the present work extends the model by incorporating a two-dimensional Computational Fluid Dynamic (CFD) analysis to account for geometry-specific effects within the hexagonal design. Results indicate that the heat transfer from the hexagonal heat pipe geometry to the coolant air flow was marginally overestimated in previous analytical calculations. Revised heat transfer rates led to a shift in the predicted temperature distributions, resulting in the need for either increased external airflow, extended condenser sections, or reduced inlet temperatures to maintain target operating conditions. Although these adjustments may result in a slight increase in system mass and parasitic power consumption, the overall impact is limited, and the heat pipe-assisted air cooling approach remains theoretically feasible. Based on the results, design modifications are proposed and their impact on thermal performance is evaluated to address the challenges of heat rejection and temperature uniformity. A modification based on variation and optimization of PHP meander lengths was evaluated using the updated model and it significantly improved temperature homogeneity across the evaporator. Full article
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25 pages, 4382 KB  
Article
Spatio-Temporal Joint Network for Coupler Anomaly Detection Under Complex Working Conditions Utilizing Multi-Source Sensors
by Zhirong Zhao, Zhentian Jiang, Qian Xiao, Long Zhang and Jinbo Wang
Sensors 2026, 26(9), 2661; https://doi.org/10.3390/s26092661 (registering DOI) - 24 Apr 2026
Viewed by 610
Abstract
Owing to the intricate mechanical coupling characteristics and the considerable difficulty in extracting synergistic spatio-temporal features from high-dimensional sensor data under fluctuating alternating loads, this study proposes a robust anomaly detection framework that combines Normalized Mutual Information (NMI) and Spatio-Temporal Graph Neural Networks [...] Read more.
Owing to the intricate mechanical coupling characteristics and the considerable difficulty in extracting synergistic spatio-temporal features from high-dimensional sensor data under fluctuating alternating loads, this study proposes a robust anomaly detection framework that combines Normalized Mutual Information (NMI) and Spatio-Temporal Graph Neural Networks (STGNN). First, NMI is utilized to quantify the nonlinear physical coupling intensity among multi-source sensors, thereby filtering out weakly correlated noise and reconstructing the spatial topological structure of the coupler system. Subsequently, a deep learning architecture incorporating Graph Convolutional Networks (GCN), Gated Recurrent Units (GRU), and one-dimensional convolutional residual connections is developed to capture the dynamic evolutionary characteristics of equipment states across both spatial interactions and temporal sequences. Finally, based on the model’s health-state predictions, a moving average algorithm is introduced to smooth the residual sequences, and an anomaly early-warning baseline is established in conjunction with the 3σ criterion. Experimental validation conducted using field service data from heavy-haul trains demonstrates that, compared to conventional serial CNN and Long Short-Term Memory (LSTM) models, the proposed method exhibits superior fitting performance and robustness against noise, effectively reducing the false alarm rate within normal working intervals. In a real-world case study, the method successfully identified variations in spatial linkage features induced by local damage and triggered timely alerts. Notably, the spatial alarm nodes were highly consistent with the fatigue crack initiation sites identified through on-site magnetic particle inspection. This study provides a viable data-driven analytical framework for the condition monitoring and anomaly identification of critical load-bearing components in heavy-haul trains. Full article
(This article belongs to the Special Issue Deep Learning Based Intelligent Fault Diagnosis)
24 pages, 823 KB  
Article
Sentiment Dynamics in Signed Social Networks as a Diffusion Process
by Zhenpeng Li, Zhihua Yan and Xijin Tang
Fractal Fract. 2026, 10(5), 278; https://doi.org/10.3390/fractalfract10050278 - 22 Apr 2026
Viewed by 192
Abstract
Understanding how sentiment propagates in signed networks is crucial for uncovering mechanisms behind opinion polarization, trust formation, and information cocoons in digital communities. This paper investigates the generation of signed edges, representing positive or negative sentiments, in online social networks. We propose an [...] Read more.
Understanding how sentiment propagates in signed networks is crucial for uncovering mechanisms behind opinion polarization, trust formation, and information cocoons in digital communities. This paper investigates the generation of signed edges, representing positive or negative sentiments, in online social networks. We propose an analytical framework that models the dynamic growth of sentiment as a diffusion process. By introducing a walker on an infinite one-dimensional lattice, we derive a time-fractional diffusion equation that captures subdiffusive, normal diffusive, and superdiffusive behaviors. The model is empirically validated using two large-scale temporal signed networks: RedditHyperlinks and Bitcoin OTC. Our findings reveal that sentiment diffusion exhibits distinct regimes depending on the stage of network evolution, providing a foundation for further theoretical analysis and applications in signed social networks. Full article
19 pages, 4324 KB  
Article
Numerical Simulation of Natural Convection in Freezing Water Droplets Using OpenFOAM
by Paria Khosravifar, Anna-Lena Ljung and T. Staffan Lundström
Water 2026, 18(8), 949; https://doi.org/10.3390/w18080949 - 16 Apr 2026
Viewed by 418
Abstract
Droplet freezing on cold surfaces plays a critical role in icing phenomena and thermal management systems. In this study, a numerical model is developed to investigate the freezing of a single water droplet, with emphasis on the influence of natural convection on internal [...] Read more.
Droplet freezing on cold surfaces plays a critical role in icing phenomena and thermal management systems. In this study, a numerical model is developed to investigate the freezing of a single water droplet, with emphasis on the influence of natural convection on internal flow dynamics. A two-phase (water–ice) solver is implemented in OpenFOAM by incorporating an enthalpy–porosity solidification model and a buoyancy model into an existing framework. The solver is verified against the analytical solution of the one-dimensional Stefan problem and validated using benchmark cases of natural convection and solidification in a cavity. Using the validated model, we examine the effects of natural convection and water density inversion on the internal flow behavior during droplet freezing. Simulations are performed for a rigid axisymmetric droplet configuration. By accounting for density inversion in the buoyancy source term, the model successfully captures the experimentally observed reversal of internal flow during freezing. The results indicate that the flow reversal occurs when the maximum droplet temperature approaches the density inversion temperature of water. While early-stage freezing follows the classical Stefan solution, comparisons with experimental data indicate that incorporating droplet impact and heat transfer to the surroundings would further enhance the model’s predictive capability. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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25 pages, 4225 KB  
Article
Canonical Spectral Transformation for Raman Spectra Enables High Accuracy AI Identification of Marine Microplastics
by Oscar Ramsés Ruiz-Varela, José Juan García-Sánchez, Roberto Narro-García, Claudia Georgina Nava-Dino, Juan Pablo Flores-De los Ríos, Luis Fernando Gaxiola-Orduño, Alain Manzo-Martínez and María Cristina Maldonado-Orozco
Microplastics 2026, 5(2), 71; https://doi.org/10.3390/microplastics5020071 - 13 Apr 2026
Viewed by 359
Abstract
The growing accumulation of microplastics in marine environments demands fast and accurate analytical methods for polymer identification. This study presents a new canonical spectral transformation (CST) strategy designed to extract the most relevant information of Raman spectra and enhance the performance of artificial [...] Read more.
The growing accumulation of microplastics in marine environments demands fast and accurate analytical methods for polymer identification. This study presents a new canonical spectral transformation (CST) strategy designed to extract the most relevant information of Raman spectra and enhance the performance of artificial intelligence (AI) models in the classification of microplastics. Using the Marine Plastic Database (MPDB) as the source of Raman spectra, five supervised models—k-Nearest Neighbor (KNN), Random Forest (RF), Extreme Gradient Boosting (XGBoost), Multilayer Perceptron (MLP), and a one-dimensional Convolutional Neural Network (CNN-1D)—were trained and evaluated under both typical (conventional methodology) and CST workflows using 500 noisy samples per category. The CST consists of representing a Raman spectra in a vector where only the magnitude peaks of the most relevant frequency bands of the spectra are retained and the remaining values are null. This CST minimizes the inclusion of non-target data reaching the AI models. All models achieved higher accuracy with CST, where CNN-1D achieved the most significant performance, increasing accuracy to 0.90. In addition, CNN-1D identified Polystyrene (PS) and Poly(methyl methacrylate) (PMMA) with a score of 100% and 99%, respectively. The results demonstrate that CST effectively enhances spectral feature extraction and can be generalized to other spectroscopic techniques, providing a scalable framework for AI-assisted microplastic identification in seawater samples. Full article
(This article belongs to the Collection Feature Papers in Microplastics)
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29 pages, 6490 KB  
Article
A Closed-Form Inverse Kinematic Analytical Method for a Humanoid Seven-DOF Redundant Manipulator
by Guojun Zhao, Ben Ye, Yunlong Tian, Juntong Yun, Du Jiang and Bo Tao
Machines 2026, 14(4), 395; https://doi.org/10.3390/machines14040395 - 4 Apr 2026
Viewed by 344
Abstract
Humanoid manipulators with kinematic redundancy offer enhanced dexterity and adaptability to complex environments. Solving their inverse kinematics (IK) is fundamental to trajectory tracking, motion planning, and real-time control. Conventional Jacobian-based iterative methods are widely used, but they are often sensitive to the initial [...] Read more.
Humanoid manipulators with kinematic redundancy offer enhanced dexterity and adaptability to complex environments. Solving their inverse kinematics (IK) is fundamental to trajectory tracking, motion planning, and real-time control. Conventional Jacobian-based iterative methods are widely used, but they are often sensitive to the initial guess, computationally expensive, and less effective in handling strict constraints. Arm-angle-based analytical parameterization reduces redundancy resolution to a single parameter. However, joint limits may lead to multiple disconnected feasible arm-angle intervals. Many existing methods still depend on a numerical search or intelligent optimization to select the arm angle. This lowers computational efficiency and provides less explicit control over branch and configuration selection. To address these issues, this paper extends the arm-angle analytical IK framework. It introduces global configuration parameters to explicitly control the shoulder-elbow-wrist configuration. It also completes the analytical derivation of the rotational relationships of the first three joints in the reference plane. In addition, a feasibility determination and modeling scheme for the arm-angle domain is established, which covers disconnected feasible intervals. The IK problem is then reformulated as a one-dimensional optimization over the feasible domain. An efficient interval-based search is employed to determine the optimal arm angle. Experimental results demonstrate high accuracy and interference-free trajectory tracking. Comparative tests on randomly sampled target poses are also performed. The results show more concentrated error distributions, shorter average computation time, and higher success rates. These results confirm the advantages of the proposed method in accuracy, robustness, and real-time performance. Full article
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23 pages, 1817 KB  
Article
The Construction and Validation of a Distributed Xin’anjiang Model for Hilly Areas Considering Non-Steady-State Evaporation
by Qifeng Song, Xi Chen and Zhicai Zhang
Water 2026, 18(7), 845; https://doi.org/10.3390/w18070845 - 1 Apr 2026
Viewed by 321
Abstract
This paper uses actual evaporation and phreatic evaporation as the upper and lower boundary fluxes, respectively. It considers the exponential change in hydraulic conductivity with depth and uses the one-dimensional Richards equation to perform vertical discretization calculations on the soil to determine soil [...] Read more.
This paper uses actual evaporation and phreatic evaporation as the upper and lower boundary fluxes, respectively. It considers the exponential change in hydraulic conductivity with depth and uses the one-dimensional Richards equation to perform vertical discretization calculations on the soil to determine soil water deficit. A semi-analytical solution method is employed to accelerate the calculation speed. Based on the relationship between groundwater depth and topographic index, the spatial distribution of soil water deficit is obtained from the spatial distribution of the topographic index. This leads to the development of a new distributed Xin’anjiang model for hilly areas that considers non-steady-state evaporation. The model is applied to simulate soil moisture content in the typical Tarrawarra catchment and compared with the storage capacity model and the DHSVM model. It is found that the new distributed Xin’anjiang model developed in this paper shows significantly better performance in simulating soil moisture content than the storage capacity model and the DHSVM model. The new distributed Xin’anjiang model developed in this paper takes into account the physical mechanisms, calculation speed, and computational accuracy. It also considers the hydrodynamic characteristics of the unsaturated zone and the impact of non-steady-state evaporation. Full article
(This article belongs to the Section Hydrology)
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18 pages, 1685 KB  
Article
Symmetric Element Stiffness and Symplectic Integration for Eringen’s Integral Nonlocal Rods: Static Response and Higher-Order Vibrations
by Zheng Yao, Changliang Zheng and Lulu Wen
Symmetry 2026, 18(4), 571; https://doi.org/10.3390/sym18040571 - 27 Mar 2026
Viewed by 280
Abstract
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration [...] Read more.
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration framework for Eringen’s two-phase (local/nonlocal mixture) integral model by embedding the constitutive operator into a Hamiltonian formulation and discretizing the influence domain in a belt-wise manner. A step-increase strategy was incorporated to allow flexible spatial marching while preserving the geometric (symplectic) structure of the transfer operation. In addition, a symmetry-explicit, element-level stiffness representation was derived for the discretized integral operator; it exposes a mirrored long-range coupling pattern and enables symmetric, energy-consistent assembly. The resulting kernel-agnostic algorithm accommodates both smooth and finite-range kernels. Static benchmarks and longitudinal vibrations are investigated for exponential, Gaussian, and triangular kernels over representative length ratios and mixture parameters. Comparisons with available analytical and asymptotic solutions show good agreement within their validity ranges, and the method yields stable higher-order eigenfrequencies when asymptotic expansions may be unreliable. The current study is limited to a linear one-dimensional rod setting, and validation is restricted to published analytical/asymptotic solutions rather than experimental calibration. Full article
(This article belongs to the Section Engineering and Materials)
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29 pages, 7087 KB  
Systematic Review
From the Reality–Virtuality Continuum to the XR Ecosystem: A Systematic Literature Review of Definitions and Conceptual Models
by Xiaoran Han, Teijo Lehtonen and Tuomas Mäkilä
Multimodal Technol. Interact. 2026, 10(3), 24; https://doi.org/10.3390/mti10030024 - 2 Mar 2026
Cited by 1 | Viewed by 964
Abstract
Extended Reality (XR) technologies are rapidly reshaping human–computer interaction; however, persistent ambiguity in the use of core terms (VR, AR, MR) hampers cumulative knowledge building, cross-study comparability, and technical standardisation. This review evaluates the XR conceptual landscape across four primary dimensions: the historical [...] Read more.
Extended Reality (XR) technologies are rapidly reshaping human–computer interaction; however, persistent ambiguity in the use of core terms (VR, AR, MR) hampers cumulative knowledge building, cross-study comparability, and technical standardisation. This review evaluates the XR conceptual landscape across four primary dimensions: the historical evolution of core definitions, the synthesis of contemporary theoretical frameworks, the critical extensions of the Reality-Virtuality (RV) Continuum, and the alignment between academic taxonomies and industry practices. This review evaluates the XR conceptual landscape across four primary dimensions: the historical evolution of core definitions, the synthesis of contemporary theoretical frameworks, the critical extensions of the Reality-Virtuality (RV) Continuum, and the alignment between academic taxonomies and industry practices. To address this issue, we conducted a PRISMA-guided systematic literature review across four major databases (IEEE Xplore, ACM Digital Library, Scopus, and Web of Science), complemented by seminal and industry sources. Of the 173,677 retrieved records, 59 studies were included in the synthesis. Using thematic synthesis, we mapped the historical evolution of definitions and conceptual models and identified recurring analytical dimensions. The results indicate a clear paradigm shift from Milgram’s one-dimensional Reality–Virtuality continuum—originally grounded in visual display technology—towards a multidimensional conceptual space that integrates subjective user-experience constructs (e.g., coherence and plausibility) with objective system characteristics. The included studies cover 1968–2025, with marked acceleration in the 2020s: 2022 alone accounts for the highest annual count (9 studies), and nearly half of the corpus (47.5%) was published in 2021–2025. We further show that industry actors pragmatically re-bound these academic concepts for product and market positioning, leading to systematic divergences between academic and industrial definitions. By distilling key turning points and synthesising core analytical dimensions into a structured lens, this review provides a historically grounded, actionable understanding of the XR conceptual landscape to support terminological alignment across research and practice. Full article
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17 pages, 2253 KB  
Article
A New Hydrogen Filling Method Based on the Analytical Solutions of Final Filling Time and Hydrogen Temperature
by Shanshan Deng, Hao Luo, Chenglong Li, Xianhuan Wu, Xu Wang, Tianqi Yang and Jinsheng Xiao
Energies 2026, 19(5), 1177; https://doi.org/10.3390/en19051177 - 26 Feb 2026
Viewed by 367
Abstract
To fill hydrogen fuel cell vehicles quickly and safely, the SAE J2601 protocol has published the MC method, which includes control of the filling speed and pressure target. The filling speed depends on the final filling time, the formula for which is obtained [...] Read more.
To fill hydrogen fuel cell vehicles quickly and safely, the SAE J2601 protocol has published the MC method, which includes control of the filling speed and pressure target. The filling speed depends on the final filling time, the formula for which is obtained by fitting simulated data. The pressure target depends on the final hydrogen temperature, whose analytical solution is derived from a thermodynamic tank model. This article derives new analytical solutions of the final filling time and hydrogen temperature based on an established lumped-parameter model of the storage tank. Based on the original MC method’s control logic, a new filling method that directly uses the analytical solutions of the final filling time and hydrogen temperature was proposed. The simulation results of the new filling method and the validated model (zone-dimensional gas and a one-dimensional tank wall, 0D1D) are compared. Under the ambient temperature conditions of the 0–20 °C and precooling temperature conditions of −20–0 °C set in this article, results show that the new filling method achieves maximum errors of 4.3 °C in its final hydrogen temperature and 0.9% in a state of charge (SOC) compared to the 0D1D model. Parameter sensitivity analysis reveals that initial pressure has the most significant impact on computational accuracy, followed by ambient and precooling temperatures. Future work may further improve prediction accuracy by incorporating correction factors for initial pressure and ambient temperature. Moreover, since the analytical solution of the final hydrogen temperature inherently includes the precooling temperature parameter, the new filling method can automatically adapt to precooling temperature variations. Full article
(This article belongs to the Special Issue Advances in New Mobility for Electric Vehicles)
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29 pages, 7039 KB  
Article
A Simplified Theoretical Model for Progressive Collapse Resistance of Steel Girders: Focusing on Load–Displacement Behavior Under Three Concentrated Loads
by Ye Li, TaeSoo Kim, SangYun Lee and SamYoung Noh
Buildings 2026, 16(5), 914; https://doi.org/10.3390/buildings16050914 - 25 Feb 2026
Viewed by 343
Abstract
Progressive collapse is characterized by disproportionate structural failure triggered by localized damage, such as column loss under extreme loading conditions. The objective of this study is to develop a simplified analytical model that is applicable in engineering practice without the need for high-fidelity [...] Read more.
Progressive collapse is characterized by disproportionate structural failure triggered by localized damage, such as column loss under extreme loading conditions. The objective of this study is to develop a simplified analytical model that is applicable in engineering practice without the need for high-fidelity nonlinear finite element analysis. Although current design guidelines (GSA and DoD) provide analytical procedures and acceptance criteria, they do not explicitly address the tensile resistance of girders after the acceptance criteria are satisfied, particularly under large deformation and connection failure. To address this limitation, this study proposes a simplified theoretical load–displacement model for a fixed-end girder subjected to three concentrated loads, considering the effects of secondary beams and focusing on the local girder response under a column-removal scenario. The proposed model incorporates moment–axial force interactions at plastic sections in the large-deformation range. Based on one-dimensional finite element analysis results, an early-developed axial force of 0.15Fp at the onset of the transition stage and a residual bending moment of 0.3Mp during the catenary action stage are explicitly introduced to better represent actual structural behavior. The girder response is idealized using five characteristic points: yielding (Y), full plasticity (P), transition initiation (T), pure catenary action initiation (C), and collapse governed by connection failure (Fconn). Stress distributions at plastic sections are analyzed using three-dimensional finite element models to establish stress-based formulations and a rational procedure for estimating axial force at collapse. The validity of the proposed model is verified through comparisons with finite element analysis results for girders with different span-to-depth ratios. The results demonstrate reasonable agreement in terms of collapse load and displacement, particularly for slender girders, confirming the applicability of the proposed model for progressive collapse assessment. Full article
(This article belongs to the Section Building Structures)
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22 pages, 2414 KB  
Article
The Algebra of Chebyshev Polynomials and the Transfer-Matrix Approach for the One-Dimensional Ising Model with a Defect
by Nicholay S. Tonchev and Daniel Dantchev
Mathematics 2026, 14(4), 741; https://doi.org/10.3390/math14040741 - 23 Feb 2026
Viewed by 399
Abstract
We investigate a random field of mutually dependent random variables (“spins”), indexed by a finite one-dimensional lattice, called in physical sciences the one-dimensional Ising model, in which the random variables can take only ±1 values (see the text for a precise definition). One [...] Read more.
We investigate a random field of mutually dependent random variables (“spins”), indexed by a finite one-dimensional lattice, called in physical sciences the one-dimensional Ising model, in which the random variables can take only ±1 values (see the text for a precise definition). One of the couplings, termed a “bond,” that describes the mutual influence of two adjacent random variables is altered—it does not equal the others, thereby introducing a single “defect” bond. This defect bond represents a localised perturbation within an otherwise uniform system. Utilising the recurrence relations of Chebyshev polynomials and the bijective map between the number of spins and the polynomial index, we present a new method for calculations and systematically explore, using it, the system’s properties across different chain lengths and boundary conditions. As an application, we derive analytical expressions for the dependence of the average values of the random variables on their position within the chain, which we refer to as the “local magnetisation profile”. From the findings related to the system with a defect bond, we present a novel result for this profile under free (Dirichlet) boundary conditions and re-derive the corresponding result for antiperiodic boundary conditions. Full article
(This article belongs to the Section E4: Mathematical Physics)
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19 pages, 563 KB  
Article
Probing Phase Transitions of Finite Directed Polymers near a Corrugated Wall via Two-Replica Analysis
by Ruijie Xu and Sergei Nechaev
Entropy 2026, 28(2), 190; https://doi.org/10.3390/e28020190 - 9 Feb 2026
Viewed by 317
Abstract
We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an N-step directed one-dimensional random walk on the half-line x0. Its interaction with the [...] Read more.
We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an N-step directed one-dimensional random walk on the half-line x0. Its interaction with the wall is described by a quenched, site-dependent, short-ranged random potential uj (j=1,,N), distributed according to Q(uj) and localized at x=0. By computing the first two disorder-averaged moments of the partition function, GN and GN2, and by analyzing the analytic structure of the resulting expressions, we derive an explicit criterion for the coincidence or distinction of the pinning transitions in annealed and quenched systems. We show that, although the transition points of the annealed and quenched systems are always different in the thermodynamic limit, for finite systems there exists a “gray zone” in which this difference is hardly detectable. Our results may help reconcile conflicting views on whether quenched disorder is marginally relevant. Full article
(This article belongs to the Section Statistical Physics)
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30 pages, 13680 KB  
Article
Multi-Dimensional Detection Capability Analysis of Surface and Surface-to-Tunnel Transient Electromagnetic Methods Based on the Spectral Element Method
by Danyu Li, Xin Huang, Xiaoyue Cao, Liangjun Yan, Zhangqian Chen and Qingpu Han
Appl. Sci. 2026, 16(3), 1560; https://doi.org/10.3390/app16031560 - 4 Feb 2026
Viewed by 289
Abstract
The transient electromagnetic (TEM) method is a key detection and monitoring technology for safe coal-mine production. Surface TEM depth penetration is limited by real geological conditions and transmitter–receiver hardware performance. Compared with the surface TEM method, the tunnel TEM method can enhance the [...] Read more.
The transient electromagnetic (TEM) method is a key detection and monitoring technology for safe coal-mine production. Surface TEM depth penetration is limited by real geological conditions and transmitter–receiver hardware performance. Compared with the surface TEM method, the tunnel TEM method can enhance the depth of exploration to some extent, but it is constrained by the limited working space of the roadway, which makes it difficult to perform the area-wide and multi-line data acquisition, and thus the lateral detection resolution is directly compromised. Consequently, either surface or tunnel TEM alone suffers inherent limitations. The multidimensional surface and surface-to-tunnel TEM method employs a single large-loop transmitter and records electromagnetic (EM) signals both on the surface and in the tunnel, enabling joint data interpretation. The joint TEM observation method effectively addresses the limitations by using a single observation mode, with the goal of achieving high-precision detection. To investigate the detection capabilities of the joint surface and surface-to-tunnel TEM method, we propose a three-dimensional (3D) joint surface and surface-to-tunnel TEM forward modeling method based on the spectral element method (SEM). The SEM, using high-order vector basis functions, enables high-precision modeling of TEM responses with complex geo-electric earth models. The accuracy of the SEM is validated through comparisons with one-dimensional (1D) TEM semi-analytical solutions. To further reveal TEM response characteristics and multi-dimensional resolution under joint surface and tunnel detection modes, we construct several typical 3D geo-electric earth models and apply the SEM algorithm to simulate the TEM responses. We systematically analyze the horizontal and vertical resolution of 3D earth model targets at different decay times. The numerical results demonstrate that surface multi-line TEM surveying can accurately delineate the lateral extent of the target body, while vertical in-tunnel measurements are crucial for identifying the top and bottom interfaces of geological targets adjacent to the tunnel. Finally, the theoretical modeling results demonstrate that compared to individual TEM methods, the multi-dimensional joint surface and tunnel TEM observation yields superior target spatial information and markedly improves TEM detection efficacy under complex conditions. The 3D TEM forward modeling based on the SEM provides the theoretical foundation for subsequent 3D inversion and interpretation of surface-to-surface and surface-to-tunnel joint TEM data. Full article
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25 pages, 506 KB  
Article
Solution Dynamics of the (1 + 1)-Dimensional Fisher’s Equation Using Lie Symmetry Analysis
by Phillipos Masindi and Lazarus Rundora
Symmetry 2026, 18(2), 279; https://doi.org/10.3390/sym18020279 - 3 Feb 2026
Viewed by 549
Abstract
Reaction–diffusion equations provide a fundamental framework for modelling spatial population dynamics and invasion processes in mathematical biology. Among these, Fisher’s equation combines diffusion with logistic growth to describe the spread of an advantageous gene and the formation of travelling population fronts. In this [...] Read more.
Reaction–diffusion equations provide a fundamental framework for modelling spatial population dynamics and invasion processes in mathematical biology. Among these, Fisher’s equation combines diffusion with logistic growth to describe the spread of an advantageous gene and the formation of travelling population fronts. In this work, we investigate the one-dimensional Fisher’s equation using Lie symmetry analysis to obtain a deeper analytical understanding of its wave propagation behaviour. The Lie point symmetries of the partial differential equation are derived and used to construct similarity variables that reduce Fisher’s equation to ordinary differential equations. These reduced equations are then solved by a combination of direct integration and the tanh method, yielding explicit invariant and travelling-wave solutions. Symbolic computations in MAPLE are employed to compute the symmetries, verify the reductions, and generate illustrative plots of the resulting wave profiles. The computed solutions capture sigmoidal fronts connecting stable and unstable steady states, providing clear information about wave speed and shape. Overall, this study demonstrates that Lie group methods, combined with hyperbolic-function techniques, offer a powerful and systematic approach for analysing Fisher-type reaction–diffusion models and interpreting their biologically relevant invasion dynamics. Full article
(This article belongs to the Special Issue Symmetry in Integrable Systems and Soliton Theories)
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