Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (9,183)

Search Parameters:
Keywords = finite-time

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
33 pages, 7181 KB  
Article
Finite-Time Disturbance Compensation for Hierarchical Formation of Dual AGVs in Smart Ports
by Qiang Zhang, Bo Yuan, Li He, Zhengfang Xu and Dudu Guo
J. Mar. Sci. Eng. 2026, 14(13), 1166; https://doi.org/10.3390/jmse14131166 (registering DOI) - 24 Jun 2026
Abstract
This paper proposes an integrated formation control framework with a finite-time nonlinear disturbance observer (FT-NDO) for automated guided vehicles (AGVs) operating in port environments, where constrained workspace, narrow formation spacing, and complex external disturbances pose significant challenges. An adaptive leader–follower formation strategy with [...] Read more.
This paper proposes an integrated formation control framework with a finite-time nonlinear disturbance observer (FT-NDO) for automated guided vehicles (AGVs) operating in port environments, where constrained workspace, narrow formation spacing, and complex external disturbances pose significant challenges. An adaptive leader–follower formation strategy with dynamic inter-vehicle spacing is developed to enhance maneuverability during turning. Within a hierarchical control structure that decouples lateral and longitudinal dynamics, two sliding mode controllers (SMCs) are designed: (a) a lateral SMC that prioritizes heading accuracy, limiting yaw angle error to within ±2°; and (b) a nonsingular terminal SMC (NTSMC) for longitudinal control, improving error convergence speed compared to conventional SMC. An FT-NDO is further incorporated into both control loops to estimate and compensate for external disturbances in real time, achieving a disturbance estimation accuracy of over 95% and significantly attenuating the impact of environmental disturbances. Validation through simulation and physical experiment of a dual-AGV formation in a realistic port scenario demonstrates that the proposed approach restricts formation deviation to 0.015 m and maintains stable operation under various disturbance conditions. This study provides a practical solution for dual-AGV collaborative transportation in spatially constrained and dynamically disturbed environments, with direct implications for improving operational efficiency and safety in port logistics. Full article
(This article belongs to the Section Ocean Engineering)
20 pages, 670 KB  
Article
Fractional-Order SEIRS-V Dynamics of Worm Propagation in Wireless Sensor Networks: Semi-Analytical and Numerical Study with Stability and Uniqueness Insights
by Mahmoud M. Mokhtar and H. M. Hamouda
Fractal Fract. 2026, 10(7), 427; https://doi.org/10.3390/fractalfract10070427 (registering DOI) - 24 Jun 2026
Abstract
This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and [...] Read more.
This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and hereditary characteristics that may influence the transmission dynamics. Consequently, their ability to represent realistic network behavior can be limited in systems where past states affect current propagation patterns. The framework divides sensor nodes into susceptible, exposed, infectious, recovered, and vaccinated classes, while explicitly incorporating worm transmission rates, temporary loss of immunity, and the impact of preventive security measures under limited resource conditions. A detailed theoretical examination is performed, covering the existence, boundedness, and uniqueness of solutions of the fractional-order system. The coupled nonlinear fractional system is solved semi-analytically by means of the Fractional Reduced Differential Transform (FRDT) technique. To confirm accuracy and robustness, the identical system is also discretized and solved using the finite difference scheme (FDS). Unlike previous studies on worm propagation models in wireless sensor networks, which are mainly limited to equilibrium point analysis and qualitative investigations without deriving explicit solutions, the present work develops an approximate semi-analytical solution for the fractional-order SEIRS-V system using the FRDTM. Comparisons between the two solution sets demonstrate excellent agreement and high precision. Numerical outcomes are presented through a series of 2D graphical profiles that illustrate the time-dependent behavior of each compartment and reveal the sensitivity of worm propagation and suppression to variations in the fractional order and key model parameters. The integrated theoretical and computational findings underscore the strong protective role of vaccination in mitigating worm outbreaks and offer valuable guidelines for strengthening cybersecurity measures in wireless sensor networks. Full article
(This article belongs to the Section Numerical and Computational Methods)
37 pages, 568 KB  
Article
Modeling Positive Seasonal Time Series with Dynamic Precision: The Generalized BPSARMA Model
by Kleber H. Santos and Francisco Cribari-Neto
Forecasting 2026, 8(4), 53; https://doi.org/10.3390/forecast8040053 (registering DOI) - 24 Jun 2026
Abstract
This paper proposes a generalized seasonal beta prime autoregressive moving average model with dynamic precision, denoted by BPSARMA, for modeling and forecasting positive-valued seasonal time series. The proposed framework extends the generalized BPARMA model by incorporating stochastic seasonal dynamics in the conditional mean [...] Read more.
This paper proposes a generalized seasonal beta prime autoregressive moving average model with dynamic precision, denoted by BPSARMA, for modeling and forecasting positive-valued seasonal time series. The proposed framework extends the generalized BPARMA model by incorporating stochastic seasonal dynamics in the conditional mean through seasonal autoregressive and moving average components while allowing a flexible autoregressive structure for the conditional precision parameter, thereby accommodating time-varying uncertainty. The model also allows the inclusion of covariates and deterministic seasonal regressors. Parameter estimation is carried out by conditional maximum likelihood, and the main inferential and diagnostic tools are discussed. Monte Carlo simulations are conducted to examine the finite-sample behavior of the estimators and associated inference procedures. The practical usefulness of the proposed approach is illustrated through hydro-environmental time series applications, where its forecasting performance is evaluated using both in-sample and out-of-sample predictive measures. The empirical results indicate that the BPSARMA specification often provides competitive or superior forecasting accuracy relative to competing models, highlighting its usefulness for modeling and prediction in positive seasonal time series. Full article
(This article belongs to the Section Environmental Forecasting)
26 pages, 5368 KB  
Article
Investigation of Seismic Responses in Large-Span Spatial Structures Using the Dynamic Substructure Approach
by Shuyu Wang, Zeqiang Wang, Mingjie Liu, Yifeng Zhao, Yan Lu and Yang Hu
Buildings 2026, 16(13), 2505; https://doi.org/10.3390/buildings16132505 (registering DOI) - 24 Jun 2026
Abstract
The feasibility of employing the dynamic substructure approach for seismic response analysis of complex structures has been widely recognized. However, the analytical accuracy of this method is affected by several factors, including the element type, the structural configuration, and the analysis method. To [...] Read more.
The feasibility of employing the dynamic substructure approach for seismic response analysis of complex structures has been widely recognized. However, the analytical accuracy of this method is affected by several factors, including the element type, the structural configuration, and the analysis method. To address these issues, four types of reticulated shell structures were designed and analyzed using the mode superposition response spectrum method (MSRSM) and the time history analysis method (THAM). The displacements of the key nodes and all member stresses were extracted to compare the simplified finite element models with the original models. The relative errors of nodal displacements calculated by the models with reduced degree of freedom (DOF) were within 1.62%. For the member stresses of the single-layer reticulated shells, the relative errors of the simplified models were within 14.35%. In the simplified models of double-layer reticulated shells, several members exhibited a relative error greater than 30%; however, these members were mainly located near the substructure boundaries and accounted for less than 0.62% of the entire structure. Three strategies are proposed to mitigate the influence of the member stress errors on the structural analysis conclusions for double-layer reticulated shell structures. In addition, the dynamic substructure method was extended to the coupled system of large-span spatial structures and point-supported glass facades. The seismic response results confirmed that this method effectively reduces computational costs while maintaining satisfactory accuracy, indicating that it is a useful tool for simplifying large-span spatial structures in extensive numerical analyses. Full article
(This article belongs to the Section Building Structures)
31 pages, 11828 KB  
Article
Experimental and Finite Element Study on the Sliding Friction Isolation System of Multi-Story Modular Container Building Structure
by Yang Zuo and Xiaoxiong Zha
Buildings 2026, 16(13), 2498; https://doi.org/10.3390/buildings16132498 (registering DOI) - 24 Jun 2026
Abstract
Given the widespread application of multi-story modular container building structures, this article proposes a new seismic isolation system called the “sliding friction isolation system (IS)” that utilizes friction energy dissipation between containers. Firstly, lateral stiffness tests were conducted on a 20 ft container, [...] Read more.
Given the widespread application of multi-story modular container building structures, this article proposes a new seismic isolation system called the “sliding friction isolation system (IS)” that utilizes friction energy dissipation between containers. Firstly, lateral stiffness tests were conducted on a 20 ft container, a 40 ft container, and 20 ft connected containers. The constraint consists of four fixed-bottom corner pieces, and the load is achieved using a symmetrical longitudinal concentrated loading method. Their stiffness values were 58.07 kN/mm, 33.41 kN/mm, and 60.03 kN/mm, respectively, providing the necessary parameters for IS. Secondly, an IS model was established, and based on the theory of random vibration, the relationship between cei (the equivalent damping of i layer of the structure) and μ (the inter-layer friction coefficient) of the system was obtained. Thirdly, a nonlinear finite element model of a six-story container building was established. Namely, the non-isolation system with standard damping ratios (NIS-sdr), the non-isolation system with equivalent damping ratio (NIS-edr), and the IS. Elastic-plastic nonlinear time-history analyses were then conducted to study the dynamic responses of three systems under strong earthquakes. The analyses yielded the top displacement of the structure, each structural layer’s maximum displacement and displacement angle, the slip of each layer, the hysteresis loops, and the cumulative dissipated energy of IS. The results show that compared to NIS sdr and NIS edr, IS can effectively reduce the maximum interlayer displacement. The largest angular displacement between the structural layer of IS and NIS-edr is far less than that of NIS-sdr. The spectral characteristics of seismic waves (the EL-Centro wave, Taft wave, and artificial wave) can significantly affect the dynamic response of IS. Additionally, the length of the sliding hole on the corner piece can be set to 35 mm based on the displacement of each layer under the Taft wave to meet the standards for container houses (T/CECS 1932-2025). Full article
(This article belongs to the Section Building Structures)
Show Figures

Figure 1

24 pages, 9851 KB  
Article
Comparative Analysis of Three- and Five-Level NPC Converters with Predictive Current Control for Reactive Power Compensation: Simulation Study and Experimental Validation of the Three-Level Topology
by Oscar Paredes, Julio Pacher, Alfredo Renault, Jorge Rodas, Leonardo Comparatore, Carlos Paredes, Paola Maidana, Christian Medina, Hugo Lezcano, Marcos Gómez, Marco Rivera and Patrick Wheeler
Appl. Sci. 2026, 16(13), 6331; https://doi.org/10.3390/app16136331 (registering DOI) - 24 Jun 2026
Abstract
This paper presents a comparative analysis of three-level (3L-NPC) and five-level (5L-NPC) Neutral-Point-Clamped converters using Finite Control Set Model Predictive Control (FCS-MPC) for reactive power compensation. The research addresses a critical gap by providing a direct performance comparison under identical operating conditions, supported [...] Read more.
This paper presents a comparative analysis of three-level (3L-NPC) and five-level (5L-NPC) Neutral-Point-Clamped converters using Finite Control Set Model Predictive Control (FCS-MPC) for reactive power compensation. The research addresses a critical gap by providing a direct performance comparison under identical operating conditions, supported by simulation and experimental validation of a 3L-NPC prototype. The study evaluates harmonic performance, dynamic response, and DC-link balance. Results demonstrate that the 5L-NPC topology significantly outperforms the 3L-NPC, achieving a simulated grid current Total Harmonic Distortion (THD) of 3.36% compared to 7.84% for the 3L-NPC. This 57.1% reduction in THD allows the 5L-NPC to comply with the IEEE Std. 519-2022 limit (<5%), whereas the 3L-NPC experimental results (9.9% THD) highlight the impact of practical non-idealities such as dead time and sensor noise. While the 5L-NPC offers superior power quality, it entails higher hardware complexity, evaluating 125 switching states compared to 27 in the 3L-NPC. These findings provide quantitative guidelines for selecting NPC topologies in high-performance grid compensation systems. Full article
Show Figures

Figure 1

40 pages, 4376 KB  
Article
Memory-Driven Anomalous Heat Transport in Heterogeneous Media: A Two-Dimensional Time-Fractional Porous Medium Approach
by Mashael Bander Alshammari, Norazrizal Aswad Abdul Rahman and Abdullah Haif Alshammari
Mathematics 2026, 14(13), 2251; https://doi.org/10.3390/math14132251 (registering DOI) - 24 Jun 2026
Abstract
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical [...] Read more.
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical spreading patterns that are not adequately represented by conventional integer-order diffusion models. In this study, a modeling and simulation framework is developed for anomalous heat transport in heterogeneous media using a two-dimensional time-fractional porous medium equation. The model combines a Caputo fractional time derivative, which represents thermal memory, with nonlinear degenerate porous-medium diffusion, spatially heterogeneous conductivity, localized volumetric heating, and Robin-type convective boundary exchange. A conservative fully discrete numerical scheme is constructed using flux-based finite differences for the heterogeneous nonlinear diffusion operator and an L1 approximation for the Caputo derivative. The nonlinear algebraic system at each time level is solved using an under-relaxed Picard frozen-coefficient iteration with non-negativity enforcement and sparse direct solution of the resulting linear systems. The numerical implementation is verified through a manufactured-solution convergence study, and additional analyses are performed to examine computational cost, Picard iteration behavior, coefficient-regularization sensitivity, strong-source effects, heterogeneous conductivity structures, and long-time thermal-footprint persistence. The results show that heterogeneous conductivity mainly redirects heat through preferential pathways and enlarges the spatial footprint while producing negligible changes in global heat content. Stronger fractional memory, represented by smaller fractional order, increases the persistence and spatial reach of moderate heating, whereas larger porous-medium exponents confine heat near the source and preserve higher local peaks. Source amplitude increases the thermal burden and footprint monotonically over the tested range, including strong forcing, without producing an abrupt localization-spreading transition. Boundary exchange remains secondary in the short-time interior-heating regime considered. These findings demonstrate that the proposed two-dimensional time-fractional porous medium framework provides a verified and physically interpretable model for non-Fourier heat transport in heterogeneous materials, where local intensity, global heat retention, and spatial thermal exposure must be assessed jointly. Full article
Show Figures

Figure 1

22 pages, 8469 KB  
Article
Mechanical Behaviour and Parametric Analysis of the Hybrid Girder Bridges Joint Between Steel-Concrete Composite Girder and Prestressed Concrete Girder
by Yiteng Lin, Qingtian Su, Fawas. O. Matanmi, Xingfei Yan and Shang Gao
Appl. Sci. 2026, 16(13), 6322; https://doi.org/10.3390/app16136322 (registering DOI) - 24 Jun 2026
Abstract
This study focuses on a novel three-span hybrid continuous beam bridge, analyzing the force performance and key design parameters of the non-cellular post-support plate joint. A finite element model and parametric analysis were used to reveal the stress distribution patterns, the load-bearing characteristics [...] Read more.
This study focuses on a novel three-span hybrid continuous beam bridge, analyzing the force performance and key design parameters of the non-cellular post-support plate joint. A finite element model and parametric analysis were used to reveal the stress distribution patterns, the load-bearing characteristics of the connectors, and the load transfer path under negative bending moments. The study shows that the axial force within the joint is equitably shared among three load paths: the top slab concrete (20.7%), the bearing plate (40.1%), and the shear connectors (39.2%). Although interfacial friction contributes approximately 27.1% to the total shear resistance, it is conservatively recommended to neglect this effect in design due to inherent uncertainties. Parametric analysis reveals distinct marginal effects and efficiency thresholds: increasing the bearing plate thickness from 20 mm to 100 mm results in a mere 1.0 MPa reduction in the peak concrete stress, while extending the joint length beyond 1.0 times the beam height renders the central connectors ineffective. Furthermore, reducing the connector stiffness effectively lowers the non-uniformity coefficient from 2.3 to below 2.0. Notably, the first row of web PBLs carries 34.8% to 47.2% of the total shear force, with a stable non-uniformity coefficient of 1.05–1.06, establishing it as the critical control section for simplified design. These findings provide a theoretical basis and practical guidance for the design of similar joints in hybrid girder bridges. Full article
Show Figures

Figure 1

21 pages, 8115 KB  
Article
Experimental Investigation of Acid-Etched Creep Behavior and Mechanical Constitutive Modeling of Carbonate Rocks
by Zehui Zhang, Ning Qi, Yuyang Shen, Yixin Lu, Shunming Zhou, Yuxin Wang, Ping Jiang and Aihua Li
Processes 2026, 14(13), 2038; https://doi.org/10.3390/pr14132038 (registering DOI) - 23 Jun 2026
Abstract
Deep and ultra-deep carbonate reservoirs commonly experience fracture closure and conductivity reduction under high-temperature and high-stress conditions. In this study, triaxial creep tests were conducted on unacid-etched and acid-etched carbonate cores under different stress levels to investigate their time-dependent deformation behavior and the [...] Read more.
Deep and ultra-deep carbonate reservoirs commonly experience fracture closure and conductivity reduction under high-temperature and high-stress conditions. In this study, triaxial creep tests were conducted on unacid-etched and acid-etched carbonate cores under different stress levels to investigate their time-dependent deformation behavior and the influence of acid etching on rock rheology. The results indicate that carbonate rocks exhibit pronounced creep behavior, including instantaneous elastic deformation, primary creep, and steady-state creep. Acid etching significantly altered the creep characteristics and rheological parameters of carbonate rocks, leading to distinct time-dependent deformation responses compared with the unacid-etched core. The Burgers constitutive model was employed to characterize the creep behavior, and all fitting correlation coefficients exceeded 0.9. Finite element simulations based on the fitted parameters successfully reproduced the experimental creep curves, verifying the reliability of the constitutive model. This study provides a theoretical and numerical basis for evaluating the long-term deformation behavior of acid-etched carbonate rocks and its implications for fracture closure and conductivity evolution. Full article
(This article belongs to the Special Issue Advanced Research on Marine and Deep Oil & Gas Development)
37 pages, 8379 KB  
Article
Symmetry-Breaking and Fault-Tolerance Analysis of a Twelve-Legged Jansen Robot Using a Hybrid FEA-ANFIS Framework
by Yusuf Coşkun, Zakir Koçak, Eren Akgüngör, Lale Özyılmaz and Yakup Hakan Özyılmaz
Symmetry 2026, 18(7), 1068; https://doi.org/10.3390/sym18071068 (registering DOI) - 23 Jun 2026
Abstract
This study presents a comprehensive symmetry-breaking analysis framework for a twelve-legged Jansen walking robot, integrating finite element analysis (FEA) with adaptive neuro-fuzzy inference system (ANFIS) surrogate modeling. A systematic dataset of 210 cases was generated by combining 21 single- and multi-leg failure scenarios [...] Read more.
This study presents a comprehensive symmetry-breaking analysis framework for a twelve-legged Jansen walking robot, integrating finite element analysis (FEA) with adaptive neuro-fuzzy inference system (ANFIS) surrogate modeling. A systematic dataset of 210 cases was generated by combining 21 single- and multi-leg failure scenarios across 10 load levels (20–200 N) on the PLA-based 3D-printed prototype. Two novel dimensionless metrics are introduced: the Resilience Index (RI), quantifying the proportional stress increase relative to the baseline, and the Asymmetry Index (AI), measuring leg-reaction force distribution imbalance. Results identify a clear fault-tolerance threshold between two- and four-leg failures: single-leg failures remain at LOW risk (RI < 0.20), while three-leg asymmetric failures (S18) reach CRITICAL level (RI = 1.13, ~97% of PLA yield strength). A hybrid machine learning framework is proposed, applying ANFIS to maximum stress (R2 = 0.817) and safety factor (R2 = 0.936) predictions, while reserving FEA tables for bimodal outputs. The ANFIS surrogate achieves approximately 106× speedup over FEA (262.6 μs vs. 5–8 min), enabling real-time fault diagnosis and digital twin applications. The framework is generalizable to other multi-legged robotic systems requiring fault-tolerance evaluation. Full article
(This article belongs to the Special Issue Finite Element Analysis, Structural Dynamics, and Symmetry/Asymmetry)
Show Figures

Figure 1

34 pages, 3799 KB  
Article
Simulation of 2D Shallow-Sea Acoustic Fields Using a Physics-Informed Residual Network
by Ziyue Wang, Lingyi Cong, Luotao Zhang, Shuyue Liu and Xiaobo Zhang
J. Mar. Sci. Eng. 2026, 14(13), 1154; https://doi.org/10.3390/jmse14131154 (registering DOI) - 23 Jun 2026
Abstract
Acoustic propagation in stratified shallow seas is governed by finite-depth waveguiding, impedance contrasts at the seawater–seabed interface, and coupled space–time wave dynamics. Conventional numerical solvers are accurate but often require detailed environmental priors, mesh generation, and explicit time marching, increasing the cost of [...] Read more.
Acoustic propagation in stratified shallow seas is governed by finite-depth waveguiding, impedance contrasts at the seawater–seabed interface, and coupled space–time wave dynamics. Conventional numerical solvers are accurate but often require detailed environmental priors, mesh generation, and explicit time marching, increasing the cost of simulations involving complex boundaries or repeated evaluations. This study proposes a physics-informed residual network (ResNet-PINN) for continuous simulation of two-dimensional acoustic fields in shallow-sea stratified media. The framework embeds a variable-density, variable-sound-speed acoustic pressure wave equation, initial and boundary constraints, and interface-focused collocation into network training. A Gaussian initial wave packet and temporal gating are incorporated through the output transformation to improve early-time physical consistency. The model is validated against SPECFEM2D simulations and a stratified semi-analytical modal benchmark. The results show that it captures source-region spreading, main wavefront evolution, and transmission–reflection structures near the seawater–seabed interface at an equivalent frequency of approximately 477 Hz. Supplementary tests with sloping and arched interfaces and modified boundary conditions indicate adaptability to smooth interface variations. Overall, the framework provides a physically consistent neural network strategy for continuous shallow-sea acoustic field simulation and a complementary basis for future extensions to higher-frequency propagation, more complex environments, and dynamically varying ocean conditions. Full article
29 pages, 3420 KB  
Article
Exact Analytical Solutions for Elliptical Flow Toward Extended Wells in Fractured Confined Aquifers: Application to Groundwater-Head Interpretation in Shale-Gas Development Areas
by Xiaoxia Chen, Shuai Huang, Nannan Lv, Xinghan Li, Taohua He, Yaohui Xu and Lei Wang
Processes 2026, 14(12), 2025; https://doi.org/10.3390/pr14122025 (registering DOI) - 22 Jun 2026
Abstract
This study develops exact analytical solutions for transient elliptical groundwater flow toward an extended well in an anisotropic fractured confined aquifer and then discusses how the resulting hydraulic response can support groundwater-head interpretation in shale-gas development areas. The environmental connection is made at [...] Read more.
This study develops exact analytical solutions for transient elliptical groundwater flow toward an extended well in an anisotropic fractured confined aquifer and then discusses how the resulting hydraulic response can support groundwater-head interpretation in shale-gas development areas. The environmental connection is made at the aquifer-protection scale: the model is not a shale-gas reservoir production model, and it does not solve contaminant transport directly. Instead, it provides a hydraulic interpretation framework for estimating anisotropy, equivalent fracture length, wellbore-storage effects, and the preferential direction of head propagation around possible leakage points, old wells, fractures, or monitoring wells. Based on Mathieu-function theory and the separation-of-variables method, constant-rate and constant-head solutions are derived in Laplace space and inverted to the time domain with the Stehfest algorithm. The analytical results are validated against COMSOL5.2 finite-element simulations, and the effects of anisotropy coefficient and wellbore storage are analyzed through drawdown and flow-rate type curves. A synthetic but field-style water-head example is included to demonstrate how monitoring records can be converted to drawdown, fitted to the elliptical-flow solution, and used to delineate a preliminary hydraulic response zone. The results show that anisotropy mainly controls early-to-middle time response, whereas wellbore storage may obscure early head changes and delay the recognition of fracture connectivity. Therefore, the solution is best regarded as a rapid hydraulic-screening and monitoring-design tool that can precede, but not replace, site-specific contaminant-transport modeling in shale-gas groundwater-protection studies. The relevant technical issues are possible head disturbances and preferential groundwater pathways associated with surface spills, flowback-water handling, old wells, faults, and fracture-connected water-bearing zones. Because verified local field-monitoring records were not available for us, the application example is explicitly described as a synthetic field-style demonstration; it is used to show the workflow and its limitations, not to claim site-specific prediction of contaminant concentration. Full article
Show Figures

Figure 1

44 pages, 535 KB  
Article
Auto Ball Covariance and Correlation for Fixed-Lag Nonlinear Dependence in Time Series
by Qiang Zhang and Chaobang Gao
Mathematics 2026, 14(12), 2233; https://doi.org/10.3390/math14122233 (registering DOI) - 22 Jun 2026
Abstract
Classical tools for time series dependence analysis are primarily designed for linear dependence and may fail to detect serial structure when a series is uncorrelated but not independent. To address this problem, we propose the auto ball covariance function and the corresponding auto [...] Read more.
Classical tools for time series dependence analysis are primarily designed for linear dependence and may fail to detect serial structure when a series is uncorrelated but not independent. To address this problem, we propose the auto ball covariance function and the corresponding auto ball correlation function for measuring lag-specific nonlinear dependence in strictly stationary time series taking values in a separable Banach space. The proposed diagnostic uses metric-ball probabilities to measure fixed-lag distributional dependence without moment requirements, making it suitable for vector-, function-, and norm-induced object-valued time series. Under suitable conditions, we show that the proposed measure is zero if and only if the lagged components are independent. We further develop sample versions of the proposed statistics and establish their large-sample properties, including strong consistency under absolute regularity and a fixed-lag null asymptotic law under a finite-range dependence condition on the lagged-pair process. Simulation studies demonstrate that the proposed method performs well in a variety of settings, especially for nonlinear, heavy-tailed time series. A real-data analysis of annual sunspot numbers further illustrates how the proposed diagnostic can reveal nonlinear residual dependence that is not visible from ordinary autocorrelation diagnostics. Full article
(This article belongs to the Section D1: Probability and Statistics)
Show Figures

Figure 1

21 pages, 4476 KB  
Article
Multiphysics Investigation on Thermal Characteristics of Internal Bio-Inspired V-Ribbed Cooling Channels for Outer Rotor PMSM
by Xin Xiong, Xiangyu Li, Shawn You, Bing Zhu, Ping Ding, Huanhuan Gao and Zongqi Hou
Biomimetics 2026, 11(6), 441; https://doi.org/10.3390/biomimetics11060441 (registering DOI) - 22 Jun 2026
Abstract
Meeting the rigorous performance standards of modern electrified transit necessitates the deployment of high-performance outer rotor PMSMs with elevated power-to-volume ratios. However, their unique internal heat source topology inherently restricts heat dissipation. This limitation risks permanent magnet demagnetization and winding insulation failure. To [...] Read more.
Meeting the rigorous performance standards of modern electrified transit necessitates the deployment of high-performance outer rotor PMSMs with elevated power-to-volume ratios. However, their unique internal heat source topology inherently restricts heat dissipation. This limitation risks permanent magnet demagnetization and winding insulation failure. To address these thermal bottlenecks, this paper proposes internal bio-inspired cooling channels. These channels feature micro-scale V-shaped ribs. This design targets a 60 kW outer rotor PMSM. The motor uses a fractional-slot concentrated winding. The analytical procedure commences with the formulation of a transient 2D numerical model utilizing the Time-Stepping Finite Element approach (TS-FEM). It is coupled with the Bertotti model to compute electromagnetic losses. This approach accurately determines losses under high-frequency rated conditions. Results reveal that stator iron loss constitutes the dominant heat source. It accounts for 76.4 percent of the total electromagnetic loss. Furthermore, these losses show severe spatial concentration at the stator teeth. Subsequently, a three-dimensional fluid-solid coupled CFD model is developed. This model evaluates the proposed internal cooling channels. The design integrates bio-inspired vein networks and V-shaped ribs. These internal ribs disrupt the near-wall thermal boundary layer. This disruption enhances the local convective heat transfer. Comparative multiphysics analyses indicate improved hydraulic and thermal performance of the bio-inspired design under the same numerical boundary conditions. The bio-inspired channel achieves a more uniform static pressure distribution and reduces severe fluid stagnation zones. In the numerical model, the maximum stator and permanent magnet temperatures are reduced to 48 °C and 42 °C, respectively. This work provides a numerical design reference for thermal management in high-performance electric aviation. Full article
(This article belongs to the Section Biomimetic Design, Constructions and Devices)
Show Figures

Figure 1

33 pages, 467 KB  
Review
Automotive Noise, Vibration, and Harshness (NVH): A Thematic Literature Review
by Waleed Faris
Vehicles 2026, 8(6), 140; https://doi.org/10.3390/vehicles8060140 (registering DOI) - 22 Jun 2026
Abstract
Automotive Noise, Vibration, and Harshness (NVH) has emerged as a critical interdisciplinary field influencing vehicle performance, passenger comfort, brand perception, and regulatory compliance. This thematic literature review synthesizes key research trends, methodological approaches, and technological developments shaping contemporary NVH studies. Drawing on 255 [...] Read more.
Automotive Noise, Vibration, and Harshness (NVH) has emerged as a critical interdisciplinary field influencing vehicle performance, passenger comfort, brand perception, and regulatory compliance. This thematic literature review synthesizes key research trends, methodological approaches, and technological developments shaping contemporary NVH studies. Drawing on 255 scholarly and industry sources, the review identifies five dominant themes: (1) sources and characterization of noise and vibration in internal combustion, hybrid, and electric vehicles; (2) advanced modeling and simulation techniques—including finite element analysis, statistical energy analysis, and machine learning–based prediction models; (3) materials, components, and structural optimization strategies for NVH mitigation; (4) the rapidly evolving landscape of electric and autonomous vehicle NVH; and (5) emerging active noise and vibration control technologies and data-driven diagnostics. The analysis highlights a definite shift toward holistic, data-driven, and multi-physics approaches, driven by lightweighting imperatives, widespread electrification, and increasingly stringent occupant comfort expectations. Key gaps in current research—including the need for unified evaluation metrics, real-time in-vehicle NVH monitoring, closer integration of subjective psychoacoustic perception with objective physical measurement, and validated simulation workflows for novel EV architectures—are identified and discussed. This review provides a consolidated and expanded framework for understanding contemporary NVH research directions and articulates opportunities for transformative innovation in next-generation vehicle development. Full article
Back to TopTop