Search Results (77)

Monitoring small water body coverage spatiotemporal evolution in karst areas of complex hydrogeology is pivotal for water resource management and disaster assessment. With recent infrastructure expansion, intensive tunnel excavation has occurred in Chongqing’s Geleshan, a typical karst region with fragile aquifers. It has disrupted hydrogeological systems, triggering ground subsidence, groundwater leakage, and subsequent reservoir desiccation, as well as threatening regional water security and ecology. Thus, monitoring reservoir coverage evolution is critical to clarify dynamics and driving mechanisms. Synthetic Aperture Radar (SAR) is ideal for water body mapping, enabling data acquisition independent of illumination and weather. However, traditional SAR-based water extraction methods are hampered by low-scatter noise and poor adaptability to hydrological fluctuations. To address this, a two-stage dual-polarization SAR clustering algorithm (TSDPS-Clus) was developed using 452 time-series Sentinel-1 images (7 February 2017–24 August 2025). Specifically, the Kolmogorov–Smirnov test via pixel-wise time-series statistics screened core water areas, built candidate regions, and mitigated noise. Subsequently, dual-polarization and positional features were fused via singular value decomposition (SVD) to generate a high-discrimination low-dimensional feature set, followed by the Iterative Self-Organizing Data Analysis Techniques Algorithm (ISODATA) clustering for high-precision extraction. Results demonstrate that the algorithm suits reservoir storage-desiccation dynamics; dual-polarization complementarity boosts accuracy and clarifies six reservoirs’ spatiotemporal evolution. Notably, post-2023, tunnel excavation-induced land subsidence increased drying frequency and duration, with a 24-month maximum cumulative desiccation period. Full article

We examine the effects from small, spatially localized permanent charges on ionic transport in narrow membrane channels. Our analysis is based on a one-dimensional steady-state Poisson–Nernst–Planck (PNP) model involving two oppositely charged ion species with constant diffusion coefficients under electroneutral boundary conditions. In the framework of geometric singular perturbation theory, the steady PNP system is reformulated as a fast–slow dynamical system amenable to boundary-layer analysis. In the limit of vanishing permanent charge, the solution exhibits a singular structure with sharp boundary-layer segments and smooth bulk segments across regions of piecewise constant charge. Assuming the permanent charge strength Q is small, we carry out a regular perturbation expansion about $Q=0$ and derive explicit first-order corrections to each ion’s flux. Closed-form expressions are obtained for both the leading-order (zero-charge) fluxes and the $O\left(Q\right)$ flux corrections, revealing how even a small fixed charge can modulate the magnitude of individual ionic fluxes as a function of the applied transmembrane voltage and boundary concentration asymmetry. These results elucidate how permanent charge enhances or inhibits specific ionic flows, thereby influencing channel selectivity. Overall, our analysis provides clear asymptotic formulas and highlights the broader relevance of this perturbative approach to electro-diffusive transport modeling in biophysical systems. Full article

This study proposes an efficient numerical scheme for simulating heat transfer governed by the diffusion equation with moving singular sources. The work addresses two-dimensional problems with line sources and three-dimensional problems with plane sources, which are prevalent in irreversible thermodynamic processes. Developed within a finite difference framework, the method employs a partitioned discretization strategy to accurately resolve the solution singularity near the heat source—a region critical for precise local entropy production analysis. In the immediate vicinity of the source, we analytically derive and incorporate the solution’s “jump” conditions to construct specialized finite difference approximations. Away from the source, standard second-order-accurate schemes are applied. This hybrid approach yields a globally second-order convergent spatial discretization. The resulting sparse system is efficient for large-scale simulation of dissipative systems. The accuracy and efficacy of the proposed method are demonstrated through numerical examples, providing a reliable tool for the detailed study of energy distribution in non-equilibrium thermal processes. Full article

The morphology of solid surfaces encodes fundamental information about the physical mechanisms that govern their formation. Here, we reinterpret scanning electron microscopy (SEM) micrographs of oxide thin films as two-dimensional self-affine morphology fields (not height-metrology) and analyze them using a multiscale statistical-physics framework that integrates spectral, multifractal, geometric, and topological descriptors. Fourier-based power spectral density (PSD) provides the spectral slope $\beta$ and apparent Hurst exponent $H$, while multifractal scaling yields the information dimensions $D_q$, the singularity spectrum $f\left(\alpha \right)$, and its width $\mathsf{\Delta }\alpha$, which quantify scale hierarchy and intermittency. Lacunarity captures intermediate-scale heterogeneity, and Minkowski functionals—especially the Euler characteristic $\chi \left(\theta \right)$—probe connectivity and identify the onset of a percolation-like network structure. Two representative surfaces with contrasting morphologies are used as model systems: one exhibiting an anisotropic, porous, strongly multifractal structure with fragmented domains; the other showing a compact, nearly isotropic, and nearly monofractal organization. The porous surface/topography displays steep PSD decay, broad multifractal spectra, and positive $\chi$, consistent with a sub-percolated, diffusion-limited, Edwards–Wilkinson-like (EW-like) growth regime. Conversely, the compact surface/topography exhibits gentler spectral slopes, narrower $f\left(\alpha \right)$, enhanced lacunarity at intermediate scales, and a $\chi \left(\theta \right)$ zero-crossing indicative of a connectivity transition where a surface becomes a percolating network, consistent with a Kardar–Parisi–Zhang-like (KPZ-like) correlated growth regime. These results demonstrate that individual SEM micrographs encode quantitative fingerprints of nonequilibrium universality classes and topology-driven transitions from fragmented surfaces to connected networks, showing that SEM intensity maps can serve as a quantitative probe for testing theories of rough surfaces and kinetic growth in experimental thin-film systems. Full article

This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying material parameters. Based on piezoelectric elasticity theory, the steady-state governing equations for the coupled system are derived. By utilizing the transfer matrix method and the Fourier integral transform, the boundary value problem is converted into a system of coupled Cauchy singular integral equations of the first and second kinds in the frequency domain. These equations are solved semi-analytically, using the least squares method combined with an iterative algorithm. Taking a power-law gradient distribution as a case study, the effects of the gradient index, relative sliding speed, and friction coefficient on the contact pressure, in-plane stress, and electric displacement are systematically analyzed. Furthermore, the contact responses of FGPM coatings with power-law, exponential, and sinusoidal gradient profiles are compared. The findings provide a theoretical foundation for the optimal design of FGPM coatings and for enhancing their operational reliability under high-speed service conditions. Full article

Extreme weather conditions, specifically typhoons and strong gusts, create a highly transient environment for wind power data collection, leading to performance degradation that significantly impacts the safety and stability of the wind power system. To accurately predict wind power trends under these conditions, this paper proposes a prediction model integrating Singular Spectrum Analysis (SSA), Temporal Convolutional Network (TCN), Convolutional Neural Network (CNN), and a global average pooling layer, combined with inverse adaptive transfer learning. First, SSA is applied to reduce noise in the collected wind power operation data and extract key information. Subsequently, a prediction model is constructed based on TCN, CNN, and global average pooling. The model employs dilated causal convolutions to capture long-term dependencies and uses two-dimensional convolution kernels to extract local mutation features. Furthermore, a domain-adaptive transfer learning module is designed to adjust the model’s parameter weights via backward optimization based on the Maximum Mean Discrepancy (MMD) between the source and target domains. Experimental validation is conducted using real-world wind power operation data from a wind farm in Guangxi, containing 3000 samples sampled at 10 min intervals specifically during severe typhoon periods. Experimental results demonstrate that even with only 60% of the target data, the proposed method outperforms the traditional TCN neural network, reducing the Root Mean Square Error (RMSE) by 58.1% and improving the Coefficient of Determination (R²) by 32.7%, thereby verifying its effectiveness in data-scarce extreme scenarios. Full article

A laser tracker is an essential tool in the field of precise geometric measurement. Its fundamental operating idea is a dual-axis rotating device that propels the laser beam to continuously align and measure the attitude of a collaborating target. Such systems provide numerous benefits, including a broad measuring range, high precision, outstanding real-time performance, and ease of use. To solve the issue of low beam recovery efficiency in typical laser trackers, this research offers a two-dimensional laser tracking system that incorporates a machine vision module. The system uses a unique off-axis optical design in which the distance measuring and laser tracking paths are independent, decreasing the system’s dependency on optical coaxiality and mechanical processing precision. A tracking head error calibration method based on singular value decomposition (SVD) is introduced, using optical axis point cloud data obtained from experiments on various components for geometric fitting. A complete prototype system was constructed and subjected to accuracy testing. Experimental results show that the proposed system achieves a relative positioning accuracy of less than 0.2 mm (spatial root mean square error (RMSE) = 0.189 mm) at the maximum working distance of 1.5 m, providing an effective solution for the design of high-precision laser tracking systems. Full article

This study examines the generalized nonlinear Hunter–Saxton (HS) model: ${\Phi }_{tx}=\Phi {\Phi }_{xx}+\gamma {\Phi }_x^2,\gamma \ne 0,$ that describes the evolution of spatial potential and angular velocity in the vector field of nematic liquid crystals. Closed-form nematicons are derived via the order reduction of the traveling wave ODE. The qualitative structures are analyzed for different values of the nonlinear parameter $\gamma$. The solutions are graphically depicted to discover rich nematicon geometries including parabolic, cuspon, kink, and singular wave structures. A comprehensive dynamic analysis of the reduced nonlinear ordinary system is performed using the phase plane method, which helps to reveal the non-isolated continuity of equilibrium and the role of singular manifolds in shaping the system’s sensitivity and stability. Bifurcation cases are investigated for distinct values of $\gamma$, and various transitions in trajectory geometry and semi-stability features are shown. The novelty appears in the comprehensive integrating of analytic and dynamic characterizations, through global phase and bifurcation analysis, of the generalized HS equation (HSE), which uncovers the control of nonlinear coefficient $\gamma$ in governing the geometry and stability of the nematicons. Also, the analysis confirms the non-chaotic nature of the associated two-dimensional system, compatible with the Poincaré–Bendixson theorem. Full article

With the evolution of social structure and the intensification of population aging, traditional community service centers struggle to meet residents’ complex needs due to their functional singularity and spatial rigidity. In response to the continuously evolving social structure and functional requirements, this research proposes a strategy based on the “Separation of Support and Infill,” distinguishing between the building’s permanent Support Structure and its replaceable Infill Components. These two parts are combined with modularization to achieve long-term spatial adaptability and sustainability throughout the entire life cycle. In terms of functional space, through the combination of vertical stratification, horizontal staggering and spatial permeability, a three-dimensional composite space system is constructed, which not only enhances the functional flexibility but also improves the environmental performance. Taking a design case in Yicheng District, Zhumadian City as an example, through a comparative analysis with the traditional building model, the comparative analysis demonstrates that this framework increases the Floor Area Ratio (FAR) by approximately 0.15 compared to traditional models. Furthermore, the modular characteristics significantly enhance demountability and reusability, reducing construction and demolition waste while lowering life-cycle costs by an estimated 15% to 25%. These studies show that the support structure and the composite functional space system can not only promote social interaction and community cohesion but also reduce the life-cycle cost and carbon emissions. The framework proposed in this paper constructs a theoretical and practical system for sustainable community buildings from the perspectives of functional compounding and low-carbon community development. Its innovation lies in its flexible spatial organization mode and the enhancement of the sustainability of community buildings. Full article

Based on the hydrodynamic description, the dynamics of nonlinear cylindrical waves in an isentropic plasma are investigated. The problem is considered in an electrostatic formulation for a two-dimensional plasma medium where ions form a stationary background. Proceeding from the particular, exact solution of hydrodynamic equations, we obtain the system of differential equations which describes the electron’s dynamics, taking into account the finite temperature of electrons. Moreover, we find the conditions when this system is reduced to the generalized Ermakov–Pinney equation which was used for analyzing electron dynamics. In the present calculations, a parabolic-in-radius temperature profile was used, associated with an electron density varying only with time. In the framework of the model that worked out, the influence of initial conditions and thermal effects on the regular and singular dynamics of excited waves are discussed. It is shown that the development of singular behavior due to intrinsic nonlinearity is avoided by taking into account thermal effects and the initial rotation of the electron flow. Full article

This paper presents soliton solutions of the fractional (2+1)-dimensional Davey–Stewartson equation based on a local fractional derivative to represent wave packet propagation in dispersive media under both spatial and temporal effects. The importance of this work is in demonstrating how fractional derivatives represent a more capable modeling tool compared to conventional integer-order methods since they include anomalous dispersion, nonlocal interactions, and memory effects typical in most physical systems in nature. The main objective of this research is to build and examine a broad family of soliton solutions such as bright, dark, singular, bright–dark, and periodic forms, and to explore the influence of fractional orders on their amplitude, width, and dynamical stability. Specific focus is given to the comparison of the behavior of fractional-order solutions with that of traditional integer-order models so as to further the knowledge on fractional calculus and its role in governing nonlinear wave dynamics in fluids, plasmas, and other multifunctional media. Methodologically, this study uses the fractional complex transform together with a new mapping technique, which transforms the fractional Davey–Stewartson equation into solvable nonlinear ordinary differential equations. Such a systematic methodology allows one to derive various families of solitons and form a basis for investigation of nonlinear fractional systems in the general case. Numerical simulations, given in the form of three-dimensional contour maps, density plots, and two-dimensional, demonstrate stability and propagation behavior of the derived solitons. The findings not only affirm the validity of the devised analytic method but also promise possibilities of useful applications in fluid dynamics, plasma physics, and nonlinear optics, where wave structure manipulation using fractional parameters can result in increased performance and novel capabilities. Full article

This paper investigates soliton solutions of the time-fractional Biswas–Arshed (BA) equation using the Extended Simplest Equation Method (ESEM). The model is analyzed under two distinct fractional derivative operators: the $\beta$-derivative and the M-truncated derivative. These approaches yield diverse solution types, including kink, singular, and periodic-singular forms. Also, in this work, a nonlinear second-order differential equation is reconstructed as a planar dynamical system in order to study its bifurcation structure. The stability and nature of equilibrium points are established using a conserved Hamiltonian and phase space analysis. A bifurcation parameter that determines the change from center to saddle-type behaviors is identified in the study. The findings provide insight into the fundamental dynamics of nonlinear wave propagation by showing how changes in model parameters induce qualitative changes in the phase portrait. The derived solutions are depicted via contour plots, along with two-dimensional (2D) and three-dimensional (3D) representations, utilizing Mathematica for computational validation and graphical illustration. This study is motivated by the growing role of fractional calculus in modeling nonlinear wave phenomena where memory and hereditary effects cannot be captured by classical integer-order approaches. The time-fractional Biswas–Arshed (BA) equation is investigated to obtain diverse soliton solutions using the Extended Simplest Equation Method (ESEM) under the $\beta$-derivative and M-truncated derivative operators. Beyond solution construction, a nonlinear second-order equation is reformulated as a planar dynamical system to analyze its bifurcation and stability properties. This dual approach highlights how parameter variations affect equilibrium structures and soliton behaviors, offering both theoretical insights and potential applications in physics and engineering. Full article

Modeling ion transport through membrane channels is crucial for understanding cellular processes, and Poisson–Nernst–Planck (PNP) equations provide a fundamental continuum framework for such ionic fluxes. We investigate a quasi-one-dimensional steady-state PNP system for two oppositely charged ion species, focusing on how large permanent charges within the channel and realistic boundary conditions impact ion transport. In contrast to classical models that impose ideal electroneutrality at the channel ends (a simplification that eliminates boundary layers near the membrane interfaces), we adopt relaxed neutral boundary conditions that allow small charge imbalances at the boundaries. Using asymptotic analysis treating the large permanent charge as a singular perturbation, we derive explicit first-order expansions for each ionic flux, incorporating boundary layer parameters $(\sigma ,\rho )$ to quantify slight deviations from electroneutrality. This analysis enables a qualitative characterization of individual cation and anion flux behaviors. Notably, we identify two critical transmembrane potentials, $V_{1c}$ and $V_{2c}$, at which the cation and anion fluxes, respectively, vanish, signifying flux-reversal thresholds that delineate distinct monotonic regimes in the flux-voltage response; these critical values depend on the permanent charge magnitude and the boundary layer parameters. We further show that both ionic fluxes exhibit saturation: as the applied voltage becomes extreme, each flux approaches a finite limiting value, with the saturation level modulated by the degree of boundary charge imbalance. Moreover, allowing even small boundary charge deviations reveals non-intuitive discrepancies in flux behavior relative to the ideal electroneutral case. For example, in certain parameter regimes, a large permanent charge that enhances an ionic current under strict electroneutral conditions will instead suppress that current under relaxed-neutral conditions (and vice versa). This new analytical framework exposes subtle yet essential nonlinear dynamics that classical electroneutral assumptions would otherwise obscure. It provides deeper insight into the interplay between large fixed charges and boundary-layer effects, emphasizing the importance of incorporating such realistic boundary conditions to ensure accurate modeling of ion transport through membrane channels. Numerical simulations are performed to provide more intuitive illustrations of our analytical results. Full article

This paper presents an innovative numerical method for solving two-dimensional weakly singular Volterra integral equations, including fractional Volterra integral equations with weak singularities. Solving these equations in higher dimensions and in the presence of fractional and weak singularities is highly challenging. The proposed approach uses Euler wavelets (EWs) within an operational matrix (OM) framework combined with advanced numerical techniques, initially transforming these equations into a linear algebraic system and then solving it efficiently. This method offers very high accuracy, strong computational efficiency, and simplicity of implementation, making it suitable for a wide range of such complex problems, especially those requiring high speed and precision in the presence of intricate features. Full article

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the $({\displaystyle \frac{G^{\prime }}{G^{\prime }+G+A}})$-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application. Full article