Search Results (581)

This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially symmetric periodic boundary conditions, achieving exponential convergence and reduced computational cost compared to traditional methods. The FGIG method uniquely combines Fourier series for spatial periodicity and Gegenbauer polynomials for temporal integration within a Galerkin framework, resulting in highly accurate numerical and semi-analytical solutions. Unlike traditional approaches, this method eliminates the need for time-stepping procedures by reformulating the problem as a system of integral equations, reducing error accumulation over long-time simulations and improving computational efficiency. Key contributions include exponential convergence rates for smooth solutions, robustness under oscillatory conditions, and an inherently parallelizable structure, enabling scalable computation for large-scale problems. Additionally, the method introduces a barycentric formulation of the shifted Gegenbauer–Gauss (SGG) quadrature to ensure high accuracy and stability for relatively low Péclet numbers. This approach simplifies calculations of integrals, making the method faster and more reliable for diverse problems. Numerical experiments presented validate the method’s superior performance over traditional techniques, such as finite difference, finite element, and spline-based methods, achieving near-machine precision with significantly fewer mesh points. These results demonstrate its potential for extending to higher-dimensional problems and diverse applications in computational mathematics and engineering. The method’s fusion of spectral precision and integral reformulation marks a significant advancement in numerical PDE solvers, offering a scalable, high-fidelity alternative to conventional time-stepping techniques. Full article

In recent years, remarkable advancements have been achieved in hyperspectral unmixing (HU). Sparse unmixing, in which models mix pixels as linear combinations of endmembers and their corresponding fractional abundances, has become a dominant paradigm in hyperspectral image analysis. To address the inherent limitations of spectral-only approaches, spatial contextual information has been integrated into unmixing. In this article, a superpixel collaborative sparse unmixing algorithm with graph differential operator (SCSU–GDO), is proposed, which effectively integrates superpixel-based local collaboration with graph differential spatial regularization. The proposed algorithm contains three key steps. First, superpixel segmentation partitions the hyperspectral image into homogeneous regions, leveraging boundary information to preserve structural coherence. Subsequently, a local collaborative weighted sparse regression model is formulated to jointly enforce data fidelity and sparsity constraints on abundance estimation. Finally, to enhance spatial consistency, the Laplacian matrix derived from graph learning is decomposed into a graph differential operator, adaptively capturing local smoothness and structural discontinuities within the image. Comprehensive experiments on three datasets prove the accuracy, robustness, and practical efficacy of the proposed method. Full article

This study investigates the multi-objective path planning problem for unmanned surface vehicles (USVs), aiming to optimize both travel distance and energy consumption in maritime environments with obstacles, sea winds, and ocean currents. The proposed method accounts for practical constraints, including collision avoidance, kinematic boundaries, and speed limitations. The problem is formulated as a nonlinear multi-objective optimization model with generalized constraints and is solved using an improved particle swarm optimization algorithm enhanced by a vector-weighted fusion strategy. The algorithm adaptively balances exploration and exploitation to obtain diverse Pareto-optimal solutions. Simulation results under varying environmental conditions, along with real-world sea trials, validate the effectiveness of the proposed approach. The outcomes demonstrate that the method enables USVs to generate energy-efficient, smooth trajectories while maintaining robustness and adaptability, offering practical value for intelligent marine navigation. Full article

Molecular dynamics (MD) simulations provide atomistic insights into nucleation and crystallization in polymers, yet interpreting their complex spatiotemporal data remains a challenge. Existing order parameters face limitations, such as failing to account for directional alignment or lacking sufficient spatial resolution, preventing them from accurately capturing the anisotropic and heterogeneous characteristics of nucleation or the surface phenomena of polymer crystallization. We introduce a novel set of local order parameters—namely, directional entropy bands— that extend scalar entropy-based descriptors by capturing first-order angular moments of the local entropy field around each particle. We compare these against conventional metrics (entropy, the crystallinity index, and smooth overlap of atomic positions (SOAP) descriptors) in equilibrium MD simulations of polymer crystallization. We show that (i) scalar entropy bands demonstrate advantages compared to SOAP in polymer phase separation at single-snapshot resolution and (ii) directional extensions (dipole projections and gradient estimates) robustly highlight the evolving crystal–melt interface, enabling earlier nucleation detection and quantitative surface profiling. UMAP embeddings of these 24–30D feature vectors reveal a continuous melt–surface–core manifold, as confirmed by supervised boundary classification. Our approach is efficient and directly interpretable, offering a practical framework for studying polymer crystallization kinetics and surface growth phenomena. Full article

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary value problems for the Helmholtz equation with complex parameters. The inverse Laplace transform is computed using a sinc quadrature along a suitably chosen contour in the complex plane. We show that due to a symmetry of the quadrature nodes, the number of stationary problems can be decreased by almost a factor of two. The influence of the integration contour parameters on the approximation error is also researched. Stationary problems are numerically solved using a boundary integral equation approach applying the Nyström method, based on the quadratures for smooth surface integrals. Numerical experiments support the expectations. Full article

The time-dependent Maxwell system in the sense of distributions is considered in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected wave. A rigorous derivation of boundary conditions for the electric and magnetic fields at temporal interfaces is provided with precise assumptions of the material parameters. In turn, this is used to obtain a general Snell’s Law at such interfaces. From this, explicit formulas for the reflection and transmission coefficients are obtained. Unlike previous works, there is no simplifying ansatz on the solution to the Maxwell system made, nor is it assumed that the fields are smooth. Material parameters which are not necessarily constant on either side of the temporal interface are also considered. Full article

Optical remote sensing images are often partially obscured by clouds due to the inability of visible light to penetrate cloud cover, which significantly limits their subsequent applications. Most existing cloud removal methods formulate the problem using low-rank and sparse priors within a discrete representation framework. However, these approaches typically rely on manually designed regularization terms, which fail to accurately capture the complex geostructural patterns in remote sensing imagery. In response to this issue, we develop a continuous blind cloud removal model. Specifically, the cloud-free component is represented using a continuous tensor function that integrates implicit neural representations with low-rank tensor decomposition. This representation enables the model to capture both global correlations and local smoothness. Furthermore, a band-wise sparsity constraint is employed to represent the cloud component. To preserve the information in regions not covered by clouds during reconstruction, a box constraint is incorporated. In this constraint, cloud detection is performed using an adaptive thresholding strategy, and a morphological erosion function is employed to ensure accurate detection of cloud boundaries. To efficiently handle the developed model, we formulate an alternating minimization algorithm that decouples the optimization into three interpretable subproblems: cloud-free reconstruction, cloud component estimation, and cloud detection. Our extensive evaluations on both synthetic and real-world data reveal that the proposed method performs competitively against state-of-the-art cloud removal methods. Full article

This paper presents a computational design method for generating discrete shell structures using sets of equivalent discrete members. This study addresses the challenge of reducing the geometrical variety in discrete shell elements by introducing a method to design and optimize constituent members considering their similarity, approximation of the double-curved architectural surface, and buildability. First, we employed a relaxation-based computational form-finding method to generate a discrete topology with planar quad faces and an approximated smooth, double-curved surface. Then, we perform clustering and optimization based on face similarities concerning the minimization of deviations from the smooth surface approximation, and the dihedral angle between the planes of neighboring elements and their optimal intersection plane. The proposed approach can reduce the geometrical differences in discrete shell elements while satisfying the user-defined error threshold. We demonstrated the viability of our method on various structured topologies with different boundary conditions, support settings, and total face counts, while explicitly controlling inter-element facing angles for assembly ready contacts. This enables mold-based prefabrication with repeatable components. Full article

Deep learning-based methods have shown great promise for synthetic aperture radar (SAR) automatic target recognition (ATR) in recent years. These methods demonstrate superior performance compared to traditional approaches across various recognition tasks. However, these methods often face significant challenges due to the limited availability of labeled samples, which is a common issue in SAR image analysis owing to the high cost and difficulty of data annotation. To address this issue, a variety of few-shot learning approaches have been proposed and have demonstrated promising results under data-scarce conditions. Nonetheless, a notable limitation of many existing few-shot methods is that their performance tends to plateau when more labeled samples become available. Most few-shot methods are optimized for scenarios with extremely limited data. As a result, they often fail to leverage the advantages of larger datasets. This leads to suboptimal recognition performance compared to conventional deep learning techniques when sufficient training data is available. Therefore, there is a pressing need for approaches that not only excel in few-shot scenarios but also maintain robust performance as the number of labeled samples increases. To this end, we propose a novel method, termed relation-guided embedding transductive propagation network with residual correction (RGE-TPNRC), specifically designed for few-shot SAR ATR tasks. By leveraging mechanisms such as relation node modeling, relation-guided embedding propagation, and residual correction, RGE-TPNRC can fully utilize limited labeled samples by deeply exploring inter-sample relations, enabling better scalability as the support set size increases. Consequently, it effectively addresses the plateauing performance problem of existing few-shot learning methods when more labeled samples become available. Firstly, input samples are transformed into support-query relation nodes, explicitly capturing the dependencies between support and query samples. Secondly, the known relations among support samples are utilized to guide the propagation of embeddings within the network, enabling manifold smoothing and allowing the model to generalize effectively to unseen target classes. Finally, a residual correction propagation classifier refines predictions by correcting potential errors and smoothing decision boundaries, ensuring robust and accurate classification. Experimental results on the moving and stationary target acquisition and recognition (MSTAR) and OpenSARShip datasets demonstrate that our method can achieve state-of-the-art performance in few-shot SAR ATR scenarios. Full article

Here, we study boundary value problems for the Laplace–Beltrami operator on a three-dimensional sphere with a circular cut, obtained by removing a smooth closed geodesic from $S^3$ embedded in ${\mathbb{R}}^4$. The presence of the cut introduces singular perturbations of the domain, and we develop an analytical framework to characterize well-posed problems in this setting. Our approach combines Green’s functions, spectral analysis, and Sobolev space methods to establish solvability criteria and uniqueness results. In particular, we identify explicit conditions for the existence of solutions with data supported near the cut, and extend the formulation to include delta-type perturbations supported on the removed circle. These results generalize earlier work on punctured two-dimensional spheres and provide a foundation for the study of PDEs on manifolds with localized singularities. Full article

Gas coolers play a critical role in CO₂ refrigeration and heat pump systems, where their thermohydraulic characteristics substantially influence the overall system performance. To improve the heat transfer performance of gas coolers, minichannels with aligned or offset fins integrated in the channel sidewalls are proposed to enlarge the heat transfer surface and intensify the flow turbulence. Unlike conventional refrigerants, supercritical CO₂ exhibits significant variations in thermophysical properties with temperature changes, which results in distinct heat transfer behavior. Three-dimensional numerical models are therefore purposely developed by employing the Shear Stress Transport k-ω turbulent model and including the entrance region effect, NIST real-gas thermophysical properties and buoyancy effect. A constant heat flux boundary is employed on the four-side channel walls to ensure that the temperature of CO₂ flowing in the channel exactly decreases from 373.15 K to 308.15 K. The results show that the fins integrated in the channel sidewalls can significantly improve the heat transfer performance, and the heat transfer coefficient significantly increases with increasing mass flux. Compared to the reference smooth channel, the heat transfer performance is enhanced by a factor of 1.85–2.15 with aligned fins and 1.44–1.61 with offset fins. Full article

To address the issue of missing constraints on control variables in the trajectory optimization problem of the differential dynamic programming (DDP) method, the adaptive projection differential dynamic programming (AP-DDP) method is proposed. The core of the AP-DDP method is to introduce adaptive relaxation coefficients to dynamically adjust the smoothness of the projection function and to effectively solve the gradient disappearance problem that may occur when the control variable is close to the constraint boundary. Additionally, the iterative strategy of the relaxation coefficient accelerates the search for a feasible solution in the initial stage, thereby improving the algorithm’s efficiency. When applied to three trajectory optimization problems, compared with similar truncated DDP, projected DDP, and Box-DDP methods, the AP-DDP method found the optimal solution in the shortest computation time, thereby proving the efficiency of the proposed algorithm. While ensuring the iterative process reaches the global optimum, the computing time of the AP-DDP method was reduced by 32.8%, 13.3%, and 18.5%, respectively, in the three examples. Full article

Aiming at the cooperative path-planning problem of multiple autonomous underwater vehicles in underwater three-dimensional terrain and dynamic ocean current environments, a hybrid algorithm based on the Improved Multi-Objective Particle Swarm Optimization (IMOPSO) and Dynamic Window (DWA) is proposed. The traditional particle swarm optimization algorithm is prone to falling into local optimization in high-dimensional and complex marine environments. It is difficult to meet multiple constraint conditions, the particle distribution is uneven, and the adaptability to dynamic environments is poor. In response to these problems, a hybrid initialization method based on Chebyshev chaotic mapping, pre-iterative elimination, and boundary particle injection (CPB) is proposed, and the particle swarm optimization algorithm is improved by combining dynamic parameter adjustment and a hybrid perturbation mechanism. On this basis, the Dynamic Window Method (DWA) is introduced as the local path optimization module to achieve real-time avoidance of dynamic obstacles and rolling path correction, thereby constructing a globally and locally coupled hybrid path-planning framework. Finally, cubic spline interpolation is used to smooth the planned path. Considering factors such as path length, smoothness, deflection Angle, and ocean current kinetic energy loss, the dynamic penalty function is adopted to optimize the multi-AUV cooperative collision avoidance and terrain constraints. The simulation results show that the proposed algorithm can effectively plan the dynamic safe path planning of multiple AUVs. By comparing it with other algorithms, the efficiency and security of the proposed algorithm are verified, meeting the navigation requirements in the current environment. Experiments show that the IMOPSO–DWA hybrid algorithm reduces the path length by 15.5%, the threat penalty by 8.3%, and the total fitness by 3.2% compared with the traditional PSO algorithm. Full article

Driven by the “dual carbon” goal, virtual power plants (VPPs) are the core vehicle for integrating distributed energy resources, but the multiple uncertainties in wind power, electricity/heat load, and electricity price, coupled with the impact of carbon-trading cost, make it difficult for traditional scheduling methods to balance the robustness and economy of VPPs. Therefore, this paper proposes an oxy-fuel combustion capture (OCC)-VPP architecture, integrating an OCC unit to improve the energy efficiency of the system through the “electricity-oxygen-carbon” cycle. Ten typical scenarios are generated by Latin hypercube sampling and K-means clustering to describe the uncertainties of source and load probability distribution, combined with the polyhedral uncertainty set to delineate the boundary of source and load fluctuations, and the stepped carbon-trading mechanism is introduced to quantify the cost of carbon emission. Then, a three-stage stochastic–robust scheduling model is constructed. The simulation based on the arithmetic example of OCC-VPP in North China shows that (1) OCC-VPP significantly improves the economy through the synergy of electric–hydrogen production and methanation (52% of hydrogen is supplied with heat and 41% is methanated), and the cost of carbon sequestration increases with the prediction error, but the carbon benefit of stepped carbon trading is stabilized at the base price of 320 DKK/ton; (2) when the uncertainty is increased from 0 to 18, the total cost rises by 45%, and the cost of purchased gas increases by the largest amount, and the cost of energy abandonment increases only by 299.6 DKK, which highlights the smoothing effect of energy storage; (3) the proposed model improves the solution speed by 70% compared with stochastic optimization, and reduces cost by 4.0% compared with robust optimization, which balances economy and robustness efficiently. Full article

In the context of the deep integration of digital art and geometric computing, this paper proposes a digital art pattern generation method with arbitrary quadrilateral tiling. The aim is to break through the limitations of traditional fixed tiling templates in terms of adaptability to irregular tiling shapes, controllability of local deformations, and naturalness of boundary transitions. By decoupling the topological stability of quadrilaterals from deformation parameters and combining the Coons surface interpolation method, a smooth invariant mapping for the fundamental region of arbitrary quadrilaterals is constructed, solving the seamless splicing problem of irregular fundamental region. This method supports real-time editing of quadrilateral shape and colors the fundamental region based on the dynamical system model to generate periodic seamless patterns with global symmetry and controllable local details. Experiments show that the proposed method can be adapted to any quadrilateral structure, from regular rectangles to non-convex polygons. By adjusting the interpolation parameters and dynamical system functions, the symmetry, texture complexity, and visual rhythm of the patterns can be flexibly regulated. The algorithm achieves efficient computation under GPU parallel optimization (with an average generation time of 0.25 s per pattern), providing a new solution for the pattern generation and personalized design of digital art patterns. Full article