Search Results (144)

Selective laser melting (SLM) offers a promising route for fabricating high-performance Cu–Sn alloys; however, the extremely transient thermal behavior of the molten pool and its influence on microstructural evolution and mechanical properties remain insufficiently understood. In this study, a finite element model based on ABAQUS was developed to simulate the transient temperature field and molten pool dynamics of Cu–10Sn alloy during the SLM process. By systematically varying the volumetric energy density (VED), the interplay among molten pool geometry, thermal characteristics, microstructure, and mechanical performance was investigated through a combination of numerical simulation and experimental investigation. The results reveal that increasing VED significantly enlarges the molten pool dimensions, elevates the peak temperature, and intensifies the maximum heating and cooling rates, thereby altering solidification conditions. At a VED of 208.33 J/mm³, the molten pool reached its maximum dimensions, with a length of 230 μm, a width of 161 μm, and a depth of 85 μm, resulting in the highest relative density within the investigated range (98.33%). Under this processing condition, the Cu–10 wt.% Sn (Cu–10Sn) alloy exhibited microhardness values of 190 HV near the solidified areas of melt pool interior and 208.4 HV near the solidified areas of melt pool boundary, accompanied by an ultimate tensile strength of 494 MPa. These findings elucidate the critical role of molten pool thermal behavior in governing microstructural refinement and mechanical properties of SLM-fabricated Cu–10Sn alloys and provide a mechanistic basis for understanding the effect of process parameters. Full article

This article investigates the numerical solution of the two-dimensional Poisson equation defined over a rectangular domain subject to a double integral nonlocal boundary condition. We propose a finite difference scheme by discretizing the integral term using the two-dimensional trapezoidal rule. The main difficulty of this problem is that, in the non-classical case, we cannot use the method of separation of variables and decompose the problem into one-dimensional problems. Our approach involves reducing the integral boundary condition from the complete domain to the interior points and strategically partitioning the computational domain into the boundary and interior points. We propose a method that allows us to find a solution by solving the Poisson equation with classical boundary conditions, and using the solutions found to construct a solution to a problem with a nonlocal integral condition. This method requires solving a linear system whose dimension is much smaller than the original. Under certain conditions on the kernel, the proposed method is correct. Full article

Accurate building roof classification from airborne LiDAR point clouds is fundamental to reliable three-dimensional (3D) urban reconstruction. While supervoxel-based methods offer efficiency and resilience to uneven point density, their performance is critically undermined by cross-boundary segmentation errors—a direct consequence of random seed initialization that merges geometrically similar yet semantically distinct objects. To address this root cause, this study proposes Interior-Anchored Mean-Shift (IAMS), a novel supervoxel segmentation framework that rethinks seed placement as a geometry-aware interior localization problem. By integrating local geometric consistency point density, and spatial correlation into a unified kernel density estimator, supplemented by density-adaptive voxel weighting and a semi-variogram-driven bandwidth, IAMS reliably anchors seeds within object interiors, yielding highly homogeneous supervoxels without post-processing. Extensive experiments on three diverse airborne LiDAR datasets demonstrated that IAMS consistently outperformed state-of-the-art baselines. On the International Society for Photogrammetry and Remote Sensing (ISPRS) Vaihingen benchmark, our approach improved roof classification completeness, correctness, and quality by up to 7.1% (per-object) over the conventional Voxel Cloud Connectivity Segmentation (VCCS) algorithm while being significantly faster than recent boundary-preserving alternatives. Critically, IAMS maintains robust performance under challenging conditions, including sparse sampling and dense vegetation occlusion, making it a practical solution for real-world urban remote sensing. Full article

Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay of solutions. To the best of our knowledge, we address this long-standing gap by presenting a fully integrated framework that simultaneously resolves both challenges. We derive the governing equation from constitutive relations and establish exact absorbing boundary conditions (ABCs) for the multi-skeleton comb model, a result absent in prior work. A transparent Dirichlet-to-Neumann (DtN) map, constructed via Laplace analysis, rigorously handles skeletal Dirac delta singularities and eliminates spurious reflections without empirical parameters. Furthermore, we propose a novel structure-preserving finite difference scheme that applies the sum-of-exponentials (SOE) approximation not only to the interior Caputo derivative but also to the convolution kernels arising from the ABCs. This yields a dramatic reduction in computational complexity, from quadratic $O\left(N_t^2\right)$ to quasi-linear $O(N_{t}log{N}_t)$, while preserving the physics of anomalous transport. We prove the well-posedness, unconditional stability, and convergence of the method. Numerical results confirm theoretical error estimates and show excellent agreement between simulated particle distributions, mean square displacement profiles, and exact asymptotics, validating both accuracy and robustness. The speedup (CPU time ratio Direct/Fast) is about $1.00\times$–$1.23\times$ for $N_t=5000$ in our tests. Our approach sets a new benchmark for simulating anomalous dynamics in fractal-inspired media. Full article

This study systematically investigated the chemical composition, microstructure, and mechanical properties of HR3C steel tubes that have been in service. The results indicate that, after nearly 70,000 h of operation, continuous lamellar M₂₃C₆ precipitates formed along grain boundaries in the HR3C steel, with needle-like or rod-like M₂₃C₆ phases extending from the grain boundaries into the grain interiors. Additionally, NbCrN and σ-phase precipitates were observed in the regions adjacent to the grain boundaries. Mechanical testing revealed a slight increase in hardness following service exposure, while the tensile strength remained largely unchanged; the yield strength, however, increased by approximately 15%. In contrast, the elongation at fracture decreased significantly—ductility declined by 64–73% relative to the as-received condition—and impact toughness dropped dramatically by 96%. These findings collectively indicate pronounced embrittlement of the HR3C steel after long-term service at 620 °C. Microstructural analysis confirms that the precipitation of M₂₃C₆ and σ phases is the primary contributor to the observed deterioration in toughness and ductility. Full article

In this paper I study a two-dimensional discrete-time evolutionary logistic-type model describing the coupled dynamics of population density and a continuously evolving trait. I provide a local bifurcation analysis of the equilibria, deriving explicit conditions for their existence and local stability. In particular, I show that the boundary and interior equilibria exchange stability through a transcritical bifurcation, and I characterize analytically the subsequent loss of stability of the interior equilibrium via period-doubling and Neimark–Sacker bifurcations. Transversality is established in all cases, and the criticality of the bifurcations is determined through normal form and Lyapunov coefficient computations. I show that the period-doubling bifurcation can be supercritical or subcritical, while the Neimark–Sacker bifurcation is generically nondegenerate and may be either supercritical or subcritical, depending on parameter values. Full article

This paper deals with several equations of mathematical physics written in explicit form with their solutions. In Theorem 1, an oblique derivative problem for the string equation is studied. More precisely, the initial-boundary value problem for the string equation is investigated. The corresponding vector field on the boundary is non-vanishing and does not have a characteristic direction, but can be tangential to some part of the boundary, and it is allowed to change sign. A classical solution exists with suitable compatibility conditions at the corner points. The picture changes significantly in the case of the wave equation with several (say two: 2D) space variables in a circular cylinder. The initial-boundary value problem turns out to be underdetermined with an infinite-dimensional kernel if the boundary vector field is orthogonal to the time axis. By prescribing extra conditions on the generatrices of the cylinder where the vector field is tangential to the cylinder, we obtain a unique classical solution. In Theorem 2, we consider the Cauchy problem in the interior of the parabola of the Lorentzian-type eikonal equation and find its unique classical solution in $\{0\le x_2\le 1/2\}\cap \{x_2\ge {\displaystyle \frac{x_1^2}{2}}\}$. Propagation of singularities for the D and 3 D hyperbolic (Klein–Gordon) equations in ${\mathbf{R}}^4$, ${\mathbf{R}}^8$ is studied in Theorem 3. In the double characteristic points, the wave front propagates either along the surface of the characteristic cone, or in the solid cone starting from $(t_0,x_0)$. Full article

In this paper, we study a nonlinear system of sequential Caputo fractional differential equations equipped with coupled mixed multi-point boundary conditions. In particular, the boundary conditions involve the values of the unknown functions at the endpoints expressed as linear combinations of their values at several interior points, forming a closed system of relations. The existence of solutions is established by applying the Leray–Schauder alternative, while uniqueness is proved using Banach’s contraction principle. In addition, we investigate the Hyers–Ulam stability of the proposed system. Several examples are included to demonstrate the applicability of the theoretical results. Some special cases of the general problem are also discussed. Full article

Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by embedding physical conditions as soft penalties into the loss function. However, the coexistence of multiple loss components often leads to gradient conflicts, degrading convergence and solution accuracy. To address this issue, we propose a dynamic domain–gradient loss reweighting PINN (DDR-PINN). The proposed method introduces a dual-residual reweighting mechanism based on gradient variations, where adaptive weights are derived from the L2 norm of the dot product between loss gradients and residuals. These weights are further normalized through a nonlinear hyperbolic tangent transformation, enabling dynamic and balanced reweighting of interior, initial, and boundary domain losses throughout training. Extensive numerical experiments on PDEs with both Dirichlet and Neumann boundary conditions demonstrate that the DDR-PINN consistently outperforms the standard PINN, APINN, and VI-PINN with the fewest trainable parameters. Full article

We investigate the application of soft-cell tessellations—a recently discovered class of curved-boundary space-filling shapes—to finite element mesh generation. Using Gmsh and scikit-fem, we compare the solution accuracy for Poisson equation benchmarks on curved domains. The results demonstrate that soft-cell meshes achieve optimal $O\left(h^2\right)$ convergence rates in $L^2$, matching conventional elements. More significantly, we identify a fundamental limitation: coarse polygon boundaries introduce systematic boundary condition (BC) error (∼3%) that does not decrease with mesh refinement. We prove analytically that the BC error scales as $O(1/n^2)$ for n-point polygon boundaries, explaining why doubling boundary points reduces the error by $4\times$. Fine spline boundaries reduce this error by 96%, with the interior solution error reduced by 97.5%. For complex organic shapes, the improvement reaches 56–80%. We establish a connection between the soft-cell softness measure $\sigma$ and FEM accuracy: a higher softness yields a lower BC error. Comparison with Isogeometric Analysis reveals that while IGA achieves exact geometry (${10}^{-16}$ error), fine spline FEM boundaries reduce the geometric error by 5–6 orders of magnitude versus coarse polygons. These results establish that the boundary representation quality fundamentally limits the FEM accuracy on curved domains, making soft-cell representations particularly valuable. Full article

Extremes of the Edgeworth box concern corner allocations and their relationship to the contract curve in a two-good, two-agent exchange economy. In the standard pure-exchange setting with well-behaved preferences, the contract curve comprises all Pareto-efficient allocations, including interior tangencies and boundary corners, where no mutually beneficial trade remains. When money is introduced as a numéraire (a medium of exchange only), real feasibility and preferences are unchanged, so the contract curve remains the benchmark for efficiency. When money provides liquidity services (is valued for holding), agents may rationally abstain from trade even near interior tangencies; short-run outcomes can therefore include inaction at corners. This entry defines these objects, outlines the efficiency conditions at boundaries, and summarizes how monetary interpretations affect short-run behavior in general equilibrium and monetary economics. The Edgeworth geometry remains a real-exchange depiction; when we discuss money as a store of value, we use it as a short-run, reduced-form outside option that proxies intertemporal motives. This does not “fix” the box; it clarifies why no-trade at or near corners can be individually rational when liquidity is valued. Full article

In freeform optical metrology, wavefront fitting over non-circular apertures is hindered by the loss of Zernike polynomial orthogonality and severe sampling grid distortion inherent in standard conformal mappings. To address the resulting numerical instability and fitting bias, we propose a unified framework curve-shortening flow (CSF)-guided progressive quasi-conformal mapping (CSF-QCM), which integrates geometric boundary evolution with topology-aware parameterization. CSF-QCM first smooths complex boundaries via curve-shortening flow, then solves a sparse Laplacian system for harmonic interior coordinates, thereby establishing a stable diffeomorphism between physical and canonical domains. For doubly connected apertures, it preserves topology by computing the conformal modulus via Dirichlet energy minimization and simultaneously mapping both boundaries. Benchmarked against state-of-the-art methods (e.g., Fornberg, Schwarz–Christoffel, and Ricci flow) on representative irregular apertures, CSF-QCM suppresses area distortion and restores discrete orthogonality of the Zernike basis, reducing the Gram matrix condition number from >900 to <8. This enables high-precision reconstruction with RMS residuals as low as $3\times {10}^{-3}\lambda$ and up to 92% lower fitting errors than baselines. The framework provides a unified, computationally efficient, and numerically stable solution for wavefront reconstruction in complex off-axis and freeform optical systems. Full article

This study presents an in silico proof of concept exploring whether deep learning models can perform conditional mitochondrial DNA (mtDNA) sequence prediction across species boundaries. A CNN–BiLSTM model was trained under a leave-one-species-out (LOSO) scheme on complete mitochondrial genomes from 21 vertebrate species, primarily archosaurs. Model behavior was evaluated through multiple complementary tests. Under context-conditioned settings, the model performed next-nucleotide prediction using overlapping 200 bp windows to assemble contiguous 2000 bp fragments for held-out species; the resulting high token-level accuracy (>99%) under teacher forcing is reported as a diagnostic of conditional modeling capacity. To assess leakage-free performance, a two-flank masked-span imputation task was conducted as the primary evaluation, requiring free-running reconstruction of 500 bp interior spans using only distal flanking context; in this setting, the model consistently outperformed nearest-neighbor and demonstrated competitive performance relative to flank-copy baselines. Additional robustness analyses examined sensitivity to window placement, genomic region (coding versus D-loop), and random initialization. Biological plausibility was further assessed by comparing predicted fragments to reconstructed ancestral sequences and against composition-matched null models, where observed identities significantly exceeded null expectations. Using the National Center for Biotechnology Information (NCBI) BLAST web interface, BLASTn species identification was performed solely as a biological plausibility check, recovering the correct species as the top hit in all cases. Although limited by dataset size and the absence of ancient DNA damage modeling, these results demonstrate the feasibility of conditional mtDNA sequence prediction as an initial step toward more advanced generative and evolutionary modeling frameworks. Full article

Subglacial topography is a critical boundary condition for ice sheet models projecting past and future ice sheet–climate interactions. Contemporary ice-sheet-wide bed topography datasets are partially derived using mass conservation, but approximately 75% of the most widely used Greenland Ice Sheet (GrIS) dataset is based on simple interpolation of airborne radio-echo sounding (RES) measurements, such as kriging or streamline diffusion. Due to limited independent validation data, the errors and biases in this approach are poorly understood, creating largely unknown uncertainties in subglacial topography. Here, we interpolated synthetic RES observations of bed topography over ice-free areas with a known topography at a 5 m spatial resolution and quantify discrepancies. We found that the absolute error in kriged bed topography increases with distance from the input data, though at a reduced rate than previously estimated. The difference between an interpolated elevation estimate and the local mean elevation is a strong predictor of real bed errors (R² = 0.72), with further improvement as input observation sparsity increases (R² > 0.82). We propose a method to quantify and reduce uncertainty in kriged bed topography in sparsely surveyed regions, reducing uncertainty for at least 56% of the kriged interior at a 99% confidence interval. Our results suggest that subglacial depth is on average 5 m deeper than previous estimates, though individual areas may be shallower or deeper (σ = 41 m). Consequently, the area grounded below sea level is likely underestimated by 2%, increasing to 29% for regions deeper than 200 m. These findings have potential implications for the future stability of the GrIS under climate change. Full article

Urban parks are fundamental to building sustainable and inclusive cities, yet the mechanisms linking their spatial configuration to human activities and social functions remain insufficiently understood. A scalable multimodal framework is developed to quantify how spatial visibility is associated with patterns of park use and the provision of social ecosystem services. A total of 94,635 geo-tagged user-generated images from 148 parks in Vancouver, Canada, were analyzed using the Contrastive Language-Image Pretraining (CLIP) model to classify user activities into six behavioral categories. Concurrently, airborne LiDAR data and space syntax analysis were used to derive three visibility metrics—Mean Isovist Area (MIA), reflecting internal openness; Mean Visual Integration (MVI), indicating visual connectivity within the park interior; and External Isovist Ratio (EIR), representing edge openness and boundary visibility. The results indicate that EIR exhibits the strongest and most consistent relationships with user activity patterns, positively associated with family recreation, social vibrancy, and physical activity, while negatively linked to nature immersion and quiet relaxation. MIA shows moderate associations with socially interactive and child-oriented activities, whereas MVI contributes little explanatory power compared to localized visibility conditions. These findings highlight spatial visibility as a critical design attribute that is closely associated with human–forest interactions. By illustrating that moderate visual openness and edge permeability are associated with more inclusive and multifunctional patterns of park use, actionable insights are provided for urban park planning and design, and the promotion of social sustainability. Full article