Search Results (102)

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

The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems produces a Fokker–Planck equation with intractable mixed partial derivatives, preventing conventional analytical solutions. This paper develops a unified computational framework for three-dimensional linear Stratonovich stochastic systems using analytical derivation for degenerate cases and physics-informed neural network (PINN) approximation for general non-degenerate scenarios. For degenerate systems, we reduce the coefficient matrix to a lower triangular form via orthogonal transformation and establish tight upper bounds based on the logarithmic growth property of the Wiener process, yielding closed-form expressions for the maximal almost sure Lyapunov exponent under all parameter sign configurations. For non-degenerate systems, we reformulate the Fokker–Planck equation in spherical coordinates and construct a customized PINN with trigonometric encoding to enforce periodic boundary conditions. The network is trained by joint loss functions of equation residuals, boundary constraints and normalization consistency, and the converged stationary density is substituted into the Furstenberg–Khasminskii formula to calculate the exponent via Gauss–Legendre quadrature. Monte Carlo simulations confirm the accuracy and robustness of the proposed method, which reliably identifies the sign of the maximal almost sure Lyapunov exponent even in near-critical regimes. Numerical experiments on a 3D stochastic Hopf bifurcation model show that noise negatively shifts the bifurcation point, with the offset linearly proportional to the squared noise intensity. This work extends Lyapunov stability analysis from two-dimensional to three-dimensional linear Stratonovich stochastic systems, offering an effective tool for stability evaluation of general three-dimensional stochastic dynamical models. Full article

In this paper, we consider the one-dimensional liquid crystal flow with a vacuum free boundary and a degenerate viscosity coefficient. The global existence and long-time dynamics of strong solutions are established under a smallness condition on the initial energy at the basic level. The main challenges come from the degeneracy near the moving boundary and the strong nonlinear coupling between the velocity and the director field. To overcome these, we obtain uniform-in-time and space point-wise bounds of the deformation variable, and we construct uniform-in-time weighted energy estimates via singular multiplier techniques. Unlike previous works, the density is allowed to vanish and the viscosity coefficient is taken to be density-dependent rather than constant. Full article

Background/Objectives: Retinal layer segmentation in optical coherence tomography (OCT) is essential for the diagnosis and monitoring of retinal diseases such as age-related macular degeneration (AMD) and diabetic macular edema (DME). Although deep learning methods have achieved strong performance, most rely on dense pixel-wise predictions and often struggle to preserve anatomical consistency, particularly in regions with low contrast or structural deformation. This study aims to address these limitations by introducing a query-based segmentation framework that explicitly models retinal layer structure. Methods: In this paper, we propose the RetiQueryNet architecture that employs encoding of retinal layers in the form of query embeddings with the use of cross attention to interact with pixel level features encoded by a transformer based encoder. The architecture integrates multi-scale features through a compact query-driven decoder with modest additional computational overhead. Normalization and resizing of OCT images preceded their usage as inputs, while the layer labels were converted to multi-class segmentation maps. In the training process, we used loss function with combination of cross entropy loss and Dice loss. Our model performance was compared with multiple state-of-the-art models such as U-Net, DeepLabV3, FPN, MANet and SegFormer, while performance metrics were Dice, IoU and mean surface distance (MSD). Results: RetiQueryNet was able to attain a mean Dice score of 0.934 ± 0.0046 and outperformed all baseline models on the main performance measures. Improvements were particularly evident in challenging retinal layers such as IBRPE and OBRPE, where boundary ambiguity is high. It should be noted that RetiQueryNet had a relatively lower MSD value, meaning that the predicted boundaries were more accurate. Furthermore, visual observations suggest that the approach generated smooth and coherent segmentations. Conclusions: The findings demonstrate that query-based modeling offers a viable approach to pixel-wise segmentation. In particular, by making use of structural priors in the form of learnable queries, RetiQueryNet improves not only segmentation accuracy but also anatomical consistency. Query-based modeling appears to be an exciting area for retinal image segmentation that could potentially be applied to other applications in medical image segmentation. Full article

This article introduces and develops a comprehensive theory of the Mixed Degenerate Gould–Hopper–Appell Type Polynomials $MDGHA$-$TPs$, constructed by embedding an Appell factor into the framework of degenerate Gould–Hopper generating functions. Beginning with the generating function formulation, we derive explicit series representations, monomial-type operational identities, recurrence relations, and a determinantal form that encodes the algebraic structure of the family. Summation identities expressed via Stirling numbers of the first kind and addition-type formulas are established. A detailed numerical investigation of the zero distributions of these polynomials is then carried out, with graphical illustrations revealing symmetry patterns and geometric arrangements in the complex plane. Connections with classical sequences of Appell, Hermite, and Gould–Hopper are explored throughout. The article concludes with remarks on open problems including the orthogonality of the $MDGHA$-$TPs$ with respect to suitable weight functions, the asymptotic behaviour of their zeros as the degree tends to infinity, and potential applications to boundary-value problems in heat diffusion, perturbation expansions in quantum mechanics, and signal processing in non-homogeneous media. Full article

Deriving rigorous elastoplastic analytical solutions for shallow tunnels subject to a gravity-induced stress gradient presents significant mathematical challenges. This paper introduces a virtual cylindrical structure model to derive a closed-form elastoplastic solution for tunnel excavation. By evaluating the static equilibrium of infinitesimal elements, the methodology explicitly determines the plastic zone boundary via the Lambert W function and yields the elastoplastic distributions of stress and displacement fields under the Mohr–Coulomb criterion. The reliability of the derivations is verified by degenerating the equations under specific boundary conditions and comparing them with classical Lamé solutions, showing agreement at low friction angles ($\varphi =5°-10°$). A case study of a 14.5 m-diameter shield tunnel in the Yangtze River Delta is conducted to demonstrate its practical application. The analytical results show that the maximum convergence displacement is controlled within 15 mm, and a ground loss rate of 1.82% corresponds to an unloading ratio of 40%. The proposed method provides a theoretical tool for preliminary estimating excavation-induced disturbances in shallow homogeneous strata. Full article

Purpose: The purpose of this study was to characterize the distribution and longitudinal evolution of intraretinal and subretinal hyperreflective foci (HF) in treatment-naive neovascular age-related macular degeneration (nAMD), and to examine associations between HF burden, hyperreflective material boundary remodeling (HRM-BR), and best-corrected visual acuity (BCVA) outcomes following bevacizumab treat-and-extend therapy. Methods: This was a retrospective observational study of 84 treatment-naive nAMD eyes receiving intravitreal bevacizumab via a treat-and-extend protocol. Spectral-domain OCT (Revo FC, Optopol) was performed at baseline (M0), month 3 (M3), and month 6 (M6). HF were quantified in the intraretinal and subretinal compartments using ImageJ software (version 1.54, National Institutes of Health, Bethesda, MD, USA) by two masked graders, with inter-rater agreement assessed by intraclass correlation coefficient (ICC). Eyes were classified into four HRM evolution patterns following the framework of Yu et al. Primary outcome was BCVA change from M0 to M6. Multivariable linear regression was performed to assess independent predictors of BCVA change. Results: Baseline intraretinal HF counts increased significantly across HRM Patterns 1 through 4 (median 0, 6, 4, and 8, respectively; Kruskal–Wallis p < 0.001; 95% CI for Spearman r = 0.471: [0.286, 0.623]). A higher baseline intraretinal HF count correlated with worse BCVA change at M6 (r = −0.300, 95% CI [−0.483, −0.092], p_adj = 0.010). In the primary multivariable model (n = 67), both intraretinal HF burden (β = −0.449, 95% CI [−0.879, −0.020], p = 0.041) and HRM width (β = −0.003, 95% CI [−0.005, −0.001], p = 0.014) were independent predictors of BCVA change. The transient M3 intraretinal HF peak in Pattern 3 eyes (median 4 → 12 → 4) was statistically confirmed by Wilcoxon signed-rank testing (M0 → M3: p = 0.004; M3 → M6: p = 0.001). Conclusions: Intraretinal HF burden is a graded marker of HRM pattern severity and an independent predictor of visual outcomes in nAMD, alongside HRM width. The statistically validated transient M3 HF peak in Pattern 3 may represent an early OCT signal of active boundary remodeling. Full article

Against the policy backdrop of high-quality development and the “Dual Carbon” goals, corporate environmental responsibility and green governance have emerged as core drivers of corporate value creation and resource allocation in capital markets. However, in practice, corporate environmental disclosure has increasingly degenerated into an impression management tool. Using a sample of China’s A-share listed companies from 2011 to 2024, this paper combines text analysis of annual reports with green patent data to systematically examine the impact of performance feedback on corporate strategic environmental decoupling, drawing upon the behavioral theory of the firm and legitimacy theory. The findings are as follows: First, negative performance feedback significantly increases corporate greenwashing propensity, whereas positive performance feedback significantly strengthens corporate brownwashing behavior. Second, government regulation amplifies the costs of falsifying environmental information, significantly suppressing the positive impact of negative performance feedback on greenwashing, but exacerbating the positive impact of positive performance feedback on brownwashing. Conversely, media attention amplifies the benefits of corporate green performances, significantly strengthening the catalytic effect of negative performance feedback on greenwashing, while effectively suppressing the positive impact of positive performance feedback on brownwashing. Third, heterogeneity analysis reveals that the impact of performance feedback on corporate strategic decoupling in environmental disclosure is more pronounced among non-state-owned enterprises, firms facing high industry competitive pressure, and those in heavily polluting industries. By integrating greenwashing and brownwashing into a unified analytical framework, this study expands the research boundaries of corporate environmental disclosure and strategic behaviors. Furthermore, it deepens the application contexts of the behavioral theory of the firm within non-financial disclosure, deconstructs the myth of homogeneous governance effects under legitimacy pressure, and provides vital implications for investors, policymakers, and fund managers. Full article

Yeast harbour more than ten different multiple drug resistance (MDR) genes encoding transporters that extrude xenobiotics from the cytoplasm into the environment. These transporters, belonging to the ATP-binding cassette (ABC) or major facilitator superfamily (MFS), exhibit broad and significantly overlapping substrate specificities, though the precise boundaries of their individual substrate ranges remain undefined. During evolution, genes with overlapping functions tend either to specialize or to degenerate into pseudogenes. Here, we propose several explanations for how this apparent redundancy of MDR efflux pumps benefits cells, and we discuss the potential individual roles of the full MDR efflux pump repertoire in the model organism Saccharomyces cerevisiae. We posit that individual MDR transporters may vary in stability under challenging environmental conditions, in the energetic cost of their synthesis and maintenance, and in their degree of specialization toward particular classes of xenobiotics. Furthermore, given that ABC transporters and MFS transporters exploit distinct driving forces for xenobiotic efflux, each class may have its own vulnerabilities. We argue that deciphering the distinct roles of MDR proteins will reveal critical weaknesses in the MDR system and guide the development of strategies to overcome multidrug resistance in pathogenic fungi. Full article

Age-related macular degeneration (AMD) is the leading cause of central vision loss in aging populations. Geographic atrophy (GA) is the advanced, non-neovascular form of AMD. Predicting the longitudinal progression of GA remains a critical challenge in ophthalmic clinical practice and clinical trial design. Forecasting the trajectory of GA is complicated by highly variable growth rates and the inherent scarcity of long-term, high-quality imaging data. To address these challenges, we introduce the Sliding Window Attention U-Net (SWAU-Net), a hybrid architecture that integrates Transformer-based temporal modeling of GA growth with precise spatial modeling of GA location with a U-Net convolutional neural network (CNN). To ensure generalization in the low-data regime, SWAU-Net embeds explicit temporal and geometric consistency priors via a weight-shared Sliding Window Attention core and feature-level regularization that preserves sparse, high-frequency lesion boundaries across frames. Experimental results demonstrate that these structural constraints prevent the model from overfitting to imaging noise, achieving a Growth Mask Dice Similarity Coefficient (DSC) of 0.66 (representing the spatial overlap between the predicted and ground truth lesion expansion regions), a significant improvement over unregularized Transformer and standard recurrent baseline models. Our framework provides a robust tool for predicting GA lesion trajectories, potentially supporting more efficient clinical trial designs and personalized patient monitoring. Full article

This study employed a Gleeble-3800TM thermal simulator to conduct thermal cycle experiments on the coarse-grained heat-affected zone (CGHAZ) of Nb-Ti-La microalloyed steel under welding heat inputs of 50, 80, 100, and 120 kJ/cm. A systematic analysis was carried out to investigate the influence of heat input on the microstructure and impact toughness of the CGHAZ. The results indicate that the microstructure of the CGHAZ across different heat inputs consists of acicular ferrite (AF), granular bainite ferrite (GBF), polygonal ferrite (PF), as well as hard phases such as M/A constituents and degenerated pearlite (DP). With increasing heat input, the content of GBF decreases monotonically, while the content of PF increases monotonically, and the amount of hard phases rises continuously. In contrast, the content of AF initially increases and then decreases, reaching its peak at 100 kJ/cm. The microstructural changes induced by higher heat input lead to increased inhomogeneity in the local microstrain, thereby causing a monotonic reduction in crack initiation energy. Regarding crack propagation energy, the optimal performance is achieved at 100 kJ/cm due to the formation of a high proportion of AF, which heterogeneously nucleates on La-rich inclusions. This structure provides a high density of high-angle grain boundaries that effectively hinder crack propagation. Consequently, under the combined influence of crack initiation and propagation behaviors, the CGHAZ exhibits the best impact toughness at a heat input of 100 kJ/cm. Full article

This paper presents an analytical model for one-dimensional consolidation analysis of multi-layered unsaturated soils under depth-dependent initial conditions. The general solutions are derived explicitly using the Laplace transform. By combining these general solutions with interfacial continuity conditions between layers and the boundary conditions, the reduced-order system is solved via the Euler method to obtain analytical solutions in the Laplace domain. Numerical inversion of the Laplace transform is then performed using Crump’s method to yield the final analytical solutions in the time domain. The model incorporates initial conditions that account for both uniform and linear distributions of initial excess pore pressure within the soil stratum. The proposed solution is verified by reducing it to degenerated cases (e.g., uniform initial pressure) and comparing it with existing analytical solutions, showing excellent agreement. This confirms the model’s correctness and demonstrates its generalization to multi-layered systems with depth-dependent initial conditions. Focusing on a double-layered unsaturated soil system, the one-dimensional consolidation characteristics under depth-dependent initial conditions are investigated by varying the physical parameters of individual layers. The proposed solution can serve as a theoretical reference for the consolidation analysis of multi-layered unsaturated soils with depth-dependent initial conditions. Full article

Background/Objectives: The aberrant subclavian artery (ASA) represents the most common congenital anomaly of the aortic arch, and is frequently associated with a Kommerell diverticulum, an aneurysmal dilation at the anomalous vessel origin. This condition carries a significant risk of rupture and dissection, and growing evidence indicates that local hemodynamic alterations may contribute to its development and progression. Computational Fluid Dynamics (CFD) provides a valuable non-invasive modality to assess biomechanical stresses and elucidate the pathophysiological mechanisms underlying these vascular abnormalities. Methods: In this study, twelve thoracic CT angiography scans were analyzed: six from patients with ASA and six from individuals with normal aortic anatomy. CFD simulations were performed using OpenFOAM, with standardized boundary conditions applied across all cases to isolate the influence of anatomical differences in flow behavior. Four key hemodynamic metrics were evaluated—Wall Shear Stress (WSS), Oscillatory Shear Index (OSI), Drag Forces (DF), and Turbulent Viscosity Ratio (TVR). The aortic arch was subdivided into Ishimaru zones 0–3, with an adapted definition accounting for ASA anatomy. For each region, time- and space-averaged quantities were computed to characterize mean values and oscillatory behavior. Conclusions: The findings demonstrate that patients with ASA exhibit markedly altered hemodynamics in zones 1–3 compared to controls, with consistently elevated WSS, OSI, DF, and TVR. The most pronounced abnormalities occurred in zones 2–3 near the origin of the aberrant vessel, where disturbed flow patterns and off-axis mechanical forces were observed. These features may promote chronic wall stress, endothelial dysfunction, and localized aneurysmal degeneration. Notably, two patients (M1 and M6) displayed particularly elevated drag forces and TVR in the distal arch, correlating with the presence of a distal aneurysm and right-sided arch configuration, respectively. Overall, this work supports the hypothesis that aberrant hemodynamics contribute to Kommerell diverticulum formation and progression, and highlights the CFD’s feasibility for clarifying disease mechanisms, characterizing flow patterns, and informing endovascular planning by identifying hemodynamically favorable landing zones. Full article

This study utilizes approximation techniques to address a boundary value problem involving a differential equation with a delayed argument. The problem is approached through analytical techniques by transforming it firstly into an equivalent integral equation. Specifically, we derive a Fredholm–Volterra integral equation that encapsulates the delayed behavior inherent in the original differential equation. The Fredholm operator in this equation features a degenerate kernel, which enables simplification and facilitates the construction of successive approximations. To solve this integral equation, we employ the two-sided convergence method, a powerful iterative technique that generates two sequences of approximate solutions—lower and upper bounds—that converge monotonically toward the exact solution. This method is particularly well-suited for problems with delayed arguments, as it ensures both stability and convergence under appropriate conditions on the kernel functions. The main objective of the study is to demonstrate the applicability and accuracy of the Simple Two-Sided Convergence Method for this class of boundary value problems. A numerical example is presented to illustrate the theoretical results, and the obtained approximations are compared with the exact analytical solution. All computations were carried out using Maple, ensuring precise numerical evaluation. Full article

Purpose: This study aims to develop a method for detecting referable (intermediate and advanced) age-related macular degeneration (AMD) and neovascular AMD, as well as providing an automatic segmentation of choroidal neovascularisation (CNV) on colour fundus retinal images. We also demonstrated that brain health risk scores estimated by AI-based Retinal Image Analysis (ARIA), such as white matter hyperintensities and depression, are significantly associated with AMD and neovascular AMD. Methods: A primary dataset of 1480 retinal images was collected from Zhongshan Hospital of Fudan University for training and 10-fold cross-validation. Additionally, two validation subdataset comprising 238 images (retinal images and wide-field images) were used. Using fluorescein angiography-based labels, we applied the InceptionResNetV2 deep network with the ARIA method to detect AMD, and a transfer ResNet50_Unet was used to segment CNV. The risks of cerebral white matter hyperintensities and depression were estimated using an AI-based Retinal Image Analysis approach. Results: In a 10-fold cross-validation, we achieved sensitivities of 97.4% and 98.1%, specificities of 96.8% and 96.1%, and accuracies of 97.0% and 96.4% in detecting referable AMD and neovascular AMD, respectively. In the external validation, we achieved accuracies of 92.9% and 93.7% and AUCs of 0.967 and 0.967, respectively. The performances on two validation sub-datasets show no statistically significant difference in detecting referable AMD (p = 0.704) and neovascular AMD (p = 0.213). In the segmentation of CNV, we achieved a global accuracy of 93.03%, a mean accuracy of 91.83%, a mean intersection over union (IoU) of 68.7%, a weighted IoU of 89.63%, and a mean boundary F1 (BF) of 67.77%. Conclusions: The proposed method shows promising results as a highly efficient and cost-effective screening tool for detecting neovascular and referable AMD on both retinal and wide-field images, and providing critical insights into CNV. Its implementation could be particularly valuable in resource-limited settings, enabling timely referrals, enhancing patient care, and supporting decision-making across AMD classifications. In addition, we demonstrated that AMD and neovascular AMD are significantly associated with increased risks of WMH and depression. Full article