A fully discrete semi-implicit numerical scheme and its optimal error estimates for Cahn-Hilliard-MHD model with variable density

Abstract There exist unique northeastward counterwind currents (CWCs) over the China shelf seas, subject to the balance between the northeastward alongshore ageostrophic (effective) pressure gradient force (PGF eff , the residual PGF after balancing the Coriolis force) and southwestward surface wind stress forcing. The underlying physics for the formation of the alongshore PGF remains largely ambiguous. We used process-oriented modeling of the China shelf seas to investigate how the alongshore PGF and subsequent CWC form. Driven by a typical alongshore variable density field and wind forcing, our numerical model produced a realistic shelf current structure and CWC. Our results show that the alongshore sea level elevation gradient, induced by an alongshore variable wind, mainly contributed to the PGF, which is consistent with arrested topographic wave theory. However, the wind-induced elevation gradient alone is insufficient to overcome the frictional effects of wind forcing to form the CWC. The alongshore density gradient, due to heterogeneous heating, enhances the PGF because of the steric effect on sea level. The enhanced PGF produced by the density gradient and wind-induced elevation gradient critically forms the CWC. In addition, the seasonally variable density gradient and wind forcing determine the spatiotemporal variability of the CWC. We found that the dominant intrinsic dynamics of the wind and buoyancy forcing are enough to trigger the CWCs, and the shelf’s topographic features further shape the structure of the CWC. The study provides new insights into the formation of CWC, which has been widely observed over the shelves globally.

An unconditionally stable hybrid discontinuous Galerkin scheme for a Cahn–Hilliard phase-field model of two-phase incompressible flow with variable densities

Tire wear particles (TWPs) are increasingly recognised as a contaminant of emerging concern, owing to their toxic and omnipresent nature. Given these characteristics, it is imperative to discuss their occurrence and fate across different environmental matrices and critically examine the current state-of-the-art technologies utilised for their sampling, detection and analysis. This review provides a comprehensive overview of the physicochemical characteristics of TWPs, their occurrence, environmental fate, and detection methodologies. It further investigates the dominant methodological bottlenecks in the detection and quantification of TWPs across different environmental matrices, highlighting key challenges in their atmospheric and waterborne cycling, including inconsistent emission estimates, a lack of standardised protocols, and a limited understanding of transport and transformation processes. Our findings revealed that TWPs are ubiquitous across all environmental matrices; however, their transport and transformation remain poorly constrained due to variable density, aggregation, ageing and additive leaching behaviour, all of which complicate modelling efforts. In addition, we also concluded that despite rapid progress in spectroscopic, thermal and mass-based approaches, there remains no standardised, matrix-independent method potent enough for achieving simultaneous chemical specificity, particle-scale resolution, and quantitative recovery. Such findings emphasise the urgent need for harmonised analytical workflows and integrative studies linking physicochemical properties to environmental mobility and toxicity. This review thus establishes a conceptual framework for bridging analytical advances with environmental process understanding, an essential step towards reliable risk evaluation of tire-derived microplastics. It further offers essential insights to researchers, policymakers, and environmental professionals determined to better comprehend and alleviate the effects of tire wear particles on ecosystems and human health.

Abstract Mapping basement relief in sedimentary basins is of great significance for resource exploration. Inverting gravity anomalies to obtain basement depth requires prior information on the mean basement depth and the density contrast between the sedimentary layer and the basement. However, these two key parameters are often difficult to determine accurately. We propose a gravity inversion method for basement depth that uses known depth control points as constraints. This method does not require prior knowledge of the mean depth and density contrast, as they are automatically updated during the iterative estimation of the basement relief. Tests on synthetic models of sedimentary basin basements confirm the validity of our proposed method. The method is unaffected by constant offsets in the gravity anomaly and requires only two depth control points to automatically estimate the basement depth. It is also applicable to models with variable density contrasts, as it automatically obtains a density contrast that matches the gravity anomalies and known depths, representing the average effect of the density contrast across the entire sedimentary basin. Our method is sensitive to noise in gravity data, so filtering of the gravity anomalies is necessary before inversion. Additionally, since the method relies on known depth control points, it is sensitive to uncertainties in the control point depths. The correctness of our proposed method is ultimately verified through its application to mapping the basement depth of the Ordos Basin.

Simulating the dispersion of high-buoyancy pollutant is challenging because of the change in fluid density. A species transport (ST) model, which accounts for variable fluid density, was first validated by simulating light and heavy gas dispersion around a cubic building using computational fluid dynamics (CFD). This validated model was then employed to study wind flow and gas dispersion with varying plume buoyancies inside a two-dimensional street canyon. The applicability of a commonly used passive scalar transport (PST) model for simulating high-buoyancy gas dispersion was evaluated through comparisons with the ST model. The simulations demonstrated that the difference between the results of PST and ST models was negligible when a small amount of high-buoyancy pollutant was released, regardless of the gas type. However, when the emission rate was high, the fluid density was significantly altered, causing the results of the PST model to deviate substantially from those of the ST model. A clockwise recirculation was observed in all cases. This recirculation was strengthened when a large amount of light gas was released because of the positive buoyancy effect, resulting in low pollution levels. In contrast, the recirculation was suppressed, leading to high pollution levels in the case of heavy gas dispersion. This study indicated that both pollutant type and emission rate must be considered when using the PST model to simulate high-buoyancy gas dispersion.

Background/Objectives: Scaphoid fractures are a common wrist injury, typically diagnosed and treated through X-ray imaging, a process that is often time-consuming. Among the various types of scaphoid fractures, occult and nondisplaced fractures pose significant diagnostic challenges due to their subtle appearance and variable bone density, complicating accurate identification via X-ray images. Therefore, creating a reliable assist diagnostic system based on deep learning for the scaphoid fracture detection and localization is critical. Methods: This study proposes a scaphoid fracture detection and localization framework based on diffusion models. In Stage I, we augment the training data set by embedding fracture anomalies. Pseudofracture regions are generated on healthy scaphoid images, producing healthy and fractured data sets, forming a self-supervised learning strategy that avoids the complex and time-consuming manual annotation of medical images. In Stage II, a diffusion-based reconstruction model learns the features of healthy scaphoid images to perform high-quality reconstruction of pseudofractured scaphoid images, generating healthy scaphoid images. In Stage III, a U-Net-like network identifies differences between the target and reconstructed images, using these differences to determine whether the target scaphoid image contains a fracture. Results: After model training, we evaluated its diagnostic performance on real scaphoid images by comparing the model’s results with precise fracture locations further annotated by physicians. The proposed method achieved an image area under the receiver operating characteristic curve (AUROC) of 0.993 for scaphoid fracture detection, corresponding to an accuracy of 0.983, recall of 1.00, and precision of 0.975. For fracture localization, the model achieved a pixel AUROC of 0.978 and a pixel region overlap of 0.921. Conclusions: This study shows promise as a reliable, powerful, and scalable solution for the scaphoid fracture detection and localization. Experimental results demonstrate the strong performance of the denoising diffusion models; these models can significantly reduce diagnostic time while precisely localizing potential fracture regions, identifying conditions overlooked by the human eye.

Over the last decade, significant progress has been made in image dehazing, particularly with the advent of deep learning-based methods. However, many of the existing dehazing approaches face critical limitations such as relying on assumptions that fail under complex atmospheric conditions. This results in poor visibility restoration. To address this, this study proposes Dehaze-Attention, an improved image dehazing model designed to handle variable haze densities while preserving essential structural information. The proposed model introduces several contributions. First, it employs advanced feature extraction through convolutional layers to capture foundational details from hazy images. Second, an attention mechanism is integrated into architecture, enabling the model to dynamically focus on relevant features and reduce information loss. Third, a multi-scale network structure is incorporated to process haze across different densities by combining global and local feature analysis. The model was evaluated on a synthesized set of hazy images derived from the UDTIRI dataset under diverse atmospheric conditions. Experimental results demonstrated that the proposed Dehaze-Attention model achieves state-of-the-art performance, with significant improvements in both quantitative metrics (PSNR and SSIM) and subjective evaluations compared to baseline models. The results highlight that the improved model can be used for applications in aerial imaging, autonomous systems, and remote sensing.

We investigate the asymptotic behavior of solutions to the Cauchy problem for a nonlinear parabolic equation with double variable density as . This equation models heat diffusion with nonlinear absorption at the critical value of the parameter . For the numerical simulations, the long-term asymptotic form of the solution was used as the initial approximation. Numerical experiments and visualizations were then performed.

Tailings dams, critical for storing mine waste and water, must maintain stability and functionality throughout their lifespan. Their design and risk assessment are complicated by significant uncertainties stemming from multivariable parameters, including material properties, loading conditions, and operational decisions. Traditional dam design and risk assessment procedures often rely on first-order probabilistic approaches, which fail to capture the complex, multi-layered nature of these uncertainties fully. This paper reviews the current tailings dam design practice and proposes the application of Bayesian networks (BNs) to analyse the epistemic and aleatory uncertainty inherent in tailings dam design parameters and risk assessment. By representing these uncertainties explicitly, BNs can facilitate more robust and targeted design strategies. The proposed approach involves several key steps, including parameterisation—design input variable probability density function and uncertainty, knowledge elicitation, and model assessment and integration. This methodology provides a sophisticated and comprehensive approach to accounting for the full spectrum of uncertainties, thereby enhancing the reliability of tailings dam designs and risk management decisions.

The design of the metro body structure must balance both safety and cost indicators. The underframe is not only the main load-bearing component of the metro body but also accounts a significant portion of its overall mass. To reduce operational costs and enhance the safety performance of the metro body, this paper focuses on optimizing the design of the underframe. A two-stage optimization approach was proposed, addressing the limitation of existing methods and the challenges in balancing realistic operating conditions with manufacturability. First, manufacturing constraints were incorporated using the variable density method, and topology optimization of the underframe sub-model was carried out with the objective of minimizing flexibility-weighted strain energy. Next, the rough topology was refined through parametric optimization after determining the approximate shape of the cross section, resulting in a more precise model. The results show that the proposed optimization method reduces underframe mass by about 4.7 % while lowering the maximum deflection of the metro car body under the maximum vertical load case by 0.601 mm. This demonstrates that the proposed framework efficiently combines optimization capabilities with simplicity.

Cementing quality is a key factor in ensuring the long-term safe production of oil and gas wells and preventing defects. Traditional cementing quality evaluation mainly relies on logging interpreters manually analyzing acoustic logging data, such as Variable Density Logging (VDL) images and acoustic amplitude curves. This process is highly dependent on personal experience, labor-intensive, and inefficient. To address these issues, this paper proposes an automated cementing quality detection method, CemQ-CNN, based on a Convolutional Neural Network (CNN). In this context, “intelligent” refers to the model’s ability to perform automatic classification from raw data, thereby increasing efficiency and consistency. This method constructs a multimodal input CNN model that can simultaneously process VDL images and acoustic logging curve data, achieving automatic, fast, and accurate classification of cementing quality. We collected and labeled 5,000 logging samples from 150 different wells across three distinct geological blocks, ensuring dataset diversity, categorizing them into three cementing quality levels: “good,” “medium,” and “poor.” By allocating 70% of the data for training, 15% for validation, and 15% for testing, our model demonstrated Good performance on the test set. Experimental results show that the proposed method achieves an overall classification accuracy of 95.7%, demonstrating robust performance across all three quality classes (‘Good’, ‘Medium’, and ‘Poor’), with a macro-average recall rate of 95.6% and a precision rate of 95.5%. Compared to models using a single data source, this multimodal model performs better. The study demonstrates that an effective intelligent method based on CNN can assist and standardize traditional manual interpretation, providing a reliable and innovative paradigm for cementing quality evaluation.

Track-etched polycarbonate (PC) membranes with nanochannels are versatile materials for electrochemical, energy-harvesting, and separation applications. Precise control over their surface charge is critical, as it governs ion selectivity, electroosmotic flow, and overall ionic transport behaviour in confined nanochannels. However, environmentally friendly and scalable strategies to precisely tune their surface charge remain limited. Amination is a practical approach for PC membrane functionalisation, as it introduces protonatable amine groups that enhance the positive surface charge and enable further chemical modifications via mild, aqueous reactions. Here, we report a simple aqueous amination method that enables systematic control of surface charge density in PC membranes between 0.0015–0.0034 C cm−2. Commercial PC membranes with nominal pore sizes of 0.015, 0.05, and 0.1 µm were functionalised with a series of amines, hexamethylenediamine (HMDA), triethylenetetramine (TETA), polyethyleneimine (PEI), and glycine (Gly), through urethane-bond formation with surface carbonyl groups under mild aqueous conditions. Elemental and spectroscopic analyses confirmed efficient functionalisation and tuneable nitrogen content (9.7–22.6 at%), related to variable surface charge density, achieved by varying reaction parameters such as concentration, time, temperature, and amine type. The highest surface charge density of 0.0034 C cm−2 was achieved using 5% w/v TETA on PC membranes with 0.1 µm diameter. This scalable, low-energy pathway for PC membrane functionalisation is even compatible with ultrasmall pores, down to ∼15 nm. The charge densities achieved through this green aqueous functionalisation are the highest among other surface charge-tuning methods, such as plasma, ultraviolet, or polymer-grafting methods. Aqueous amination-based functionalisation is suitable for fabricating charge-tuneable, ion-selective membranes for nanofluidic energy conversion, electrochemical sensing, and other surface-charge-governed applications.

ObjectivesTo evaluate the feasibility and manufacturing robustness of integrating the novel β-lactam/β-lactamase inhibitor combination cefepime/enmetazobactam (FEP/META) which has been approved by FDA, EMA and MHRA, into Bruker’s antimicrobial susceptibility testing (AST) devices. Specifically, we investigated the accuracy, stability and production compatibility of FEP/META within broth microdilution-based AST systems using both manual and automated methodologies.MethodsAn initial feasibility assessment was performed using 96-well microbroth dilution plates, manually filled with FEP/META solution and vacuum-dried. Susceptibility testing was conducted using four quality control strains: Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, E. coli ATCC 35218 and Klebsiella pneumoniae ATCC 700603. Each strain was tested in biological triplicates with variable inoculum densities. MICs were determined both visually and using two photometers. To evaluate solution stability, testing was repeated after 28 days using the same preparation. Subsequently, an automated filling process was employed to simulate production-scale manufacturing under two distinct methods (Parameter A and Parameter B). AST was conducted using the previously mentioned strains as biological triplicates with variations in inoculum density over 3 days, and MICs recorded visually and photometrically.ResultsOf the 288 MIC values generated during the manual feasibility study, 100% fell within CLSI-defined quality control (QC) ranges. After 28 days of storage, 287/288 MIC results remained within QC, confirming the solution's short-term stability. The single deviation was attributed to a photometer anomaly, not compound degradation. Under automated production, 861 out of 864 MIC results (99.7%) were within QC ranges across both production parameters. All deviations were traced to a single skipped well, consistently identified across visual and photometric readings, suggesting an isolated technical anomaly with a frequency of 1 in 288 biological data points (3 out of 864 total readings). While both production settings yielded equivalent QC compliance, parameter B demonstrated more uniform MIC distribution within target ranges and was selected for future use.ConclusionsThis multi-phase in-vitro study demonstrated that FEP/META can be effectively and reliably integrated into Bruker’s AST devices using both manual and automated processes. Across three independent experiments and 1440 total MIC readings, 99.7% fell within CLSI QC ranges, confirming analytical robustness. Additionally, FEP/META antibiotic solution showed stability over at least 28 days. Based on comparative performance, production process parameter B was chosen for continued development. These efforts will support the deployment of FEP/META in AST platforms as a reliable option for detecting susceptibility in Enterobacterales and P. aeruginosa.

This study investigates the delineation of human agglomerations within the framework of ensuring compliance with the Urban Wastewater Treatment Directive. Focusing on the case study of Craiova agglomeration, the analysis examines the critical parameters that define urban areas requiring enhanced wastewater treatment infrastructure. By assessing demographic, geographic, and administrative boundaries, the study identifies key factors that influence the classification of urban settlements as eligible for directive-specific sanitation improvements. The research employs a mixed-method approach, incorporating both qualitative and quantitative analyses. Spatial data mapping and field observations underscore the challenges faced by urban planning authorities in delineating boundaries consistent with EU regulatory standards. These challenges include rapid urbanization, variable population densities, and resource allocation disparities, which complicate the effective management of wastewater treatment systems. Methodical evaluation of human agglomerations, based on standardized metrics, can facilitate improved implementation of wastewater treatment policies. The results further suggest that local governments need to adopt integrative planning strategies that consider the evolving dynamics of urban growth. Ultimately, this study contributes to a better understanding of urban boundary setting and provides recommendations for policy adjustments to ensure sustainable urban wastewater management practices.

This paper investigates the evolution of a blast wave propagating through a self-gravitating, non-ideal gaseous medium subjected to an azimuthal magnetic influence. A power series approach is applied to formulate approximate solutions for the primary flow quantities, utilizing Sakurai's analytical technique. The study presents both zeroth- and first-order approximations, including explicit expressions for the zeroth-order terms. To examine the nature of the resulting flow structure across the shock boundary, graphical analyses are conducted for key variables such as density, velocity, pressure, magnetic influence, and mass distribution, based on the zeroth-order profiles.

Rapid and precise intervention in disaster and medical-aid scenarios demands aerial platforms that can both survey and physically interact with their environment. This study presents the design, fabrication, modeling, and experimental validation of a one-piece, 3D-printed quadcopter with an integrated six-degree-of-freedom aerial manipulator robotic arm tailored for emergency response. First, we introduce an ‘X’-configured multi-rotor frame printed in PLA+ and optimized via variable infill densities and lattice cutouts to achieve a high strength-to-weight ratio and monolithic structural integrity. The robotic arm, driven by high-torque servos and controlled through an Arduino-Pixhawk interface, enables precise grasping and release of payloads up to 500 g. Next, we derive a comprehensive nonlinear dynamic model and implement an Extended Kalman Filter-based sensor-fusion scheme that merges Inertial Measurement Unit, barometer, magnetometer, and Global Positioning System data to ensure robust state estimation under real-world disturbances. Control algorithms, including PID loops for attitude control and admittance control for compliant arm interaction, were tuned through hardware-in-the-loop simulations. Finally, we conducted a battery of outdoor flight tests across spatially distributed way-points at varying altitudes and times of day, followed by a proof-of-concept medical-kit delivery. The system consistently maintained position accuracy within 0.2 m, achieved stable flight for 15 min under 5 m/s wind gusts, and executed payload pick-and-place with a 98% success rate. Our results demonstrate that integrating a lightweight, monolithic frame with advanced sensor fusion and control enables reliable, mission-capable aerial manipulation. This platform offers a scalable blueprint for next-generation emergency drones, bridging the gap between remote sensing and direct physical intervention.

Abstract We performed a detailed time-resolved spectral study of GRS 1915+105 during its low-flux rebrightening phase using the broadband capabilities of AstroSat and NuSTAR in 2019 May–June. The AstroSat light curves revealed erratic X-ray flares with count rates rising by a factor of ∼5. Flares with simultaneous LAXPC and SXT coverage were segmented and fitted using two degenerate but physically motivated spectral models: a reflection-dominated model (hereafter model A) and an absorption-dominated model (hereafter model B). In model A, the inner disk radius ( R in ) shows a broken power-law dependence on flux, indicating rapid inward motion of the disk at higher flux levels. In contrast, model B shows variable column density in the range of 10 23 –10 24 cm −2 , displaying a strong anticorrelation with flux. Both models exhibit significant variation in the ionization parameter between low- and high-flux segments. The total unabsorbed luminosity in the 0.7–30 keV energy range ranged from 6.64 × 10 36 to 6.33 × 10 38 erg s −1 . Across both models, several spectral parameters exhibited step-function-like behavior around flux thresholds of 5–10 × 10 −9 erg cm −2 s −1 , indicating multiple spectral regimes. The disk flux contribution, more evident in model B, increased with total flux, supporting an intrinsic origin for the variability. These findings point to a complex interplay between intrinsic disk emission, structured winds, and variable local absorption in driving the flare activity.

In aerospace engineering, structural lightweight remains one of the core design objectives. Here, a design methodology combining topology optimization (TO) with honeycomb materials is proposed to achieve lightweight for a typical aircraft double-lug joint structure (DLJS). The initial DLJS is topologically optimized using the variable density method to identify optimal material distribution. The optimized result is then reconstructed into a regular geometric model using the three dimensional (3D) modeling software SolidWorks 2022. In the reconstructed DLJS, the lower stress regions are replaced with honeycomb materials possessing superior mechanical properties or either removed to further enhance stiffness-to-weight ratio. Numerical strength verifications are performed on the final designed DLJS, demonstrating that the maximum stresses designed DLJS remain below the material yield strength under three typical load cases, meeting both strength requirements and safety margins. The mass of the designed DLJS is 38.44 kg, achieving a weight reduction rate of 59.7% compared to the initial DLJS (95.38 kg). Finally, the fabrication feasibility of the designed DLJS is evaluated, and a scaled-down DLJS specimen is fabricated using 3D printing technology with photopolymer resin. This work demonstrates the effectiveness and potential of TO combined with honeycomb materials in lightweighting complex 3D engineering components, providing valuable insights for the lightweight design of intricate 3D structures.

ABSTRACT Spiral solid fins are extensively used for the removal of waste heat from exhaust gases. However, they undergo thermal degradation due to high‐temperature conditions. This setback is addressed by the use of porous media. Hence, in this study, we used spiral fins made of high‐porosity metallic foam samples. The thermal and hydrodynamic performance of these fins was evaluated in a three‐dimensional domain using computational fluid dynamics technique. The foam samples were subjected to analysis using the Darcy–Brinkman–Forchheimer and local thermal nonequilibrium models. The foam samples had variable pore densities ranging from 5 to 40 pores per inch (PPI) and differing porosities. The study focused on spiral fin pitch ( P f ) between 2.4 and 6.4 mm. Turbulent flow conditions were modeled using the realizable κ–ϵ model in ANSYS Fluent. Samples with variable pore densities were first evaluated for their thermal and flow parameters. Flow streamlines reveal a vortex formation near the fin base that intensifies with fin spacing. The overall performance study recommends the use of a 20‐PPI foam sample due to its superior performance compared to others. To study the effect of porosity, samples with porosity varying between 0.9005 and 0.978 were used. It was observed that the resistance offered by a specific foam sample is crucial in determining the pressure drop, while the heat transfer depends on the specific surface area of the porous sample. The overall performance analysis of all foam samples based on the area goodness factor and the ratio of heat transfer per unit temperature difference to the pumping power of the assembly ( Z / E) recommends the use of a 20‐PPI foam sample with a porosity of 0.9005. On the other hand, the samples with the highest flow resistance and lowest specific surface area are termed undesirable due to their higher pressure drop and lower heat transfer rate.