The stationary version of the Boussinesq system with a general gravitational acceleration term is considered. Under suitable assumptions on this term, as well as on the external forces acting on each equation of this coupled system, we first establish the existence of weak solutions in the natural energy space H(center dot)1(& Ropf;3). The uniqueness of these solutions is a challenging open problem. Within this framework, our first main contribution is to show that any weak H(center dot)1-solution exhibits an analytic smoothing effect in the Gevrey class. Our second main contribution is to show that the Gevrey class regularity can also be used to study the uniqueness problem, provided that these solutions satisfy a suitable low-frequency control. As a byproduct, we also obtain new regularity results and a new Liouville-type result for weak H(center dot)1-solutions of the classical Navier-Stokes equations. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
This paper analyses the water flow in curved channels, which may present particular hydrodynamic patterns such as streamline alteration, cross-wave formation, recirculation zones and possible contour flow separations, all of which require detailed hydrodynamic analysis. The analysis focuses on a case study of a hydroelectric power plant intake with a side grate, which includes a curved (small-radius) gravel-removing channel connecting the intake works to two desanding chambers. This design results in an unequal distribution of flow to the desanding chambers, causing neither chamber to function properly, and a recirculation zone upstream of the left desanding chamber. The methodology uses three-dimensional numerical modelling in OpenFOAM, based on prototype data. The model was calibrated with a flow rate of 8,8 m3/s. Subsequently, the transit of the design flow of 13 m3/s was simulated and an uneven flow distribution in the desanding chambers was verified. To address this problem, and considering the higher-velocity streamlines, two groups of alternatives were considered: the first consisted of placing two panels of different special shapes (straight, broken, and curved) in the desilting chamber; the second examined the flow behavior with an increased number of panels and alteration aspect ratio. For the first group, the scenarios tested did not modify the flow distribution in the sand removal chambers; however, the panels locally changed the hydrodynamic conditions and successfully altered the recirculation zone location. The scenarios in the second group yielded the best operational results regarding flow distribution.
Car accidents remain a leading cause of death worldwide, with drowsiness and distraction accounting for roughly 25% of fatal crashes in Ecuador. This study presents a real-time driver monitoring system that uses computer vision and deep learning to detect fatigue, distraction, and emotions from facial expressions. It combines a MobileNetV2-based CNN trained on RAF-DB for emotion recognition and MediaPipe’s 468 facial landmarks to compute the EAR (Eye Aspect Ratio), the MAR (Mouth Aspect Ratio), the gaze, and the head pose. Tests with 27 participants in both real and simulated driving environments showed strong results. There was a 100% accuracy in detecting distraction, 85.19% for yawning, and 88.89% for eye closure. The system also effectively recognized happiness (100%) and anger/disgust (96.3%). However, it struggled with sadness and failed to detect fear, likely due to the subtlety of real-world expressions and limitations in the training dataset. Despite these challenges, the results highlight the importance of integrating emotional awareness into driver monitoring systems, which helps reduce false alarms and improve response accuracy. This work supports the development of lightweight, non-invasive technologies that enhance driving safety through intelligent behavior analysis.
Non-wood agro-residues can reduce the environmental and cost burdens of papermaking, yet process alkalinity often drives impacts. Pineapple crowns were valorized as fiber feedstock and evaluated partial substitution of NaOH with NaHCO3 during processing, using NaOH-NaHCO3 ratios of 1:0, 3:1, and 1:1 (P100:0, P75:25, P50:50). Physical (grammage, thickness, porosity, burst, pH, water uptake) and instrumental characterizations, including Fourier-transform infrared spectroscopy (FTIR), thermogravimetric and derivative thermogravimetric analysis (TGA/DTGA), and scanning electron microscopy (SEM), were coupled with cradle-to-gate life-cycle (CF: carbon footprint; WF: water footprint) and unit-cost analyses. P75:25 achieved the highest grammage (71.86 + 0.49 g/ m2) and balanced network consolidation, while P100:0 maximized burst (19.53 + 0.91 psi); P50:50 increased porosity and moisture uptake. TGA/DTGA indicated effective polysaccharide/lignin breakdown for P100:0 and P75:25, with elevated high-temperature residue in P50:50, aligning with SEM-resolved fiber compaction. Envi-ronmental results decreased monotonically with sodium-bicarbonate substitution: total CF = 0.25, 0.22 (-12 %), and 0.19 kg CO2-eq for P100:0, P75:25, and P50:50. WF per sheet was 6.56, 3.72, and 3.28 L for P100:0, P75:25, and P50:50, respectively. Despite lab-scale costs (approximate to 4.0 USD/sheet), sensitivity indicates reagent price and electricity as main levers. Overall, P75:25 offers the best performance-to-impact trade-off preserving mechanical integrity while lowering CF and WF vs P100:0 supporting pineapple-crown papers as credible candidates for lightweight pack-aging and printing.
This article is devoted to the mathematical study of a new Navier-Stokes-alpha model with a nonlinear filter equation. For a given indicator function, this filter equation was first considered by W. Layton, G. Rebholz, and C. Trenchea in [Modular Nonlinear Filter Stabilization of Methods for Higher Reynolds Numbers Flow, J. Math. Fluid Mech. 14: 325-354 (2012)] to select eddies for damping based on the understanding of how nonlinearity acts in real flow problems. Numerically, this nonlinear filter equation was applied to the nonlinear term in the Navier-Stokes equations to provide a precise analysis of numerical diffusion and error estimates. Mathematically, the resulting alpha-model is described by a doubly nonlinear parabolic-elliptic coupled system. We therefore undertake the first theoretical study of this system by considering periodic boundary conditions in the spatial variable. Specifically, we address the existence and uniqueness of weak Leray-type solutions, their rigorous convergence to weak Leray solutions of the classical Navier-Stokes equations, and their long-time dynamics through the concept of the global attractor and some upper bounds for its fractal dimension. Handling the nonlinear filter equation together with the well-known nonlinear transport term makes certain estimates delicate, particularly when deriving upper bounds on the fractal dimension. For the latter, we adapt techniques developed for hyperbolic-type equations.
