This paper investigates density-driven flow in porous media, focusing on the roles of viscosity contrast, density contrast, and linear adsorption. In this setup, the fluid on top is heavier and more viscous than the fluid below. Under the effect of gravity, this system becomes unstable, and finger-like structures appear. The phenomenon is described mathematically by coupling Darcy's law with a convection-diffusion reaction equation. The nonlinearity in this model arises mainly from the concentration dependence of viscosity and the convective transport term. The existence of a unique pair of weak solutions is shown using the Galerkin approximation method and truncation technique. Moreover, an application of the maximum principle shows non-negativity of the concentration. Additionally, we analyze the long-time behavior of the solution and prove that the concentration converges exponentially to zero in the U-norm for all 1 <= p <= infinity as t -> infinity. To complement the theoretical analysis, we perform numerical simulations based on a pressure formulation. By tracking total kinetic energy and mixing measures over time, we discuss the instability and the mixing efficiency, respectively. The present study reveals that although increasing the density contrast amplifies the total kinetic energy, the marginal impact diminishes with successive increments of density contrast. Similarly, while adsorption acts to suppress mixing, its efficiency in doing so tends to saturate with further increases. These behavior are consistent with the numerical simulations.
Climate change is gradually affecting the quality, reliability and safety of potable water throughout the world. Rising temperatures, excess rainfall and changing hydrological cycles are altering the physical, chemical and biological characteristics of water sources,. This in turn poses serious challenges to drinking water facilities and water distribution systems. Artificial intelligence (AI), machine learning (ML) and internet of things (IoT) have emerged as powerful tools for better water quality (WQ) monitoring, optimisation of treatment and management of infrastructure. This review is a critical assessment of the recent developments of AI-based approaches for the evaluation and remediation of drinking water quality under changing climatic conditions. It involves management of chlorination, adsorption, membrane filtration and the risk foreseen for the water distribution network in a city. The review addresses a critical gap by synthesising an integrated AI‑driven framework to mitigate climate‑induced WQ variability and support resilient potable water systems. It also examines the integration of AI with IoT-enabled sensor systems for real-time monitoring and predictive risk management. Furthermore, the review discusses current limitations, operational challenges, and sustainability implications of AI-based water management systems. The outcome demonstrates a growing potential of data-driven technologies to facilitate adaptive decision-making, enhance the efficiency of water treatment systems. It also portrays the resiliency of drinking water systems under climate change pressures.
Bioresorbable polymeric coronary stents (BCSs) offer transformative potential for cardiovascular therapy by providing temporary vascular support before degrading, yet structural performance and complex processing hinder their clinical translation. Single-shot net-shape fabrication via micro-injection molding (µIM) offers a cost-effective, high-throughput solution with minimal material waste in cleanroom settings. To overcome mold underfilling in high L/t ratio (> 650) geometries, this study introduces a multiphysics computational framework combining finite element analysis for structural validation with computational fluid dynamics for melt-flow simulation. The objective is to optimize BCS designs for mechanical integrity and manufacturability, enabling scalable µIM-based net-shape production. The framework systematically evaluates seven BCS designs, including four CE-marked geometries, two patented novel variants, and one reported design under uniform processing conditions using different grades of PLA. Structural parameters including radial strength, bending resistance, and elastic recoil, were analyzed alongside manufacturability outcomes such as mold-filling efficiency, pressure requirement, and defect formation. Key findings reveals that the manufacturability via µIM depends not only on L/t ratio and gate configuration but also on the detailed geometric profile of the stent. Intricate designs demand prohibitively high injection pressures ( 1500 MPa) due to extremely fine features and impractical profiles which impeding melt propagation, whereas the patented Diamond-4 geometry achieves comparable radial strength, lower elastic recoil, and slightly higher bending stiffness, with complete cavity filling at substantially lower injection pressures and the least shrinkage among all evaluated designs. Coupling structural and melt flow analysis, the methodology links clinical needs like vascular patency and endothelialisation with µIM process challenges including high polymer viscosity, premature solidification, and demolding issues. This dual-validation approach aligns mechanical performance with processing constraints, offering a predictive tool for net-shape fabrication of next-generation polymeric BCS. It minimizes costly experimental trials and accelerates scalable stent development.
Expansive soils exhibit significant volume changes due to moisture variations, necessitating soil stabilization. Conventional stabilizers, such as lime and cement, have environmental drawbacks due to their carbon emissions. In this study, wollastonite powder (WP), a natural silicate mineral, and polyester fiber (PF), a synthetic reinforcing material, were used to improve the strength properties of expansive soil. Experimental investigations were conducted on the collected soil samples with varying percentages of WP (0-12
In this article, we address the valuation of a European vulnerable options within a structural framework. Specifically, we model the underlying asset and the asset of the option writer using a joint Hawkes jump-diffusion model with two-factor stochastic volatility. We derive a general analytical integral formula for prices of European options, applicable under any modeling framework as long as the joint characteristic function of asset prices associated with the underlying and option writer is available analytically. Distinguished from the pricing formulae in the literature, especially in a jump-diffusion framework, which is either in the form of the expectation over the jump process or requires evaluating several layers of infinite sums, our formula is significantly simplified and computationally efficient. Moreover, our model dynamics encompasses a wide range of commonly used models as special cases, for which we provide explicit analytical forms of the joint characteristic functions. Finally, we present numerical experiments demonstrating the accuracy and computational efficiency of our formula, along with sensitivity analysis to highlight the impact of various model parameters on the option prices.
