A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations

We consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\phi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\rm 94}$, $61-66 ({\rm 1984})$]. By taking an $L^{\infty}$ norm of the energy of the full binary system, designated as $E_{\infty}$, we have shown that $\int_{0}^{t}E_{\infty}(\tau)\,d\tau$ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs), of the 3D CHNS equations, for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with $128^3$ to $512^3$ collocation points and over the duration of our DNSs, confirm that $E_{\infty}$ remains bounded as far as our computations allow.Comment: 11 pages, 3 figure

The role of BKM-type theorems in 3D3D Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis

The Beale-Kato-Majda theorem contains a single criterion that controls the behaviour of solutions of the $3D$ incompressible Euler equations. Versions of this theorem are discussed in terms of the regularity issues surrounding the $3D$ incompressible Euler and Navier-Stokes equations together with a phase-field model for the statistical mechanics of binary mixtures called the $3D$ Cahn-Hilliard-Navier-Stokes (CHNS) equations. A theorem of BKM-type is established for the CHNS equations for the full parameter range. Moreover, for this latter set, it is shown that there exists a Reynolds number and a bound on the energy-dissipation rate that, remarkably, reproduces the $Re^{3/4}$ upper bound on the inverse Kolmogorov length normally associated with the Navier-Stokes equations alone. An alternative length-scale is introduced and discussed, together with a set of pseudo-spectral computations on a $128^{3}$ grid.Comment: 3 figures and 3 table

Assessment of Air and Water Quality in Opencast Mines

Mining Industry is one of the most important and revenue-generating industries of our country. It’s pivotal for the industry to thrive and grow to ensure that the manufacturing sector also develops at the required pace. But the detrimental effects of mining are far more dangerous than we can perceive and must be kept under check to reduce the polluting consequences on environment. Mining of any ore leads to befoulment of water bodies and also air contamination. The sources of air pollution in open cast mines are drilling and blasting of ore bodies, loading and haulage of blasted ore, handling of material and maintenance. The standards for air pollution have been set by National Ambient Air Quality Standards(NAAQS) and it’s based on criteria like PM2.5, PM10, SPM etc. PM2.5 and PM10 are the standards acceptable for respirable dust and pollutants. The water that runs off the mines can have detrimental effect on the water bodies that are in and around the mining areas. The seepage from ore bodies, mining waste rocks and treatment of effluents pose a great threat to the water bodies and the aquatic life associated with them. This project will assess the various parameters of water that decide the pollution level of the water body and will also focus on the dependency of ore type on the pollution level of the water bodies

Analyzing the Impact of Offer Load, Mobility and Energy Related Issues on Simulation Areas of Reactive and Proactive Routing Protocols in Manets

MANETS is a collection of Independent mobile nodes that can communicate through each other via radio waves. The mobile nodes that are in radio range can directly communicate where as the other needs the aid of intimidate node to route the packets. These networks are fully disturbed and can work with any place without the help of any Infrastructure this property makes these networks highly flexible and robust. In this Project we analyzed the impact of offer load, mobility and energy related issues with respect to simulation areas for reactive and proactive routing protocols for MANETS by using NS2 simulator to measure the different parameters like Routing Overhead, Rout load, packet delivery ratio energy consume, energy remaining

Antimycobacterial mechanism of vanillin involves disruption of cell-surface integrity, virulence attributes, and iron homeostasis

AbstractObjective/BackgroundTuberculosis (TB) remains a global threat, claiming one-third of the population annually. The ever increasing emergence of multidrug-resistant TB (MDR-TB) is the major impediment to effective anti-TB therapy. Under such circumstances, deciphering the antimycobacterial potential of natural compounds has gained considerable prominence. This study evaluated the antimycobacterial activity of vanillin (Van), a natural food-flavoring agent and preservative, along with its potential mechanisms of action.MethodsDrug susceptibilities were performed using broth microdilution, spot, and filter-disc assays. Membrane damage was studied by nitrocefin hydrolysis and electron microscopy. Virulence attributes were assessed by biofilm formation and cell adherence. Iron availability was estimated by enzymatic (ferroxidase) assay.ResultsWe found that the antimycobacterial activity of Van against Mycobacterium smegmatis (a surrogate of Mycobacterium tuberculosis) is 125μg/mL. Additionally, we observed disruption of membrane homeostasis in the presence of Van, as revealed by enhanced membrane permeability and transmission electron microscopy images showing a disturbed cell envelope. Concomitant with our findings, we also observed that Van leads to enhanced drug susceptibility to membrane targeting known anti-TB drugs. Furthermore, Van affects significant virulence traits of Mycobacterium by inhibiting biofilm formation and cell adhesion. Finally, we observed that Van disrupted iron homeostasis as displayed by hypersensitivity to iron deprivation.ConclusionThe results established for the first time that Van could be an effective antimycobacterial agent that could be exploited further in treating mycobacterial infections