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This paper studies a stabilized virtual element method for the unsteady Navier-Stokes problems on polygonal meshes. Using "equal-order" virtual elements in space and the Crank-Nicolson scheme in time, we give a fully discrete formula. By introducing the local-projection type stabilizations, the method can not only circumvent the discrete inf-sup condition but also control spurious oscillations caused by high Reynolds numbers. Stability and error estimates for velocity and pressure are analyzed. Particularly, error estimates are derived in which the constants are independent of the negative powers of the viscosity. Several numerical experiments are simulated to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies non-inf-sup stable virtual element methods for the Navier-Stokes problems based on "equal-order" virtual elements. Two equivalent pressure stabilizations are considered, which contain neither second-order derivative terms nor extra coupling terms. In addition, the methods are parameter-free. We obtain optimal error estimations in the H 1 -norm for velocity and the L 2 -norm for velocity and pressure. Several numerical experiments in two-dimension for different polynomial degrees and different polygonal meshes are offered which certify the theoretical results and display excellent stability. [ABSTRACT FROM AUTHOR]

Cd 0.3 Pb 0.7 S (CdPbS) aqueous quantum dots (AQDs) made with 3-mercaptoproprionic acid (MPA) as a ligand have the advantages of emitting near-infrared light, well above 800 nm, that completely circumvents interference from tissue autofluorescence and have significant amounts of ligands for bioconjugation. However, retaining the right amount of MPA became a challenge when using CdPbS AQDs for bioimaging because retaining too much MPA could lead to significant nonspecific staining in cell imaging while insufficient MPA could cause AQDs instability in biological systems. Here we examined PEGylation (i.e. chemically linking amine-functionalized polyethylene glycol (PEG)) to modify MPA on the AQDs surface to improve AQDs stability and reduce nonspecific staining. In addition, for conjugation with antibodies, a bifunctional PEG with a carboxyl functionality was used to permit chemical linkage of a PEG to an antibody on the other end. It was found that performing PEGylation at the thiol concentration where the zeta potential becomes saturated stabilized the CdPbS AQDs suspension and reduced nonspecific binding to cells. Furthermore, with the bifunctional PEG, the CdPbS AQDs were conjugated with antibodies and the AQD-Ab conjugates were shown to stain cancer cells specifically against normal cells with a signal-to-noise ratio of 8., (Creative Commons Attribution license.)