The Two Dimensional Euler Equation: A Statistical Study

We construct surface type measures on the level sets for the renormalized energy, which is an invariant quantity for the two dimensional periodic Euler flow, and prove the existence of weak solutions living on such level sets. Other classes of invariant measures for the motion are also introduced. Received: 3 December 1997 / Accepted: 20 August 1998     

Amphoteric 2-(sulfonylamino)benzaldehydes,secondary amines and isocyanides in the multicomponent synthesis of elusive N-alkyl-2,3-diaminoindoles

A novel interrupted Ugi reaction between ortho-sulfonylaminated aryl aldehydes, secondary amines, and isocyanides affords in good to high yields N-alkyl-2,3-diaminoindoles, providing access to a so far unexplored area of the indole chemical space. With only one single chemical operation, this novel reaction affords a broad gamma of substituted 2,3-diaminoindoles with five points of diversity. The success of this novel multicomponent transformation lies in presence of the amphoteric sulfonylamino group, which sequentially acts as a Brønsted acids and as a nucleophile the lack of need for additional catalysts and the high atom economy, with the loss of only one molecule of water, renders this approach a very effective one.     

Silver nanoparticles as potential antiviral agents

Virus infections pose significant global health challenges, especially in view of the fact that the emergence of resistant viral strains and the adverse side effects associated with prolonged use continue to slow down the application of effective antiviral therapies. This makes imperative the need for the development of safe and potent alternatives to conventional antiviral drugs. In the present scenario, nanoscale materials have emerged as novel antiviral agents for the possibilities offered by their unique chemical and physical properties. Silver nanoparticles have mainly been studied for their antimicrobial potential against bacteria, but have also proven to be active against several types of viruses including human imunodeficiency virus, hepatitis B virus, herpes simplex virus, respiratory syncytial virus, and monkey pox virus. The use of metal nanoparticles provides an interesting opportunity for novel antiviral therapies. Since metals may attack a broad range of targets in the virus there is a lower possibility to develop resistance as compared to conventional antivirals. The present review focuses on the development of methods for the production of silver nanoparticles and on their use as antiviral therapeutics against pathogenic viruses.     

Discovery of novel anti-HIV active G-quadruplex-forming oligonucleotides

A series of d((5')TGGGAG(3')) sequences, 5'-conjugated with a variety of aromatic groups through phosphodiester linkages, were synthesized, showing CD spectra diagnostic of parallel-stranded, tetramolecular G-quadruplex structures. When tested for anti-HIV-1 and HIV-2 activity, potent inhibition of HIV-1 infection in CEM cell cultures was found, associated with high selectivity index values. Surface Plasmon Resonance assays revealed specific binding to HIV-1 gp120 and gp41.     

Optimization of a 2D photonic crystal add/drop multiplexer based on contra-directional coupling

We present a highly integrated add/drop multiplexer, where the contra-directional coupling is realized by phase matching two photonic crystal waveguides. The device band structure, the corresponding transmission and drop spectra, and the coupling length are carefully analysed. Different device configurations are discussed and by tailoring the coupling factor, we optimize the frequency response of the filter, obtaining a -sized channel selector, characterized by a very high drop efficiency.     

Batching in single operation manufacturing systems

We introduce a new decision problem important to the efficient operation of resources in manufacturing systems. This problem of ‘batching’ is considered for single machine activities. It is shown that even for these simple models, lot splitting may occur and that these batching decisions may have a dramatic impact on the manufacturing lead time of items to be processed.     

A large deviations principle for stochastic flows of viscous fluids

We study the well-posedness of a stochastic differential equation on the two dimensional torus ${\mathbb{T}}^2$, driven by an infinite dimensional Wiener process with drift in the Sobolev space $L^2(0,T;H^1\left({\mathbb{T}}^2\right))$. The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier–Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.     

Boundary layer problem: Navier–Stokes equations and Euler equations

This work is concerned with the boundary layer turbulence, which is an outstanding problem in fluid mechanics. We consider an incompressible viscous fluid in 2D domains with permeable walls. The permeability is described by the Yudovich condition. The goal of the article is to study the fluid behavior at vanishing viscosity (large Reynold’s numbers). We show that the vanishing viscous limit is a solution of the Euler equations with the Yudovich condition on the inflow region of the boundary.     

Microrheology and electrical conductivity of a dilute PNIPAM suspension

We study on a suspension of poly(N-isopropylacrylamide) at a low concentration using particle-tracking microrheology in two modalities: at constant temperatures and during a heating ramp. The dilute suspensions do not present a glass state at low temperatures, and at high temperatures, the polymer particles collapse, giving rise to entropic forces that induce aggregation of the tracking colloids. The viscoelastic moduli of the system, which drastically change with temperature, allow us to follow this dynamics. Furthermore, the viscosity of the system remains approximately constant with temperature but suddenly increases as it passes the lower critical solution temperature (LCST). Such effect is probably associated to hydration before the collapse of the polymer, as verified by electrical conductivity measurements.