A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.     

On the solvability of initial boundary value problems for nonlinear time-dependent Schrödinger equations

In this paper, we study the initial boundary value problems for a nonlinear time-dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin’s method.     

A new free and immobilized pyrylogen electron transfer sensitizer

The synthesis, photophysical, and electrochemical characterization of N-allyl-2,6-diphenyl-4,4′-pyrylogen bis tetrafluoroborate is reported. The pyrylogen is reduced under dissolving metal reduction conditions with formation of the radical cation. In addition, it can be copolymerized with styrene and divinylbenzene to generate a polymer bound reagent that facilitates its separation from photochemically induced electron-transfer reaction mixtures.     

A law of large numbers result for a bifurcating process with an infinite moving average representation

This paper derives a law of large numbers theorem for bifurcating processes defined on a perfect binary tree. This theorem can be viewed as a generalization of some results that have already appeared in the literature. For instance, all that is required of the bifurcating process is an infinite moving average representation with geometrically decaying coefficients and a finite moment assumption. In addition, the summands are assumed to belong to a flexible class of functions that satisfy a generalized Lipschitz type condition. These two criteria allow for an expansive range of applicability. Two examples are given as corollaries to the theorem.     

Effect of conjugated core building block dibenzo[a,c]phenazine unit on π‐conjugated electrochromic polymers: Red‐shifted absorption

A comparative investigation was undertaken for the electrosynthesis and electrochemical properties of three different electroactive polymers having a conjugated core building block, dibenzo[a,c]phenazine. A series of monomers has been synthesized as regards to thiophene based units; thiophene, 3‐hexyl thiophene, and 3,4‐ethylenedioxythiophene. The effects of different donor substituents on the polymers' electrochemical properties were examined by cyclic voltammetry. Introducing highly electron‐donating (ethylene dioxy) group to the monomer enables solubility while also lowering the oxidation potential. The planarity of the monomer unit enhances π‐stacking and consequently lowering the E_g from 2.4 eV (PHTP) to 1.7 (PTBP). Cyclic voltammetry and spectroelectrochemical measurements revealed that 2,7‐bis(4‐hexylthiophen‐2‐yl)dibenzo[a,c]phenazine (HTP) and 2,7‐bis(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)dibenzo[a,c]phenazine (TBP) possessed electrochromic behavior. The colorimetry analysis revealed that while PTBP have a color change from red to blue, PHTP has yellow color at neutral state and blue color at oxidized state. Hence the presence of the phenazine derivative as the acceptor unit causes a red shift in the polymers' absorption to have a blue color. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1714–1720, 2010     

Application of computer algebra to Jones polynomials

In this paper we apply computer algebra (Maple) techniques to calculate Jones polynomial of graphs of K(2,q)-Torus knots. For this purpose, a computer program was developed. When a positive integer q is given, the program calculate Jones polynomial of graph of K(2,q)-Torus knots.     

Electrochemical Detection of a Cancer Biomarker mir‐21 in Cell Lysates Using Graphene Modified Sensors

In the present study, the voltammetric and impidimetric detection of microRNA‐21, mir‐21 from cell lysates was investigated for the first time by using graphene modified disposable pencil graphite electrodes (GME). The surface characterization of GME was performed via electrochemical impedance spectroscopy (EIS) and scanning electron microscopy (SEM). Upon passive adsorption of inosine substituted antimicroRNA‐21, antimir‐21 probe, InP, onto the surface of GME and then solid phase hybridization of InP with mir‐21, the target, the electrochemical detection was performed by using Differential Pulse Voltammetry (DPV) and EIS techniques. This developed biosensor, GME has presented a 2.77 times lower detection limit of 2.09 µg/mL (3.12 pmol) with respect to unmodified pencil graphite electrode (GE). Moreover it is capable of analyzing mir‐21 in the cell lysates of mir‐21 positive breast cancer cell line (MCF‐7) contrast to mir‐21 negative hepatoma cell line (HUH‐7). The proposed electrochemical yes‐no system does not require any purification and/or amplification step prior to fast detection of mir‐21 from real samples.     

(−)‐Englerin A is a Potent and Selective Activator of TRPC4 and TRPC5 Calcium Channels

Current therapies for common types of cancer such as renal cell cancer are often ineffective and unspecific, and novel pharmacological targets and approaches are in high demand. Here we show the unexpected possibility for the rapid and selective killing of renal cancer cells through activation of calcium‐permeable nonselective transient receptor potential canonical (TRPC) calcium channels by the sesquiterpene (?)‐englerin A. This compound was found to be a highly efficient, fast‐acting, potent, selective, and direct stimulator of TRPC4 and TRPC5 channels. TRPC4/5 activation through a high‐affinity extracellular (?)‐englerin A binding site may open up novel opportunities for drug discovery aimed at renal cancer.     

In vitro swelling studies in simulated physiological solutions and biocompatibility of NIPAM-based hydrogels with some biochemical parameters of human sera

In modern medicine, commonly used biomaterials originating from metals, ceramics and polymers have shown biocompatibility with blood, tissues, cells, etc., in the human body. Polymeric biomaterials are usually understood as polymeric materials and articles made from them which are used in medicine, biotechnology biomedicine, bioengineering, pharmaceutical, veterinary, food industry, agriculture and related fields. In this in vitro study, swellings and the biocompatibility of environmentally sensitive N-isopropyl acrylamide-based (ES) hydrogels such as N-isopropyl acrylamide/acrylamide (ES/0), and N-isopropyl acrylamide/acrylamide/ carboxylic acids (ES/XAc) prepared by free radical polymerization in aqueous solutions has been investigated. Selected carboxylic acids for this study were acrylic, methacrylic, crotonic, itaconic, maleic, mesaconic and aconitic acid. The equilibrium swelling of the hydrogels are investigated in simulated physiological fluids or crystalloid solutions such as HCl-KCl buffer (pH = 1.1), universal buffer (pH = 5.5), phosphate buffer (pH = 7.4), urea, isotonic NaCl, isotonic KCl, 5% dextrose, 5% dextrose+isotonic NaCl, Ringer's lactate, human blood serum and human serum albumin solution at 37°C. For the analysis of biocompatibility, ES hydrogels are incubated in 5 different human sera and their biocompatibilities with some biochemical parameters have been investigated for 24 h at 37°C. No significant differences in values before and after the test procedures have been found. It is therefore concluded that environmentally sensitive N-isopropyl acrylamide-based hydrogels are biocompatible for biochemical parameters of human sera.