Asymptotic behavior of spreading fronts in the anisotropic Allen–Cahn equation on Rn

We consider the Cauchy problem for the anisotropic (unbalanced) Allen–Cahn equation on ${\mathbb{R}}^n$ with $n\ge 2$ and study the large time behavior of the solutions with spreading fronts. We show, under very mild assumptions on the initial data, that the solution develops a well-formed front whose position is closely approximated by the expanding Wulff shape for all large times. Such behavior can naturally be expected on a formal level and there are also some rigorous studies in the literature on related problems, but we will establish approximation results that are more refined than what has been known before. More precisely, the Hausdorff distance between the level set of the solution and the expanding Wulff shape remains uniformly bounded for all large times. Furthermore, each level set becomes a smooth hypersurface in finite time no matter how irregular the initial configuration may be, and the motion of this hypersurface is approximately subject to the anisotropic mean curvature flow $V_{\gamma }={\kappa }_{\gamma }+c$ with a small error margin. We also prove the eventual rigidity of the solution profile at the front, meaning that it converges locally to the traveling wave profile everywhere near the front as time goes to infinity. In proving this last result as well as the smoothness of the level surfaces, an anisotropic extension of the Liouville type theorem of Berestycki and Hamel (2007) for entire solutions of the Allen–Cahn equation plays a key role.     

HPLC/DAD,Antibacterial and Antioxidant Activities of Plectranthus Species (Lamiaceae) Combined with the Chemometric Calculations

The increase in antibiotic resistance and the emergence of new bacterial infections have intensified the research for natural products from plants with associated therapy. This study aimed to verify the antibacterial and antioxidant activity of crude extracts of the genus Plectranthus species, being the first report on the modulation of aminoglycosides antibiotic activity by Plectranthus amboinicus extracts. The chemical composition was obtained by chemical prospecting and High-Performance Liquid Chromatography with diode arrangement detector (HPLC/DAD). The antibacterial activities of the extracts alone or in association with aminoglycosides were analyzed using the microdilution test. The antioxidant activity was evaluated by 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radical scavenging. The phytochemical prospection allowed the flavonoids, saponins, tannins and triterpenoids to be identified. Quercetin, rutin, gallic acid, chlorogenic acid, caffeic acid, catechin, kaempferol, glycosylated kaempferol, quercitrin, and isoquercitrin were identified and quantified. The principal component analysis (PCA) observed the influence of flavonoids and phenolic acids from Plectranthus species on studied activities. Phytochemical tests with the extracts indicated, especially, the presence of flavonoids, confirmed by quantitative analysis by HPLC. The results revealed antibacterial activities, and synergistic effects combined with aminoglycosides, as well as antioxidant potential, especially for P. ornatus species, with IC₅₀ of 32.21 µg/mL. Multivariate analyzes show that the inclusion of data from the antioxidant and antibacterial activity suggests that the antioxidant effect of these species presents a significant contribution to the synergistic effect of phytoconstituents, especially based on the flavonoid contents. The results of this study suggest the antibacterial activity of Plectranthus extracts, as well as their potential in modifying the resistance of the analyzed aminoglycosides.     

Substituent effect of fluorine atom on benzothiadiazole bridging unit in dye sensitized solar cells

Dye sensitized solar cells performances using two organic dyes with fluorinated-benzothiadiazole spacer, 3-{5-[7-(5-{4-[Bis(9,9-dimethyl-9H-fluoren-2-yl)-amino]-5-fluoro-phenyl}thiophen-2-yl)benzo-[1,2,5]thiadiazol-4-yl]thiophen-2-yl}-2-cyano acrylic acid (JK-311) and 3-{5-[7-(5-{4-[Bis(9,9-dimethyl-9H-fluoren-2-yl)-amino]-5,6-difluorophe-nyl}thiophen-2-yl)benzo-[1,2,5]thiadiazol-4-yl]thiophen-2-yl}-2-cyano acrylic acid (JK-312), were systematically investigated by solar simulation equipment, stepped light-induced transient measurements of photocurrent and voltage, and electrochemical impedance spectroscopy. To investigate substituent effect of fluorine atom on benzothiadiazole, molecular orbital calculations of two dyes using a time dependent density functional theory model with B3LYP/3-31G* were also carried out. JK-312 showed a unique electronic transition from HOMO-1 to LUMO. Short circuit current and open-circuit voltage in DSSCs performances were increased by the introduction of fluorine atom into spacer segment, compared to fluorine-free dyes.     

Synthesis of a new zirconium catalyst for ethylene polymerization

A novel complex dichlorobis(2‐ethyl‐3‐hydroxy‐4‐pyrone)zirconium(IV) (ZrCl₂(ethylpyrone)₂) was synthesized. Complexation of the pyrone ligand to the zirconium was confirmed by UV, ¹H and ¹³C‐NMR, and electrochemical studies. NMR showed the presence of four isomers and density functional theory calculations indicated that the main isomer had a cis configuration. The catalyst was shown to be active in ethylene polymerization in the presence of the cocatalyst methylaluminoxane. The highest catalyst activity for the zirconium complex was achieved at Al/Zr = 2500, 70 °C and when a small concentration of catalyst was used (1 μmol). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3830–3841, 2008     

Numerical simulation of non-Abelian particle-field dynamics

Numerical 1D-3V solutions of the Wong-Yang-Mills equations with anisotropic particle momentum distributions are presented. They confirm the existence of plasma instabilities for weak initial fields and of their saturation at a level where the particle motion is affected, similar to Abelian plasmas. The isotropization of the particle momenta by strong random fields is shown explicitly, as well as their nearly exponential distribution up to a typical hard scale, which arises from scattering off field fluctuations. By variation of the lattice spacing we show that the effects described here are independent of the UV field modes near the end of the Brioullin zone.     

Hexadecapole deformation studies in<Superscript>148,150</Superscript>Nd

Theγ-ray yields from inelastically excited 2⁺ and 4⁺ levels of^{144,146,148,150}Nd nuclei using¹⁶O beam at near barrier energies in coincidence with the back-scattered projectiles were measured. The 2⁺ and 4⁺ level cross-sections were deduced from the measuredγ-ray yields and fitted to the DWBA calculations to obtain the reduced transition matrix elementsM(E4: 0⁺ → 4⁺). The deducedM(E4) values for¹⁴⁸Nd and¹⁵⁰Nd nuclei, 0.16(0.05) and 0.22(0.12) eb², respectively are consistent with theoretical predictions.     

Isotopomeric characterization of N2O produced, consumed, and emitted by automobiles

Fossil fuel combustion is the second largest anthropogenic source of nitrous oxide (N2O) after agriculture. The estimated global N2O flux from combustion sources, as well as from other sources, still has a large uncertainty. Herein, we characterize automobile sources using N2O isotopomer ratios (nitrogen and oxygen isotope ratios and intramolecular site preference of 15N, SP) to assess their contributions to total global sources and to deconvolute complex production/consumption processes during combustion and subsequent catalytic treatments of exhaust. Car exhaust gases were sampled under running and idling state, and N2O isotopomer ratios were measured by mass spectrometry. The N2O directly emitted from an engine of a vehicle running at constant velocity had almost constant isotopomer ratios (delta15Nbulk = -28.7 +/- 1.2 per thousand, delta18O = 28.6 +/- 3.3 per thousand, and SP = 4.2 +/- 0.8 per thousand) irrespective of the velocity. After passing through catalytic converters, the isotopomer ratios showed an increase which varied with the temperature and the aging of the catalysts. The increase suggests that both production and consumption of N2O occur on the catalyst and that their rates can be comparable. It was noticed that in the idling state, the N2O emitted from a brand new car has higher isotopomer ratios than that from used cars, which indicate that technical improvements in catalytic converters can reduce the N2O from mobile combustion sources. On average, the isotopomeric signatures of N2O finally emitted from automobiles are not sensitive to running/idling states or to aging of the catalysts. Characteristic average isotopomer ratios of N2O from automobile sources are estimated at -4.9 +/- 8.2 per thousand, 43.5 +/- 13.9 per thousand, and 12.2 +/- 9.1 per thousand for delta15Nbulk, delta18O, and SP, respectively.     

Numerical analysis of thermal lens effect for sensitive detection on microchips

Thermal lens microscope (TLM) is a sensitive detection method for nonfluorescent molecules and widely applied to detection in a capillary or on a microchip. In this paper, we developed a flexible design tool for TLM systems to meet various applications utilizing a microspace. The TL effect was modeled, including signal processing, and calculated by combining fluidic dynamics and wave optics software. The coincidence of the calculations and experiments was investigated by measuring the effects of optical path length or focus positions of the excitation beams on TL signals which are quite difficult to calculate by a conventional method. Good agreement was shown and the applicability of the TLM design tool was verified.     

Use of biotin-streptavidin system for developing a viable, sensitive and specific antigen heterologous assay for hapten

The present study demonstrates improvement in sensitivity and specificity of hapten assay by using antigen heterology in conjunction with low molecular weight biotin label as compared to high molecular weight horseradish peroxidase (HRP) label. For generation of antiserum, cortisol-3-O-carboxylmethyl-oxime-bovine serum albumin (F-3-CMO-BSA) was used as immunogen whereas, for the preparation of primary label, corticosterone-3-carboxymethyl oxime (B-3-CMO) was coupled with biotinylcaproylhydrazide and HRP by employing N-hydroxysuccinimide mediated carbodiimide reaction. The data of the present study revealed that the antigen heterologous assay which employed high molecular weight HRP label showed 100% cross-reaction with corticosterone. On the contrary, when HRP was replaced with low molecular weight biotin label, less than 0.1% cross-reaction was observed with all analogous C₁₈, C₁₉, C₂₁ and C₂₇ steroids including corticosterone (0.2%). Moreover, the sensitivity of the later assay was 0.09 μg/dL, which is appreciable as compared to previously reported enzyme based assays. The recovery of the exogenously spiked serum pools lies in the range of 90.3-104.2%. The intra-assay and inter-assay coefficient of variation (CVs) ranged from 3.3% to 7.8% and 2.3% to 7.7%, respectively. The serum cortisol values obtained by this method correlated well with those obtained by radioimmunoassay; r = 0.9 (n = 50). The use of much stable biotin label in place of HRP has made the antigen heterologous enzyme linked immunosorbent assay (ELISA) of cortisol assay highly specific and sensitive.