Boundary layer solutions for some nonlinear elastic membrane problems

Summary The method of matched asymptotic expansions is used to describe finite axisymmetric deformations of two thin elastic membrane problems: a circular membrane with a small radial traction at the edge, an annular membrane with a small circular hole at the center. In both problems, the surface load is assumed to be an axial pressure. There is a boundary layer at the outer edge in the first problem, and at the hole in the second problem.

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Zusammenfassung Mit Hilfe der in der singulären Störungsrechnung benutzten Methode einer inneren und äußeren asymptotischen Entwicklung werden endliche, axialsymmetrische Deformationen bei zwei Membranproblemen beschrieben: eine dünne elastische Kreismembran mit kleiner radialer Zugspannung am Rande, und eine Kreisringmembran mit einem kleinen konzentrischen Loch. In beiden Problemen wird die Belastung als ein axial gerichteter Oberflächendruck angenommen. Im ersten Problem zeigt die Lösung am äußeren Rand Grenzschichtverhalten, welches im zweiten Problem am Lochrand vorliegt.

     

Fluorine in optics

Fluorine occupies an original and strategic position in modern optics. The F₂ excimer lasers are unrivaled sources of deep UV light for semiconductors, microphotolithography and micromachining which has brought on the development of single crystal calcium fluoride optics. Due to the weak polarisability of the fluoride ion, fluoride materials have low refractive index suitable for thin film antireflective coatings specially in IR optics. Transparent magnesium fluoride ceramics, prepared by fine grains hot pressing, are transparent in the mid IR where the transparency windows of the atmosphere are located. They are used as IR domes for missiles guidance. Fluoride glasses when elaborated as optical fibers or channel waveguides and when doped with appropriate lanthanides, are original optical devices for laser operations lying from the mid IR to the UV region where light emission is characterized by up-conversion phenomena. The same devices have also found industrial applications in telecommunications as a new generation of optical amplifiers operating in the ultra-transparency window of the silica fiber.     

Polymer surface patterning by laser scanning

Proposed work develops method of polymer surface patterning, suggested in our laboratory. Surface structures with different symmetry and shape are prepared on PMMA and photoresist (Su-8) surface. For surface modification, periodic laser scanning from confocal microscope was used. For optical response improvement meso tetraphenylporphyrine was added either in the polymer bulk or on the top of pristine polymer by vacuum evaporation method. Applications of vacuum deposition methods allow increasing applicability of the technique and preparation of more complex structure. Parameters of the created structures were studied with the aim to better understand the driving forces of the surface modification. Application of prepared structures in photonics as diffraction grating or light coupling elements is also given.     

An Isoperimetric Theorem in Plane Geometry

Abstract. Let P be a simple polygon. Let the vertices of P be mapped, according to a counterclockwise traversal of the boundary, into a strictly increasing sequence of real numbers in [0, 2π) . Let a ray be drawn from each vertex so that the angle formed by the ray and a horizontal line pointing to the right equals, in measure, the number mapped to the vertex. Whenever the rays from two consecutive vertices intersect, let them induce the triangular region with extreme points comprising the vertices and the intersection point. It is shown that there is a fixed α such that if all of the assigned angles are increased by α , the triangular regions induced by the redirected rays cover the interior of P . This covering implies the standard isoperimetric inequalities in two dimensions, as well as several new inequalities, and resolves a question posed by Yaglom and Boltanskii.     

The design and testing of kinetically-appropriate operando spectroscopic cells for investigating heterogeneous catalytic reactions

This tutorial review discusses some of the current designs of reaction cells used for operando spectroscopy (X-ray absorption, UV-vis, Raman, transmission FTIR and DRIFTS) and the relation to the apparent reaction kinetics. Beam effects, the control of the catalyst bed temperature and bed by-pass are some of the potential problems that may lead to flawed activity measurements. Finally, four examples are given in which a good agreement was obtained between the activity of a powdered catalyst measured in a conventional reactor and in a spectroscopic cell. It is proposed that such comparison between reactors should become a standard procedure, to ensure the correctness of the data collected over typically non-ideal spectroscopic reaction cells.     

Macromolecular Diffusion in Self-Assembling Biodegradable Thermosensitive Hydrogels

Hydrogel formation triggered by a change in temperature is an attractive mechanism for in situ gelling biomaterials for pharmaceutical applications such as the delivery of therapeutic proteins. In this study, hydrogels were prepared from ABA triblock polymers having thermosensitive poly(N-(2-hydroxypropyl) methacrylamide lactate) flanking A-blocks and hydrophilic poly(ethylene glycol) B-blocks. Polymers with fixed length A blocks (~22 kDA) but differing PEG-midblock lengths (2, 4 and 10 kDa) were synthesized and dissolved in water with dilute fluorescein isothiocyanate (FITC)-labeled dextrans (70 and 500 kDA). Hydrogels encapsulating the dextrans were formed by raising the temperature. Fluorescence recovery after photobleaching (FRAP) studies showed that diffusion coefficients and mobile fractions of the dextran dyes decreased upon elevating temperatures above 25 °C. Confocal laser scanning microscopy and cryo-SEM demonstrated that hydrogel structure depended on PEG block length. Phase separation into polymer-rich and water-rich domains occurred to a larger extent for polymers with small PEG blocks compared to polymers with a larger PEG block. By changing the PEG block length and thereby the hydrogel structure, mobility of FITC-dextran could be tailored. At physiological pH the hydrogels degraded over time by ester hydrolysis, resulting in increased mobility of the encapsulated dye. Since diffusion can be controlled according to polymer design and concentration, plus temperature, these biocompatible hydrogels are attractive as potential in situ gelling biodegradable materials for macromolecular drug delivery.     

An Enhanced Process for the Production of a Highly Purified Extracellular Lipase in the Non-conventional Yeast <Emphasis Type="Italic">Yarrowia lipolytica</Emphasis>

Yarrowia lipolytica LgX64.81 is a non-genetically modified mutant that was previously identified as a promising microorganism for extracellular lipase production. In this work, the development of a fed-batch process for the production of this enzyme in this strain was described. A lipolytic activity of 2,145 U/mL was obtained after 32 h of batch culture in a defined medium supplemented with 10 g/L of tryptone, an enhancer of lipase expression. To maximize the volumetric productivity, two different fed-batch strategies had been investigated. In comparison to batch process, the intermittent fed-batch strategy had not improved the volumetric lipase productivity. In contrast, the stepwise feeding strategy combined with uncoupled cell growth and lipase production phases resulted in a 2-fold increase in the volumetric lipase productivity, namely, the lipase activity reached 10,000 U/mL after 80 h of culture. Furthermore, this lipase was purified to homogeneity by anion exchange chromatography on MonoQ resin followed by gel filtration on Sephacryl S-100. This process resulted in an overall yield of 72% and a 3.5-fold increase of the specific lipase activity. The developed process offers a great potential for an economic production of Lip2 at large scale in Y. lipolytica LgX64.81.     

First emission studies of Tc2X8(2-) systems (X = Cl, Br)

The emission spectra of the solids [n-Bu(4)N](2)Tc(2)X(8) (X = Cl, Br) have been investigated at room temperature and 77 K. In each case, the emission originates in the (1)δ-δ* excited state, as with the rhenium homologues, but has a shorter lifetime.     

Synthesis of a new hydrophilic poly(ethylene glycol)-ionic liquid and its application in peptide synthesis

The synthesis of a new hydrophilic ammonium-based poly(ethylene glycol)-ionic liquid (PEG-IL) is reported; the structure was assigned by NMR ((1)H, (13)C) and MALDI mass spectrometry. The viscosity and thermal stability were also studied, as well as its polarity. Its application as an alternative solvent in the synthesis of dipeptides under microwave irradiation is also described.     

An automated instrument for human STR identification: design, characterization, and experimental validation

The microfluidic integration of an entire DNA analysis workflow on a fully integrated miniaturized instrument is reported using lab‐on‐a‐chip automation to perform DNA fingerprinting compatible with CODIS standard relevant to the forensic community. The instrument aims to improve the cost, duration, and ease of use to perform a “sample‐to‐profile” analysis with no need for human intervention. The present publication describes the operation of the three major components of the system: the electronic control components, the microfluidic cartridge and CE microchip, and the optical excitation/detection module. Experimental details are given to characterize the level of performance, stability, reliability, accuracy, and sensitivity of the prototype system. A typical temperature profile from a PCR amplification process and an electropherogram of a commercial size standard (GeneScan 500?, Applied Biosystems) separation are shown to assess the relevance of the instrument to forensic applications. Finally, we present a profile from an automated integrated run where lysed cells from a buccal swab were introduced in the system and no further human intervention was required to complete the analysis.