Superconvergence Analysis of Galerkin FEM and SDFEM for Elliptic Problems with Characteristic Layers

We analyse the superconvergence properties of the Galerkin FEM and of the streamline-diffusion finite element method (SDFEM) using bilinear functions in the case of elliptic problems with characteristic layers. To resolve the layers we use appropriate Shishkin meshes. For the SDFEM we give an optimal choice for the streamline-diffusion parameter δ for maximal stability in the induced streamline-diffusion norm. In the characteristic layers we are able to show that δ can be chosen of order δ = Cε- N^–2 which is con.rmed by numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ionic Liquids - New Solvents in the Free Radical Polymerization

Summary: The analysis of the influence of ionic liquids (ILs) in polymer synthesis as an alternative for common organic solvents is still an active field of research. 1 Using ILs as solvents for free radical polymerizations implies a significant increase in polymerization rates and molecular weights which can be observed. In this work we examined the copolymerization behaviour of styrene (S) and methyl methacrylate (MMA), glycidyl methacrylate (GMA) and 2-hydroxypropyl methacrylate (HPMA) with acrylonitrile (AN) in 1-etyhl-3-methylimidazolium ethylsulfate ([EMIM]EtSO₄). ILs are liquids with comparable high polarities and viscosities. These two characteristic properties are strongly correlated with the rate coefficients of propagation k_p and termination k_t. 2 - 4 The rate constant of termination k_t decreases when the IL concentration and therefore the viscosity of the reaction mixture is increased, whereas the propagation rate coefficient k_p increases with increasing IL content. The viscosity of the IL can be varied by either working with mixtures of IL with conventional organic solvents – here the IL [EMIM]EtSO₄ was mixed with DMF – or by variation of the temperature. The influence of the viscosity of the IL ([EMIM]EtSO₄) on polymerization kinetics of methyl methacrylate (MMA) and styrene/acrylonitrile (S/AN) was investigated.     

ABS-Modified Epoxy Resins – Curing Kinetics,Polymerization Induced Phase Separation,and Resulting Morphologies

Summary : A commercial diglycidylether of bisphenol A (DGEBA) was modified with an acrylonitrile-butadiene-styrene-copolymer (ABS) and cured with the diamine hardener 4,4′-diaminodiphenylsulfone (DDS). The curing kinetics was followed by DSC- and PVT-measurements. The polymerization induced phase separation (PIPS) was studied using light microscopy and electron microscopy. While the cloud point analyzed by light microscopy is independent of the ABS content, the curing is accelerated by the presence of ABS. The non-linear dependency of the curing rate on the ABS content must have its origin in the different morphologies developed due to PIPS.     

Approximation to Nonlinear Schrodinger Equation of the Complex Generalized Ginzburg-Landau Equation

In this paper, we prove that in the inviscid limit the solution of the generalized derivative Ginzburg-Landau equations converges to the solution of derivative nonlinear Schrödinger equation, we also give the convergence rates for the difference of the solution.     

Poly­[copper(II)-μ-pyrazine-μ3-squarato]

In the structure of the title compound, [Cu(C₄O₄)(C₄H₄N₂)]_n, each copper cation is surrounded by three squarate (3,4-di­hydroxy-3-cyclo­butene-1,2-dioate) anions and two pyrazine ligands, all of which are located in special positions. The copper cation and all atoms of the squarate anion are located on a mirror plane, whereas the pyrazine ligand is located around a mirror plane which is perpendicular to the ring plane. The cations are connected via the squarate anions and the pyrazine ligands, forming sheets parallel to (001).     

A continuum model accounting for defect and mass densities in solids with inelastic material behaviour

In this paper the analysis of structures with inelastic material behaviour is considered taking into account the evolution of defects and changes in mass density. The underlying kinematical concept of an oriented continuum is general enough to describe the micro- and macrobehaviour of material bodies appropriately. Based on the logical and consistent variational arguments for a Lagrangian functional the dynamic balance laws, boundary and transversality conditions, all related to the evolution of defect density and mass changes, are derived for macro- and microstresses of deformational as well as of configurational type. The adopted procedure, which formally leaves the balance laws unaltered, leads to the additional balance law for changes in defect density and additional boundary conditions for the changes in mass and defect densities. Driving forces or affinities, associated with the evolution of defect and mass densities, and a generalization of the J-integral representing the thermodynamic forces on defects are obtained. A nonlocal constitutive model accounting for changes in the defect density is presented.     

Measurements of concentration per size class in a dense polydispersed jet using planar laser-induced fluorescence and phase Doppler techniques

In dense two-phase flows, it is well known that phase Doppler anemometry is not well suited for the measurement of concentration and mass flux. Laser diagnostics based on fluorescence can provide the dispersed phase concentration but without discrimination between size classes. We present a new method of coupling the two techniques, in order to extract the local value of concentration and flux per size class. The method is applied to an axisymmetric turbulent jet, laden with polydispersed droplets 1–90 μm. Droplet concentration profiles are obtained in the development zone (x/d ₀ < 20) of the dense jet and are used to study droplet dispersion. The results are then introduced into the momentum transport equations to analyze the influence of droplets on the carrier phase. We show that the local decrease of the rate of variation of mean momentum with mass loading is due both to an increase in interfacial transfer rate and to a decrease in turbulent diffusion effects. Received: 20 November 2000 / Accepted: 3 April 2001     

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.     

Development of Non-Hydrolysable Oligosaccharide Activity-Based Inactivators for Endoglycanases: A Case Study on α-1,6 Mannanases

There is a vast genomic resource for enzymes active on carbohydrates. Lagging far behind, however, are functional chemical tools for the rapid characterization of carbohydrate-active enzymes. Activity-based probes (ABPs) offer one chemical solution to these issues with ABPs based upon cyclophellitol epoxide and aziridine covalent and irreversible inhibitors representing a potent and widespread approach. Such inhibitors for enzymes active on polysaccharides are potentially limited by the requirement for several glycosidic bonds, themselves substrates for the enzyme targets. Here, it is shown that non-hydrolysable trisaccharide can be synthesized and applied even to enzymes with challenging subsite requirements. It was found that incorporation of carbasugar moieties, which was accomplished by cuprate-assisted regioselective trans-diaxial epoxide opening of carba-mannal synthesised for this purpose, yields inactivators that act as powerful activity-based inhibitors for α-1,6 endo-mannanases. 3-D structures at 1.35–1.47 Å resolutions confirm the design rationale and binding to the enzymatic nucleophile. Carbasugar oligosaccharide cyclophellitols offer a powerful new approach for the design of robust endoglycosidase inhibitors, while the synthesis procedures presented here should allow adaptation towards activity-based endoglycosidase probes as well as configurational isosteres targeting other endoglycosidase families.