Discrete approximations of BV solutions to doubly nonlinear degenerate parabolic equations

Summary. In this paper we present and analyse certain discrete approximations of solutions to scalar, doubly nonlinear degenerate, parabolic problems of the form under the very general structural condition . To mention only a few examples: the heat equation, the porous medium equation, the two-phase flow equation, hyperbolic conservation laws and equations arising from the theory of non-Newtonian fluids are all special cases of (P). Since the diffusion terms a(s) and b(s) are allowed to degenerate on intervals, shock waves will in general appear in the solutions of (P). Furthermore, weak solutions are not uniquely determined by their data. For these reasons we work within the framework of weak solutions that are of bounded variation (in space and time) and, in addition, satisfy an entropy condition. The well-posedness of the Cauchy problem (P) in this class of so-called BV entropy weak solutions follows from a work of Yin [18]. The discrete approximations are shown to converge to the unique BV entropy weak solution of (P). Received November 10, 1998 / Revised version received June 10, 1999 / Published online June 8, 2000     

Environmental adaptation of proteins: Regression models with simple physicochemical properties

Bio-sequences from ortholog proteins are well suited for statistical inference when the sequences can be divided into ordinal groups based on known environmental features or traits of the host organisms. In this paper two new regression models are described for extracting proteomic trends of extreme environments. The approach is based on physicochemical properties of the amino acids, and may also utilise stratification of the data. We are especially looking for connections of temperature adaptation between the organism and its molecular level. To show the applicability of the methods, we present analyses of genomic data from proteobacteria orders, where we examine the cold adaptation of membrane proteins, intracellular proteins, and the enzyme endonuclease I. Our results confirm earlier findings that redistribution of charge and increase of surface hydrophobicity might be some of the most important signatures for cold adaptation.     

WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

The main purpose of this paper is two-fold:(i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71(2011), pp. 2014–2047];(ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58(2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

Addition of diazomethane and sulfur ylides to the oxo-group in derivatives of ketoses and aldoses : I. Reactions of 2,3-O-isopropylidene-D-glyceraldehyde

The reaction between 2,3-O-isopropylidene-D-glyceraldehyde and diazomethane, dimethylsulfonium methylide and dimethyloxosulfonium methylide has been studied. The sulfur ylides yield two epimeric epoxides, 1,2-anhydro-3,4-O-isopropylidene-D-erythritol and 1,2-anhydro-3,4-O-isopropylidene-D-threitol, with a slight preference for the erythro isomer.The reaction with diazomethane yields in addition to the epoxides a methyl ketone, 1-deoxy-3,4-O-isopropylidene-D-glycero-tetrulose. The relative yields of the three products have been discussed on the basis of mechanisms previously proposed for the reactions. The yield of methyl ketone was lowest when the reaction was carried out in pure diethyl ether solution. This solvent also gives the greatest preference for the erythro isomer of the two epoxides. Constitution and stereochemistry for the three products have been shown by synthesis.     

Mechanism of propylene insertion using bis(phenoxyimine)-based titanium catalysts: an unusual secondary insertion of propylene in a group IV catalyst system

A highly regioselective secondary enchainment of propylene in a group IV catalyst system is reported. End-group analysis of polypropylene formed using the phenoxyimine-based titanium catalysts revealed a reversal in the regioselectivity of insertion for this class of catalysts. To the best of our knowledge, bis(phenoxyimine)-based titanium complexes are the only known group IV catalysts that insert propylene with exclusive 2,1-regiochemistry. Insertion of propylene into the initiating titanium hydride occurs with high 1,2-regiochemistry. Subsequent insertions into primary titanium alkyls are regiorandom, while insertions into secondary titanium alkyls proceed with high 2,1-regioselectivity. Cyclopolymerization and ethylene/propylene copolymerization strategies are employed to support this proposal.     

Stochastic Breakeven Points

When the probability of a negative unit contribution is non-negligible, desirable and undesirable data configurations may map into the same breakeven point. In the general case, the decision relevance of a breakeven point probability distribution is rather obscure. Assuming bivariate normality, with a "small" probability of a negative denominator, then an approximation procedure based on the Geary-Hinkley transformation is a convenient and powerful means of obtaining information about the breakeven point probability distribution. Hence, for practical purposes it may be unnecessary to resort to computer simulation or to numerical integration of the complex exact density function of the breakeven point.     

GDOES,XPS, and SEM with EDS analysis of porous coatings obtained on titanium after plasma electrolytic oxidation

In the paper, the glow discharge optical emission spectroscopy, X‐ray photoelectron spectroscopy, scanning electron microscopy, and energy‐dispersive X‐ray spectroscopy results of a commercial purity titanium grade 2 after plasma electrolytic oxidation (PEO), also known as micro arc oxidation (MAO), are presented. The PEO treatment was performed in the electrolyte containing concentrated (85%) phosphoric acid with copper nitrate at the voltage of 450 ± 10 V for 1 min. For the electrolyte, copper nitrate addition from 300 to 600 g/l was used. Porous coatings of specific properties were obtained. The measurements results allow to state that the copper and nitrogen ions can be introduced into the surface layer formed on pure titanium by the plasma electrolytic oxidation. The distributions of these elements were detected to depend on the electrolyte composition, with the highest amounts revealed in the coating created in the electrolyte containing 600 g Cu(NO₃)₂ in 1 l H₃PO₄. Three sub‐layers of the coating, displayed in this work by two models, were developed in the study. The analysis performed shows that under the PEO treatment in each of the electrolytes used, the formation of coating with the top sub‐layers always enriched in copper compounds was found. Copyright © 2016 John Wiley & Sons, Ltd.     

A numerical investigation of aerofoil boundary-layer manipulator profile for cruise-flight conditions

A computational study has been conducted to determine the variation of device drag with profile shape and angle of attack for aerofoil boundary-layer manipulators (LEBUs) operating at high subsonic Mach numbers. Calculations have been made at a free-stream Mach number of 0.80 for both symmetrical and asymmetrical NACA-00xx and 44xx series devices including an inverted cambered NACA-4409 profile. The LEBUs considered were located in a turbulent boundary-layer at a mid-chord heighth equivalent to 0.67 from the wall. The present investigations sought to confirm suggestions based upon experimental observations that there may be some advantage in replacing a symmetrical device by an inverted asymmetrical profile form.The computations were performed using an unstructured adaptive-mesh 3D Navier-Stokes code incorporating a Lam and Bremhorst low-Reynolds number two-equationk — turbulence model. The calculated flow field around a NACA-0009 aerofoil at zero angle of attack was initially verified against experimental interferometric data.The calculated device drag coefficient at zero incidence was 0.026 for the NACA-0009, similar to that measured in experiments. However predicted drag for an inverted NACA-4409 was 0.085, this being considerably higher than anticipated. The results suggested that a slightly positive angle of attack may help minimise device drag but neither profile is appropriate for use in transonic conditions. Improved results may be obtained from inverted flat-topped profiles designed to minimise losses associated with localised shocks.