Error analysis for finite element methods for steady natural convection problems

We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (u p T), which we also establish.     

Mass and momentum conservation of the least-squares spectral collocation method for the Navier-Stokes equations

From the literature, it is known that the Least-Squares Spectral Element Method (LSSEM) for the stationary Stokes equations performs poorly with respect to mass conservation but compensates this lack by a superior conservation of momentum. Furthermore, it is known that the Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the stationary Stokes equations. In the present paper, we consider mass and momentum conservation of the LSSCM for time-dependent Stokes and Navier-Stokes equations. We observe that the LSSCM leads to improved conservation of mass (and momentum) for these problems. Furthermore, the LSSCM leads to the well-known time-dependent profiles for the velocity and the pressure profiles. To obtain these results, we use only a few elements, each with high polynomial degree, avoid normal equations for solving the overdetermined linear systems of equations and introduce the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero. Furthermore, we combined the transformation of Gordon and Hall (transfinite mapping) with the least-squares spectral collocation scheme to discretize the internal flow problems.     

Renin inhibition by substituted piperidines: a novel paradigm for the inhibition of monomeric aspartic proteinases?

BACKGROUND: The aspartic proteinase renin catalyses the first and rate-limiting step in the conversion of angiotensinogen to the hormone angiotensin II, and therefore plays an important physiological role in the regulation of blood pressure. Numerous potent peptidomimetic inhibitors of this important drug target have been developed, but none of these compounds have progressed past clinical phase II trials. Limited oral bioavailability or excessive production costs have prevented these inhibitors from becoming new antihypertensive drugs. We were interested in developing new nonpeptidomimetic renin inhibitors. RESULTS: High-throughput screening of the Roche compound library identified a simple 3, 4-disubstituted piperidine lead compound. We determined the crystal structures of recombinant human renin complexed with two representatives of this new class. Binding of these substituted piperidine derivatives is accompanied by major induced-fit adaptations around the enzyme's active site. CONCLUSIONS: The efficient optimisation of the piperidine inhibitors was facilitated by structural analysis of the renin active site in two renin-inhibitor complexes (some of the piperidine derivatives have picomolar affinities for renin). These structural changes provide the basis for a novel paradigm for inhibition of monomeric aspartic proteinases.     

Stick-slip of the three-phase line in measurements of dynamic contact angles

Contact angles of a series of n-alkanes (i.e., n-heptane to n-hexadecane) are studied on two functionalized maleimide copolymers (i.e., poly(ethene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ETMF) and poly(octadecene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ODMF)). On the homogeneous ETMF films, all liquids show a smooth motion of the three-phase line. In contrast, on ODMF surfaces that are found to consist of mainly fluorocarbons and small patches of hydrocarbons, short-chain n-alkanes show a stick-slip pattern. By increasing the chain length of the probe liquids, stick-slip is reduced significantly. The phenomenon is discussed in the framework of the Cassie equation. It is found that the upper limit of contact angles in the stick-slip pattern is given by the advancing angle that would be obtained on the pure fluorocarbon surface, whereas the lower limit of the stick-slip pattern is given by the Cassie angle.     

Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia

Iron oxide colloidal nanomagnets generate heat when subjected to an alternating magnetic field. Their heating power, governed by the mechanisms of magnetic energy dissipation for single-domain particles (Brown and Néel relaxations), is highly sensitive to the crystal size, the material, and the solvent properties. This study was designed to distinguish between the contributions of Néel and Brownian mechanisms to heat generation. Anionic nanocrystals of maghemite and cobalt ferrite, differing by their magnetic anisotropy, were chemically synthesized and dispersed in an aqueous suspension by electrostatic stabilization. The particles were size-sorted by successive electrostatic phase separation steps. Parameters governing the efficiency of nanomagnets as heat mediators were varied independently; these comprised the particle size (from 5 to 16.5 nm), the solvent viscosity, magnetic anisotropy, and the magnetic field frequency and amplitude. The measured specific loss powers (SLPs) were in quantitative agreement with the results of a predictive model taking into account both Néel and Brown loss processes and the whole particle size distribution. By varying the carrier fluid viscosity, we found that Brownian friction within the carrier fluid was the main contributor to the heating power of cobalt ferrite particles. In contrast, Néel internal rotation of the magnetic moment accounted for most of the loss power of maghemite particles. Specific loss powers were varied by 3 orders of magnitude with increasing maghemite crystal size (from 4 to 1650 W/g at 700 kHz and 24.8 kA/m). This comprehensive parametric study provides the groundwork for the use of anionic colloidal nanocrystals to generate magnetically induced hyperthermia in various media, including complex systems and biological materials.     

Papierchromatographische Trennungen von Alkaloidgemischen an Succinylzellulose-Papieren

Zusammenfassung Das früher beschriebene¹ Succinylzellulose-Papier wird als Ionenaustauscher zur weiteren papierchromatischen Trennung von Basengemischen verwendet. Getrennt wurden die Alkaloide der Morphingruppe und deren Abwandlungsprodukte, ferner die Alkaloide der Strychnin-, der Tropin-, der Cocaingruppe und andere Alkaloide.

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Summary The succinyl-cellulose paper described previously¹ is used as ion exchanger for additional paper chromatographic separations of mixtures of bases. Separations were accomplished of the alkaloids of the morphine group and their modification products, and also of the alkaloids of the strychnine-, tropine- and cocaine groups and other alkaloids.

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Résumé On utilise le papier à la succinyl-cellulose déjà décrit¹, comme écharigeur d'ions pour d'autres séparations par chromatographie sur papier de mélanges basiques. On a séparé ainsi les alcaloïdes du groupe de la morphine et leurs produits d'évolution, et en outre, les alcaloïdes des groupes de la strychnine, de la tropine et de la cocaïne et d'autres alcaloïdes.

     

Einsatz von Hochleistungs-Trennkapillaren in der GC.-EIMS./GC.-CIMS.-Analyse: Eine Möglichkeit zur massenspektrometrischen Doppelbindungscharakterisierung in komplexen Monoalkengemischen

In an attempt to determine position and substitution of double bonds in complex mixtures of straight-chain and branched monoalkenes without actually isolating the constituents, GC.-MS. analysis is performed after in-batch preparation of derivatives of a judiciously chosen type. Cyclic phenylboronates (4,5-substituted 2-phenyl-1,3,2-dioxaborols) are prepared from 1,2-diols which are, in turn, obtained from the original alkenes by treatment with osmium tetroxide. Chemical ionization mass spectrometry (CIMS.) is used in addition to conventional electron impact techniques (EIMS.) in sequential GC./CIMS.- and GC./EIMS.runs, yielding complementary structural information for the single components of the mixture. In order to cope with the potential severity of the separation problem, high-efficiency glass capillary columns were employed throughout. The performance of the system used is demonstrated by a complete double bond analysis of a 35-component mixture of monoalkenes in the C₅ to C₉ range.