A subdomain boundary element method for high‐Reynolds laminar flow using stream function‐vorticity formulation

The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd.     

Bestimmung der molaren Masse und der Ladungszahl von Polymerelektrolyten mit der Ultrazentrifuge

Zusammenfassung In der vorliegenden Arbeit wird das Sedimentationsgleichgewicht der Systeme Na₆[H₂W₁₂O₄₀]—NaCI—H₂O und Na₆[H₂W₁₂O₄₀]—NaClO₄— H2O untersucht. Die scheinbare molare Masse Mapp des Natriummetawolframats wird in beiden Systemen als Funktion der Natriummetawolfrarnat-Anfangspartialdichte ₀ ^PX _z gemessen. Durch lineare Extrapolation der Funktion Mapp = Mapp (PP,, ) auf die Polymerelektrolyt-Anfangspartialdichte Null können die Grenzwerte der scheinbaren molaren Masse (Mapp)o ermittelt werden. Aus den (Mapp)o-Werten wird die Abhängigkeit der Größe (ln _PXz /m _BX ) _mPXz von der NaCI- bzw. NaClO₄-Molalität berechnet.Die Bestimmung der molaren Masse und der (stöchiometrischen) Ladungszahl eines Polymerelektrolyten aus den experimentell ermittelten (Mapp)o-Werten unter Anwendung der Lamm-Williams-Gleichung wird diskutiert. Zur Ermittlung der beiden Größen müssen mehrere Versuchsreihen mit zwei verschiedenen Fremdelektrolyten durchgeführt werden. Externe Messungen sind nicht erforderlich.Man erhält auf diese Weise verläßliche Werte so-wohl der molaren Masse als auch der (stächiometrischen) Ladungszahl.

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Summary The sedimentation equilibria of the systems sodium metatungstate-sodium chloride-water and sodium metatungstate-sodium perchlorate-water are investiated. In both systems the apparent molecular mass Mapp of sodium metatungstate (PX _z) is measured in dependence on partial density ₀ ^PX _z before centrifugation. By linear extrapolation of the function Mapp = Mapp ( ₀ ^PX _z the limiting value (Mapp)o for ₀ ^PX _z = 0 is obtained. The variation with sodium chloride and sodium perchlorate molality of the quantity (ln _{PX z} ^m _BX )mPX_z is calculated from (Mapp)o data.The determination of the molecular mass and the algebraic valency of a polymeric ion by means of the (Mapp)o values calculated by Lamm-Williams equation is discussed. In order to obtain these two quantities at least two series of experiments are required, each of which using a different supporting electrolyte. External measurements are not necessary. In this way reliable values for the molecular mass as well as for the stoichiometric valency are obtained.

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Mit 5 Abbildungen und 3 Tabellen     

Trace-Aktivitätskoeffizienten und Ionenassoziation von Natriummetawolframat im System Natriummetawolframat-Natriumperchlorat-Wasser

Zusammenfassung In der vorliegenden Arbeit wird das Sedimentations-gleichgewicht des Systems Na₆[H₂W₁₂O₄₀]-NaClO₄-H₂O bei 25 °C untersucht. Die scheinbare Ladungszahl des Natriummetawolframats wird als Funktion der NaClO₄-MolalitätmNaClO₄ ermittelt. Aus dieser Abhängigkeit kann für die summarische Dissoziation des NatriummetawolframatsNa₂[H₂W₁₂O_4o] 6Na⁺ + [H₂W₁₂O₄₀]^6– die DissoziationskonstanteK in Gegenwart von NaClO₄ als Fremdelektrolyt zuK=0,08 mol⁶·kg^–6 bestimmt werden.Der Kreuzdifferentialquotient ( _PXz , ist der Trace-Aktivitätskoeffizient des Natriummetawolframats) wird ebenfalls als Funktion der NaClO₄-Molalität ermittelt.Die Konzentrationsabhängigkeit des Trace-Aktivitätskoeffizienten zeigt einen Verlauf, wie er unseres Wissens nach noch nicht von anderen Autoren beobachtet wurde.

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Summary An ultracentrifugal study of the sedimentation equilibrium of the system Na₂[H₂W₁₂O₄₀]-NaClO₄-H₂Oat 25 °C is presented. The dependency of the apparent charge of the sodium metatungstate on NaClO₄-molality is investigated. From these data the dissociation constant for the dissociation of the sodium metatungstate in the presence of NaClO₄ according to the equationNa[H₂W₁₂O₄₀] 6Na⁺ + [H₂W₁₂O₄₀]^6– is calculated toK=0.08 mol⁶·kg^–6. The cross differential quotient ( _PXz is the trace activity coefficient of the sodium metatungstate) shows a behavior in its dependence on NaClO₄-molality which to our knowledge has not yet been reported by other authors.

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Mit 5 Abbildungen und 1 Tabelle     

Manifestations of group covariance in a metric theory

Foundations of Physics - The requirement to present Dirac's Large Number Hypothesis in one system of units in which the resulting modifications to Einstein's theory are exhibited, led to...     

Magnetic behavior of amorphous Fe−Ni−Zr alloys and their response to radiation damage

The magnetic properties of two amorphous Fe?Ni?Zr alloys, Fe_89.7Ni_0.03Zr₁₀ and Fe₇₀Ni₂₀Zr₁₀, both in the “as cast” and neutron irradiated states were investigated by Mössbauer spectroscopy and dc magnetic susceptibility measurements. The upper magnetic ordering temperatures of Fe_89.7Ni_0.03Zr₁₀ are 232K and 246K for the “as cast” and irradiated samples, respectively. The magnetic ordering temperature for Fe₇₀Ni₂₀Zr₁₀ was about 478K for both the “as cast” and irradiated samples. Both compositions yield magnetic hyperfine spectra, which show a considerable relaxation effect that must be explicitly considered in the calculation of the average local Fe moments. When this is done, these values derived from Mössbauer spectra are in good agreement with the dc susceptibility values. The effects of neutron irradiation on the magnetic properties of these alloys are small.     

Raman and SERS study of metoclopramide at different pH values

Conjugate acid–base forms of the drug metoclopramide were investigated by Raman spectroscopy in aqueous solutions and by surface‐enhanced Raman scattering (SERS), when the molecules were adsorbed on colloidal silver surfaces. Raman spectra were recorded at pH values below 8, metoclopramide being poorly water soluble at higher pH values. The SERS spectra of metoclopramide were recorded in the 3–11 pH range, even in spite of its low solubility at basic pH values. The Raman and SERS spectra were assigned by means of density functional theory (DFT) calculations. By monitoring several SERS marker bands, the protonated, neutral or the coexistence of both molecular species adsorbed on the colloidal silver particles could be evidenced. The adsorbate orientation was deduced to be perpendicular to the metal surface for the protonated molecular species and tilted for the neutral metoclopramide molecular species. Copyright © 2009 John Wiley & Sons, Ltd.     

Severi varieties on blow-ups of the symmetric square of an elliptic curve

We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces.