Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.     

Preparation of unsymmetrical disulfides by using sulfines1

Acidolytic cleavage of unsymmetrically substituted dithioacetal monoxides, ArCH(SR)S(O)Me has been used to prepare linear unsymmetrical disulfides RSSMe. Disproportionation was suppressed by the addition of a small amount of benzyl mercaptan. The required starting materials were conveniently obtained from appropriately substituted sulfines ArC(=SO)SR and methyl lithium. The following disulfides were prepared: R =n-C₄H₉ (73.5%), n-C₇H₁₅ (78%), Ph (77.3%), AcO(CH₂)₁₀ (81.5%).The unsymmetrical dithioacetal PhCH(SEt)SC₇H₁₅-n gave upon oxidation with one equivalent of peracid a mixture of two dithioacetal monoxides which on treatment with HClO₄ led to three disulfides. This result is discussed in term of the mechanism of acidolysis.     

Die Deprotonierung von Metallaquoionen II: Aquochrom(III)-ion. Zur Struktur aktiver Chromhydroxide

On alkalinization of solutions of the chromiun(III)-aquo ion simple deprotonation takes place first. The degree of hydroxylation n _OH however can be brought up to only about 1 (the exact value depending on the total concentration [Cr]_t), before the uncharged complex Cr(OH)₃(OH₂)₃ is precipitated. The structure of the very sparingly soluble complex (solubility ～10^?7M ) is held together by hydrogen bonds of type I between the molecules, so that its formula may be written as Cr(OH)₂H_6/2-lattice. The formation of the well ordered structure is extremely fast. On aging, the metallic centers become connected by μ-hydroxo-bridges (type II) and the substances become amorphous and very insoluble. The dinuclear (H₂O)₄Cr(OH)₂Cr(OH₂)₄⁴⁺ behaves similar on deprotonation. Concerning the various equilibria constants see Table 1.     

Radon-222 and 226Ra concentrations in mineralized groundwaters of Gorzanów (Kłodzko Basin, Sudeten Mountains, SW Poland)

This work characterizes the occurrence of radionuclides ²²²Rn and ²²⁶Ra in the mineralized groundwaters of Gorzanów. The village is situated in the Sudeten Mountains, which are known in Poland for having increased concentrations of the aforesaid radionuclides in their groundwaters. However, in Gorzanów, the measured concentrations of ²²⁶Ra were low both in the reservoir rocks and mineralized waters. Consequently, the ²²²Rn concentration in the groundwaters also turned out to be low. The ²²⁶Ra content of these waters should mainly be associated with the dissolution of this nuclide, together with other main ions, at large depths, at slightly enhanced temperature. Radon-222, on the other hand, penetrates into the water during its outflow to the surface, in the zones of intensive friable deformations near fault zones. Thus, in the groundwaters of Gorzanów, the concentrations of these nuclides, subsequent in the uranium series, do not have a common genesis and they are not correlated with each other.     

On a new method for constructing good point sets on spheres

We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-space (d 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated byN segments of equal length.Editors' note: We learned with sadness of Gerold Wagner's untimely death as a result of an avalanche in the Alps shortly after the submission of this paper. When one of the referees, Joram Lindenstrauss, suggested that Wagner's results might be extended to dimensions >6, we invited Professor Lindenstrauss to submit a paper containing that extension which we would publish alongside the Wagner paper. The result is the paper by Bourgain and Lindenstrauss that follows the present one.     

The identification of nitrated polycyclic aromatic hydrocarbons in diesel particulate extracts and their potential formation as artifacts during particulate collection

Summary The highly complex matrix of diesel particulate extracts was analyzed for nitrated polycyclic aromatic hydrocarbons (nitro-PAH) using fused-silica capillary-column gas chromatography along with a thermionic nitrogen-phosphorus detector (TID) and high-performance liquid chromatography followed by on-line catalytic reduction of the nitro-PAH to amino-PAH and subsequent fluorescence detection. Positive isomer identification and quantitation of nitro-PAH are from retention times of authentic standards and their mass spectra. The ease of nitro-PAH formation by nitration of PAH raises the question regarding the origin of these species, whether they are produced as “native” products during the engine combustion process and/or in the exhaust, or instead, formed as the result of chemical conversion to produce artifacts during the sampling procedure. This problem is assessed examing 1-nitropyrene-concentration in particulates of three light-duty diesel engines for different sampling times. 1-Nitropyrene concentrations show only a moderate increase with sampling time under average sampling conditions. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Der Einflu\ der Bestrahlung auf das dielektrische Verhalten von Polyvinylchlorid

Ohne Zusammenfassung Herrn Prof. Dr.W. Holzmütter danke ich für sein stetes Interesse an dieser Arbeit und seine wertvollen Ratschl?ge. Au\erdem bin ich Herrn Dr.G. Geppert und seiner Mitarbeiterin, Frl.C. Roth, für die Unterstützung beim Aufnehmen der Ultrarotspektren zu Dank verpflichtet. Für die überlassung von Probematerial m?chte ich folgenden Firmen danken: Eilenburger Celluloidwerk, Chemische Werke Buna, Badische Anilin- & Sodafabriken, Ludwigshafen, Kalle & Co., Wiesbaden.     

Dielectric Shielding of Ionic Charges in Aqueous Solutions of Different Ionic Strength

The thermodynamic functions of the proton transfer H₂tn²⁺+tn → 2 Htn⁺ (tn = 1,3-diaminopropane) have been determined in aqueous solutions containing different amounts of KCl (0.05 ? μ ? 3.01). The free energy (?ΔG) of the process decreases, whereas the enthalpy (-ΔH) increases with μ. There is reason to believe that the reaction is entirely controlled by the Coulomb forces between the two protonic charges. The electrostatic energy involved can be described in terms of a model incorporating an effective dielectric constant εe, such that δε_e/δμ and δ²ε_e/δμδT are both positive. The polarisation of pure water is produced by orientation of hydrogen-bonded dipole molecules H₂O, whereas the electrolyte solution is polarised in addition by dislocation of the ions K⁺ and Cl^?. Our results demonstrate that the former type of polarisation is much more temperature dependent than the latter.