Calculation of impulsively started incompressible viscous flows

The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.     

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When β-bell particles (particles occupying β contiguous lattice sites) are placed in a random manner on a one-dimensional array of N compartments, we are simultaneously creating sequences of 1, 2, 3, …, β ? 1, vacant compartments. Clearly, after a long period of time a saturation situation arises in which the probability of placing a β-bell particle on such an array becomes zero even though the coverage has not attained the value of one. It is shown that v(β, N), the average fraction of vacant compartments when β-bell particles are placed in a random manner on a linear array of N compartments is exactly described by the recursion relation:

$\text{v(β, N)=}\text{N ? β}\text{N(N ? β + 1}\text{[(N ? 1) v(β, N ? 1) + 2v(β, N ? β)]}$

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Radionuclides in biota collected near a dicalcium phosphate plant, southern Catalonia, Spain

Industrial waste containing radioactive U-decay series isotopes was released into the Ebro River, Spain, over a period of >20 years from a dicalcium phosphate (DCP) plant. This release raised activities of several natural radionuclides (e.g. ²³⁸U, ²³⁴U, ²³⁰Th, ²³²Th and ²²⁶Ra) in biota taken from the area near the DCP plant. Plants and animals selected for this study included the green algae (Cladophora glomerata), the blue mussel (Mytilus edulis), the zebra mussel (Dreissena polymorpha) and the scavenger catfish (Silurus glanis) because they are all common in the area. Multiple sampling points were chosen for this study: (1) a site in the Riba-Roja Reservoir, above the DCP plant’s area of influence, (2) four sites in the area surrounding the DCP plant, close to the town of Flix, and (3) a location in the Ebro Delta Estuary in Fangar Bay. Significant differences in the activities (in Bq kg^?1 of dry weight) for the radioisotopes included in this study among samples were attributed to sample location and the species evaluated. For instance, relatively high activities for uranium and radium were obtained in algae collected around the DCP plant, compared to results obtained for algae samples taken from the unimpacted Riba-Roja Reservoir. In contrast, for zebra mussels, enhanced activities were observed for all radionuclides and, in particular, for thorium and radium isotopes within the area of influence. Among catfish samples, activity values from different locations were not significantly different, though slightly higher activities were observed at the sampling point just downstream of the DCP factory.     

Synthesis of amphidinolide Y precursors

The Negishi coupling between a chiral C3 synthon and an iodoalkene arising from 3-butyn-1-ol, which gave the C3–C9 fragment of amphidinolide Y, was the starting point of a formal total synthesis of this marine natural product. By means of Sharpless ADH and TADDOL-mediated crotylation, the full western fragment (C1–C11) was obtained, which was coupled with the eastern fragment (3-hydroxyoxolane derivative). The penultimate step (ring-closing metathesis, with G-II, H–G-II, or Nitro-Grela reagents, under several conditions) posed great difficulties. The cyclization was achieved with 15c (7,9-bis-O-TES) and 15d (7-O-TES, 9-O-TBS); more than stoichiometric amounts of the H–G-II Ru complex were required for complete conversion.     

Selective and mild oxidation of sulfides to sulfoxides by H_2O_2 using DBUH-Br_3 as catalyst

<正>DBUH-Br_3 catalyzed selective conversion of sulfides to sulfoxides in the presence of H_2O_2 as oxidizing agent is described.The reaction was performed selectively at room temperature and relatively short reaction times.     

Multi-component, regio-selective aldol addition of β-ketoesters to aldehydes: scope and applications

Simple and effective multi-component one-pot aldol addition/protection reactions of β-ketoesters to a series of aldehydes in the presence Me(3)SiCl and i-Pr(2)EtN have been described. The analysis of the scope of the reaction revealed a dramatic dependence of the reactivity on the substrates used. Thus the effect of a catalytic amount of DMF and different reaction conditions was widely investigated. Further transformations of the aldol adducts were particularly useful to give valuable diols and compounds with quaternary stereocenters, while X-ray structural analysis gave also important stereochemical information about this challenging reaction.     

A new dinuclear Ru-Hbpp based water oxidation catalyst with a trans-disposition of the Ru-OH

The bis(2-pyridyl)ethylamine (bpea) ligand has been used as a starting material for the synthesis of dinuclear Ru complexes of general formula trans,fac-{[Ru(n)X(bpea)](2)(μ-bpp)}(m+) (for X = Cl, n = II, m = 1, trans-Ru(II)-Cl, 1(+); for X = OH, n = III, m = 3, trans-Ru(III)-OH, 2(3+)) where the 3,5-bis(2-pyridyl)pyrazolate anionic ligand (bpp) acts as bridging dinucleating ligand, the bpea ligand coordinates in a facial manner and the monodentate ligands X are situated in a trans fashion with regard to one another. These complexes have been characterized in solution by 1D and 2D NMR spectroscopy, UV-vis and electrochemical techniques and in the solid state by X-ray diffraction analysis. The reaction of 1(PF(6)) with Ag(+) generates the corresponding solvated complex where the Cl ligand has been removed as insoluble AgCl, followed by the oxidation of Ru(II) to Ru(III) to generate the corresponding dinuclear complex trans-Ru(III)-OH, 2(PF(6))(3). The latter has been shown to catalytically oxidize water to molecular dioxygen using Ce(IV) as oxidant. Quantitative gas evolution as a function of time has been monitored on line by both manometry and mass spectroscopy (MS) techniques. Relative initial velocities of oxygen formation together with structural considerations rule out an intramolecular O-O bond formation pathway.     

How many Langmuirs are required for monolayer formation?

In the present work, we provide the exact answer to the title question employing a probabilistic approach. The average number of Langmuirs L required for monolayer formation was found to be equal to (1/i), i.e., the armonic series up to the nth term, where n is the number of adsorption sites. This result is particularly useful when a reduced number of adsorption sites is considered, such as adsorption on small terraces of nanoscopic dimensions where the value of n could be in the range of a few thousands sites. In this case, the use of integrated equations derived from the mean-field approach would provide completely misleading results.