Algebraic multigrid methods for the solution of the Navier–Stokes equations in complicated geometries

The application of standard multigrid methods for the solution of the Navier–Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection–diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. © 1998 John Wiley & Sons, Ltd.     

Structural, infrared, and density functional theory studies of N,N,N',N'-Tetramethylimidazolidinium dichloride: a model for cation-anion association of headgroups and counterions in the interfacial regions of gemini micelles

N,N,N',N'-Tetramethylimidazolidinium dichloride (1-Im-1 2Cl) has been studied as a model system for cation-anion interactions in the interfacial regions of gemini micelles by X-ray crystallography, density functional theory (DFT) calculations, and infrared spectroscopy. Single crystals of 1-Im-1 2Cl contain 1-Im-1 dications, whose five-membered rings adopt a distorted envelope conformation. Eight chloride anions surround each dication, two of which are cradled above and below the five-membered ring (apical) and six of which are dispersed about the periphery of the ring (equatorial). The cations and anions are linked in the solid state by an extensive network of weak C-H...Cl hydrogen bonds that involve all of the H atoms of the dication. The calculated (DFT at the 6-31+G(d) level) structure of the asymmetric unit, which consists of a dication and two apical chloride ions, closely resembles the equivalent unit in the crystal structure with respect to bond distances and angles, the conformation of the 1-Im-1 ring, and the nature and location of the C-H...Cl hydrogen bonds. The calculated IR spectrum predicts a number of absorptions in the 3000 cm(-1) region, assigned as C-H...Cl stretching modes, which are consistent with the presence of an intense band in the observed IR spectrum of the crystals. Over all, this study supports the notion that apical chloride ions interact more strongly with gemini surfactant headgroups by forming multiple hydrogen bonds in ion pairs of a type that cannot be present in the corresponding ion pairs of quaternary headgroups with counterions of single-chain surfactants.     

单位圆内代数体函数的T半径

应用Ahlfors覆盖曲面的方法,在单位圆内构造了代数体函数的一个新的奇异半径(称为T半径),并应用无穷级的型函数推广了亚纯函数奇异方向的相关结论.     

Large t elastic proton-proton scattering at √s = 53 GeV

New experimental results are presented on proton-proton elastic scattering in the range of momentum transfer 0.8GeV² < ?t < 9 GeV² at a centre-of-mass energy of √s = 53 GeV. The data are obtained sing the Split-Field- Magnet Detector at the CERN Intersecting Storage Rings. The cross section has well-known minimum at ?t = (1.34±0.02) GeV² but no further minimum or change of slope is observed between 2 and 6.5 GeV².     

Conformations of highly hindered aryl ethers: IX. Dipole moment evidence for an intramolecular donor-acceptor complex

In a search for evidence that a π cloud proximal halogen interaction is of importance to the mode of action of the thyroid hormones, the dipole moments of the 1'-naphthyl (I), (4.29 D), 4'-carboxymethylphenyl (II), (2.90 D), 2'-bromo4'-carboxymethylphenyl (III), (3.56 D), and methyl (IV), (3.24 D) ethers of 2,4dinitro-6-bromophenol were determined in benzene at 25 °C. The moments of (I), (II) and (III) are approximated best by those calculated for the twisted conformation in which the bromine closely approaches the face of the other ring. That of the naphthyl ether (I) can, however, be explained only by inclusion of an intramolecular electron donor-acceptor charge-transfer moment of 1.6 D directed from the π cloud of the naphthyl ring to the proximal nitro group of the other ring, or of 2.8 D to the proximal bromine of that ring. In the preferred conformation of the methyl ether (IV), the methoxy group is coplanar with the ring while the 2-nitro group is twisted 90° from coplanarity to accomodate it. A mesomeric moment of 2.3 D is estimated from this for the 2,4-dinitro-6-bromophenoxy moiety and is used in calculating the expected moments of the other ethers.     

ACTIVATION ENERGY OF DESORPTION OF DIBENZOFURAN ON ACTIVATED CARBONS

1. INTRODUCTION With the development of municipalization in China, more and more cities are challenged by the problem of how to dispose of the dramatically increased municipal waste. Generally, most of municipal solid waste is landfilled or dumped openly in the suburbs. It causes not only land waste, but also serious environment pollution. In order to solve efficiently the environment pollution caused by municipal solid waste, incineration technique was introduced in some big cities such…