Measuring the Effects of Artificial Viscosity in SPH Simulations of Rotating Fluid Flows

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for quantifying its effect include approximate analytic formulae and disc-averaged be- haviour in specific ring-spreading simulations, based on the kinematic effects produced by the artificial viscosity. These methods have disadvantages, in that they typically are applicable to a very small range of physical scenarios, have a large number of simplifying assumptions, and often are tied to specific SPH formulations which do not include corrective (e.g., Balsara) or time-dependent viscosity terms. In this study we have developed a simple, generally applicable and practical technique for evaluating the local effect of artificial viscosity directly from the creation of specific entropy for each SPH particle. This local approach is simple and quick to implement, and it al- lows a detailed characterization of viscous effects as a function of position. Several advantages of this method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability. In order to compare this new method with ex- isting ones, simple disc flow examples are used. Even in these basic cases, the very roughly approximate nature of the previous methods is shown. Our local method pro- vides a detailed description of the effects of the artificial viscosity throughout the disc, even for extended examples which implement Balsara corrections. As a further use of this approach, explicit dependencies of the effective viscosity in terms of SPH and flow parameters are estimated from the example cases. In an appendix, a method for the initial placement of SPH particles is discussed which is very effective in reducing numerical fluctuations.Comment: 15 pages, 9 figures, resubmitted to MNRA

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Homogeneous CO Hydrogenation: Ligand Effects on the Lewis Acid-Assisted Reductive Coupling of Carbon Monoxide

Structure-function studies on the role of pendent Lewis acids in the reductive coupling of CO are reported. Cationic rhenium carbonyl complexes containing zero, one, or two phosphinoborane ligands (Ph_2P(CH_2)_nB(C_8H_(14)), n=1-3) react with the nucleophilic hydride [HPt(dmpe)_2]^+ to reduce [M-CO]^+ to M-CHO; this step is relatively insensitive to the Lewis acid, as both pendent (internal) and external boranes of appropriate acid strength can be used. In contrast, whether a second hydride transfer and C-C bond forming steps occur depends strongly on the number of carbon atoms between P and B in the phosphinoborane ligands, as well as the number of pendent acids in the complex: shorter linker chain lengths favor such reductive coupling, whereas longer chains and external boranes are ineffective. A number of different species containing partially reduced CO groups, whose exact structures vary considerably with the nature and number of phosphinoborane ligands, have been crystallographically characterized. The reaction of [(Ph -2P(CH_2)_2B(C_8H_(14)))_2Re(CO)4]^+ with [HPt(dmpe)_2]^+ takes place via a “hydride shuttle” mechanism, in which hydride is transferred from Pt to a pendent borane and thence to CO, rather than by direct hydride attack at CO. Addition of a second hydride in C_6D_5Cl at -40 ºC affords an unusual anionic bis(carbene) complex, which converts to a C-C bonded product on warming. These results support a working model for Lewis acid-assisted reductive coupling of CO, in which B (pendent or external) shuttles hydride from Pt to coordinated CO, followed by formation of an intramolecular B-O bond, which facilitates reductive coupling

Trialkylborane-Assisted CO_2 Reduction by Late Transition Metal Hydrides

Trialkylborane additives promote reduction of CO_2 to formate by bis(diphosphine) Ni(II) and Rh(III) hydride complexes. The late transition metal hydrides, which can be formed from dihydrogen, transfer hydride to CO_2 to give a formateborane adduct. The borane must be of appropriate Lewis acidity: weaker acids do not show significant hydride transfer enhancement, while stronger acids abstract hydride without CO_2 reduction. The mechanism likely involves a pre-equilibrium hydride transfer followed by formation of a stabilizing formateborane adduct

Homogeneous CO Hydrogenation: Dihydrogen Activation Involves a Frustrated Lewis Pair Instead of a Platinum Complex

During a search for conditions appropriate for Pt-catalyzed CO reduction using dihydrogen directly, metal-free conditions were discovered instead. A bulky, strong phosphazene base forms a “frustrated” Lewis pair (FLP) with a trialkylborane in the secondary coordination sphere of a rhenium carbonyl. Treatment of the FLP with dihydrogen cleanly affords multiple hydride transfers and C−C bond formation