Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Reconstruction of the (110) surface of III–V semiconductor compounds

We have used ab initio quantum chemical methods to determine the structure of the clean (110) surface of the nine III–V compounds with III = B, Al or Ga, and V = N, P or As. The theoretical results for small clusters give geometries in good agreement with the experimental geometry for GaAs (the only case for which an experimental structure is available), supporting the use of such clusters in studying the reconstruction of the other systems. We find in all cases that the reconstruction of these (110) surfaces is determined by local valence hybridization forces on the surface atoms. To show the effects of these valence forces we have also carried out extensive calculations on the trihydrides of the above-mentioned elements, for which we have calculated bond distances, bond angles, and the variation of the total energy with bond angle, leading to inversion barriers for the trihydrides of column V elements.     

Nucleophilic ligand substitution in triply deprotonated tetrapeptide complexes of copper(II) and nickel(II) with 1,10-phenanthroline and 2,2-bipyridine

Ligand substitution of the triply deprotonated tetrapeptide ligand with bulky α-carbon substituents, in the tetrapeptide complexes of Cu(II) and Ni(II) by the bidentate ligands 2,2-bipyridine and 1,10-phenanthroline has been studied. The mechanism in the Cu^II(H_-3A₄)^2? and the Cu^II(H_-3F₄)^2? complexes shows a proton-assisted nucleophilic attack, and the Cu^II(H_-3V₄)^2? shows both proton-assisted and direct equatorial nucleophilic attack by the bidentate ligands. A factor of ten decrease in the rate of substitution from Cu^II(H_-3A₄)^2? to Cu^II(H_-3V₄)^2?, and also Cu^II(H_-3F₄)^2? is an indication of a steric hindrance on the substitution rate because of atom overcrowding due to the size of the α-carbon substituents in the Cu^II(H_-3V₄)^2? and Cu^II(H_-3F₄)^2? complexes. The substitution of the triply deprotonated tetrapeptide ligand in Ni^II(H_-3A₄)^2? by 2,2-bipyridine and 1,10-phenanthroline shows a kinetic behaviour completely different to that of the Cu(II)-tetrapeptide complexes. Only a direct equatorial nucleophilic attack by the bidentate ligands has been observed.     

Palladium (II) complexes chelated by 1-substituted-4-pyridyl-1H-1,2,3-triazole ligands as catalyst precursors for selective ethylene dimerization

A series of neutral as well as cationic palladium methyl complexes bearing 1-substituted-4-pyridyl-1H-1,2,3-triazole ligands were prepared and fully characterized by a range of analytical techniques. Conventional and 2D NMR spectroscopy as well as single-crystal X-ray diffraction analysis unambiguously determined the molecular structure of the complexes. The neutral complexes activated by methylaluminoxane were found to be effective catalysts in the ethylene dimerization reaction. The catalyst performance of the in-situ-generated active species was compared with the discrete cationic complexes of the same ligand scaffold. Activities and selectivities for the two systems were remarkably similar, pointing to similarities in the nature of the active species. Both catalytic systems showed a strong correlation of activity and selectivity with the nature of the ligand scaffold. Highest activities were attained when electron-withdrawing groups were incorporated into the triazole ring, while increasing steric bulk in the ortho-position on the pyridyl ring of the ligand led to the almost exclusive dimerization of ethylene with selectivities up to 94% observed toward 1-butene.