Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

The effect of constraints on the initial steps of adsorption of nitrogen atoms on the silicon surface as modeled by the cluster [Si9H12 + N]

The effect of constraints on the initial steps of the incorporation of nitrogen on silicon has been assessed by calculations with the [Si₉H₁₂ + N] model cluster using density functional theory with the hybrid functional B3LYP, and two basis sets that differ significantly in size. The relative stability of the various stationary points is dependent on the type of constraints imposed on the cluster. Constrained calculations have predicted the structure with the nitrogen symmetrically bonded to the dimer silicons as the global minimum, however, if no constraint is imposed and the whole cluster is optimized, as done in this work, a structure with the nitrogen inserted between the dimer and the first layer and bonded to three silicon atoms is predicted to be the most stable one by about 17 kcal/mol by either the doublet or quartet route. The whole process is very exothermic and reaction barriers in the intermediate steps are easily overcome. Calculations with the smaller basis do not essentially change the major conclusion about the relative stability of the various stationary points. The most stable structure and frequency calculations are consistent with a planar NSi₃ moiety and its asymmetrical stretching frequency.     

Adaptive mesh refinement and coarsening for aerodynamic flow simulations

A new mesh refinement technique for unstructured grids is discussed. The new technique presents the important advantage of maintaining the original grid skewness, thanks to the capability of handling hanging nodes. The paper also presents an interpretation of MacCormack's method in an unstructured grid context. Results for a transonic convergent–divergent nozzle, for a convergent nozzle with a supersonic entrance and for transonic flow over a NACA 0012 airfoil are presented and discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Polar actions on compact rank one symmetric spaces are taut

We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z ₂-coefficients.The second author was supported in part by FAPESP and CNPq.     

Path integral and transactional interpretation

The concept of transaction, introduced by Cramer in his realistic nonlocal interpretation of quantum mechanics (QM), is herein reformulated in the language of the Feynman graphs' technique.     

Probing the mechanism of the Petasis olefination reaction by atmospheric pressure chemical ionization mass and tandem mass spectrometry

Atmospheric pressure chemical ionization mass (APCI-MS) and tandem mass spectrometry (APCI-MS/MS) is used to probe the mechanism of the Petasis olefination reaction. Oxatitanacycle intermediates 4 were transferred from solution to the gas phase, detected as 4H+ by APCI-MS with characteristic Ti-isotopic patterns, and structurally characterized by APCI-MS/MS. Detection of 4H+, which upon collision activation dissociates to both 3H+ and Cp(2)TiOH+, fully supports the Hughes mechanism as depicted above. [reaction: see text]     

Studies on the synthesis of heterocyclic compounds. XI. Cleavage of 1,3-benzodioxoles by magnesium bromide-acetic anhydride

The cleavage reaction of some 1,3-benzodioxole derivatives with magnesium bromide and acetic anhydride has been studied. The reactions have been carried out in acetonitrile solution at room temperature. In all of the 1,3-benzodioxoles studied, the opening of the heterocyclic ring with formation of bromides, alkenes and their corresponding products of hydrolysis have been observed. The competitive electrophilic substitution on the benzene ring was very limited and was insignificant when a large excess of the cleavage reagent was used. The structures of newly prepared compounds have been determined by elemental analysis, spectroscopic data and comparison with authentic samples.     

Fine tuning of the electronic coupling between metal centers in cyano-bridged mixed-valent trinuclear complexes

We report the synthesis, characterization, and spectroscopic properties of a family of trinuclear cyano-bridged mixed-valent compounds, trans-[Ru(II)L(4)[NCFe(III)(CN)(5)](2)](4-), trans-[Ru(II)L(4)[CNFe(III)(CN)(5)](2)](4-), and cis-[Ru(II)(bpy)(2)[NCFe(III)(CN)(5)](2)](4-) (L = pyridine, 4-tert-butylpyridine, and 4-methoxypyridine). Tetraphenylphosphonium salts of complexes trans-[Ru(II)L(4)[NCFe(III)(CN)(5)](2)](4-) (L = pyridine and 4-tert-butylpyridine) crystallize in the space groups C2 and P2(1)/c, respectively, and show a linear arrangement of the metal units and an almost completely eclipsed configuration of the equatorial ligands. An intense band (epsilon approximately 2000-9000 M(-1) cm(-1)) is observed for all of the compounds in the NIR region of the spectrum, not present in the separated building blocks, and strongly solvent dependent. We assign it as a metal-to-metal charge transfer (MMCT) from the Ru(II) to the terminal Fe(III) moieties in the context of a simplified three-center model. The electrochemistry measurements reveal a splitting of the redox waves for the reduction of the iron centers for some of the complexes with a trans configuration between the metal units, ranging from 100 to 260 mV, depending on the substituting pyridine ligand and the solvent, suggesting long-range metal-metal interactions. These interactions are rationalized in terms of the energy matching between the pi-symmetry orbitals of the metals and the cyanide bridge. The one- and two-electron reduced species derived from compounds trans-[Ru(II)L(4)[NCFe(III)(CN)(5)](2)](4-,5-,6-) were characterized in methanolic solution. The mixed-valent Fe(II)-Ru(II)-Fe(III) system exhibits an intense red shifted band in the NIR region of the spectrum, arising from the superposition of MMCT bands from the central Ru(II) to the terminal Fe(III) fragments and from the 1 nm distant Fe(II) to Fe(III) centers.