Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms

Electrochemical Characterization and CO2 Reduction Reaction of a Family of Pyridazine-Bridged Dinuclear Mn(I) Carbonyl Complexes

Three recently synthesized neutral dinuclear carbonyl manganese complexes with the pyridazine bridging ligand, of general formula [Mn2(μ-ER)2(CO)6(μ-pydz)] (pydz = pyridazine; E = O or S; R = methyl or phenyl), have been investigated by cyclic voltammetry in dimethylformamide and acetonitrile both under an inert argon atmosphere and in the presence of carbon dioxide. This family of Mn(I) compounds behaves interestingly at negative potentials in the presence of CO2. Based on this behavior, which is herein discussed, a rather efficient catalytic mechanism for the CO2 reduction reaction toward the generation of CO has been hypothesized

Dinuclear Re(I) Complexes as New Electrocatalytic Systems for CO2 Reduction

A family of dinuclear tricarbonyl rhenium (I) complexes containing bridging 1,2-diazine ligand and halide anions as ancillary ligands and able to catalyze CO2 reduction is presented. Electrochemical studies show that the highest catalytic efficiency is obtained for the complex containing the 4,5-bipenthyl-pyridazine and iodide as ancillary halogen ligands. This complex gives rise to TOF=15 s−1 that clearly outperforms the values reported for the benchmark mononuclear Re(CO)3Cl(bpy) (11.1 s−1). The role of the substituents on the pyridazine ligand and the nature of the bridging halide ligands on the catalytic activity have been deeply investigated through a systematic study on the structure-properties relationship to understand the improved catalytic efficiencies of this class of complexes

Dinuclear rhenium pyridazine complexes containing bridging chalcogenide anions : synthesis, characterization and computational study

The synthesis of a series of neutral dinuclear rhenium complexes of the general formula [Re2(m-ER)2(CO)6- (m-pydz)] (pydz = pyridazine; E = S, Se or Te; R = methyl or phenyl; the TeMe is not included) has been carried out via new, either one-pot or two-step, procedures. The one-pot synthesis consists of the oxidative addition of RE\u2013ER across the Re\u2013Re bond of [Re2(CO)10], in the presence of 1 equivalent of pyridazine, and affords the corresponding dinuclear complexes in high yields (ca. 85%). Furthermore, a general two-step procedure has been carried out, which involves the synthesis of heterocubane-like [Re4(m3-ER)4(CO)12] molecules and their reaction with pyridazine, quantitatively affording the corresponding dinuclear species through a symmetric [2+2] fragmentation pathway. The molecular structure of the complexes has been elucidated by single crystal XRD analysis, and TD-DFT calculations predicted the existence of conformers differing in the orientation of the chalcogen substituents with respect to the pyridazine ligand. The relative stabilities and the activation barriers for the interconversion have been calculated, observing a regular trend that has been rationalized depending on the hybridization of the chalcogen atom. Variable temperature NMR studies experimentally confirmed the theoretical prediction, showing, in solution, two conformers with different relative amounts and different interconversion rates between them, depending on the chalcogen nature. From the electrochemical point of view the S, Se and Te complexes display a bi-electronic reversible oxidation peak, differently from the two mono-electronic irreversible oxidation peaks previously observed for the O derivatives. Moreover, a progressive narrowing of the HOMO\u2013LUMO gap on going from O to Te, arising from the increase of the HOMO level, has been observed. This is in line with the decreasing electron-withdrawing strength of the chalcogenide bridging ligand, so that the energy gap for the telluride derivative is 1.64 eV, the smallest value in the whole family of the di-rhenium pyridazine complexes. The spectroscopic HOMO\u2013LUMO gap parallels this trend, with a significant red-shift of the metal-to-ligand charge transfer absorption, making the telluride complex highly promising as a photosensitizer in the field of solar energy conversion. In agreement with the narrow HOMO\u2013LUMO gap, no photoluminescence has been observed upon optical excitation

Tilt-over mode in a precessing triaxial ellipsoid

The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J. Fluid Mech., 33, 739 (1968)] are extended to this more complex geometry, which corresponds to a tidally deformed spinning astrophysical body. As confirmed by three-dimensional numerical simulations, the proposed analytical model provides an accurate description of the stationary flow in an arbitrary triaxial ellipsoid, until the appearance at more vigorous forcing of time dependent flows driven by tidal and/or precessional instabilities.Comment: http://link.aip.org/link/doi/10.1063/1.350435

The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow

The behavior of a spheroidal vesicle, in a plane shear flow bounded from one side by a wall, is analysed when the distance from the wall is much larger than the spheroid radius. It is found that tank treading motions produce a transverse drift away from the wall, proportional to the spheroid eccentricity and the inverse square of the distance from the wall. This drift is independent of inertia, and is completely determined by the characteristics of the vesicle membrane. The relative strength of the contribution to drift from tank-treading motions and from the presence of inertial corrections, is discussed.Comment: 16 pages, 1 figure, Latex. To appear on J. Phys. A (Math. Gen.