Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Mössbauer and PAC studies of nanocrystalline Fe

High-purity Fe powder was mechanically milled under argon at ambient temperature using an SPEX 8000 mill. The local atomic and magnetic structure was studied using⁵⁷Co/Fe Mössbauer and¹¹¹In/Cd perturbed angular correlations (PAC) spectroscopies. After 32 hours of milling, X-ray diffraction revealed effective grain diameters of 18 nm and energy-dispersive X-ray analysis indicated a Cr impurity concentration of 5%, presumably introduced by mechanical attrition of steel ball bearings used for milling. In addition to a spectral component very similar to bulk iron metal, the Mössbauer spectra exhibited hyperfine field shifts attributed to the Cr impurities. PAC spectra on Fe milled for 5 h, with no contamination, exhibited two components: (1) A slightly broadened magnetic interaction attributed to interior, defect-free sites of In/Cd probes with a mean hyperfine field slightly greater than in macroscopic grains. The defect-free site fraction grew appreciably during milling, even though In is essentially insoluble in Fe. (2) An indistinct signal due to mixed magnetic and quadrupole interactions attributed to probes at surface or other defect sites.     

Synthetic Applications of the beta-Lithiation of beta-Aryl Secondary Amides: Diastereoselective and Enantioselective Substitutions

The sequence of beta-lithiation and electrophilic substitution of beta-aryl secondary amides is reported. The lithiations occur regioselectively at the beta-position, and the resulting lithiated intermediates can be reacted with a wide range of electrophiles to give substituted products. Reactions of beta-lithiated amides bearing an alpha-substituent provide substituted products with high diastereoselectivity. Electrophilic substitutions of beta-lithiated N-methylamides in the presence of the chiral diamine (-)-sparteine provide highly enantioenriched products. The methodology is used to synthesize enantioenriched beta-aryl beta-substituted amides, acids, and lactones.     

The coupling of supercritical fluid chromatography and field ionization time-of-flight high-resolution mass spectrometry for rapid and quantitative analysis of petroleum middle distillates

We report the first coupling of supercritical fluid chromatography (SFC) with field ionization time-of-flight high-resolution mass spectrometry (FI-ToF HRMS), in parallel with ultraviolet (UV) detection and flame ionization detection (FID), for rapid and quantitative analysis of petroleum middle distillates. SFC separates petroleum middle distillates into saturates and 1- to 3-ring aromatics. FI generates molecular ions for hydrocarbon species eluted from the SFC. The high resolution and exact mass measurements by ToF mass spectrometry provide elemental compositions of the molecules in the petroleum product. The amounts of saturates and aromatic ring types were quantified using the parallel SFC-FID assisted by SFC-UV. With a proper carbon-number calibration, the detailed composition of the petroleum middle distillate was rapidly determined.