Large eddy simulation of temporally developing juncture flows

Large eddy simulation (LES) results are reported for temporally developing solid–solid and solid–rigid-lid juncture flows. A MacCormack-type scheme that is second-order in time, and fourth-order in space for the convective terms and second-order in space for the viscous terms, is used. The simulations are obtained for a low subsonic Mach number. The subgrid-scale stresses (SGS) are modeled using the dynamic modeling procedure. The turbulent flow field generated on a flat-plate boundary layer is used to initialize the juncture flow simulations. The results of the flat-plate boundary layer simulations are validated with experimental and direct numerical simulations (DNS) data. In juncture flow simulations, the presence of an adjacent solid-wall/rigid-lid boundary altered the mean and the turbulent field, setting up gradients in the anisotropy of normal Reynolds stresses resulting in the formation of turbulence-induced secondary vortices. The relative size of these secondary vortices and the distribution of mean and turbulent quantities are in qualitative agreement with the experimental observations for the solid–solid juncture. The overall distribution of the mean and turbulence quantities showed close resemblance between the solid–solid and the solid–rigid-lid junctures; except for the absence of a second vortical region near the rigid-lid boundary. In agreement with the experimental observations, it was found that the normalized anisotropy term exhibited similarity when plotted against the distance from the boundary, regardless of the type of boundary, i.e. solid-wall or rigid-lid. The turbulent kinetic energy increased near the rigid-lid boundary. While the surface normal velocity fluctuations decreased to zero at the rigid-lid boundary, the other two velocity components showed an increase in their energy, which is also consistent with the experimental observations. © 1998 John Wiley & Sons, Ltd.     

On the modularity of elliptic curves over -adic exercises

We complete the proof that every elliptic curve over the rational numbers is modular.

     

Flow injection with chemical reaction interface-isotope ratio mass spectrometry: an alternative to off-line combustion for detecting low levels of enriched 13C in mass balance studies

We have evaluated the potential of flow injection chemical reaction interface isotope-ratio mass spectrometry to replace radioactive labeling techniques in material balance studies. A sample is flow injected and transmitted through a desolvation system followed by combustion to form ¹³CO₂ with a microwave-powered chemical reaction interface. We can detect trace amounts of a ¹³C-labeled drug (3′-azido-3′-deoxythymidine, AZT) in urine or feces. Our ability to quantify less than 100 ng/mL of excess ¹³C (∼1 μg/mL of ¹³C-labeled AZT) from a sample equivalent to 10 μL of urine is superior to previous detection limits for ¹³C in urine that use off-line combustion methods. Parallel studies using ¹⁴C-labeled AZT showed that our stable isotope method provides comparable percent excretion data for urine and feces. These results support previous findings that mass balance studies could be carried out with isotope-ratio mass spectrometer, here using doses as low as 1–2 mg/kg.     

Reactions of 1,1,3,3-tetrakis(dimethylamino)-1λ5,3λ5-diphosphete with diphenylchlorophosphane and methyl iodide

1,1,3,3-Tetrakis(dimethylamino)-1λ⁵,3λ⁵-diphosphete, 1, reacts with diphenylchlorophosphane to yield 1,1,3,3-tetrakis(dimethylamino)-4-diphenylphosphanyl-1,2-dihydro-3λ⁵-[1,3]diphosphetium chloride, 2, or, depending on the reaction conditions, the isomer compound 3. The cation of 2 is deprotonated by LiN[Si(CH₃)₃]₂ to give the diphenylphosphanyl-substituted derivative of 1, i.e., compound 4. Methyl iodide adds to 1 to form 1,1,3,3-tetrakis(dimethylamino)-4-methyl-1,2-dihydro-3λ⁵-[1,3]diphosphetium iodide, 6. Deprotonation of 6 with n-butyllithium leads to the monomethyl derivative of 1, i.e., compound 7. Physical properties, NMR spectra, and mass spectra of compounds 2–4, 6, and 7 are described. The results of the X-ray structural analysis of 6 are reported and discussed. © 1996 John Wiley & Sons, Inc.     

Heavier Alkaline-Earth Catalyzed Dehydrocoupling of Silanes and Alcohols for the Synthesis of Metallo-Polysilylethers

The dehydrocoupling of silanes and alcohols mediated by heavier alkaline-earth catalysts, [Ae{N(SiMe₃)₂}₂⋅(THF)₂] ( I – III ) and [Ae{CH(SiMe₃)₂}₂⋅(THF)₂], ( IV – VI ) (Ae=Ca, Sr, Ba) is described. Primary, secondary, and tertiary alcohols were coupled to phenylsilane or diphenylsilane, whereas tertiary silanes are less tolerant towards bulky substrates. Some control over reaction selectivity towards mono-, di-, or tri-substituted silylether products was achieved through alteration of reaction stoichiometry, conditions, and catalyst. The ferrocenyl silylether, FeCp(C₅H₄SiPh(OBn)₂) ( 2 ), was prepared and fully characterized from the ferrocenylsilane, FeCp(C₅H₄SiPhH₂) ( 1 ), and benzyl alcohol using barium catalysis. Stoichiometric experiments suggested a reaction manifold involving the formation of Ae–alkoxide and hydride species, and a series of dimeric Ae–alkoxides [(Ph₃CO)Ae(μ₂-OCPh₃)Ae(THF)] ( 3 a – c , Ae=Ca, Sr, Ba) were isolated and fully characterized. Mechanistic experiments suggested a complex reaction mechanism involving dimeric or polynuclear active species, whose kinetics are highly dependent on variables such as the identity and concentration of the precatalyst, silane, and alcohol. Turnover frequencies increase on descending Group 2 of the periodic table, with the barium precatalyst III displaying an apparent first-order dependence in both silane and alcohol, and an optimum catalyst loading of 3 mol % Ba, above which activity decreases. With precatalyst III in THF, ferrocene-containing poly- and oligosilylethers with ferrocene pendent to- ( P1 – P4 ) or as a constituent ( P5 , P6 ) of the main polymer chain were prepared from 1 or Fe(C₅H₄SiPhH₂)₂ ( 4 ) with diols 1,4-(HOCH₂)₂-(C₆H₄) and 1,4-(CH(CH₃)OH)₂-(C₆H₄), respectively. The resultant materials were characterized by NMR spectroscopy, gel permeation chromatography (GPC) and DOSY NMR spectroscopy, with estimated molecular weights in excess of 20,000 Da for P1 and P4 . The iron centers display reversible redox behavior and thermal analysis showed P1 and P5 to be promising precursors to magnetic ceramic materials.     

Coupled Si and O isotope measurements of meteoritic material by laser fluorination isotope ratio mass spectrometry

We present a procedure for the determination of the isotopic ratios of silicon and oxygen from the same aliquot of anhydrous silicate material. The sample is placed in a bromine pentafluoride atmosphere as it is heated with a CO₂ laser system releasing silicon tetrafluoride and oxygen gasses. The oxygen gas is then purified to remove other reaction by‐products through several liquid nitrogen traps before being captured onto a molecular sieve and transferred to an isotope ratio mass spectrometer. The silicon tetrafluoride gas is then purified using a supplementary line by repeatedly freezing to ?196°C with liquid nitrogen and then thawing with an ethanol slurry at ?110°C through a series of metal and Pyrex traps. The purified gas is then condensed into a Pyrex sample tube before it is transferred to an isotope ratio mass spectrometer for silicon isotope ratio measurements. This system has silicon yields of greater than 90% for pure quartz, olivine, and garnet standards and has a reproducibility of ±0.1‰ (2σ) for pure quartz for both oxygen and silicon isotope measurements. Meteoritic samples were also successfully analyzed to demonstrate this system's ability to measure the isotopic ratio composition of bulk powders with precision. This unique technique allows for the fluorination of planetary material without the need for wet chemistry. Though designed to analyze small aliquots of meteoritic material (1.5 to 3 mg), this approach can also be used to investigate refractory terrestrial samples where traditional fluorination is not suitable.