DNS of backward‐facing step flow with fully turbulent inflow

Direct numerical simulation (DNS) has been performed to study the channel flow over a backward‐facing step at a Reynolds number Re_b=5600 based on the step height h and the inflow bulk velocity U_b. A dynamic method has been used in order to generate realistic turbulent inflow conditions. The results upstream of the step compared well with the fully developed channel flow. Downstream of the step our results show excellent agreement with experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Relative Oscillation Theory,Weighted Zeros of the Wronskian,and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm–Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein’s spectral shift function is established. Research supported by the Austrian Science Fund (FWF) under Grant No. Y330.     

On the Possibility of Glucose Sensing Using Boronic Acid and a Luminescent Ruthenium Metal-Ligand Complex

We describe a new approach to optical sensing of glucose based on the competitive interactions between a ruthenium metal ligand complex, a boronic acid derivative and glucose. The metal-ligand complex [Ru(2,2-bipyridine)₂(5,6-dihydroxy-1,10-phenanthroline)](PF₆)₂ at pH 8 forms a reversible complex with 2-toluylboronic acid or 2-methoxyphenyl boronic acid. Complexation is accompanied by a several-fold increase in the luminescent intensity of the ruthenium complex. Addition of glucose results in decreased luminescent intensity, which appears to be the result of decreased binding between the metal-ligand complex and the boronic acid. Ruthenium metal-ligand complexes are convenient for optical sensing because their long luminescent decay times allow lifetime-based sensing with simple instrumentation.     

The synthesis of (+)-preussin and related pyrrolidinols by diastereoselective Paternò-Büchi reactions of chiral 2-substituted 2,3-dihydropyrroles

The N-alkoxycarbonyl substituted 2,3-dihydropyrroles 3 and 8 are converted to 2-benzyl-3-pyrrolidinols by the Paternò - Büchi reaction followed by hydrogenolysis. Since the addition of the photoexcited benzaldehyde at the unsaturated heterocycle proceeds in a syn fashion, the benzyl group at C-2 and the hydroxy group at C-3 of the product are cis oriented. The simple and facial diastereoselectivities of the Paternò-Büchi reaction were studied more closely and the relative configuration of the products was elucidated. The thermodynamically less stable endo product is formed as a result of simple diastereoselection. The face differentiation in 2-substituted 2,3-dihydropyrroles is presumably due to the nonplanarity of these heterocycles, which forces attack of the carbonyl group on the face with the existing substituent. All-cis-pyrrolidinols are consequently formed after hydrogenolysis. Following this route, a total synthesis of the pyrrolidinol alkaloid (+)-preussin (1) was conducted, which yielded the target compound in a total yield of 11% over nine steps starting from L-pyroglutaminol (11).     

Observation of the decay τ → πv

The decay of the heavy lepton τ into πv has been established using the magnetic detector PLUTO. The branching ratio is determined to be BR(τ→πv)=(9.0 ± 2.9)% with an additional systematic uncertainty of 2.5%. This value is in good agreement with the theoretical prediction.