Torque on a sphere inside a rotating cylinder

Summary The couple on a sphere in the centre of a finite rotating circular cylinder is measured over a wide range of Reynolds numbers for both Newtonian and non-Newtonian fluids. Wall effects are calculated. Experimental results are compared with Collins' analysis. Secondary flow is made visible. For non-Newtonian fluids the apparatus determines accurately the zero shear rate viscosity.

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Résumé Le couple sur une sphère dans un cylindre circulaire rotatoire est mesuré pour des divers nombres de Reynolds et pour des fluides Newtoniens et non-Newtoniens. L'effet des parois sur le couple est calculé. Les resultats obtenus sont comparés avec l'analyse de Collins. Pour les fluides non-Newtoniens l'appareil determine la viscosité de zéro cisaillement.

     

π‐Conjugated [2]Catenanes Based on Oligothiophenes and Phenanthrolines: Efficient Synthesis and Electronic Properties

Novel π‐conjugated topologies based on oligothiophenes and phenanthroline have been assembled by combining their outstanding electronic and structural benefits with the specific properties of the topological structure. Macrocycles and catenanes are prepared by using an optimized protocol of transition metal‐templated macrocyclization followed by efficient Pd‐catalyzed cross‐coupling reaction steps. By using this method, [2]catenanes comprising two interlocked π‐conjugated macrocycles with different ring sizes have been synthesized. The structures of the [2]catenanes and corresponding macrocycles are confirmed by detailed ¹H NMR spectroscopy and high resolution mass spectrometry. Single crystal X‐ray structural analysis of the quaterthiophene–diyne macrocycle affords important insight into the packing features and intermolecular interaction of the new systems. The fully conjugated interlocked [2]catenanes are fully characterized by spectroscopic and electrochemical measurements.     

<Emphasis Type="Italic">xPert</Emphasis>: computer algebra for metric perturbation theory

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the nth order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n = 4 or n = 5 within seconds, or reach n = 10 with timings below 1 h.     

Cube-type nitrido complexes containing titanium and zinc/copper

Several azaheterometallocubane complexes containing [MTi3N4] cores have been prepared by the reaction of [{Ti(eta5-C5Me5)(mu-NH)}3(mu3-N)] (1) with zinc(II) and copper(I) derivatives. The treatment of 1 with zinc dichloride in toluene at room temperature produces the adduct [Cl2Zn{(mu3-NH)3Ti3(eta5-C5Me5)3(mu3-N)}] (2). Attempts to crystallize 2 in dichloromethane gave yellow crystals of the ammonia adduct [(H3N)Cl2Zn{(mu3-NH)Ti3(eta5-C5Me5)3(mu-NH)2(mu3-N)}] (3). The analogous reaction of 1 with alkyl, (trimethylsilyl)cyclopentadienyl, or amido zinc complexes [ZnR2] leads to the cube-type derivatives [RZn{(mu3-N)(mu3-NH)2Ti3(eta5-C5Me5)3(mu3-N)}] (R = CH2SiMe3 (5), CH2Ph (6), Me (7), C5H4SiMe3 (8), N(SiMe3)2 (9)) via RH elimination. The amido complex 9 decomposes in the presence of ambient light to generate the alkyl derivative [{Me3Si(H)N(Me)2SiCH2}Zn{(mu3-N)(mu3-NH)2Ti3(eta5-C5Me5)3(mu3-N)}] (10). The chloride complex 2 reacts with lithium cyclopentadienyl or lithium indenyl reagents to give the cyclopentadienyl or indenyl zinc derivatives [RZn{(mu3-N)(mu3-NH)2Ti3(eta5-C5Me5)3(mu3-N)}] (R = C5H5 (11), C9H7 (12)). Treatment of 1 with copper(I) halides in toluene at room temperature leads to the adducts [XCu{(mu3-NH)3Ti3(eta5-C5Me5)3(mu3-N)}] (X = Cl (13), I (14)). Complex 13 reacts with lithium bis(trimethylsilyl)amido in toluene to give the precipitation of [{Cu(mu4-N)(mu3-NH)2Ti3(eta5-C5Me5)3(mu3-N)}2] (15). Complex 15 is prepared in a higher yield through the reaction of 1 with [{CuN(SiMe3)2}4] in toluene at 150 degrees C. The addition of triphenylphosphane to 15 in toluene produces the single-cube compound [(Ph3P)Cu{(mu3-N)(mu3-NH)2Ti3(eta5-C5Me5)3(mu3-N)}] (16). The X-ray crystal structures of 3, 8, 9, and 15 have been determined.     

Screening method for pesticides in air by gas chromatography/tandem mass spectrometry

A multiresidue method for determining more than 70 pesticides in air has been validated using a single injection with gas chromatography/tandem mass spectrometry (GC/MS/MS). The method validation considered both stages of sampling and analysis. The sampling method, based on active sampling using sorption in sorbent cartidges, was validated by generating standard atmospheres. Performance parameters of the method were evaluated, with a reduction in the limits of quantification by injecting a higher volume of sample extract, and increase of selectivity by the use of MS/MS detection mode. The method was based on solid-phase extraction, which permits a degree of automation. The best adsorbents were found to be Chromosorb 106 and Tenax TA. The retention capacity of these sampling sorbents allows up to 1440 L of air to be sampled without any breakthrough for most of the compounds. Data were generated for assessing the potential exposure of bystanders. The application of the method to the analysis of the air in urban locations near agricultural areas showed that pesticides were present in most of the samples.     

On the Bayesian Mixture Model and Identifiability

This article is concerned with Bayesian mixture models and identifiability issues. There are two sources of unidentifiability: the well-known likelihood invariance under label switching and the perhaps less well-known parameter identifiability problem. When using latent allocation variables determined by the mixture model, these sources of unidentifiability create arbitrary labeling that renders estimation of the model very difficult. We endeavor to tackle these problems by proposing a prior distribution on the allocations, which provides an explicit interpretation for the labeling by removing gaps with high probability. We propose a Markov chain Monte Carlo (MCMC) estimation method and present supporting illustrations.     

Numerical solution of the finite horizon stochastic linear quadratic control problem

The treatment of the stochastic linear quadratic optimal control problem with finite time horizon requires the solution of stochastic differential Riccati equations. We propose efficient numerical methods, which exploit the particular structure and can be applied for large‐scale systems. They are based on numerical methods for ordinary differential equations such as Rosenbrock methods, backward differentiation formulas, and splitting methods. The performance of our approach is tested in numerical experiments.