The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics

We investigate the regularization of Moore’s singularities by surface tension in the evolution of vortex sheets and its dependence on the Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing up at finite time t ₀, grows exponentially fast up to a O(We) limiting value close to t ₀. We describe the analytic structure of the solutions and their self-similar features and characteristic scales in terms of the Weber number in a O(We⁻¹) neighborhood of the time at which, in absence of surface tension effects, Moore’s singularity would appear. Our arguments rely on asymptotic techniques and are supported by full numerical simulations of the PDEs describing the evolution of vortex sheets.     

Reduced order models based on local POD plus Galerkin projection

A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained via POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estimate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calculate the right hand side of the Galerkin system; and (c) introducing a second error estimate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg–Landau equation.     

An Introduction to Electrochemistry for Undergraduates: Detection of Vitamin C (Ascorbic Acid) by Inexpensive Electrode Sensors

This paper describes an undergraduate laboratory for general chemistry that can be used to supplement the teaching of oxidation–reduction reactions. The laboratory experiment also introduces students to basic electrochemical techniques and instrumentation. Using inexpensive materials to make carbon-paste electrodes, ascorbic acid (vitamin C) is oxidized with the cyclic voltammetry technique. The students learn to operate the potentiostat, prepare electrodes from inexpensive materials, and oxidize the vitamin C in over the counter tablets.     

Aqua­bis­(benzo­nitrile)(o‐benzo­quin­one di­imine)(tri­phenyl­phosphine)­ruthenium(II) bis­(tetra­fluoro­borate) hydrate

The Ru atom in the title compound, [Ru(C₆H₅CN)₂{P(C₆H₅)₃}{C₆H₄(NH)₂}(H₂O)](BF₄)₂·H₂O, has six‐coordinate octahedral geometry, with a trans arrangement of the tri­phenyl­phosphine ligand and the water mol­ecule. The asymmetric unit contains one complex cation, two tetra­fluoro­borate anions and one solvent water mol­ecule, which is disordered over two sites (ratio of occupancies 0.70:0.30).     

Measurement uncertainty in analytical methods in which trueness is assessed from recovery assays

We propose a new procedure for estimating the uncertainty in quantitative routine analysis. This procedure uses the information generated when the trueness of the analytical method is assessed from recovery assays. In this paper, we assess trueness by estimating proportional bias (in terms of recovery) and constant bias separately. The advantage of the procedure is that little extra work needs to be done to estimate the measurement uncertainty associated to routine samples. This uncertainty is considered to be correct whenever the samples used in the recovery assays are representative of the future routine samples (in terms of matrix and analyte concentration). Moreover, these samples should be analysed by varying all the factors that can affect the analytical method. If they are analysed in this fashion, the precision estimates generated in the recovery assays take into account the variability of the routine samples and also all the sources of variability of the analytical method. Other terms related to the sample heterogeneity, sample pretreatments or factors not representatively varied in the recovery assays should only be subsequently included when necessary. The ideas presented are applied to calculate the uncertainty of results obtained when analysing sulphides in wine by HS-SPME-GC.     

Propellanes—From a Chemical Curiosity to “Explosive” Materials and Natural Products

Propellanes are a unique class of compounds currently consisting of well over 10 000 representatives, all featuring two more or less inverted tetrahedral carbon atoms that are common to three bridging rings. The central single bond between the two bridgeheads is significantly weakened in the smaller entities, which leads to unusual reactivities of these structurally interesting propeller-like molecules. This Review highlights the synthesis of such propellanes and their occurrence in material sciences, natural products, and medicinal chemistry. The conversion of [1.1.1]propellane into bridgehead derivatives of bicyclo[1.1.1]pentane, including oligomers and polymers with bicyclo[1.1.1]penta-1,3-diyl repeat units, is also featured. A selection of natural products with larger propellane subunits are discussed in detail. Heteropropellanes and inorganic propellanes are also addressed. The historical background is touched in brief to show the pioneering work of David Ginsburg, Günther Snatzke, Kenneth B. Wiberg, Günter Szeimies, and others.     

Stereocontrolled Synthesis of 1,4‐Dicarbonyl Compounds by Photochemical Organocatalytic Acyl Radical Addition to Enals

We report a visible‐light‐mediated organocatalytic strategy for the enantioselective acyl radical conjugate addition to enals, leading to valuable 1,4‐dicarbonyl compounds. The process capitalizes upon the excited‐state reactivity of 4‐acyl‐1,4‐dihydropyridines that, upon visible‐light absorption, can trigger the generation of acyl radicals. By means of a chiral amine catalyst, iminium ion activation of enals ensures a stereoselective radical trap. We also demonstrate how the combination of this acylation process with a second catalyst‐controlled bond‐forming event allows to selectively access the full matrix of all possible stereoisomers of the resulting 2,3‐substituted 1,4‐dicarbonyl products.