Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Evolved gas analysis (EGA) of brick clays

Using a system based on non-dispersive infrared (NDIR) detectors, evolved gas analysis (EGA) was able to identify and quantify the principal volatiles produced by heating powdered samples of UK brick clays. From these results, atmospheric emissions likely to result from brick production can be predicted. In addition, EGA results for extruded brick clay test pieces are significantly different from those of powdered samples. Within an extruded brick clay body, evolved gases are contained within a pore system and evolved gas-solid phase reactions also occur. This EGA study provides further evidence on the nature of firing reactions within brick clay bodies. The qualitative and quantitative influence of heating rate — a key process condition in brick manufacture — on gas release is also outlined.Dedicated to Dr. Robert Mackenzie on the occasion of his 75th birthday     

Pseudo-epitaxial C60 films prepared by a hot-wall method

We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C₆₀ evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C₆₀ planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C₆₀ is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy.     

Prediction of chromatographic retention of metal complexes from stability constants measured by ion chromatography

Chromatographia - A theoretical model is used to predict retention times of divalent metal cations in single-column ion chromatography using one or more ligands in the eluent. Stability constants...     

Linearization of column responses by correlation chromatography. Separation improvement and reduction of undesired adsorption effects

Summary Experiments and simulations prove that correlation chromatography can greatly reduce the disadvantage of a non-linear response of the chromatographic column. A factor that has been accepted as being an important source of error in correlation or multiplex chromatography, has been shown not to be. Separations affected, improve dramatically when correlation chromatography is used, and a substantial amount of correlation noise only arises when there is a large difference in separation between a conventional chromatogram and a correlogram.A model has been developed for simulating these nonlinearities. It is shown that, especially for correlation chromatography, the simulation results match the practical measurements very well.     

Recent developments in the chemistry of stable doubly bonded germanium compounds

During the last 10 years, several compounds of the type Ge=X (X = C, Ge, N, P, S) have been isolated as monomers. The stabilization of such derivatives, which are generally highly polymerizable, was achieved by using very bulky groups both on the germanium atom and on the heteroelement X. Conjugation (particularly in a few germenes and germaimines) and intramolecular or intermolecular coordination with oxygen or nitrogen, also contributes, in some cases, to the stabilization. The X-ray analyses of such compounds show a significant bond shortening of the double bond (8–10%) relative to the corresponding single bond and a planar or nearly planar germanium. These doubly bonded germanium derivatives are usually thermally stable but must be handled in an inert atmosphere because of their high sensitivity to oxygen and moisture; they are extremely reactive, much more than the corresponding carbon analogues. Nearly quantitative additions on the double bond have been observed with electrophiles and nucleophiles, and various types of cycloadditions also occur. Except in one case, a germylene behavior has not been observed, proving that such compounds retain their structural integrity in solution.