A posteriori control of modelling errors in linear elasticity

The concept of adaptive error control for finite element Galerkin discretizations has more recently been extended from the pure treatment of the discretization errors [1], [2] also to the control of modelling errors [4], [5]. These techniques can be employed for a rigorous justification of the local choice of the model out of a given hierarchy with increasing complexity. In the present paper the concept is exemplified by a hierarchy of linear-elastic models, consisting of a basic model with constant E modulus and an improved model with oscillating E modulus. Significant reduction of the computational complexity can be achieved by a proper choice of the model in different subdomains, automatically chosen by the error estimators. Several error indicators are investigated in the context of goal oriented error estimation. Their efficiency is compared by means of finite element simulations [3] of an elementary example. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ein Kommutativitätskriterium für unendliche auflösbare Gruppen

Ohne Zusammenfassung     

Dielectric spectroscopy on aqueous solutions of some zwitterionic amino acids

The complex (electric) permittivity of aqueous solutions of dipolar solutes has been measured as a function of frequency between 1 MHz and 40 GHz. Solutes are the isomers DL-2-aminobutyric acid, DL-3-aminobutyric acid, and 4-aminobutyric acid, and also 6-aminohexanoic acid. The measured dielectric spectra show two dispersion/dielectric loss regions, one due to the orientational diffusion of the solute molecules the other one due to the dielectric relaxation of the solvent water. A relaxation spectral function based on a model of the solutions has been fitted to the measured frequency dependence of the complex permittivity. The values for the electric dipole moment and reorientation time of the zwitterionic part of the solute particles derived by this analysis from the measurements fairly agree with theoretical predictions. Quite remarkably, the dipole moment in solution of 4-aminobutyric acid and 6-aminohexanoic acid up to remarkably high solute concentrations is nearly constant. A noteworthy result for the hydration water of the amino acids is, that its relaxation time is almost independent of the solute dipole moment.     

New Synthetic Route to Polyhedral Organylsilsesquioxanes

Hydrosilation of methylenecyclohexane and hex-1-ene by octa(hydridosilsesquioxane) catalysed by hexachloroplatinic acid is a new route to polyhedral organylsilsesquioxanes. Quantitative yield of octa(cyclohexylmethylsilsesquioxane) is reached. This reaction opens a vast field of yet unknown polyhedral silsesquioxanes.     

Zn location in the W‐type hexagonal ferrite SrZnCoFe16O27

The title compound, SrZnCoFe₁₆O₂₇ (ZnCo‐W), strontium zinc cobalt hexadecairon oxide, crystallizes in space group P6₃/mmc, with the Sr atom at a site with symmetry and Zn²⁺ located at two tetrahedral sites (4e and 4f, each with 3m symmetry) of the spinel blocks. The Zn occupancy is 36% on equipoint 4e and 14% on 4f. The enrichment of diamagnetic ions on one of seven sublattices is thought to be responsible for the high temperature dependence of the saturation magnetization.     

The Temperature-Composition Phase Equilibria in the HgTe–HgI2 Pseudobinary System

The temperature-composition phase diagram of the HgTe—HgI₂ pseudobinary system was determined between 25 and 670°C using differential scanning calorimetry, differential thermal analysis, Debye-Scherrer powder X-ray diffraction techniques, and metallographic analysis methods. Solid solutions of HgTe and HgI₂ with the cubic, zinc blende-type structure exist above 300°C, having a maximum solubility of 11.7±0.8 Mol-% HgI₂ in HgTe at 501±5°C. The monoclinic intermediate phase Hg₃Te₂I₂ is formed by a peritectic reaction upon cooling at 501±5°C, with the peritectic point at approximately 37±4 Mol-% HgI₂. The previously unknown cubic phase Hg₃TeI₄ (a = 6.240±0.003 Å) is formed by a eutectoid reaction at 238±3°C and is stable up to 273±3°C, where it melts by a peritectic reaction with the peritectic point at approximately 79±3 Mol-% HgI₂. Between Hg₃TeI₄ and HgI₂ is a eutectic point at 82±3 Mol-% HgI₂ and 250±3°C. The α to β transition of HgI₂ at 133±3°C is independent of sample composition between 33.3 and 100 Mol-% HgI₂.