Frequency based preconditioning and smoothing for shape optimization

In this paper, we present a smoothing technique which can be understood as a Quasi-Newton method. The idea of this preconditioner is that it approximates the symbol of the inverse Hessian, which has smoothing behavior. This symbol is derived analytically for the Stokes equations and investigated numerically for a flow with a Reynolds number of 80. The resulting symbol is then approximated by differential operators, which will lead to a method similar to Sobolev Smoothing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks

The thermal fracture of a bimaterial consisting of a homogeneous material and a functionally graded material (FGM) with a system of internal cracks and an interface crack is investigated. The bimaterial is subjected to a heat flux. The thermal properties of FGM are assumed to be continues functions of the thickness coordinate, while the elastic properties are constants. The method of the solution is based on the singular integral equations. For a special case where the interface crack is much larger than the internal cracks in the FGM the asymptotic analytical solution of the problem is obtained as series in a small parameter (the ratio between sizes of the internal and interface crack) and the thermal stress intensity factors (TSIFs) are derived as functions of geometry of the problem and material characteristics. A parametric analysis of the effects of the location and orientation of the cracks and of the inhomogeneity parameter of FGM’s thermal conductivity on the TSIFs is performed. The results are applicable to such kinds FGMs as ceramic/ceramic FGMs, e.g., TiC/SiC, MoSi₂/Al₂O₃ and MoSi₂/SiC, and also some ceramic/metal FGMs.     

Simulation of crack propagation in alumina with ab initio based polarizable force field

We present an effective atomic interaction potential for crystalline α-Al(2)O(3) generated by the program potfit. The Wolf direct, pairwise summation method with spherical truncation is used for electrostatic interactions. The polarizability of oxygen atoms is included by use of the Tangney-Scandolo interatomic force field approach. The potential is optimized to reproduce the forces, energies, and stresses in relaxed and strained configurations as well as {0001}, {1010}, and {1120} surfaces of Al(2)O(3). Details of the force field generation are given, and its validation is demonstrated. We apply the developed potential to investigate crack propagation in α-Al(2)O(3) single crystals.     

Untersuchung von Bier, Bierroh- und Zwischenerzeugnissen

Ohne Zusammenfassung     

Kondensation von Naphtalaldehydsäure mit Methyl-m-tolylketon,Pinakolin und Acenaphtenon

Ohne ZusammenfassungIch schließe, indem ich meinem hochverehrten Lehrer, Herrn Prof. G. Goldschmiedt, für die liebenswürdige Hilfe, die er mir bei der Vollendung dieser Arbeit in Rat und Tat angedeihen ließ, den herzlichsten Dank ausspreche.     

Untersuchungen über die natürlichen Gleichungen krummer Flächen

Ohne Zusammenfassung     

Über das Glykol und Aldol aus Isobutyr- und Isovaleraldehyd

Ohne ZusammenfassungAn dieser Stelle erfüllen wir mit grosser Freude die angenehme Pflicht, unserem hochverehrten Lehrer, Herrn Hof-rath Professor Dr. Adolf Lieben, für vielfache Anregung und lebhaftes Interesse, welches er unserer Arbeit entgegenbrachte, unseren tiefgefühlten Dank auszusprechen.