A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L₂ norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H² regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-called‘matching function’. A numerical example supports the anisotropic error analysis.     

Continuity properties of the integrated density of states on manifolds

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation.     

Deposition and Characterization of Metastable Cu3N Layers for Applications in Optical Data Storage

 Cu₃N films for optical data storage were deposited on Si(100) wafers and 0.6 mm thick polycarbonate DVD base material discs at a temperature of 50 °C by reactive magnetron sputtering. A copper target was sputtered in rf mode in a nitrogen plasma. For basic investigations concerning the composition and structure of Cu₃N, Si wafers were used as substrate material. To study the suitability of Cu₃N as an optical data storage medium under technical conditions, Cu₃N/Al bilayers were deposited on polycarbonate discs. The composition and structure of the films were investigated by X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD). The decomposition of Cu₃N into metallic copper and nitrogen was induced and characterized with a dynamic tester consisting of an optical microscope with an integrated high power laser diode. The change in reflectivity induced by the laser pulses was measured by a high sensitivity photo detector. Optimized Cu₃N films could be decomposed into metallic copper at pulse lengths of 200 ns. The reflectivity change from 3.2% to 33.2% for completely transformed areas and to 12% for single bits as well as the maximum write data rate of 3.3 Mbit/s demonstrated the suitability of Cu₃N for write once optical data storage. Especially the carrier to noise ratio of 41 dB shows an increase of a factor of 3 for this novel material as compared to conventional optical data storage media.     

Nickel and palladium complexes of enolatefunctionalised N-heterocyclic carbenes

The reaction of chloroethyltrimethylsilylether with 1-methylimidazole furnishes an ionic liquid that undergoes methanolysis to crystalline 2-hydroxyethylimidazolium chloride (crystal structure presented). Conversion to defined hydroxyethylimidazol-2-ylidene nickel complexes failed, but was accomplished with 1-methyl-3-acetophenyl-imidazolium bromide. The bis(NHC^⋂O⁻) nickel(II) chelate is formed, rather than a methallylnickel monochelate, but with nickelocene a monochelate NiCp complex was detected. The bulky 1-(2,6-diisopropylphenyl)-3-(2’-phenyl-enolato)-imidazol-2-ylidene allylpalladium chloride was obtained in pure form. Attempts to generate catalysts for ethylene oligomerization by in situ techniques have failed so far whereas P^⋂O⁻ ligands, comparable by the P-C diagonal relationship, provide active catalysts.