Edelmetalle

Ohne Zusammenfassung     

Variational formulations for scattering in a three‐dimensional acoustic waveguide

Variational formulations for direct time‐harmonic scattering problems in a three‐dimensional waveguide are formulated and analyzed. We prove that the operators defined by the corresponding forms satisfy a Gårding inequality in adequately chosen spaces of test and trial functions and depend analytically on the wavenumber except at the modal numbers of the waveguide. It is also shown that these operators are strictly coercive if the wavenumber is small enough. It follows that these scattering problems are uniquely solvable except possibly for an infinite series of exceptional values of the wavenumber with no finite accumulation point. Furthermore, two geometric conditions for an obstacle are given, under which uniqueness of solution always holds in the case of a Dirichlet problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Coalescence analysis for evolving foams via optical flow computation on projection image sequences

A novel image‐processing procedure is proposed for the analysis of sequences of two‐dimensional projection images. Sudden events like the merging of bubbles in an evolving foam can be detected and spatio‐temporally located in a given projection image sequence. The procedure is based on optical flow computations extended by a forward–backward check for each time step. Compared with prior methods, efficient suppression of noise or false events is achieved owing to uniform foam motion, and the reliability of detection is thus increased. The applicability of the proposed procedure in combination with synchrotron radiography is illustrated by a series of characteristic studies of foams of different kind. First, the detection of single‐bubble collapses in aqueous foams is considered. Second, a spatial distribution of coalescence events in metals foamed in casting molds is estimated. Finally, the structural stability of polymer foams containing admixed solid nanoparticles is examined.     

Overlap Dirac operator at nonzero chemical potential and random matrix theory

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma5 Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.     

Polytypism in GaAs nanowires: determination of the interplanar spacing of wurtzite GaAs by X‐ray diffraction

In GaAs nanowires grown along the cubic [111]_c direction, zinc blende and wurtzite arrangements have been observed in their stacking sequence, since the energetic barriers for nucleation are typically of similar order of magnitude. It is known that the interplanar spacing of the (111)_c Ga (or As) planes in the zinc blende polytype varies slightly from the wurtzite polytype. However, different values have been reported in the literature. Here, the ratio of the interplanar spacing of these polytypes is extracted based on X‐ray diffraction measurements for thin GaAs nanowires with a mean diameter of 18–25 nm. The measurements are performed with a nano‐focused beam which facilitates the separation of the scattering of nanowires and of parasitic growth. The interplanar spacing of the (111)_c Ga (or As) planes in the wurtzite arrangement in GaAs nanowires is observed to be 0.66% ± 0.02% larger than in the zinc blende arrangement.     

Formation and chemical behaviour of silylated phosphanes

Abstract

Our investigations to be presented here have their origin in a number of former results: The formation of [(Me₃Si)₂P]₂SiMe₂ [1] and its rearrangement to P₄(SiMe₂)₆ (a molecule with adamantane structure) and P(SiMe₃)₃, the formation of P₇(SiMe₃)₃ and of some cyclic phosphanes by the thermally induced rearrangement of [(Me₃Si)₂)P]₂SiMe₂ [3], and the formation of P₇(SiMe₃)₃ by reacting P₄ with Na/K-alloy and Me₃SiCl. After finding LiP(SiMe₃)₂ to be such a versatile reagent we turned to elucidate synthesis and chemical behaviour of LiP[P(SiMe₃)₂]₂.     

Statistical properties at the spectrum edge of the QCD Dirac operator

The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the spectral rigidity, are investigated. While the spectral fluctuations at the edge are suppressed to the same extent as in the bulk, the spectra are more rigid at the edge. To study this effect, we introduce a microscopic unfolding procedure to separate the variation of the microscopic spectral density from the fluctuations. For the unfolded data, the number variance shows oscillations of the same kind as before unfolding, and the average spectral rigidity becomes larger than the one in the bulk. In addition, the short-range statistics at the origin is studied. The lattice data are compared to predictions of chiral random-matrix theory, and agreement with the chiral Gaussian Symplectic Ensemble is found. Received: 6 November 1997 / Revised version: 19 January 1998