Investigation of potential flow using the soap film analogy – a historical review

The soap film analogy is a tool for analysing potential flow in complex geometries. It has been used around 1960 in Dresden to investigate the flow in high-pressure turbine cascades. The present paper briefly reviews the technique and reports on the comparison between historical results, achieved with the soap film analogy, and numerical simulations. It illustrates the capabilities of the method and the historical progress made since then. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assembly of π‐Conjugated Phosphole Azahelicene Derivatives into Chiral Coordination Complexes: An Experimental and Theoretical Study

Aza[n]helicene phosphole derivatives have been prepared from aza[n]helicene diynes by the Fagan–Nugent route. Their photophysical properties (UV/Vis absorption and emission behavior) have been evaluated. Their behavior as P,N chelates towards coordination to Pd^II and Cu^I has been investigated: metal–bis(aza[n]helicene phosphole) assemblies are formed by a highly stereoselective coordination process, as demonstrated by X‐ray crystallography. An aza[6]helicene phosphole bearing an enantiopure helicene part has been obtained, which allows the preparation of enantiopure Pd^II and Cu^I complexes with original topologies and high molar rotation (MR) and circular dichroism (CD). The structure–property relationship established from the experimental data has been studied in detail by theoretical studies (TDDFT calculations of UV/Vis, CD, and MR). Aza[n]helicene phosphole derivatives show π conjugation extended over the entire molecule, and its influence on the MR of aza[6]helicene phosphole 5 c has been demonstrated. Finally, it has been shown that the nature of the metal (coordination geometry and electronic interaction) can have a great impact on the amplitude of the chiroptical properties in metal–bis(aza[n]helicene phosphole) assemblies.     

Efficient temperature compensation strategies for guided wave structural health monitoring

The application of temperature compensation strategies is important when using a guided wave structural health monitoring system. It has been shown by different authors that the influence of changing environmental and operational conditions, especially temperature, limits performance. This paper quantitatively describes two different methods to compensate for the temperature effect, namely optimal baseline selection (OBS) and baseline signal stretch (BSS). The effect of temperature separation between baseline time-traces in OBS and the parameters used in the BSS method are investigated. A combined strategy that uses both OBS and BSS is considered. Theoretical results are compared, using data from two independent long-term experiments, which use predominantly A₀ mode and S₀ mode data respectively. These confirm that the performance of OBS and BSS quantitatively agrees with predictions and also demonstrate that the combination of OBS and BSS is a robust practical solution to temperature compensation.     

A new characterization of for countable spectra of (LB)-spaces

The derived projective limit functor Proj¹ is a very useful tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations).

We provide a new characterization for vanishing Proj¹ on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.

     

An Adaptive Wavelet–Vaguelette Algorithm for the Solution of PDEs

The paper first describes a fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function. This approach permits to compute the decomposition of a function into a lacunary wavelet basis, i.e., a basis constituted of a subset of all basis functions up to a certain scale, without modification. The construction is then extended to operator-adapted biorthogonal wavelets. This is relevant for the solution of certain nonlinear evolutionary PDEs where a priori information about the significant coefficients is available. We pursue the approach described in (J. Fröhlich and K. Schneider,Europ. J. Mech. B/Fluids13,439, 1994) which is based on the explicit computation of the scalewise contributions of the approximated function to the values at points of hierarchical grids. Here, we present an improved construction employing the cardinal function of the multiresolution. The new method is applied to the Helmholtz equation and illustrated by comparative numerical results. It is then extended for the solution of a nonlinear parabolic PDE with semi-implicit discretization in time and self-adaptive wavelet discretization in space. Results with full adaptivity of the spatial wavelet discretization are presented for a one-dimensional flame front as well as for a two-dimensional problem.