Ansprache bei der Überreichung der Manuskripte des Festbandes am 14. Mai 1946

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Erratum to Laplacian Instability of Planar Streamer Ionization Fronts—An Example of Pulled Front Analysis

Streamer ionization fronts are pulled fronts that propagate into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long-time attractor out of a continuous family. A stability analysis for perturbations in the transverse direction has to take these features into account. In this paper we show how to apply the Evans function in a weighted space for this stability analysis. Zeros of the Evans function indicate the intersection of the stable and unstable manifolds; they are used to determine the eigenvalues. Within this Evans function framework, we define a numerical dynamical systems method for the calculation of the dispersion relation as an eigenvalue problem. We also derive dispersion curves for different values of the electron diffusion constant and of the electric field ahead of the front. Numerical solutions of the initial value problem confirm the eigenvalue calculations. The numerical work is complemented with an analysis of the Evans function leading to analytical expressions for the dispersion relation in the limit of small and large wave numbers. The paper concludes with a fit formula for intermediate wave numbers. This empirical fit supports the conjecture that the smallest unstable wave length of the Laplacian instability is proportional to the diffusion length that characterizes the leading edge of the pulled ionization front. G. Derks acknowledges a travel grant of the Royal Society, which initiated this research, and a visitor grant of the Dutch funding agency NWO and the NWO-mathematics cluster NDNS⁺ to finish the work. The work was also supported by a CWI PhD grant for B. Meulenbroek.     

Comparison of operator- and computer-controlled scanning electron microscopy of particles from different atmospheric aerosol types

Analytical and Bioanalytical Chemistry - Individual aerosol particles from an urban background site in Mainz (Germany), a traffic hotspot site in Essen (Germany), the free troposphere in the Swiss...     

Self‐Assembly of Imidazolium‐Based Rodlike Ionic Liquid Crystals: Transition from Lamellar to Micellar Organization

By using aryl‐amination chemistry, a series of rodlike 1‐phenyl‐1H‐imidazole‐based liquid crystals (LCs) and related imidazolium‐based ionic liquid crystals (ILCs) has been prepared. The number and length of the C‐terminal chains (at the noncharged end of the rodlike core) and the length of the N‐terminal chain (on the imidazolium unit in the ILCs) were modified and the influence of these structural parameters on the mode of self‐assembly in LC phases was investigated by polarizing microscopy, differential scanning calorimetry, and X‐ray diffraction. For the single‐chain imidazole derivatives nematic phases (N) and bilayer SmA₂ phases were found, but upon increasing the number of alkyl chains the LC phases were lost. For the related imidazolium salts LC phases were preserved upon increasing the number and length of the C‐terminal chains and in this series it leads to the phase sequence SmA–columnar (Col)–micellar cubic (Cub_I/Pm3n). Elongation of the N‐terminal chain gives the reversed sequence. Short N‐terminal chains prefer an end‐to‐end packing of the mesogens in which these chains are separated from the C‐terminal chains. Elongation of the N‐terminal chain leads to a mixing of N‐ and C‐terminal chains, which is accompanied by complete intercalation of the aromatic cores. In the smectic phases this gives rise to a transition from bilayer (SmA₂) to monolayer smectic (SmA) phases. For the columnar and cubic phases the segregated end‐to‐end packing leads to core–shell aggregates. In this case, elongation of the N‐terminal chains distorts core–shell formation and removes Cub_I and Col phases in favor of single‐layer SmA phases. Hence, by tailoring the length of the N‐terminal chain, a crossover from taper‐shaped to polycatenar LC tectons was achieved, which provides a powerful tool for control of self‐assembly in ILCs.     

Simultaneous diode-laser-based in situ measurement of liquid water content and oxygen mole fraction in dense water mist environments

We performed what we believe are the first simultaneous in situ measurements of liquid water and oxygen concentrations in a dense water mist environment. Direct absorption tunable diode laser absorption spectroscopy was used to make oxygen concentrations and simultaneously quantify the liquid water via optical density measurements. This spectrometer with an absorption path length of only 36.8 cm was successfully tested during full-scale fire suppression tests with scattering losses up to 99.9%. The simultaneous oxygen and liquid water concentration measurements agree with fire suppression model calculations.     

Wavelets on S3 and SO(3)—Their construction,relation to each other and Radon transform of wavelets on SO(3)

The paper at hand is concerned with creating a flexible wavelet theory on the three sphere S³ and the rotation group SO(3). The theory of zonal functions and reproducing kernels will be used to develop conditions for an admissible wavelet. After explaining some preliminaries on group actions and some basics on approximation theory, we will prove reconstruction formulas of linear and bilinear wavelet transformed L²‐functions on S³. Moreover, specific examples will be constructed and visualized. Second, we deal with the construction of wavelets on the rotation group SO(3). It will be shown that the Radon transform of a wavelet packet on SO(3) gives a wavelet packet on S² for every fixed detection direction. Copyright © 2010 John Wiley & Sons, Ltd.