Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Papierchromatographische Trennungen von Alkaloidgemischen an Succinylzellulose-Papieren

Zusammenfassung Das früher beschriebene¹ Succinylzellulose-Papier wird als Ionenaustauscher zur weiteren papierchromatischen Trennung von Basengemischen verwendet. Getrennt wurden die Alkaloide der Morphingruppe und deren Abwandlungsprodukte, ferner die Alkaloide der Strychnin-, der Tropin-, der Cocaingruppe und andere Alkaloide.

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Summary The succinyl-cellulose paper described previously¹ is used as ion exchanger for additional paper chromatographic separations of mixtures of bases. Separations were accomplished of the alkaloids of the morphine group and their modification products, and also of the alkaloids of the strychnine-, tropine- and cocaine groups and other alkaloids.

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Résumé On utilise le papier à la succinyl-cellulose déjà décrit¹, comme écharigeur d'ions pour d'autres séparations par chromatographie sur papier de mélanges basiques. On a séparé ainsi les alcaloïdes du groupe de la morphine et leurs produits d'évolution, et en outre, les alcaloïdes des groupes de la strychnine, de la tropine et de la cocaïne et d'autres alcaloïdes.

     

Numerical stability of biorthogonal wavelet transforms

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL . These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.     

Calculation of muon level-crossing resonance spectra for Si∶B and Si∶Al

The spin dynamics of muons interacting with acceptor impurity nuclei in silicon is investigated. Using values of electric field gradients obtained from ab-initio calculations, the field dependence of the longitudinal muon polarization is calculated for SiB and SiAl and compared to the contributions from paramagnetic bond-center muonium.