Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Resonantly photo-pumped Fe16+ soft X-ray laser

A resonantly photo-pumped soft x-ray laser process is studied for neon-like iron ions with an automatic line match scheme. The special advantages of this scheme are shown. The temporal characteristics of lasing gains and their dependences on the pump strength and electron density are investigated. Unlike the electron-collisional excitation and some other photo-pumped excitation schemes, it is demonstrated that main photopumped gains come from 2p-4d-3p-3s transition channels. Using the experimental data of pump strengths from a non-LTE plasma produced in our experiment as input data, our model yields a peak gain of 5.6 cm^–1, 2.8 cm^–1 and 1.9 cm^–1 on the dominant lasing transitions at 38.74 nm, 25.47 nm and 20.46 nm.     

Embedded solutions for exterior minimal surface problems

We construct area minimizing hypersurfaces in ℝⁿ⁺¹ which satisfy a Plateau or free boundary condition and become asymptotic to a plane (n≥2) or to the half of a catenoid (n=2). For n≤6 these surfaces are free from singularities.     

Optimization strategy for simulated moving bed systems

Simulated moving bed (SMB) systems are of rising interest in the purification of pharmaceuticals or specialty chemicals (racemic mixtures, proteins, organic acids, etc.). This is particularly due to their advantage in solvent reduction, obtained productivity and purities as well as investment costs in comparison to eluent chromatography. This paper evolved from the need for a readily available algorithm in order to find optimal operating conditions for SMB chromatography systems with nonlinear or coupled adsorption isotherms. The herein developed algorithm is based on a semi-deterministic two-step approach. First, optimal operating conditions with regard to an objective function are found by knowing adsorption measurements only. In a second step actual SMB results are used to adapt the initial isotherm measurements and match the simulation with the experiment. The algorithm is verified on a bench-scale SMB unit applied for the separation of a racemic epoxide with Chiralcel-OD as stationary phase. The developed algorithm improved the productivity of the investigated experimental design by 24%.     

Revidierte Struktur des Makrodiolids Colletodiol

Revised Structure of the Macrodiolide Colletodiol An X-ray analysis shows that the vicinal glycol unit of colletodiol has the threo-rather than the previously assigned erythro-configuration (see 1 , Fig. 1 and Fig. 3). Together with the correlative assignments of (2R)- and (8R)-absolute configurations by MacMillan & Simpson the centers of chirality of colletodiol 1 are now established to be (2R, 8R, 10R, 11R).     

Doppelt und dreifach funktionalisierte,enantiomerenreine C4-Synthesebausteine aus β-Hydroxybuttersäure, Äpfelsäure und Weinsäure

Enantiomerically Pure Synthetic Building Blocks with Four C-Atoms and Two or Three Functional Groups from β-Hydroxy-butanoic, Malic, and Tartaric Acid The pool of chiral, non-racemic electrophilic building blocks, which are available from simple natural products in both enantiomeric forms is enlarged by the epoxides 3, 5 , and 10 , by the tosylate 12a , and by the aldehydes 18 (cf. symbols A-D , 14 , and Scheme 1). Key steps of the conversions leading from hydroxyacids to the building blocks are: epoxide-opening by triethylborohydride ( 1 → 2a ) and tosylate reduction ( 12a → 12b ); the Mitsunobu inversion ( 2a → 4a ); the reduction of (R, R)-tartaric ester to (R)-malic ester by NBS (N-bromosuccinimide) opening of the benzaldehyde acetal 8 and tin hydride reduction ( 6c → 7c ); the enantiomer enrichment of optically active ethyl β-hydroxy-butanoate through the crystalline dinitrobenzoate 21b . Detailed procedures are given for large scale preparations of the key intermediates. The enantiomeric purities of the building blocks are secured by correlations.     

Characteristics of an x-ray preionized TEA CO laser

A cryogenically cooled sealed-off x-ray preionized self-sustained discharge CO laser was succesfully operated. It was found that 20 to 40% higher output energies could be obtained using x-ray instead of uv preionization. A maximum output energy of 2.9 J per pulse could be extracted from a 2×2×40cm³ discharge volume. The maximum electrical efficiency proved to be 12.6%.