A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

Electronic structure of the radicals NF and NCl. III. The radiative lifetimes of the bΣ and aΔ states

The radiative lifetimes of the b¹Σ⁺ and a¹Δ states have been evaluated by perturbation expansions including X³Σ⁻, a¹Δ, b¹Σ⁺, 1^3,1Π, 2^3,1Π, 2³Σ⁻ and 2¹Σ⁺ states. All wavefunctions result from large MRD CI calculations. The b—X transition is dominated by the parallel transition moment; it is found to be much stronger than the a—X transition. The calculated radiative lifetimes of τ(¹Σ⁺)=18 ms, τ(¹Δ)=2.2 s for NF and τ(¹Σ⁺)=2.5–3.5 ms for NCl are in good accord with corresponding experimentally deduced values. The lifetime for the a¹Δ state in NCl is found to be τ(¹Δ)=1.1 s, ie. much longer than derived from a recent experiment. Its magnitude is consistent with the τ(b¹Σ⁺)/τ(a¹Δ) ratio of similar systems and with the decrease in lifetime from NF to NCl and is thus believed to be quite reliable. A detailed analysis of all contributions of the perturber states to the transition mechanism is made and comparison with the related data in SO, O₂ and S₂ is undertaken. The b-a transition probability dominated by the quadrupole transition is fairly constant in all the systems in the order of A = 0.013 (NF) - 0.0013 (S₂) s⁻¹.     

Totalsynthese des macrodiolids (r,r)-(−)-grahamimycin a1

The title compound is synthesized by use of the easily accessible aldehyde for establishing both chiral centres and of ketenylidentriphenylphosphorane for cyclization. In contrast to literature our product is not an antibiotic.     

Multinuclear enantiopure titanium self‐assembly complexes—synthesis,characterization and application to organic synthesis

Hexa‐ and nonanuclear titanium complexes were obtained by self‐assembly of titanium(IV)‐tert‐butoxide and D ‐mandelic acid. Suitable single crystals of these complexes were characterized by X‐ray structure analysis. When used with these complexes, aldol adducts were isolated with a high degree of regioselectivity in direct aldol additions of aromatic and aliphatic aldehydes to functionalized unsymmetrical ketones. High syn‐diastereoselectivities were obtained in aldol additions of enolizable aldehydes with hydroxyacetone and methoxyacetone. Copyright © 2007 John Wiley & Sons, Ltd.     

Gewöhnliche lineare Differentialgleichungen zweiter Ordnung mit Distributionskoeffizient

Zusammenfassung Läßt man in der gew. lin. Dgl. zweiter Ordnung einen Distributionskoeffizient zu, der Ableitung einerL _loc ² -Funktion ist, so existieren eindeutig festlegbare, stetige Lösungen derart, daß die in der Dgl. auftretenden Produkte definiert werden können. Mit einer Regularisierung des Distr.-Koeffizienten können die Lösungen durchC -Funktionen approximiert werden. Es wird der Sturmsche Vergleichssatz verallgemeinert. Hieraus und aus den Eigenschaften der mit zwei Basislösungen gebildeten Lösungskurve folgt die Gültigkeit des Ljapunovschen Satzes über die Eigenwertverteilung der verallgemeinerten Hillschen Dgl. mit positivem Distr.-Koeffizient, falls eine zusätzliche Bedingung erfüllt ist. Die vorliegende Arbeit enthält einige Ergebnisse meiner Dissertation [6] (weitere Resultate und Details finden sich dort).