On quasilinear parabolic evolution equations in weighted L p -spaces II

Our study of abstract quasi-linear parabolic problems in time-weighted L _p -spaces, begun in Köhne et al. (J Evol Equ 10:443–463, 2010), is extended in this paper to include singular lower-order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell–Stefan diffusion, and to geometric evolution equations like the surface diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

In Situ Quench Reactions of Enantioenriched Secondary Alkyllithium Reagents in Batch and Continuous Flow Using an I/Li-Exchange

We report a practical in situ quench (ISQ) procedure involving the generation of chiral secondary alkyllithiums from secondary alkyl iodides (including functionalized iodides bearing an ester or a nitrile) in the presence of various electrophiles such as aldehydes, ketones, Weinreb amides, isocyanates, sulfides, or boronates. This ISQ-reaction allowed the preparation of a broad range of optically enriched ketones, alcohols, amides, sulfides and boronic acid esters in typically 90–98 % ee. Remarkably, these reactions were performed at −78 °C or −40 °C in batch. A continuous flow set-up permitted reaction temperatures between −20 °C and 0 °C and allowed a scale-up up to a 40-fold without further optimization.