Finite element methods for a class of continuum models for immiscible flows with moving contact lines

In this paper, we present a finite element method for two‐phase incompressible flows with moving contact lines. We use a sharp interface Navier–Stokes model for the bulk phase fluid dynamics. Surface tension forces, including Marangoni forces and viscous interfacial effects, are modeled. For describing the moving contact lines, we consider a class of continuum models that contains several special cases known from the literature. For the whole model, describing bulk fluid dynamics, surface tension forces, and contact line forces, we derive a variational formulation and a corresponding energy estimate. For handling the evolving interface numerically, the level‐set technique is applied. The discontinuous pressure is accurately approximated by using a stabilized extended finite element space. We apply a Nitsche technique to weakly impose the Navier slip conditions on the solid wall. A unified approach for discretization of the (different types of) surface tension forces and contact line forces is introduced. Results of numerical experiments are presented, which illustrate the performance of the solver. Copyright © 2016 John Wiley & Sons, Ltd.     

On the approximation of high-dimensional differential equations in the hierarchical Tucker format

The hierarchical Tucker format is a way to decompose a high-dimensional tensor recursively into sums of products of lower-dimensional tensors. The number of degrees of freedom in such a representation is typically many orders of magnitude lower than the number of entries of the original tensor. This makes the hierarchical Tucker format a promising approach to solve ordinary differential equations for high-dimensional tensors. In order to propagate the approximation in time, differential equations for the parameters of the hierarchical Tucker format are derived from the Dirac-Frenkel variational principle. We prove an error bound for the dynamical approximation in the hierarchical Tucker format by extending previous results of Koch and Lubich for the non-hierarchical Tucker format.     

Oxidative-Insertion Reactivity Across a Geometrically Constrained Metal→Borane Interaction

While interest in cooperative reactivity of transition metals and Lewis acids is receiving significant attention, the scope of known reactions that directly exploit the polarized reverse-dative σ-bond of metal-borane complexes (i.e., M → BR₃) remains limited. Described herein is that the platinum (boryl)iminomethane (BIM) complex [Pt(κ²-N,B-^Cy2BIM)(CNAr^Dipp2)] can effect the oxidative insertion of a range of unsaturated organic substrates, including azides, isocyantes, and nitriles, as well as CO₂ and elemental sulfur (S₈). In addition, alkyl migration processes available to the BIM framework allow for post-insertion reaction sequences resulting in product release from the metal center.     

Die Kristallstruktur von Kaliummonomethylcarbonat

Crystal Structure of Potassium Monomethylcarbonate Potassium monomethylcarbonate KCH₃CO₃ was obtained from reaction of dimethylcarbonate with potassium hydroxide in methanole. The crystal structure was determined (triclinic, P1 (no. 2), Z = 2, a = 380.9(2) pm, b = 558.9(3) pm, c = 985.3(3) pm, α = 100.71(2)°, β = 90.06(3)°, γ = 92.48(3)°, V = 205.9(2) · 10⁶ pm³, wR(F²) = 0.054, wR_obs(F) = 0.022). Structural relations between potassium monomethylcarbonate and potassium hydrogencarbonate are discussed.     

Steplength optimization and linear multigrid methods

Summary Recently steplength parameters have been used in linear multigrid methods. In this paper we give a theoretical analysis of the effects of steplength optimization in a rather general framework which covers two different implementations of steplength optimization in standard multigrid methods.     

Colchicine Models: Synthesis and Binding to Tubulin of Tertamethoxybiphenyls

Syntheis of tetramethoxybiphenyl 21 was accomplished from 4-phenylcylohexane-1,3-dione 13 by aromatization to biphenyl 19 and reductive removal of the phenolic OH group as phenyltetrazolyl ether. Tertramethoxybiphenyls 34 and 40 were obtained from 4-phenylcyclohexenone 26 via ester 27 . The tetramethoxybiphenyls 21, 34 , and 40 , and analogs 28, 29 , and 31 were evaluated for antitubulin activity and as antimitotic agents with L1210 murine leukemia cells. Compounds 31 and 34 had significant effects on the in-vitro polymerization of tubulin. Compound 31 was the most cytotoxic of the six new biphenyls studied (IC₅₀ for cell growth, 0.6M ) and caused the accumulation of cells in metaphase arrest.     

Tetracyclic phenothiazines IV . Synthesis of 1,2,3,4-Tetrahydro-azepino [3,2,1-kl] phenothiazin -4-one

The synthesis of 1,2,3,4-tetrahydroazepine[3,2,1-kl]phenothiazin-4-one was accomplished by cyclization of phenothiazine-10-butanoic acid using phosphorus pentoxide and absolute ethanol. The title compound represents the first reported example of the azepino[3,2,1-kl]phenothiazine ring system. A vastly improved malonic ester-type synthesis of the precursor acid has also been developed.     

Analysis of (particle,xn) reactions on tantalum and gold: (II). 181Ta, 197Au(3He,xn) excitation functions and equilibrium statistical model analysis

Excitation functions for the reactions ${}^{197}\text{Au}\text{(}{}^3\text{He}\text{, x}\text{n}\text{)}{}^{\mathrm{200?x}}\text{Tl}\text{(x = 3, … 7)}$ and ${}^{181}\text{Ta}\text{(}{}^3\text{He}\text{, x}\text{n}\text{)}{}^{\mathrm{184?x}}\text{Re}\text{(x = 3, … 7)}$ were measured at bombarding energies up to 75 MeV. The data are compared to the results of an equilibrium statistical model calculation including angular momentum conservation and γ-ray competition. Satisfactory agreement was found except for the high energy tails.     

Synthese und Eigenschaften von 6-Desoxy-6-halogen-Derivaten der L-Ascorbinsäure

Synthesis and Properties of 6-Deoxy-6-halogeno-Derivatives of L -Ascorbic Acid 6-Deoxy-6-chloro-, -6-bromo-, -6-iodo- and -6-fluoro derivatives of L -ascorbic acid have been synthesized and characterized. The physiological properties of the chloro derivative have been investigated. It shows a high antiscurvy activity. The chloro- and bromo-derivatives have been reduced to the corresponding deoxy compound, which is an interesting chiral intermediate for the preparation of rare ω-deoxy sugars.