Influence of the substrate,metal overlayer and lattice neighbors on the focusing properties of colloidal microspheres

Calculations of the field distribution in colloidal SiO₂ microspheres are presented. Two cases are considered: small particles on a Si substrate irradiated by the 266 nm light, and larger ones, covered with a gold film and irradiated at 800 nm. Substrate, neighboring spheres and sputtered metal overlayer all significantly modify the field pattern and magnitude. Reflected light is focused inside the spheres, which may lead to their damage. The results can be useful in the analysis of microspheres-assisted nano-patterning.     

Ultrasonic radiation in dynamic force microscopy

In dynamic force microscopy the cantilever of an atomic force microscope is vibrated at ultrasonic frequencies in the range of several 10 kHz up to several MHz while scanning a sample surface. The amplitude and phase of the cantilever vibration as well as the shift of the cantilever resonance frequencies provide information about local sample surface properties. In several operation modes of dynamic force microscopy, for example force modulation microscopy, tapping mode or atomic force acoustic microscopy, the sensor tip is in contact with the sample at least during a fraction of its vibration cycle. The periodic indentation of the tip with the sample surface generates ultrasonic waves. In this paper, the ultrasonic radiation of a vibrating cantilever into a sample and its contribution to the damping of the cantilever vibration are calculated. The theoretical results are compared to experiments.     

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.