On the Influence of Polynomial De-aliasing on Subgrid Scale Models

In this work we investigate the interplay of polynomial de-aliasing and sub-grid scale models for large eddy simulations based on discontinuous Galerkin discretizations. It is known that stability is a major concern when simulating underresolved turbulent flows with high order nodal collocation type discretizations. By changing the interpolatory character of the nodal collocation type discretization to a projection based discretization by increasing the number of quadrature points (polynomial de-aliasing), one is able to remove the aliasing induced stability problems. We focus on this effect and on the consequence for large eddy simulations with explicit subgrid scale models. Often, subgrid scale models have to achieve two possibly conflicting tasks in a single simulation: firstly stabilizing the numerics and secondly modeling the physical effect of the missing scales. Within a discontinuous Galerkin approach, it is possible to use either a fast (but potentially aliasing afflicted) nodal collocation discretization or a projection-based (but computationally costly) variant in combination with an explicit subgrid scale model. We use this framework to investigate the effect on the appropriate model parameter of a standard Smagorinsky subgrid scale model and of a Variational Multiscale Smagorinsky formulation. For this we first consider the 3-D viscous Taylor-Green vortex example to investigate the impact on the stability of the method and second the turbulent flow past a circular cylinder to investigate and compare the accuracy of the results. We show that the aliasing instabilities of collocative discretizations severely limit the choice of the model constant, in particular for high order schemes, while for de-aliased DG schemes, the closure model parameters can be chosen independently from the numerical scheme. For the cylinder flow, we also find that for the same model settings, the projection-based results are in better agreement with the reference DNS than those of the collocative scheme.     

Multicomponent one-pot synthesis of (dihydro-1H-benzo[d]imidazole) phosphonate

Abstract

We present a multicomponent reaction strategy to synthesize a (dihydro-1H-benzo[d]imidazole)phosphonate family of compounds, using benzimidazoles, diethyl chlorophosphate and aliphatic amines as starting reactants. Giving its simplicity, our procedure involves reaction times of only few hours and avoid the usage of any catalyst agent. All the newly synthesized compounds were characterized by Nuclear Magnetic Resonance spectroscopy (¹H, ¹³C and ³¹P) and mass spectrometry by the DART method.     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

Organoselenido Complexes of Tungsten

Organometallic tungsten selenido complexes of the type [cpW(CO)₃]₂Se_m; m = 2 (1), 3 (2), 4 (3), can be easily synthesized via insertion of selenium into the alkali-metal tungsten bond of LiWcp(CO)₃ in appropriate ratios and subsequent oxidation of the produced W-selenolates with O₂/SiO₂. In contrast, reactions of K₂Se₆ with [cpW(CO)₃Cl] and 18-crown-6 in DMF lead to a mixture óf [cpW(CO)₃]₂Se₄ (3), the η¹ Se-bonded selenocarbamato complex [cpW(CO)₃SeC(O)NMe₂] (4) and the ionic complex [(18-crown-6)K]⁺[cpW(Se₄)₂]^? (5). The crystal structures of 3 and 4 together with their ⁷⁷Se NMR data are presented.     

Palladium(II) complexes bearing N‐alkylpiperidoimidazolin‐2‐ylidene derivatives: Effect of alkyl chain length of ligands on catalytic activity

A series of piperidoimidazolinium salts which differ in the chain lengths (butyl, octyl, dodecyl, octadecyl) and their Pd–N‐heterocyclic carbene complexes with pyridine were synthesized and characterized using elemental analysis and spectroscopic methods. The effects of these ligands on catalyst activation and the performance of the complexes were studied in Suzuki–Miyaura reactions of arylboronic acid with aryl chlorides. The complex with the ligand having the longest chain length was found to be most active. The results demonstrated that the length of the alkyl chain of the piperidoimidazolin‐2‐ylidene controlled the dispersion and composition of the nanoparticles and it affected the catalytic activity. The impact of alkyl chain length of piperidoimidazolin‐2‐ylidene on the Suzuki–Miyaura reactions of arylboronic acid with aryl halides was systematically investigated.     

Radiometrische Bandwaage mit Rechnerschaltkreis zur Signalaufbereitung

Es wird eine radiometrische Bandwaage zur Koksaustragsmengen-Messung in BHT-Kokereien beschrieben. Voranstellend werden einige analytische Ausdrücke zur theoretischen Behandlung dieses Bandwaagentyps mitgeteilt. Die Waage zeichnet sich durch hohe Stabilität der Anzeige, durch die Möglichkeit des routinemäßigen Umsetzens von Meßstelle zu Meßstelle innerhalb kurzer Zeit und durch einen relativ kleinen Wägefehler (Meßunsicherheit ≦ 2,9%) aus. Die Signalaufbereitung innerhalb der Elektronik erfolgt durchgängig digital unter Verwendung eines Rechnerschaltkreises.     

New chiral dopants for ferroelectric liquid crystals

New chiral dopants for application in ferroelectric liquid crystal mixtures are presented. They derive from chirally modified biphenylcyclohexylcarbonitriles, lactates and optically active 2-cyano-2-methylalkanoates. Synthetic routes to the new compounds are shown and the physical properties of the new compounds in a non-chiral smectic C host are reported.