Stretching of polymers in isotropic turbulence: a statistical closure

We present a new closure for the mean rate of stretching of a dissolved polymer by homogeneous isotropic turbulence. The polymer is modeled by a bead-spring-type model (e.g., Oldroyd B, FENE-P, Giesekus) and the analytical closure is obtained assuming the Lagrangian velocity gradient can be modeled as a Gaussian, white-noise stochastic process. The resulting closure for the mean stretching depends upon the ratio of the correlation time for strain and rotation. Additionally, we derived a second-order expression for circumstances when strain and rotation have a finite correlation time. Finally, the base level closure is shown to reproduce results from direct numerical simulations by simply modifying the coefficients.     

Modeling Abrasive Wear Caused by Small Solid Particles of Different Sizes

Abrasive wear is one of the mechanisms which cause the decrease of efficiency of hydraulic machines. The working fluid of a hydraulic machine, e.g., a turbine of a hydroelectric power plant, transports small solid particles of different sizes. Those small particles damage the surface of the hydraulic machine when contacting. In contrast to classical approaches in fluid dynamics, here, we present an approach where only mesh-free methods are applied. The Smoothed Particle Hydrodynamics (SPH) method is used for modeling the fluid in this study. The SPH method is a mesh-free method which has its advantages in describing transient fluid flows with free surfaces and large motions. The loading of the fluid consists of small solid particles of different sizes. A coupled approach for describing the loading is used. For the larger abrasive particles the Discrete Element Method and for smaller ones a transport equation is utilized. In doing so it is possible to model a loading of the fluid consisting of small particles of different sizes. The abrasive wear is described with an abrasive wear model. The wear model takes into account different parameters like the size, the velocity of the abrasive particles, and of course material parameters of both the target and the particles. On impact of an abrasive particle, the amount of removed material is stored at the boundary and in doing so the removed material over time is identified. In this work, a representative numerical example is presented. The simulations were performed with the code Pasimodo, developed at the Institute of Engineering and Computational Mechanics. It is the aim of this work to point out that it is possible to model abrasive wear due to abrasive particles with different sizes with a mesh-free approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of mixed thiolate/thioether versus dithiolate coordination on the accessibility of the uncommon +I and +III oxidation states for the nickel ion: an experimental and computational study

Sulfur-rich nickel metalloenzymes are capable of stabilizing Ni(I) and Ni(III) oxidation states in catalytically relevant species. In an effort to better understand the structural and electronic features that allow the stabilization of such species, we have investigated the electrochemical properties of two mononuclear N(2)S(2) Ni(II) complexes that differ in their sulfur environment. Complex 1 features aliphatic dithiolate coordination ([NiL], 1), and complex 2I is characterized by mixed thiolate/thioether coordination ([NiL(Me)]I, 2I). The latter results from the methylation of a single sulfur of 1. The X-ray structure of 2I reveals a distorted square planar geometry around the Ni(II) ion, similar to what was previously reported by us for 1. The electrochemical investigation of 1 and 2(+) shows that the addition of a methyl group shifts the potentials of both redox Ni(II)/Ni(I) and Ni(III)/Ni(II) redox couples by about 0.7 and 0.6 V to more positive values. Through bulk electrolyses, only the mononuclear dithiolate [Ni(I)L](-) (1(-)) and the mixed thiolate/thioether [Ni(III)L(Me)](2+) (2(2+)) complexes were generated, and their electronic properties were investigated by UV-vis and EPR spectroscopy. For 1(-) (Ni(I), d(9) configuration) the EPR data are consistent with a d(x(2))(-)(y(2)) based singly occupied molecular orbitals (SOMOs). However, DFT calculations suggest that there is also pronounced radical character. This is consistent with the small g-anisotropy observed in the EPR experiments. The spin population (Mulliken analysis) analysis of 1(-) reveals that the main contribution to the SOMO (64%) is due to the bipyridine unit. Time dependent density functional theory (TD-DFT) calculations attribute the most prominent features observed in the electronic absorption spectrum of 1(-) to metal to ligand charge transfer (MLCT) transitions. Concerning 2(2+), the EPR spectrum displays a rhombic signal with g(x) = 2.236, g(y) = 2.180, and g(z) = 2.039 in CH(3)CN. The g(iso) value is larger than 2.0, which is consistent with metal based oxidation. The unpaired electron (Ni(III), d(7) configuration) occupies a Ni-d(z(2)) based molecular orbital, consistent with DFT calculations. Nitrogen hyperfine structure is observed as a triplet in the g(z) component of the EPR spectrum with A(N) = 51 MHz. This result indicates the coordination of a CH(3)CN molecule in the axial position. DFT calculations confirm that the presence of a fifth ligand in the coordination sphere of the Ni ion is required for the metal-based oxidation process. Finally, we have shown that 1 exhibits catalytic reductive dehalogenation activity below potentials of -2.00 V versus Fc/Fc(+) in CH(2)Cl(2).     

Epimerization,transacylation and bromination of dihydroquercetin acetates; synthesis of 8-bromodihydroquercetin

Dihydroquercetin (dhq) and its 3-acetate react with acetic anhydride in the absence of a base catalyst to yield mixtures of partially acetylated products. Three new esters were characterized by NMR spectroscopy as dhq 3,7,3′-triacetate, 3,7,4′-triacetate and 5,7,3′,4′-tetraacetate. At its melting point neat dhq 3,7,3′,4′-tetraacetate is partially converted to dhq 3,3′,4′-triacetate and dhq pentaacetate by intermolecular acetyl transfer. Dhq 7,3′,4′-triacetate yields exclusively dhq 3′,4′-di- and 3,7,3′,4′-tetraacetate under these conditions. The acetylation/deacetylation reactions are accompanied by partial epimerization: 3 new acetates with 2,3-cis stereochemistry (dhq 3-, 3,7,3′,4′-tetra- and penta-) were identified. Dhq and its 3,7,3′,4′-tetraacetate undergo regiospecific dibromination at C-6 and C-8 with excess N-bromosuccinimide in polar solvents, and 6,8-dibromo-dhq can be regioselectively debrominated to 8-bromo-dhq with sodium sulfite.     

Analysis of repeated impacts on a steel rod with visco-plastic material behavior

In machine dynamics impacts are usually common phenomena, resulting from collisions of moving bodies. Even low velocity impacts might produce high stresses in the contact region, which result in inelastic deformation. Thereby, visco-plastic materials, such as steel, show a significant increase of the yield stress with the strain rate. In machine dynamics repeated collisions occur, resulting in repeated impacts on a previously deformed contact area. Then, inelastic deformation and the resulting residual stresses produced by previous impacts have an influence on the behavior of the following impacts. Thus, the impact behavior varies with the number of impacts. This paper presents a numerical and experimental evaluation of repeated impacts with identical impact velocity up to 3 m/s, whereby the deformation history of the contact area, due to previous impacts, is included. The approach is applied to longitudinal impacts of an elastic steel sphere on a steel rod with distinct visco-plastic material behavior which is identified by Split Hopkinson Pressure Bar tests. A Finite Element analysis and experimental verification using two Laser-Doppler-Vibrometers are performed. It is shown that for an accurate impact simulation the FE model must include the visco-plastic material behavior of the steel. Further it is found that the maximal contact force, the rebound velocity and the coefficient of restitution increase with the number of impacts, while the contact duration decreases with the number of impacts. After several impacts these quantities show saturation to a constant value, indicating no significant additional inelastic deformation in the later impacts. Further, the residual stress distribution, the maximal von Mises stress distribution and the local deformation at the contact point are evaluated and a characteristic force-deformation diagram is obtained. Finally, an analysis is performed to describe the relation between maximal force and remaining crater at the contact point.     

Radius Theorems for Monotone Mappings

Set-Valued and Variational Analysis - For a Hilbert space X and a mapping $F: X\rightrightarrows X$ (potentially set-valued) that is maximal monotone locally around a pair $(\bar {x},\bar {y})$ in...