Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

四磺酸基酞菁锌在水和非水溶剂中的电化学性质研究

在非水溶剂（二甲基亚砜（ＤＭＳＯ）及Ｎ,Ｎ＿二甲基甲酰胺（ＤＭＦ））中的伏安曲线．呈现三对电流峰,表明存在三个可逆或准可逆酞菁配体的单电子转移过程,而在水溶液中则不呈现准可逆行为,且波形改变很大．此外,还比较了四磺酸基酞菁锌的水溶液在自然光和红光（６００～７００ｎｍ）照射下的循环伏安曲线,其氧化还原峰的数目和峰电位基本不变,但在红光照射下比自然光照射下的峰电流明显增大．     

Stable edge dislocations in finite crystals

Dislocations have been considered as mechanically unstable defects in bulk crystals, ignoring the Peierls oscillations. Eshelby [J. Appl. Phys. 24 (1953) p.176] had showed that a screw dislocation can be stable in a thin cylinder. In the current work, considering Eshelby's example of an edge dislocation in a single crystalline plate, we show that an edge dislocation can be stable in a finite crystal. Using specific examples, we also show that the position of stability of an edge dislocation can be off-centre. This shift in the stability from the centre marks the transition from a stable dislocation to an unstable one. The above-mentioned tasks are achieved by simulating edge dislocations using the finite element method.     

The Determination of Trace Elements by Flame Atomic Absorption Spectrometry: Effect of the Composition of Standard Solution Matrices

Abstract

The effect of using solution matrices in calibration standards different from those employed for the extraction steps in the determination of Cd, Cr, Cu, Ni and Zn were tested. Cu and Zn are little affected by matrix effects but, if the extractant is ammonium acetate, the use of other matrices may result in too high Cd, Cr and Ni values.     

Probenchemische Methode zur Bestimmung von 15N an in Gesteinen fixiertem Stickstoff

Zur Klärung geologischer Prozesse werden in zunchmendem Maße die Isotopenvariationen des Stickstoffs herangezogen. Da der größte Teil des Stickstoffs der Gesteine in gebundener Form als Ammoniumstickstoff [1–6] vorliegt, kommt der Untersuchung der Isotopenvariationen desselben eine große Bedeutung zu.     

Note on the Design Differentiability of the Static Response of Elastic Structures

This paper provides a new proof of design sensitivity of the static response of some typical structures. These structures (beams, plates, and plane elastic solids) have been described previously. A proof of design sensitivity of the inverse state operator was provided there, and design sensitivity of static response was derived. The proof presented here is simpler and self-contained.     

Dislocation density crystalline plasticity modeling of lath martensitic microstructures in steel alloys

A three-dimensional multiple-slip dislocation density-based crystalline formulation, specialized finite-element formulations and Voronoi tessellations adapted to martensitic orientations were used to investigate large strain inelastic deformation modes and dislocation density evolution in martensitic microstructures. The formulation is based on accounting for variant morphologies and orientations, retained austenite and initial dislocation densities that are uniquely inherent to martensitic microstructures. The effects of parent austenite orientation and retained austenite were also investigated for heterogeneous fcc/bcc crystalline structures. Furthermore, the formulation was used to investigate microstructures mapped directly from SEM/EBSD images of martensitic steel alloys. The analysis indicates that variant morphology and orientations have a direct effect on dislocation density accumulation and inelastic localization in martensitic microstructures, and that lath directions, orientations and arrangements are critical characteristics of high strength martensitic deformation and behavior.     

Spectroscopic studies and crystal structure of a dimeric Zn(II) complex with diethyl (pyridin-2-ylmethyl)phosphate

The crystal structure of [Zn₂(2-pmOpe)₂Cl₄] (2-pmOpe?=?diethyl (pyridin-2-ylmethyl)phosphate) was determined by X-ray-diffraction method. The compound was also characterized by IR, far-IR, 1H, and ³¹P NMR spectroscopy. In this compound, 2-pmOpe is a bidentate N,O-bridging ligand and Zn(II) are slightly distorted tetrahedral ZnNOCl₂. Zn(II) ions are doubly bridged by the 2-pmOpe ligands, resulting in a dinuclear species. The structure is stabilized by intermolecular C–H?···?O and C–H?···?Cl hydrogen bonds. The spectral properties are in agreement with the structural data.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.