Three-dimensional phase field simulations of grain growth in materials containing finely dispersed second-phase particles

Phase field modelling has proven to be a versatile tool for simulating microstructural evolution phenomena, such as grain growth in polycrystalline materials. However, the computational requirements of a phase field model impose strong limitations on the number of phase field variables employed in a practical implementation. In this paper, a bounding box algorithm is proposed allowing the use of a large number of phase field variables without excessive computational requirements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Fractional Clifford-Fourier Transform

In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived. In the case of even dimension, also an explicit expression for the kernel in terms of Bessel functions is obtained. Finally, the analytic properties of this new integral transform are studied in detail.     

Special functions and systems in Hermitian Clifford analysis: Higher codimension

In this paper, we investigate a Cauchy–Kowalevski (CK) extension problem that arises naturally within the framework of Hermitian Clifford analysis, which concerns the study of Dirac‐like operators in several complex variables. The work presented here includes CK extensions of higher codimension and in particular the CK extension of the Gauss distribution in several complex variables. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of Water-in-Crude-Oil Emulsion Stability Using Critical Electric Field: Effect of Emulsion Preparation Procedure and Crude Oil Properties

The critical electrical field has been used as a tool to probe water in crude emulsion stability to electrical fields in many previous studies. Given the increasing importance of this metric, this study investigates factors that are important to the reproducibility of the measurement and the effect of emulsion preparation variables on the critical electric field. It was observed that the emulsion preparation procedure has a strong effect on the measured critical electric field due to droplet size effects. Furthermore, the effect of crude oil properties on the critical electric field was investigated using emulsions from different oils but with the same average droplet diameter, where it was found that the measurement was dominated by crude oil viscosity.     

The Class of Clifford-Fourier Transforms

Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical Fourier transform. This is applied to the so-called Clifford-Fourier transform (see Brackx et al., J. Fourier Anal. Appl. 11:669–681, 2005). The integral kernel of this transform is a particular solution of a system of PDEs in a Clifford algebra, but is, contrary to the classical Fourier transform, not the unique solution. Here we determine an entire class of solutions of this system of PDEs, under certain constraints. For each solution, series expressions in terms of Gegenbauer polynomials and Bessel functions are obtained. This allows to compute explicitly the eigenvalues of the associated integral transforms. In the even-dimensional case, this also yields the inverse transform for each of the solutions. Finally, several properties of the entire class of solutions are proven.     

Random Function Iterations for Consistent Stochastic Feasibility

We study the convergence of iterated random functions for stochastic feasibility in the consistent case (in the sense of Butnariu and Flåm [Numer. Funct. Anal. Optimiz., 1995]) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point mappings. The iterations are Markov chains and, for the purposes of this study, convergence is understood in very restrictive terms. We show that sufficient conditions for geometric (linear) convergence in expectation of stochastic projection algorithms presented in Nedi? [Math. Program, 2011], are in fact necessary for geometric (linear) convergence in expectation more generally of iterated random functions.     

Wetting of a self-assembled 1,4-benzenedimethanethiol monolayer on gold and silver: An adhesion force spectroscopy study

Using atomic force microscopy we investigated how local capillary phenomena are affected by the deposition of a self-assembled 1,4-benzenedimethanethiol (BDMT) layer on epitaxially grown Au(1 1 1) and Ag(1 1 1) films. Force-distance curves monitored at varying relative humidity show clear differences in the adhesion forces on the different samples, which can be explained in terms of a change in the wetting behavior due to the presence of the molecules. Moreover, we found that not only the chemical structure of the molecules but also their orientation strongly influences the strength of the capillary forces. A detailed analysis of the measurements shows that condensation of water vapor on Au(1 1 1) films is drastically enhanced due to the vertically aligned BDMT molecules, while on Ag(1 1 1) water condensation is reduced due to a parallel molecule orientation.     

Ruthenium complexes bearing bidentate Schiff base ligands as efficient catalysts for organic and polymer syntheses

A concise overview is given on mononuclear and dinuclear, bidentate Schiff base ruthenium complexes with different additional ligands and on their applications in various chemical transformations such as Kharasch addition, enol-ester synthesis, alkyne dimerization, olefin metathesis and atom transfer radical polymerization. These new ruthenium complexes, conveniently prepared from commonly available ruthenium compounds, are very stable, exhibit a good tolerance towards organic functionalities, air and moisture and display high activity and chemoselectivity in chemical transformations. Relevant features of coordination chemistry connected with the reaction mechanism and chemoselectivity are also fully described. Since the nature of Schiff bases can be changed in a variety of ways, appealing routes for designing and preparing novel ruthenium complexes can be foreseen in the future.     

Dilithiation of Bis(benzene)molybdenum and subsequent isolation of a molybdenum-containing paracyclophane

The homoleptic sandwich complex bis(benzene)molybdenum, [Mo(eta6-C6H6)2], was successfully dilithiated by employing an excess of BuLi in the presence of N,N,N',N'-tetramethylethylenediamine (up to 6 equiv each) at slightly elevated temperatures furnishing the highly reactive, ring metalated species [Mo(eta6-C6H5Li)2].tmeda in high yields. Alternatively, this compound was synthesized upon prolonged sonication with 5 equiv of tBuLi/tmeda without heating. An X-ray crystal structure determination revealed a symmetrical, dimeric composition in the solid state, i.e., a formula of [Mo(eta6-C6H5Li)2]2.(thf)6, where the six-membered rings are connected by two pairs of bridging lithium atoms. The synthesis of an elusive ansa-bridged complex failed in the case of a [1]bora and a [1]sila bridge due to the thermal lability of the resulting compounds. Instead, reverse addition of the dilithio precursor to an excess of the appropriate element dihalide facilitated the isolation of several unstrained, 1,1'-disubstituted derivatives, namely, [Mo{eta6-C6H5(BN(SiMe3)2X)}2] (X = Cl, Br) and [Mo{eta6-C6H5(SiiPr2Cl)}2], respectively. However, the incorporation of a less congesting [2]sila bridge was accomplished. In addition to the formation of [Mo{(eta6-C6H5)2Si2Me4}], a molybdenum-containing paracylophane complex was isolated and characterized by means of crystal structure analysis. The ancillary formation of 1 equiv of bis(benzene)molybdenum strongly suggests that this species is generated by deprotonation of the ansa-bridged complex by the dilithiated precursor and subsequent reaction with a second equivalent of the disilane.     

Stability studies of high-stable water-in-oil model emulsions

Different compositions and emulsification protocols were used to prepare stable water-in-oil (w/o) emulsions. Water, mineral oil, and a mixture of Span 80 and Tween 80 surfactants were combined to form emulsions that can be used as reference for electrolyte-free systems. Here, we have proposed emulsions wherein different properties were evaluated. Electrical conductivity measurements indicated that conductivity increases linearly with increasing surfactant content. The emulsions’ flow curves and viscoelastic behaviors were delineated by rheological measurements. Stability studies by centrifugal testing have shown that smaller the surfactant content, lower the stability, for any used stirring speeds. Furthermore, higher the applied mixing rate to make the emulsion, higher the stability, regardless of the amount of surfactant. Electrical field stability analysis showed, for all systems, that critical electric field (CEF) values were dependent on either surfactant amount and emulsion elastic modulus.