A posteriori error estimates for a time discrete scheme for a phase-field system of Penrose-Fife type

A time discrete scheme is used to approximate the solution toa phase field system of Penrose–Fife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data.     

On the Spectra of Carbon Nano-Structures

An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.     

Konstruktion von Fundamentallösungen für Convolutoren in roumieuschen Ultradistributionsräumen

Fundamental solutions in a space D(M_p) of Roumieu ultradistributions are constructed for convolutors f whose Fourier transform is slowly decreasing. The solutions are of exponential growth if satisfies a stronger condition. These results include a constructive proof of the known existence theorem of Chou. For families of convolutors our method yields solutions which depend continuously on parameters.     

Cobalt Chalcogenide Clusters. Synthesis,Characterization and DFT Calculations of [Co4Se2(CO)10] and [Co4Te2(CO)11]. Crystal Structure of [Co8Se4(CO)16(μ‐dppa)2]

The reactions of [Co₂(CO)₈] with E(SiMe₃)₂ (E = Se, Te) in CH₂Cl₂ result in the formation of the compounds [Co₄Se₂(CO)₁₀]> ( 1 ) and [Co₄Te₂(CO)₁₁] ( 2 ), respectively. Both cluster complexes have similar molecular structures in which the cobalt atoms form four‐membered rings with μ₄‐bridging chalcogen atoms (Se and Te) above and below the plane of the metal atoms and the carbonyl ligands as either terminal or μ₂‐bridging ligands. DFT‐calculations for both compounds have been carried out in order to obtain some more information about their electronic distribution. In the presence of the phosphine Ph₂PC≡CPPh₂ (dppa), the reaction of [Co₂(CO)₈] with Se(SiMe₃)₂ leads to the formation of [Co₈Se₄(CO)₁₆(μ‐dppa)₂] ( 3 ). During the reaction two molecules of [Co₂(CO)₈] have been added to the acetylene groups of the dppa ligands, whilst the remaining cobalt atoms coordinate to the phosphorus atoms of the phosphine. In this compounds the selenium atoms act as μ₃‐ligands, bridging the metal atoms bonded to the phosphorus with those bonded to the acetylene groups.     

A comparison of viscoelastic and empirical rheological models in context of squeeze flows

This work compares the behavior of a Giesekus and Carreau-Yasuda fluid in a squeeze flow between two circular plates. In order to do this the Carreau-Yasuda model is fitted to the shear viscosity curve of the Giesekus model and the squeeze stress is compared over the process time. The investigations are performed numerically with a 2.5 dimensional wedge model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New engineering polymers for blow-moulding

The combination of using high performance flexible engineering polymers and their processing by blow moulding technology allows traditional rubber and rubber-metal composite parts to be replaced to obtain improved performance, lower cost and greater design freedom. Two examples of automobile applications are detailed to support this concept - constant velocity joint boots and engine air ducting.     

Yang–Mills instantons and dyons on group manifolds

We consider Euclidean SU(N)$\mathrm{SU}(N)$ Yang–Mills theory on the space G×R$G\times \mathbb{R}$, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang–Mills equations. For gauge fields invariant under the adjoint G  -action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G=SU(2)≅S³$G=\mathrm{SU}(2)\cong S^3$, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on G×R$G\times \mathbb{R}$ to Minkowski and construct finite-energy dyon-type Yang–Mills solutions. The special case of G=SU(2)×SU(2)$G=\mathrm{SU}(2)\times \mathrm{SU}(2)$ may be used in heterotic flux compactifications.     

Atomic-Scale Insights into Electrode Surface Dynamics by High-Speed Scanning Probe Microscopy

Atomic-scale processes at electrode surfaces in liquid electrolytes are central elemental steps of electrochemical reactions. Detailed insights into the structure of these interfaces can be obtained with in situ scanning tunnelling and atomic force microscopy. By increasing the time resolution of these methods into the millisecond range, highly dynamic processes at electrode surfaces become directly observable. This review gives an overview of in situ studies with video-rate scanning probe microscopy techniques. Firstly, quantitative investigations into the dynamic behaviour of individual adsorbed atoms and molecules are described. These reveal a complex dependence of adsorbate surface diffusion on potential and co-adsorbed species and provide data on adsorbate–adsorbate and adsorbate–substrate interactions in a liquid environment. Secondly, results on collective dynamic phenomena are discussed, such as molecular self-assembly, the dynamics of nanoscale structures, nucleation and growth, and surface restructuring due to phase-formation processes.     

Actinide Organometallic Complexes with π-Ligands

Recent developments and results from the organometallic chemistry of the actinides are reviewed. In the last one and a half years the structural data of about 15 organometallic complexes of transuranium actinides (Np or Pu) have been published, all involving π-ligands in the coordination sphere of the metal ion. On the basis of these data, a comparison of these molecules is presented. Depending on the steric demands of the ligands, effects like the actinide contraction seem to be stronger or weaker in the structural features. This indicates that the interplay between the actinide ion and the π-ligand is rather flexible, enabling the formation of stable bonds over a broad range of actinide ion oxidation states.