A constructive approach to nodal splines

In the context of local spline interpolation methods, nodal splines have been introduced as possible fundamental functions by de Villiers and Rohwer in 1988. The corresponding local spline interpolation operator possesses the desirable property of reproducing a large class of polynomials. However, it was remarked that their definition is rather intricate so that it seems desirable to reveal the actual origin of these splines. The real source can be found in the Martensenoperator which can be obtained by two-point Hermite spline interpolation problem posed and proved by Martensen [Darstellung und Entwicklung des Restgliedes der Gregoryschen Quadraturformel mit Hilfe von Spline-Funktionen, Numer. Math. 21(1973)70–80]. On the one hand, we will show how to represent the Hermite Martensen spline recursively and, on the other hand, explicitly in terms of the B-spline by using the famous Marsden identity. Having introduced the Martensenoperator, we will show that the nodal spline interpolation operator can be obtained by a special discretization of the occurring derivatives. We will consider symmetric nodal splines of odd degree that can be obtained by our methods in a natural way.     

Patch coupling with the isogeometric dual mortar approach

The use of a common set of basis functions for design and analysis is the main paradigm of isogeometric analysis. The characteristics of the commonly used non-uniform rational B-splines (NURBS) surfaces require methods to handle non-conforming meshes to attain an efficient computational framework. The isogeometric mortar method uses constrained approximation spaces to enforce a coupling of deformations at the interface between patches in a weak manner. This method neither requires additional degrees of freedom nor the choice of empirical parameters. The main drawback of the standard isogeometric mortar approach is the non-local support of the mortar basis functions along the interface. This yields a large number of nodes per element for elements adjacent to the interface. Thus, the computational costs increase significantly for mesh refinement. This issue is remedied by the use of dual basis functions for the mortar method, which is referred to as dual mortar method. In this contribution several choices for the dual basis functions for B-splines are proposed and compared. A special focus is set on the support of the dual basis functions and on the support of the resulting mortar basis functions. Numerical examples show the influence of the choice for the dual basis functions on the accuracy of the global stress distribution, on the fulfillment of the interface conditions and on numerical efficiency. The use of approximate dual basis functions is shown to be competitive to computations of conforming meshes in terms of accuracy and efficiency. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nanotextured multicrystalline Al‐BSF solar cells reaching 18% conversion efficiency using industrially viable solar cell processes

We report recent achievements in adapting industrially used solar cell processes on nanotextured surfaces. Nanostructures were etched into c‐Si surfaces by dry exothermic plasma‐less reaction of F species with Si in atmospheric pressure conditions and then modified using a short post‐etching process. Nanotextured multicrystalline wafers are used to prepare Al‐BSF solar cells using industrially feasible solar cell proc‐ essing steps. In comparison to the reference acidic textured solar cells, the nanostructured cells showed gain in short circuit current (J_sc) of up to 0.8 mA/cm² and absolute gain in conversion efficiency of up to 0.3%. The best nanotextured solar cell was independently certified to reach the conversion efficiency of 18.0%. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Monotone multigrid methods for elliptic variational inequalities II

Summary. We derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements. The coarse grid corrections are computed from certain obstacle problems. The actual constraints are fixed by the preceding nonlinear fine grid smoothing. This new approach allows the implementation as a classical V-cycle and preserves the usual multigrid efficiency. We give estimates for the asymptotic convergence rates. The numerical results indicate a significant improvement as compared with previous multigrid approaches. Received March 26, 1994 / Revised version received September 22, 1994     

The Baum-Connes conjecture via localisation of categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the Baum-Connes assembly map for other equivariant homology theories. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting.     

Ternäre Thallium-Indium-Sulfide: Eine Zusammenfassung

Ternary Thallium Indium Sulfides: A Summary Combined thermal and X-Ray analyses in the ternary system Thallium—Indium—Sulfur show, that the two binary sections Tl₂S? In₂S₃ and TlS? InS contain ternary compounds with unique crystal structures. The chemical formulas of these ternary solids are TlIn₅S₈, TlIn₃S₅, TlInS₂ and Tl₃InS₃ for the section Tl₂S? In₂S₃ and TlIn₅S₆ as well as Tl₃In₅S₈ (metastable high temperature phase) for the section TlS? InS respectively. With TlIn₅S₇ an additional ternary solid could be detected, which is located outside the two sections. It is derived from the binary mixed valence compound In₆S₇ by complete substitution of In⁺ by Tl⁺. The following ionic formulations make the mixed valence character of the ternary Thallium—Indium-Sulfides reasonable: TlIn₅S₈ = Tl⁺(In³⁺)₅(S^2?)₈, TlIn₃S₅ = Tl⁺ (In³⁺)₃(S^2?)₅, TlInS₂ = Tl⁺In³⁺(S^2?)₂, Tl₃InS₃ = (Tl⁺)₃In³⁺ · (S^2?)₃, TlIn₅S₆ = Tl⁺([In₂]⁴⁺)₂In³⁺ (S^2?)₆, Tl₃In₅S₈ = 4 × [(Tl⁺)_0,75 · (In⁺)_0,25In³⁺(S^2?)₂], TlIn₅S₇ = Tl⁺[In₂]⁴⁺ (In³⁺)₃(S^2?)₇. All compounds contain Tl⁺-ions in a characteristic “lone pair coordination” of S^2? ions. Indium atoms however occur with the oxidation numbers +2 (formal, In₂ dumb bells with covalent In? In bonding) and +3 (with In³⁺ in tetrahedral and octahedral coordination of S^2?). Chemical preparation, crystal chemistry and general properties of the ternary solids are discussed, summarized and compared to each other.     

Trans-cis isomerization is responsible for the red-shifted fluorescence in variants of the red fluorescent protein eqFP611

An important class of red fluorescent proteins (RFPs) feature a 2-iminomethyl-5-(4-hydroxybenzylidene)imidazolinone chromophore. Among these proteins, eqFP611 has the chromophore in a coplanar trans orientation, whereas the cis isomer is preferred by other RFPs such as DsRed and its variants. In the photoactivatable protein asFP595, the chromophore can even be switched from the nonfluorescent trans to the fluorescent cis state by light. By using X-ray crystallography, we have determined the structure of dimeric eqFP611 at high resolution (up to 1.1 A). In the far-red emitting eqFP611 variant d2RFP630, which carries an additional Asn143Ser mutation, the chromophore resides predominantly (approximately 80%) in the cis isomeric state, and in RFP639, which has Asn143Ser and Ser158Cys mutations, the chromophore is found completely in the cis form. The pronounced red shift of excitation and emission maxima of RFP639 can thus unambiguously be assigned to trans-cis isomerization of the chromophore. Among RFPs, eqFP611 is thus unique because its chromophore is highly fluorescent in both the cis and trans isomeric forms.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.