Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence

We show that the nonlinear bending theory of shells arises as a Γ-limit of three-dimensional nonlinear elasticity. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Single‐Molecule Spin Switch Based on Voltage‐Triggered Distortion of the Coordination Sphere

Here, we report on a new single‐molecule‐switching concept based on the coordination‐sphere‐dependent spin state of Fe^II species. The perpendicular arrangement of two terpyridine (tpy) ligands within heteroleptic complexes is distorted by the applied electric field. Whereas one ligand fixes the complex in the junction, the second one exhibits an intrinsic dipole moment which senses the E field and causes the distortion of the Fe^II coordination sphere triggering the alteration of its spin state. A series of complexes with different dipole moments have been synthesized and their transport features were investigated via mechanically controlled break‐junctions. Statistical analyses support the hypothesized switching mechanism with increasing numbers of junctions displaying voltage‐dependent bistabilities upon increasing the Fe^II complexes’ intrinsic dipole moments. A constant threshold value of the E field required for switching corroborates the mechanism.     

Current density analysis of electron transport through molecular wires in open quantum systems

The current density in molecular wires connected to contacts is investigated within the nonequilibrium Green's function formalism combined with the Landauer approach. Energy-dependent and total current density through a series of molecular junctions are calculated in real space representation. A rich variety of current patterns including pronounced ring currents (“vortices”) are found even in the defect-free minimal building blocks of molecular devices. The influences of contact positions, functional groups as well as atomic defects on the transport properties are examined systematically for prototypical ortho-, meta-, and para-substituted benzenes as well as heteroaromatic systems. It is found that substitutional functional groups mainly shift the molecular levels and retain characteristic transport channels, while a significant change of electronic pathways and conductance is induced by hetero-aromaticity. The current distribution is used to calculate the static magnetic field distribution in the carbon-based conductors. © 2017 Wiley Periodicals, Inc.     

An explicit norm representation for the analysis of multilevel methods

In the present paper we develop a representation of a norm frequently used in the analysis of multilevel methods. This allows us to examine the convergence of additive Schwarz schemes also in the case of non-nested subspaces. We demonstrate the usefulness of the given norm representation by studying in detail the stability of sparse grid splittings due to Griebel and Oswald, which turns out to be a special case of our unified theory. Further applications concerning approximation spaces and non-nested finite element spaces are given. This revised version was published online in August 2006 with corrections to the Cover Date.     

Selbstadjungierte Operatoren als „dual rein atomare“ Skalaroperatoren

Ohne Zusammenfassung     

Application de la RMN du 13C a la determination de la configuration de centres quaternaires en serie alicyclique et hydrate de carbone a chaine ramifiee

Configurational assignments to quaternary centres of 2-(l,3-dithianyl) branched-chain carbohydrates, important intermediates for the synthesis of carbohydrate-containing antibiotics, have been made through natural abundance ¹³C NMR spectroscopy. Configurations of quaternary carbons in 21, 24 and 26 were assigned by comparison with ¹³C spectra of structurally-related alicyclic derivatives 1–16.