Convergence to equilibrium for delay-diffusion equations with small delay

It is shown that for scalar dissipative delay-diffusion equationsu _t–u=f(u(t),u(t–)) with a small delay, all solutions are asymptotic to the set of equilibria ast tends to infinity.     

Synthese,Röntgenstrukturanalyse und Multikern‐NMR‐spektroskopische Untersuchung einiger intramolekular stickstoffstabilisierter Bor‐, Aluminium‐ und Galliumorganyle

Synthesis, X‐Ray Structure, and Multinuclear NMR Investigation of some intramolecularly Nitrogen stabilized Organoboron, ‐aluminum, and ‐gallium Compounds The intramolecularly nitrogen stabilized organoaluminum‐ and organoboron compounds Me₂Al(CH₂)₃NMe₂ ( 1 ), Me₂AlC₁₀H₆‐8‐NMe₂ ( 2 ), ⁱPr₂Al(CH₂)₃NEt₂ ( 3 ), (CH₂)₅Al(CH₂)₃NMe₂ ( 4 ), and (CH₂)₅B(CH₂)₃NMe₂ ( 5 ) are synthesized from Me₂AlCl and the corresponding organolithium compounds and from AlCl₃ or BCl₃, the lithium alkyl and ⁱPrMgCl or BrMg(CH₂)₅MgBr, respectively. AlCl₃ and GaCl₃ react with Li(CH₂)₃NMe₂ or LiCH₂CHMeCH₂NMe₂ forming Cl₂AlCH₂CHMeCH₂NMe₂ ( 6 ), Cl₂Al(CH₂)₃NMe₂ ( 8 ), and Cl₂Ga(CH₂)₃NMe₂ ( 9 ). The reaction of 6 and of 8 or 9 with BrMg(CH₂)₅MgBr and BrMg(CH₂)₆MgBr, respectively, yields (CH₂)₅AlCH₂CHMeCH₂NMe₂ ( 7 ), (CH₂)₆Al(CH₂)₃NMe₂ ( 10 ), and (CH₂)₆Ga(CH₂)₃NMe₂ ( 11 ). MeAlCl₂, made by the redistribution reaction of AlCl₃ with Me₂AlCl, reacts with 2 equivalents of Li(CH₂)₃NMe₂ yielding MeAl[(CH₂)₃NMe₂]₂ ( 12 ) and with MeN[(CH₂)₃MgCl]₂ under formation of MeAl[(CH₂)₃]₂NMe ( 13 ). MeAlCl₂, MeGaCl₂, or GaCl₃ accordingly react with one equivalent of organolithium reagent to give the intramolecularly nitrogen stabilized organoaluminum and organogallium chlorides MeClAl(CH₂)₃NMe₂ ( 14 ), MeClGa(CH₂)₃NMe₂ ( 15 ), MeClGaC₆H₄‐2‐CH₂NMe₂ ( 16 ) as well as Cl₂GaC₆H₄‐2‐CHMeNMe₂ ( 17 ). The compounds were characterized by elemental analyses, mass spectroscopy, ¹H, ¹¹B, ¹³C and ²⁷Al NMR investigations. Single crystal X‐ray structure analyses of 1 , 2 , 4 , 5 and 17 reveal the monomeric molecular structures with intramolecular nitrogen coordination.     

Activation of surface hydroxyl groups by modification of H-terminated Si(111) surfaces

Chemical functionalization of semiconductor surfaces, particularly silicon oxide, has enabled many technologically important applications (e.g., sensing, photovoltaics, and catalysis). For such processes, hydroxyl groups terminating the oxide surface constitute the primary reaction sites. However, their reactivity is often poor, hindering technologically important processes, such as surface phosphonation requiring a lengthy postprocessing annealing step at 140 °C with poor control of the bonding geometry. Using a novel oxide-free surface featuring a well-defined nanopatterned OH coverage, we demonstrate that hydroxyl groups on oxide-free silicon are more reactive than on silicon oxide. On this model surface, we show that a perfectly ordered layer of monodentate phosphonic acid molecules is chemically grafted at room temperature, and explain why it remains completely stable in aqueous environments, in contrast to phosphonates grafted on silicon oxides. This fundamental understanding of chemical activity and surface stability suggests new directions to functionalize silicon for sensors, photovoltaic devices, and nanoelectronics.     

Direct Microfabrication of Topographical and Chemical Cues for the Guided Growth of Neural Cell Networks on Polyamidoamine Hydrogels

Cell patterning is an important tool for organizing cells in surfaces and to reproduce in a simple way the tissue hierarchy and complexity of pluri‐cellular life. The control of cell growth, proliferation and differentiation on solid surfaces is consequently important for prosthetics, biosensors, cell‐based arrays, stem cell therapy and cell‐based drug discovery concepts. We present a new electron beam lithography method for the direct and simultaneous fabrication of sub‐micron topographical and chemical patterns, on a biocompatible and biodegradable PAA hydrogel. The localized e‐beam modification of a hydrogel surface makes the pattern able to adsorb proteins in contrast with the anti‐fouling surface. By also exploiting the selective attachment, growth and differentiation of PC12 cells, we fabricated a neural network of single cells connected by neuritis extending along microchannels. E‐beam microlithography on PAA hydrogels opens up the opportunity of producing multifunctional microdevices incorporating complex topographies, allowing precise control of the growth and organization of individual cells.

     

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.     

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).     

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

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