A convergent adaptive finite element method for an optimal design problem

The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It eventually leads to a degenerate convex minimisation problem. The numerical analysis is therefore delicate for possibly multiple primal variables u but unique derivatives σ : = DW(D u). Even fine a posteriori error estimates still suffer from the reliability-efficiency gap. However, it motivates a simple edge-based adaptive mesh-refining algorithm (AFEM) that is not a priori guaranteed to refine everywhere. Its convergence proof is therefore based on energy estimates and some refined convexity control. Numerical experiments illustrate even nearly optimal convergence rates of the proposed AFEM. Supported by the DFG Research Center MATHEON “Mathematics for key technologies” in Berlin.     

IDENTIFICATION OF MEMBRANE PROTEINS IMAGED BY ATOMIC FORCE MICROSCOPY USING A TEMPLATE MATCHING ALGORITHM

The atomic force microscope allows to image biological samples in their native environment. But the identification and the topography of individual randomly distributed membrane proteins is still a challenge. We used membranes of isolated vacuoles of barley mesophyll cells. Images at low resolution indicate that vacuoles spontaneously attach, rupture and finally adsorb completely as planar membrane to mica. Height profiles indicate that the membrane at the peripheral boundary exposes the extravacuolar surface to the scanning tip. At molecular resolution a template matching correlation algorithm was used to identify the most abundant membrane protein, the vacuolar H⁺-ATPase by the characteristic extravacuolar head of the transport molecule. The data indicate the possibility to analyse single randomly distributed membrane proteins in their native environment with the knowledge of a suitable template.     

Synthesis of the selective antimuscarinic agent 4-{[cyclohexylhydroxy(2-methoxyphenyl)silyl]-methyl}-1,1-dimethylpiperazinium methyl sulfate (o-methoxy-sila-hexocyclium methyl sulfate)

The synthesis of the potent and highly selective silicon-containing antimuscarinic agent o-methoxysila-hexocyclium methyl sulfate and its corresponding tertiary amine (isolated as the dihydrochloride) is described. The quarternary compound is an o-methoxy derivative of sila-hexocyclium methyl sulfate, which represents one of the tools currently used in experimental pharmacology for the subclassification of muscarinic receptors. The o-methoxy derivative, the pharmacological profile of which differs substantially from that of the nonmethoxy compound, is also recommended as a tool for the investigation of muscarinic receptor heterogeneity.     

Photoinduced Luminescence Blinking and Bleaching in Individual Single‐Walled Carbon Nanotubes

The temporal evolution of photoluminescence in individual single‐walled carbon nanotubes (SWNT) under strong laser irradiation is studied and pronounced blinking and bleaching is observed, caused by photoinduced oxidation that subsequently quenches mobile excitons. The nanotubes are isolated with sodium cholate and spun onto either a glass or mica surface. Their bleaching behavior is investigated for variable laser intensities in air and argon atmosphere. The decay rate for luminescence bleaching generally increases with higher laser intensity, however saturating on mica substrates, which is attributed to limited availability of oxygen in the vicinity of the nanotubes. Step‐like events in the luminescence time traces corresponding to single oxidation events are analyzed regarding relative step height and suggest an exciton diffusion range of about 105 nm.     

Precipitates originating from tungsten crucible parts in AlN bulk crystals grown by the PVT method

In order to evaluate the possible involvement of crucible materials in the growth of AlN bulk crystals grown by physical vapor transport, we applied growth conditions with a high vertical thermal gradient and hence high supersaturation of aluminum vapor. Under these conditions, precipitates formed causing diffuse grayish substructures at the initial growth interface and in the crystal body, decorating dislocations. Electron microscopy studies revealed that the precipitates are elongated, single‐phase particles with sizes of 50–500 nm of commensurate structure, oriented along the <110> direction. Chemical analysis of the precipitates showed tungsten as well as carbon and oxygen. The lattice parameters of the precipitates are in close agreement to hexagonal tungsten hemicarbide (W₂C). The possible transport from the tungsten parts and its conversion into tungsten hemicarbide precipitates is discussed. We thus conclude that the W₂C precipitates may contribute to the decoration of dislocations, even in growth with moderate thermal gradients.     

Cybotactic nematic phases of photoisomerisable hockey-stick liquid crystals

New five-ring hockey-stick liquid crystalline materials with 4-bromoresorcinol as the central core unit and an azobenzene-based side arm were synthesised and their mesophase behaviour was investigated by polarising optical microscopy, differential scanning calorimetry, X-ray diffraction and under a triangular wave electric field. Additional structural modification was done by introducing a lateral fluorine atom in the terminal ring of one of the side arms. It is found that regardless of the alkyl chain length or the lateral fluorine substitution, all of the prepared materials are liquid crystalline exhibiting nematic phases composed of cybotactic clusters of the SmC-type (N_CybC) in addition to a monotropic SmC phase for the longest homologue.     

Non-symmetric ether-linked liquid crystalline dimers with a highly polar end group

A new class of non-symmetric dimeric compounds derived from 4-cyano-4′-hydroxybiphenyl in which two rigid parts are connected via flexible spacers have been designed and synthesised. These materials possess trialkoxy chains attached at one end of the molecule, while the other end consists of a biphenyl moiety terminated with the highly polar cyano group. The molecular structures of these dimers have been confirmed by elemental analysis and spectroscopic data and their phase behaviour has been characterised by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). Almost all of the synthesised materials exhibit liquid crystalline properties depending on the number of carbon atoms in the terminal chains, where all short chains derivatives form nematic phases and depending on the length of the internal spacer long terminal chains homologues display crystalline or unidentified smectic phase.