A variational view at the time-dependent minimal surface equation

We present a global variational approach to the L ²-gradient flow of the area functional of cartesian surfaces through the study of the so-called weighted energy-dissipation (WED) functional. In particular, we prove a relaxation result which allows us to show that minimizers of the WED converge in a quantitatively prescribed way to gradient-flow trajectories of the relaxed area functional. The result is then extended to general parabolic quasilinear equations arising as gradient flows of convex functionals with linear growth.     

A New Minimum Principle for Lagrangian Mechanics

We present a novel variational view at Lagrangian mechanics based on the minimization of weighted inertia-energy functionals on trajectories. In particular, we introduce a family of parameter-dependent global-in-time minimization problems whose respective minimizers converge to solutions of the system of Lagrange’s equations. The interest in this approach is that of reformulating Lagrangian dynamics as a (class of) minimization problem(s) plus a limiting procedure. The theory may be extended in order to include dissipative effects thus providing a unified framework for both dissipative and nondissipative situations. In particular, it allows for a rigorous connection between these two regimes by means of Γ-convergence. Moreover, the variational principle may serve as a selection criterion in case of nonuniqueness of solutions. Finally, this variational approach can be localized on a finite time-horizon resulting in some sharper convergence statements and can be combined with time-discretization.     

Properties of polythiophene and related conjugated polymers: a density-functional study

Using a parameter-free, density-functional method that has been developed explicitly for the theoretical treatment of infinite, periodic, isolated, helical polymers we study various polymers related to polythiophene. In particular we discuss how the electronic properties of polythiophene are changed when replacing some of the H atoms by CH3 group, by incorporating vinylene bridges into the backbone, or when replacing some or all the CH units of the backbone by N atoms. We observe the weakest effects for the methyl-substitution and the strongest for the N-incorporation. The latter leads to an overall downward shift of all bands, but in contrast to the case for polyacetylene, the unrelaxed compound with N atoms does not have N lone-pair orbitals as the highest occupied ones. Instead these occur at somewhat deeper energies. When comparing the aromatic and quinoid forms we found for the pure compound as well as for the methyl-containing one that the gap closes when passing from the one to the other form which was not found for any of the other materials of the present study. Moreover, the energy of the HOMO was found to depend stronger on the bond-length alternation than the energy of the LUMO, ultimately giving that polarons will induce two asymmetrically placed gap states with the energetically lower one appearing deeper in the gap than the other one.     

Über das Verhalten unterstöchiometrischer Übergangsmetallcarbide als Katalysatoren in Dehydrierungsprozessen

Zusammenfassung Messungen an unterstöchiometrischen Übergangsmetallcarbiden (Gruppe IV, V) im Hinblick auf deren Eignung als Katalysatoren für den Dehydrierungsprozeß Aethylbenzol Styrol zeigen eine Abhängigkeit der Dehydrierungsrate von der Konzentration des Kohlenstoffs im Metallgitter und von der Struktur der Carbidphase. Einige technische Anwendungsmöglichkeiten werden angeführt.

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The catalytic behaviour of substoichiometric transition metal carbides on dehydrogenation processes

The catalytic activities of substoichiometric carbides of transition metals (group IV, V) on the dehydrogenation process of ethylbenzene to styrene are described. The results show the dependence of the dehydrogenation rate versus the concentration of carbon in the metal lattice and of the structure of the used carbides. Some technical applications are mentioned.

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Mit 4 Abbildungen

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Herrn Prof. Dr.H. Nowotny gewidmet.     

(C2N2H10)2Mg(HP2O7)2·2H2O synthesis and crystal structure

(C₂N₂H₁₀)₂Mg(HP₂O₇)₂·2H₂O, is a new inorganic organic hybrid structure. It has been synthetized using wet chemistry. Its crystal structure consists of cis- and trans-edge sharing [MgO₄(H₂O)₂] octahedra resulting in chains, which are linked via [HP₂O₇] units to form [Mg(HP₂O₇)₂(H₂O)₂]⁴⁻ layers. The Mg²⁺ cations and the ethylendiammonium cations are located on centers of inversion. The ethylendiammonium cations are alternately located in the interlayer space. The cohesion of the crystal is well ensured by coulombic interactions between anions and cations and by several hydrogen bonds. The diphosphate anion shows an eclipsed conformation.     

Crystal structures of a pair of diastereomeric 3-(N,N-dimethylammonium)-1,1-diphenyl-1-butanol O,O′-di-p-toloyl hydrogen tartrates

The crystal structures of a pair of diastereomeric salts of (–)-(2R, 3R)-O, O-di-p-toloyl tartaric acid and (–)- and ( + )-3-N,N-dimethylamino-1,1-diphenyl-1-butanol have been determined. Crystal data: 3: (-)-(R)-C₁₈HC₂₄NO⁺(-)-(2R,3R)-C₂₀H₁₇O^- ₈ orthorhombic, P2₁2₁2₁, a = 7.873(2), b = 15.343(3), c = 28.76(1) Å, V = 3474(2) ų, Z = 4, and D _calc = 1.254 g cm^–3. 4: (+)- (S)-C₁₈H₂₄NO⁺, (-)-(2R,3R)-C₂₀H₁₇O^- ₈orthorhombic, P2₁2₁2₁, a = 7.504(1), b = 17.215(2), c = 26.490(4) Å, V = 3422.0(8) ų,Z = 4, and D _calc = 1.273 g cm^–3. The geometries and the conformational energies of the solid state conformations of the cations have been compared with global and local energy minimum conformations determined by molecular mechanics calculations. In the solid state, one conformation with and one without an intramolecular hydrogen bond are observed. The calculated global energy minimum conformation in aqueous solution contains the intramolecular hydrogen bond.     

Crystal structures of a pair of diastereomeric 3-(N,N-dimethylammonium)-1,1-diphenyl-1-butanol hydrogen tartrates

The crystal structures of a pair of diastereomeric salts of (2R, 3R)- (+)-tartaric acid and (–)-and (+)-3-N,N-dimethylamino-1,1-diphenyl-1-butanol have been determined. Crystal data: 1: (R)-(–)-C₁₈H₂₄NO⁺, , C2, a = 38.198(7), b = 5.841(2), c = 9.993(2)Å, = 102.63(1)°, V = 2175.6(1) ų, Z = 4, D _calc = 1.281 g cm^–3. 2: (S)-(+)-C₁₈H₂₄NO⁺, P2₁2₁2₁, a = 6.037(2), b = 8.5947(8), c = 39.74(1)Å, V = 2062.0(9) ų, Z = 4, D _calc = 1.351 g cm^–3. The conformations of the 3-(N,N-dimethylammonium)-1,1-diphenyl-1-butanol cations in the two salts are almost mirror images of each other, but the cation in 2 has an intramolecular hydrogen bond. The hydrogen tartrate ions adopt an extended conformation. The hydrogen bonding networks in the two salts are very different. The absolute configuration of (–)-3-(N,N-dimethylamino)-1,1-diphenyl-1-butanol (1) was established as R.     

Full-field supercritical angle fluorescence microscopy for live cell imaging

We introduce a full-field fluorescence imaging technique with axial confinement of about 100 nm at the sample/substrate interface. Contrary to standard surface imaging techniques, this confinement is obtained through emission filtering. This technique is based on supercritical emission selectivity. It can be implemented on any epifluorescence microscope with a commercial high numerical aperture objective and offers a real-time surface imaging capability. This technique is of particular interest for live cell membrane and adhesion studies. Using human embryonic kidney cells, we show that one can observe simultaneously the surface and in-depth cell phenomena.     

Weighted energy-dissipation functionals for doubly nonlinear evolution

This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.     

The disordered molecular structure of (3aRS,7aRS)‐1,3‐dinitrosooctahydro‐1H‐benzimidazole

The title compound, C₇H₁₂N₄O₂, was obtained by nitrosation of the aminal cage (2R,7R,11S,16S)‐1,8,10,17‐tetraazapentacyclo[8.8.1.1^8,17.0^2,7.0^11,16]icosane. The crystal structure is a racemic mixture of RR and SS enantiomers. The asymmetric unit contains two crystallographically independent half‐molecules, one having two partially occupied conformers with refined occupancy factors of 0.747 (3) and 0.253 (3). The molecules sit across twofold axes. The unique molecules each form chains parallel to [001], with molecules connected by intermolecular C—H...O hydrogen bonds. The bonding between adjacent chains is weak. The analysis of eight different crystals confirmed the presence of disordered and nondisordered molecules in the same structure as a regular feature.