Slow flow between concentric cones

This paper considers the low-Reynolds-number flow of an incompressiblefluid contained in the gap between two coaxial cones with coincidentapices and bounded by a spherical lid. The two cones and thelid are allowed to rotate independently about their common axis,generating a swirling motion. The swirl induces a secondary,meridional circulation through inertial effects. For specificconfigurations complex eigenmodes representing an infinite sequenceof eddies, analogous to those found in two-dimensional cornerflows and some three-dimensional geometries, form a componentof this secondary circulation. When the cones rotate these eigenmodes,arising from the geometry, compete with the forced modes todetermine the flow near the apex. This paper studies the relative dominance of these two effectsand maps out regions of parameter space, with attention to howshear and overall rotation can destroy the infinite sequenceof eddies that may be present when only the lid is rotated.A qualitative picture of the number of eddies visible in themeridional circulation is obtained as a function of the rotationrates of cones and lid, for various choices of angles. The resultsare discussed in the context of previous work, including theirsignificance for applications to the mixing of viscous fluidsin this geometry.     

On angles and distances between subspaces

The angles and distances between two given subspaces of are investigated on the basis of a joint decomposition of the corresponding orthogonal projectors. Several new results are established, with the particular attention paid to the notions of inclinedness and minimal angle. To demonstrate the usefulness of the approach utilized, some results known to be valid in Hilbert space are reestablished in , either in generalized form or with considerably shorter proofs than in the original sources.     

Comparing reaction orders of anthracite chars with bituminous coal chars at high temperature oxidation conditions

The influence of concentration of oxygen on the oxidation rates of 5 anthracite chars is investigated at gas temperatures ranging from 1223 K to 1673 K. Reaction orders and kinetic parameters are determined with a multivariable optimization method in which modeled burnout profiles are fitted to experimental burnout profiles from a 4 m isothermal plug flow reactor operating at industrially realistic heating rates, i.e., 10⁴–10⁵ K/s. The determined reaction orders are compared to reaction orders of 10 bituminous coal chars investigated at similar conditions in a previous study. The results show that the optimized reaction order of the anthracite chars is zero, while the reaction order of the bituminous coal char is one. The difference in the reaction orders cannot be explained by using the two semi-global oxidation reactions: C(O) + O₂ → CO/CO₂ and C(O) → CO. However, by also considering 2C(O) → CO₂ + C as a possible reaction step, the reaction order difference between the anthracite chars and the bituminous coal chars can be explained. In addition, a first attempt to apply the same multivariable optimization method to determine the reaction order for a biomass char is presented.     

Modern Trends in Organic Light-Emitting Devices (OLEDs)

Summary. Synthesis of crosslinkable small and large organic molecules having OLED properties will be presented. Three strategies for the construction of multilayer devices will be described. In the first case small, well-defined OLED-molecules are functionalized with oxetanes as crosslinker. The second case deals with polymers having OLED active units in the main chain and pendant crosslinkers and finally it was shown that styrene polymers with pendant OLED functions and crosslinkers can be applied for the construction of such multilayer and multicolour devices.     

On a subspace metric based on matrix rank

The metric between subspaces M,N⊆C_n,1, defined by δ(M,N)=rk(P_M-P_N), where rk(·) denotes rank of a matrix argument and P_M and P_N are the orthogonal projectors onto the subspaces M and N, respectively, is investigated. Such a metric takes integer values only and is not induced by any vector norm. By exploiting partitioned representations of the projectors, several features of the metric δ(M,N) are identified. It turns out that the metric enjoys several properties possessed also by other measures used to characterize subspaces, such as distance (also called gap), Frobenius distance, direct distance, angle, or minimal angle.     

Kreisverwandtschaften in der hyperbolischen Geometrie

Ohne Zusammenfassung     

The effect of molecular topology on π-molecular-orbital energies

Three models for constructing topologically related pairs of molecular isomers are discussed at length. The topological-effect-on-molecular-orbitals (TEMO) theorem is presented in detail and illustrated with experimental data; this theorem demonstrates that molecular topology imposes constraints in the form of general interlacing rules on the MO energy patterns of topologically related molecules. Further, non-empirical SCF MO calculations have been performed for topologically related o- and p-divinylbenzenes, difluorobenzenes, benzoquinones, and benzoquinodimethanes in standard and optimized geometries using various basis sets. In most cases, the SCF -MO eigenvalue patterns of topological related isomers are in complete agreement with the TEMO theorem, thus demonstrating the dominant influence of topology on the -MO energies. A modified version of the generalized perturbationalvariational Rayleigh-Ritz (PV-RR) procedure is described which is used to study the occasional observed deviations from the TEMO predictions; this procedure had been combined with the concept of critical (i.e. the threshold value of the perturbation parameter at which the TEMO order of a pair of MO eigenvalues starts to invert), thus enabling us to analyze in quantitative detail the physical factors which compete with molecular topology in conditioning the ab initio MO energy patterns.Part 10 of the TEMO series; for Part 9, see Ref. [9b].Dedicated to Prof. Dr. Günther Wilke on the occasion of his 60th birthday