Smoothness equivalence properties of univariate subdivision schemes and their projection analogues

We study the following modification of a linear subdivision scheme S: let M be a surface embedded in Euclidean space, and P a smooth projection mapping onto M. Then the P-projection analogue of S is defined as T := P ◦ S. As it turns out, the smoothness of the scheme T is always at least as high as the smoothness of the underlying scheme S or the smoothness of P minus 1, whichever is lower. To prove this we use the method of proximity as introduced by Wallner et al. (Constr Approx 24(3):289–318, 2006; Comput Aided Geom Design 22(7):593–622, 2005). While smoothness equivalence results are already available for interpolatory schemes S, this is the first result that confirms smoothness equivalence properties of arbitrary order for general non-interpolatory schemes.     

Influence of a Large-Eddy-Breakup-Device on the Turbulent Interface of Boundary Layers

The effects of implementing a large-eddy break-up device (LEBU) in a turbulent boundary layer on the interaction with the boundary layer is investigated with particular emphasis on the turbulent/non-turbulent interface (TNTI). The simulation data is taken from a recent well-resolved large eddy simulation (Chin et al. Flow Turb. Combust. 98, 445–460 2017), where the LEBU was implemented at a wall-normal distance of 0.8 δ (local boundary layer thickness) from the wall. A comparison of the TNTI statistics is performed between a zero-pressure-gradient boundary layer with and without the LEBU. The LEBU is found to delay the growth of the turbulent boundary layer and also attenuates the fluctuations of the TNTI. The LEBU appears to alter the structure size at the interface, resulting in a narrower and shorter dominant structure (in an average sense). Further analysis beneath the TNTI using two-point correlations shows that the LEBU affects the turbulent structures in excess of 100 δ downstream of the LEBU.     

Generalized Newtonian fluids in moving domains

In this paper we prove the existence of weak solutions for the equations describing the unsteady motion of an incompressible, viscous and homogeneous generalized Newtonian fluid in a non-cylindrical domain ${?}_{t\in I}\{t\}\times \mathrm{\Omega }(t)$.     

Q-Band Loop-Gap Resonator for EPR Applications with Broadband-Shaped Pulses

Recently, Q-band-pulsed electron paramagnetic resonance spectroscopy has strongly advanced its performance by the introduction of high-power microwave amplifiers and the use of shaped pulses. For such applications, the resonator Q value has to be low enough to achieve sufficient bandwidth for short microwave pulses and to reduce the ring-down time after the pulses. However, a low Q value reduces the detection sensitivity as well as the conversion efficiency of the microwave input power to the magnetic field strength at the sample position. Therefore, the resonator Q value has to be optimized for a given microwave input power and specific application. We designed a three-loop/two-gap resonator using CST Microwave Studio for such applications, and tested its performance in comparison with a standard Bruker D2 Q-band microwave resonator by accomplishing broadband SIFTER experiments on a nitroxide model compound.     

Static versus dynamic DEA in electricity regulation: the case of US transmission system operators

In this paper a dynamic DEA-model (data envelopment analysis) is developed that takes up Nemoto and Goto’s (Econ Lett 64(1):51–56, 1999) concept of quasi-fixed inputs but can dispense with price-information as it solely deals with technical efficiencies that are derived in an additive-model type of setting. This model is applied to the data of 50 of the largest US electric transmission system operators in the period 2000–2006 in order to show that the static DEA-models that are usually employed by electricity regulators can lead to wrong conclusions about the enterprises’ efficiency since they ignore the short-run fixity of essential inputs like transmission lines.     

Fine-tuning of relative metal-metal distances within highly ordered chiral 2D nanopatterns

The two-dimensional nanopatterning of a series of neutral alkoxy/alkyl-functionalised bis(salicylaldehydato)/bis(aldiminato)copper(II) and -palladium(II) complexes at a liquid/solid (highly oriented pyrolytic graphite, HOPG) interface has been studied by scanning tunnelling microscopy (STM). The relative metal-metal distances were tuned stepwise in two dimensions by ligand design. Exchange of the carbonyl O-atom for NH or N-alkyl units effects different intermolecular interactions such as weak hydrogen bonds and steric effects that determine, together with the van der Waals forces between the alkyl chains, the relative arrangements of the complexes. Further variation of the length and position of the alkoxy side chains as well as the exchange of CuII for PdII affords an absolute fine-tuning of the surface structures. Highly resolved STM images of the resultant highly ordered adlayers allow us to establish detailed models of the molecular 2D arrays and to classify them into three basic chiral pattern types. Homochirality within the individual domains is induced by the highly regular deposition of the prochiral complexes from the same enantiotopic face. In the case of the C12 O-substituted bis(salicylaldiminato) (NH) Cu(II) complex Cu5, a secondary structure occurs as a racemic mixture of two chiral surface species deposited in a distinct alternating order.     

Decacyclene as complexation manifold: synthesis, structure and properties of its Fe2 and Fe4 slipped triple-decker complexes

Reaction of [(eta(5)-Me4EtC5)Fe(II)Cl(tmeda)] (tmeda = N,N,N'N'-tetramethylethylenediamine) with a polyanion solution of decacyclene (1) results in the formation of the triple-deckers [{(eta(5)-Me4EtC5)Fe}2-mu2-(eta(6):eta(6)-decacyclene)] (3) and [{(eta(5)-Me4EtC5)Fe}4-mu4-(eta(6):eta(6):eta(6):eta(6)-decacyclene)] (4). Metal complexation in 3 and 4 occurs on opposite faces of the pi perimeter in an alternating mode. The decacyclene ring adopts a gently twisted molecular propeller geometry with twofold crystallographic symmetry (C2). Complex 4 crystallizes in the chiral space group C222(1); the investigated crystal only contains decacyclene rings with M chirality. The handedness can be assigned unambiguously to the presence of the iron atoms. Cyclovoltammetric studies revealed quasireversible behavior of the redox events and a strong interaction of the Fe atoms in 3 and 4, exemplified by potential differences deltaE of 660 and 770(780) mV between the first and the second individual oxidation processes. This corresponds to a high degree of metal-metal interaction for 3 and 4. The successful syntheses of 3 and 4 together with earlier results from our laboratory proves that all five- and six-membered pi subunit sets of 1 are prone to metal complexation. A clear site preference in 1 towards the complexation of [Cp(R)]iron, -cobalt, and -nickel fragments exists.     

Minimum Stiffness Criteria for Edge Reinforcements of Elastically Clamped Plates

In many structural situations, e.g. in aerospace engineering, composite plates with edge reinforcements are used, for example as stiffeners of a fuselage section of an airplane. Based on an explicit analysis of the buckling behavior of the laminate plate, a minimum stiffness criterion is presented in this contribution. A transformation of the governing equations into a dimensionless system is used, that proved to be very advantageous. Besides a minimum stiffness criterion that can be used for generation of minimum stiffness diagrams, an absolute minimum stiffness is found that enables the reinforcement to act like a simple support for arbitrarily slender plates. The relevance of the criteria for stiffener design is discussed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation order of interpolatory nonlinear subdivision schemes

Linear interpolatory subdivision schemes of C^r smoothness have approximation order at least r+1. The present paper extends this result to nonlinear univariate schemes which are in proximity with linear schemes in a certain specific sense. The results apply to nonlinear subdivision schemes in Lie groups and in surfaces which are obtained from linear subdivision schemes. We indicate how to extend the results to the multivariate case.