Julia directions of meromorphic functions and their derivatives

We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to ￥ \infty then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is o(?{ | z | }) o(\sqrt{\mid z \mid}) or O(?{ | z | }) O(\sqrt{\mid z \mid}) on a path to ￥ \infty . Further we disprove a conjecture of Frank and Wang by means of a counterexample.     

Integrated optical components on atom chips

We report on the integration of small-scale optical components into silicon wafers for use in atom chips. We present an on-chip fibre-optic atom detection scheme that can probe clouds with small atom numbers. The fibres can also be used to generate microscopic dipole traps. We describe our most recent results with optical microcavities and show that a sufficiently high finesse can be achieved to enable single-atom detection on an atom chip. The key components have been fabricated by etching directly into the atom chip silicon substrate.     

Invariant subsets of scattered trees and the tree alternative property of Bonato and Tardif

A tree is scattered if it does not contain a subdivision of the complete binary tree as a subtree. We show that every scattered tree contains a vertex, an edge, or a set of at most two ends preserved by every embedding of T. This extends results of Halin, Polat and Sabidussi. Calling two trees equimorphic if each embeds in the other, we then prove that either every tree that is equimorphic to a scattered tree T is isomorphic to T, or there are infinitely many pairwise non-isomorphic trees which are equimorphic to T. This proves the tree alternative conjecture of Bonato and Tardif for scattered trees, and a conjecture of Tyomkyn for locally finite scattered trees.     

C1-continuous time integration based on cubic Hermite interpolation

We discuss a C¹-continuous time integration method based on piecewise cubic Hermite approximation. This method, denoted as p2-scheme, belongs to a class of one-step integration methods derived recently [1]. It exhibits a convergence rate of order four and shows properties similar to variational integrators, such as an excellent long-term energy preservation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bis(2-pyridylimino)isoindolato iron(II) and cobalt(II) complexes: structural chemistry and paramagnetic NMR spectroscopy

Condensation of phthalodinitrile and 2-amino-5,6,7,8-tetrahydroquinoline gave the bis(2-pyridylimino)isoindole protioligand 1 (thqbpiH) in high yield. Deprotonation of thqbpiH (1) using LDA in THF at -78 °C yields the corresponding lithium complex [Li(THF)(thqbpi)] (2) in which the lithium atom enforces almost planar arrangement of the tridentate ligand, with an additional molecule of THF coordinated to Li. Reaction of cobalt(II) chloride or iron(II) chloride with one equivalent of the lithium complex 2 in THF led to formation of the metal complexes [CoCl(THF)(thqbpi)] (3a) and [FeCl(THF)(thqbpi)] (3b). The paramagnetic susceptibility of 3a,b in solution was measured by the Evans method (3a: μ(eff) = 4.17 μ(B); 3b: μ(eff) = 5.57 μ(B)). Stirring a solution of 1 and cobalt(II) acetate tetrahydrate in methanol yielded the cobalt(II) complex 4 which was also accessible by treatment of 3a with one equivalent of silver or thallium acetate in DMSO. Whereas 3a,b were found to be mononuclear in the solid state, the acetate complex 4 was found to be dinuclear, the two metal centres being linked by an almost symmetrically bridging acetate. For all transition metal complexes paramagnetic (1)H as well as (13)C NMR spectra were recorded at variable temperatures. The complete assignment of the paramagnetic NMR spectra was achieved by computation of the spin densities within the complexes using DFT. The proton NMR spectra of 3a and 3b displayed dynamic behaviour. This was attributed to the exchange of coordinating solvent molecules by an associative mechanism which was analysed using lineshape analysis (ΔS(≠)= -154 ± 25 J mol(-1) K(-1) for 3a and ΔS(≠) = -168 ± 15 J mol(-1) K(-1) for 3b).     

Computational chemistry and molecular simulations of phosphoric acid

Quantum mechanics (QM) calculations, molecular dynamics (MD) simulations using the condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, and the atom‐centered density matrix propagation (ADMP) approach have been used to investigate properties of phosphoric acid (PA). QM using B3LYP/6‐31++G(d,p) density functional theory were used to calculate gas‐phase proton affinities and interaction energies of PA and its derivatives. Detailed single coordinate driving, followed by quadratic synchronous transit optimization was used to determine energy barriers for different proton transfer (PT) pathways. Determined energy barrier heights in ascending order are (unit: kJ/mol): H₃O⁺→H₃PO₄ (0); H₄P₂O₇→H₃PO₄ (2.61); H₃PO₄→H₂PO (5.31); H₄PO→H₃PO₄ (～7.33); H₃PO₄→H₄P₂O₇/H₃PO₄→H₃PO₄ (15.99); H₄P₂O₇→H₂O (28.61); H₃PO₄→H₂O (47.14). The COMPASS force field was used to study condensed‐phase properties of PA. Good agreement between experimental data and MD results including density, radial distribution functions, and self‐diffusion coefficient at different temperatures provides validation of the COMPASS force field for PA. Finally, preliminary ADMP studies on a cluster of three PA molecules shows that the ADMP approach can reasonably describe the PT and self‐dissociation processes in PA. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Finiteness obstructions and Euler characteristics of categories

We introduce notions of finiteness obstruction, Euler characteristic, L²-Euler characteristic, and Möbius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FPR) is a class in the projective class group K₀(RΓ); the functorial Euler characteristic and functorial L²-Euler characteristic are respectively its RΓ-rank and L²-rank. We also extend the second author's K-theoretic Möbius inversion from finite categories to quasi-finite categories. Our main example is the proper orbit category, for which these invariants are established notions in the geometry and topology of classifying spaces for proper group actions. Baez and Dolan's groupoid cardinality and Leinster's Euler characteristic are special cases of the L²-Euler characteristic. Some of Leinster's results on Möbius–Rota inversion are special cases of the K-theoretic Möbius inversion.     

Nanoscale laser-induced forward transfer through patterned Cr films

The resolution enhancement of laser-induced forward transfer (LIFT) is investigated through the pre-patterning of Cr on the donor substrate. 85 nm dots are first patterned on a microscope slide, and an 800 nm wavelength and 130 fs pulse laser with a beam waist of ～9 μm is used to transfer the Cr dots to an acceptor substrate. The threshold fluence is found to be ～0.15 the threshold fluence of a similar continuous film, which is thought to be due to the fact that no force is needed to tear away Cr from the film itself, unlike in a continuous film experiment. Since the volume of the material limits the transfer feature sizes instead of the laser parameters, as in a continuous film system, minimum transferable feature diameters are significantly lower compared to the continuous film case. Also, the transferred feature diameters are not dependent on the laser parameters, so the diameters are consistent across a wide range of fluences. The force per unit area generated by the laser at threshold fluence is estimated to be ～3 GPa, which is consistent with previous results in the literature. The simplified model that our pre-patterned Cr LIFT experiment represents would make it an ideal case for benchmarking molecular dynamics simulations of femtosecond laser ablation.     

Characterization of polymeric light emitting diodes by SIMS depth profiling analysis

SIMS depth profiling experiments have been used to elucidate the layered structure, the impurity distribution, and current induced changes in polymeric light emitting diodes (LEDs). In the first investigated system (ITO/PPV/Al), a poly-p-phenylene-vinylene (PPV) layer has been deposited onto an indium/tin oxide (ITO) glass support, and covered by an aluminium top electrode. A well defined aluminium oxide interlayer has been found in between the polymer and the Al overlayer. Furthermore, an enrichment of chlorine has been detected at both electrode-polymer interfaces, a residue from the polymer preparation process. This observation points to a chemical reaction between the electrodes and elimination products that are liberated during the thermal decomposition of the polymer precursor. In the second system, three different polymeric layers have been spin-coated onto an ITO substrate, i.e. a pure poly-methylphenylsilane (PMPS) layer, a second PMPS layer doped with an organic dye, and finally a polystyrene (PS) layer containing an oxadiazole derivative. By the addition of a bromine containing label into the first layer, it can be shown that the two PMPS layers have been diffusing into each other, whereas the PMPS and the PS regions have remained well separated. As found with the single layer devices, the formation of an interfacial oxide layer between the PS layer and the Al top electrode has been observed. Investigations of driven multilayer LEDs have provided evidence for drastic current-induced degradation effects.     

On the Kondo-effect in dilute alloys of iron and nanoscaled copper

Electric resistivity measurements in nanocrystalline Cu-samples alloyed with Fe in the concentration regime of C _Fe ～ 0.17 - 0.37 at - % and nanocrystallite sizes of 6 nm to 24 nm show a Kondo minimum at ～ 30 K. Resistivity does not saturate at low temperature but passes over a maximum at ～ 10 K, which may be due to a spin glass transition. An applied magnetic field of 0.5T shifts the minimum to lower T, but does not destroy the maximum. The curves measured are rather spiky in contrast to curves obtained from polycrystalline samples which is possibly due to non-selfaveraging effects. Further indication for such effects is a non-monotonuous dependence of the resistivity minimum as a function of average crystallite size.