On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

The dose dependence of cyclobutane dimer induction and repair in UVB-irradiated human keratinocytes

UVB and UVA components of the solar spectrum or from artificial UV-sources might be important etiological factors for the induction and development of skin cancer. In particular, deficiencies in the capacity to repair UV-induced DNA-lesions have been linked to this phenomenon. However, until now only limited data are available on the biological and physical parameters governing repair capacity. We have, therefore, developed a flowcytometric assay using fluorescence-labeled monoclonal antibodies to study the dose-dependence of induction and repair of UVB-induced cyclobutane pyrimidine dimers in a spontaneously immortalized keratinocytic cell line (HaCaT). Our results show that the kinetics of recognition and incision of UVB-induced DNA lesions slows down by a factor of about 3 in a dose range of 100-800 J m-2. Furthermore, a thorough analysis of repair kinetics indicates that this reduction in repair capacity might not be dependent on saturation of enzymatic repair capacity (Michaelis-Menten) but may be caused by a UV-induced impairment of enzymes involved in DNA repair. Because this effect is evident in vitro at doses comparable to the minimal erythemal dose in vivo, our results might have significant impact on risk assessment for UV-induced carcinogenesis.     

Azadepsipeptides: synthesis and evaluation of a novel class of peptidomimetics

A general route to azadepsipeptides, a new class of pseudopeptides, has been established. The methodology was applied to the synthesis of a bis-aza analogue of the antiparasitic cyclooctadepsipeptide PF1022A. Comparison of the X-ray crystal structures of natural PF1022A (8) and the chimeric aza analogue 9 revealed that the introduction of nitrogen in the backbone of PF1022A results in almost complete conservation of the 3D structure with only minor deviations at the new nitrogen positions.     

AES-depth-profiling of thin annealed Pt-films on Si(100)

Thin PtSi films can be grown by evaporating Pt on Si(100) at RT and subsequent annealing of the system at 600–700 K. Contaminants like oxygen are known to have a strong influence on this reaction. In the present study we concentrate on the effect of oxygen partial pressure during the annealing on the silicide growth process. Under proper vacuum conditions annealing at 500 K leads to a homogeneous Pt₂Si film which reacts around 600 K completely to PtSi. A substantial oxygen partial pressure ( 0.1 mbar) in contrast results in an incomplete reaction in the same temperature range: unreacted platinum remains at the surface separated from the silicide by an oxygen enriched layer.Presented at the Seminar on Secondary Electrons in Electron Spectroscopy, Microscopy, and Microanalysis, Chlum (The Czech Republic), 21–24 September, 1993.This work was supported by Deutsche Forschungsgemeinschaft (DFG) through Sonderforschungsbereich 292.We thank Dr. W. Platz (Deutsche Aerospace AG, Ottobrunn) for providing us with Pt evaporated Si-wafers and Th. Hierl (Lehrstuhl für Angewandte Physik, University of Erlangen-Nürnberg), who performed the RBS measurements for AES calibration.     

Schwingungsspektren der Clusterverbindungen (M6X)X · 8 H2O,M = Nb,Ta; Xi = CI,Br; Xa = CI,Br, I

Vibrational Spectra of the Cluster Compounds (M₆X₁₂ⁱ) · 8H₂O, M = Nb, Ta; Xⁱ = Cl, Br; X^a = Cl, Br, I IR and, for the first time, Raman spectra at 80 K of the cluster compounds (M₆X)X · 8H₂O; M = Nb, Ta; Xⁱ = Cl, Br; X^a = Cl, Br, I, have been recorded, characterized by typical frequencies of the (M₆X) unit, which are only slightly influenced by the terminal X^a ligands. The most intense line with the depolarisation ≈? 0.2 in all Raman spectra is caused by inphase movement of all atoms and assigned to the symmetric metal-metal vibration v₁, observed for the clusters (Nb₆Cl) at 233–234, for (Nb₆Br) at 186–187, for (Ta₆Cl) at 199–203, and for (Ta₆Br) at 176–179 cm^?1. The IR spectra exhibit in the same series intense bands at 233, 204, 207, and 179 cm^?1, assigned to the antisymmetric metal-metal vibration. The metal-metal frequencies are significantly higher than discussed before. The tantalum clusters show on excitation with the krypton line 647.1 nm in the region of a d–d transition at 645 nm a resonance Raman effect with series of overtones and combination bands. In case of (Ta₆Br) another polarisized band is observed at 229 cm^?1 and assigned to the Ta? Brⁱ vibration v₂. From the progressions of v₁ and v₂ anharmonicity constants of about ?3 cm^?1 are calculated indicating a strong distortion of the potential curves.     

Practical and quality-control aspects of multi-element analysis with quadrupole ICP–MS with special attention to urine and whole blood

Two screening methods were developed for rapid analysis of a great number of urine and blood samples within the framework of an exposure check of the population after a firework explosion. A total of 56 elements was measured including major elements. Sample preparation consisted of simple dilution. Extensive quality controls were applied including element addition and the use of certified reference materials. Relevant results at levels similar to those found in the literature were obtained for Co, Ni, Cu, Zn, Sr, Cd, Sn, Sb, Ba, Tl, and Pb in urine and for the same elements except Ni, Sn, Sb, and Ba in blood. However, quadrupole ICP–MS has limitations, mainly related to spectral interferences, for the analysis of urine and blood, and these cause higher detection limits. The general aspects discussed in the paper give it wider applicability than just for analysis of blood and urine—it can for example be used in environmental analysis.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.     

Insight into Oxide‐Bridged Heterobimetallic Al/Zr Olefin Polymerization Catalysts

Reaction of (TBBP)AlMe ? THF with [Cp*₂Zr(Me)OH] gave [(TBBP)Al(THF)?O?Zr(Me)Cp*₂] (TBBP=3,3’,5,5’‐tetra‐tBu‐2,2'‐biphenolato). Reaction of [DIPPnacnacAl(Me)?O?Zr(Me)Cp₂] with [PhMe₂NH]⁺[B(C₆F₅)₄]^? gave a cationic Al/Zr complex that could be structurally characterized as its THF adduct [(DIPPnacnac)Al(Me)?O?Zr(THF)Cp₂]⁺[B(C₆F₅)₄]^? (DIPPnacnac=HC[(Me)C=N(2,6‐iPr₂?C₆H₃)]₂). The first complex polymerizes ethene in the presence of an alkylaluminum scavenger but in the absence of methylalumoxane (MAO). The adduct cation is inactive under these conditions. Theoretical calculations show very high energy barriers (ΔG=40–47 kcal mol^?1) for ethene insertion with a bridged AlOZr catalyst. This is due to an unfavorable six‐membered‐ring transition state, in which the methyl group bridges the metal and ethene with an obtuse metal‐Me‐C angle that prevents synchronized bond‐breaking and making. A more‐likely pathway is dissociation of the Al‐O‐Zr complex into an aluminate and the active polymerization catalyst [Cp*₂ZrMe]⁺.