Optical nanofibers and spectroscopy

We review our recent progress in the production and characterization of tapered optical fibers with a sub-wavelength diameter waist. Such fibers exhibit a pronounced evanescent field and are therefore a useful tool for highly sensitive evanescent wave spectroscopy of adsorbates on the fiber waist or of the medium surrounding. We use a carefully designed flame pulling process that allows us to realize preset fiber diameter profiles. In order to determine the waist diameter and to verify the fiber profile, we employ scanning electron microscope measurements and a novel accurate in situ optical method based on harmonic generation. We use our fibers for linear and nonlinear absorption and fluorescence spectroscopy of surface-adsorbed organic molecules and investigate their agglomeration dynamics. Furthermore, we apply our spectroscopic method to quantum dots on the surface of the fiber waist and to cesium vapor surrounding the fiber. Finally, toward dispersive measurements, we present our first results on building and testing a single-fiber bimodal interferometer.     

Existence of weak solutions for the incompressible Euler equations

Using a recent result of C. De Lellis and L. Székelyhidi Jr. (2010) [2] we show that, in the case of periodic boundary conditions and for arbitrary space dimension d?2, there exist infinitely many global weak solutions to the incompressible Euler equations with initial data v₀, where v₀ may be any solenoidal L²-vectorfield. In addition, the energy of these solutions is bounded in time.     

On the Extension of Onsager’s Conjecture for General Conservation Laws

Journal of Nonlinear Science - The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this...     

Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper, DiPerna and Majda (Commun Math Phys 108(4):667–689, 1987) introduced the notion of a measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.     

Substituted Bisphosphanylamines as Ligands in Gold(I) Chemistry – Synthesis and Structures

Dimethyl 5‐aminoisophthalate, which is a building block of amino‐substituted tetralactam macrocycles, was used as ligand in gold(I) chemistry to form model complexes for macrocyclic gold compounds. Reaction of dimethyl 5‐aminoisophthalate with chlorodiphenylphosphine gave the diphosphine compound dimethyl 5‐[N,N‐bis(diphenylphosphanyl)amino]isophthalate (dmbpaip). This compound can further be reacted with [AuCl(tht)] (tht = tetrahydrothiophene) to give the dinuclear complex [Au₂Cl₂(dmbpaip)]. In contrast, treatment of dmbpaip with [Au(tht)₂]ClO₄ resulted in the ionic compound [Au₂(dmbpaip)₂](ClO₄)₂ in which the cation forms an eight‐membered Au₂P₄N₂ heterocycle. In both gold(I) compounds Au···Au interactions are observed. All new compounds were characterized by single‐crystal X‐ray diffraction.     

A remark on the constructibility of real root representations of quivers using universal extension functors

In this paper we consider the following question: Is it possible to construct all real root representations of a given quiver Q using universal extension functors, starting with a real Schur representation? We give a concrete example answering this question negatively.     

Lyapunov exponents from quantum dynamics

We extract classical Lyapunov exponents from the time dependence of quantum mechanical expectation values. Classical chaos is revealed as a quantum transient with a liftetime ～? ln ?. Our strategy is shown to work for the example of a periodically kicked top.     

Dynamical scaling law for jet tomography

Medium modifications of parton fragmentation provide a novel tomographic tool for the study of the hot and dense matter created in ultrarelativistic nucleus-nucleus collisions. Their quantitative analysis, however, is complicated by the strong dynamical expansion of the collision region. Here we establish for the multiple scattering induced gluon radiation spectrum a scaling law which relates medium effects in a collision of arbitrary dynamical expansion to that in an equivalent static scenario. Based on this scaling, we calculate for typical kinematical values of the RHIC and LHC heavy ion programming medium-modified fragmentation functions for collisions with realistic dynamical expansion.     

Bildung und thermische stabilität von rhodium-oxiden

Thermoanalytical and X-ray studies were carried out on rhodium and on rhodium compounds. They proved that the orthorhombic β-Rh₂O₃ is the most stable oxide under normal pressure. The low temperature form (χ-Rh₂O₃) with corundum structure was formed only in the decomposition of rhodium compounds (hydroxide, nitrate, sulfate). It transforms slowly and irreversibly to the high temperature modification (β-Rh₂O₃) upon heating in the range 750-1000°C. The rutile-type oxide RhO₂ could be prepared also under normal pressure at about 450-600°C by decomposition of Rh-nitrate or Rh-hydroxide. It decomposes irreversibly and probably topotactically to χ-Rh₂O₃ at higher temperatures. The thermal decomposition of Rh₂O₃ depends on the oxygen pressure, it decreases from 1130°C at 760 torr to 900°C at 10 torr. This pressure dependence was determined by TG and DTG and was used for calculating the heat of dissociation of Rh₂O₃. For a medium temperature ΔH^o₁₂₈₇=92.7 kcal mol^?1 which is in the order of the heat of formation of Rh₂O₃. Both χ- and β-Rh₂O₃ are decomposed readily to Rh in reducing atmosphere at about 100-150°C. The linear thermal expansion of the Rh-sesquioxides is very similar, about 5.5 × 10^?6 in the average.Die wichtigsten Ergebnisse der hier beschriebenen thermoanalytischen Untersuchungen über die Bildung und die Stabilität der Rhodiumoxide sind folgende:Die Aufoxidation von metallischem Rhodium findet je nach Korngrösse im Bereich von etwa 300-1000°C statt. Beim Rhodiummohr bildet sich dabei zuerst die metastabile Korundform (χ-Rh₂O₃), sonst immer gleich die stabile, orthorhombische Hochtemperaturform (β-Rh₂O₃).Die Zersetzung von Rhodiumhydroxid, Rh-nitrat, und Rh-sulfat geht immer über das α-Rh₂O₃ zum β-Rh₂O₃, wobei diese polymorphe Umwandlung äusserst träge abläuft. Bei kurzzeitigem Erhitzen ist χ-Rh₂O₃ auch noch bei 1000°C stabil.     

Thermoanalytische und massenspektrometrische Untersuchung der Zersetzung von Zinkoxalat-Dihydrat. Thermoanalytische Untersuchungen XII

The dehydration and pyrolysis of zinc oxalate dihydrate are re-examined by thermo-analytical methods at linearily increasing temperature in air, nitrogen, water vapour, and high vacuum. Simultaneous analysis of the gaseous decomposition products by means of mass spectrometry confirms previous authors' results obtained with other methods. The activation energy of the thermal decomposition of ZnC₂O₄ above 340° has been found to be 40,4 ± 2,6 kcal/mol. The rehydration of ZnC₂O₄ has been investigated at various water vapour pressures. In an atmosphere virtually saturated with moisture, the rehydration leads to the dihydrate and is easily controlled on the thermobalance. The dihydrate itself takes up an ill-defined fraction of surplus water. The thermal effects resulting from surface water on the dihydrate have been investigated by DTA (freezing and melting peaks). They disappear below 5% w/w of surplus water in the dihydrate. The surface of cristallites of the decomposition products calculated from particle size (from X-ray line broadening) is much larger than the surface determined by the BET-method. However, for ZnO in its state immediately after decomposition of ZnC₂O₄, both methods give similar results. Thus, dihydration of ZnC₂O₄ · 2 H₂O produces a considerable inner surface of ZnC₂O₄ not accessible to gas adsorption. This surface is considered to be covered by adsorbed water, which would explain the remarkable amount of water retained during dehydration. The final product, ZnO, sinters rapidly at temperatures higher than 500–600°.