Schwarzschild black hole as moving puncture in isotropic coordinates

The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1 + log coordinate condition. We compute stationary 1 + log slices of the Schwarzschild spacetime in isotropic coordinates in order to investigate the coordinate singularity that the numerical methods have to handle at the puncture. We present an alternative integration method to obtain isotropic coordinates that simplifies numerical integration and that gives direct access to a local expansion in the isotropic radius near the puncture. Numerical results have shown that certain quantities are well approximated by a function linear in the isotropic radius near the puncture, while here we show that in some cases the isotropic radius appears with an exponent that is close to but unequal to one. This paper is dedicated to the memory of Jürgen Ehlers. I have known JE for a number of years, in particular during his time as founding director of the Albert Einstein Institute in Potsdam. JE was the mentor of my habilitation thesis in 1996, and I am deeply thankful for many insightful discussions. JE combined great breadth and physical intuition with sharp analytical thought. His example inspired me to look beyond the numerical methods and results of numerical relativity to the analytic foundations. For example, while at the AEI, S. Brandt and I introduced “puncture initial data” for the numerical construction of general multiple black hole spacetimes [3]. While the puncture construction starts with an analytic trick of the sort that numerical relativists may devise, it is fair to say that the keen interest in analytical relativity created by JE at the AEI induced us to push our analysis one step further. As a result [3] connects to [26] for an existence and uniqueness proof for such black hole initial data, using weighted Sobolev spaces (see also [4–6]). The present work and its predecessors [9–12] represent an example where numerical experiments led to the discovery of an analytic solution for the 1 + log gauge for the Schwarzschild solution, and the present result, although modest, is of the type which I believe JE would have appreciated.     

Solar Thermal Energy Storage in a Photochromic Macrocycle

The conversion and efficient storage of solar energy is recognized to hold significant potential with regard to future energy solutions. Molecular solar thermal batteries based on photochromic systems exemplify one possible technology able to harness and apply this potential. Herein is described the synthesis of a macrocycle based on a dimer of the dihydroazulene/vinylheptafulvene (DHA/VHF) photo/thermal couple. By taking advantage of conformational strain, this DHA–DHA macrocycle presents an improved ability to absorb and store incident light energy in chemical bonds (VHF–VHF). A stepwise energy release over two sequential ring‐closing reactions (VHF→DHA) combines the advantages of an initially fast discharge, hypothetically addressing immediate energy consumption needs, followed by a slow process for consistent, long‐term use. This exemplifies another step forward in the molecular engineering and design of functional organic materials towards solar thermal energy storage and release.     

Optical and redox properties of a series of 3,4-ethylenedioxythiophene oligomers

The optical and redox properties of a series of 3,4-ethylenedioxythiophene oligomers (EDOTn, n=1-4) and their beta,beta'-unsubstituted analogues (Tn, n=1-4) are described. Both series are end capped with phenyl groups to prevent irreversible alpha-coupling reactions during oxidative doping. Absorption and fluorescence spectra of both series reveal a significantly higher degree of intrachain conformational order in the EDOTn oligomers. Oxidation potentials (E(PA1) and E(PA2)) determined by cyclic voltammetry reveal that those of EDOTn are significantly lower than the corresponding Tn oligomers as a consequence of the electron-donating 3,4-ethylenedioxy substitution. Linear fits of E(PA1) and E(PA2) versus the reciprocal number of double bonds reveal significantly steeper slopes for the EDOTn than for the Tn oligomers. This could indicate a more effective conjugation for the EDOTn series, confirmed by the fact that coalescence of E(PA1) and E(PA2) is reached already at relatively short chain lengths ( approximately 5 EDOT units) in contrast to the Tn series (>10 thiophene units). The stepwise chemical oxidation of the EDOTn and Tn oligomers in solution was carried out to obtain radical cations and dications. The energies of the optical transitions of the radical cations and dications as determined by UV/Vis/NIR spectroscopy were similar for the two series. These spectroscopic observations are consistent with quantum-chemical calculations performed on the singly charged molecules. Cooling solutions containing T2.+, T3.+, EDOT2.+, and EDOT3.+ revealed the reversible formation of dimers, albeit with a somewhat different tendency, expressed in the values for the dimerization enthalpy.     

Solid supported fluoronitroaryl triazenes as immobilized and convertible Sanger reagents--synthesis and SNAr reactions towards a novel preparation of 1-alkyl-5-nitro-1H-benzotriazoles

Synthesis of novel fluoronitroaryl triazenes in liquid phase and on solid support have been described; mild displacement of the fluoride ion with various nucleophiles provides access to substituted arenes which in turn can be cleaved to provide a unique access to 1-alkyl-5-nitro-1H-benzotriazole.     

High-throughput approaches for the discovery and optimization of new olefin polymerization catalysts

The discovery of new olefin polymerization catalysts is currently a time-intensive trial-and-error process with no guarantee of success. A fully integrated high-throughput screening workflow for the discovery of new catalysts for polyolefin production has been implemented at Symyx Technologies. The workflow includes the design of the metal-ligand libraries using custom-made computer software, automated delivery of metal precursors and ligands into the reactors using a liquid-handling robot, and a rapid primary screen that serves to assess the potential of each metalligand-activator combination as an olefin polymerization catalyst. "Hits" from the primary screen are subjected to secondary screens using a 48-cell parallel polymerization reactor. Individual polymerization reactions are monitored in real time under conditions that provide meaningful information about the performance capabilities of each catalyst. Rapid polymer characterization techniques support the primary and secondary screens. We have discovered many new and interesting catalyst classes using this technology.     

Characterization and quantification of metallothionein isoforms by capillary electrophoresis–inductively coupled plasma–isotope-dilution mass spectrometry

In a new approach to the characterization and quantification of metallothionein isoforms an on-line isotope-dilution method in combination with the coupling of capillary electrophoresis (CE) to an inductively coupled plasma-sector field mass spectrometer (ICP-SFMS) is reported. Metallothionein (MT) isoforms are separated by CE and the elements Cu, Zn, Cd, and S are detected simultaneously by use of ICP-SFMS in the medium resolution mode. On-line isotope dilution is performed by continuous introduction of an isotopically enriched, species-unspecific spike solution after the separation step. MT from rabbit liver and a further purified MT-1 isoform were quantified by determination of sulfur, and the stoichiometric compositions of the metalloprotein complexes are characterized by determination of their sulfur-to-metal ratios.     

Charge transfer and dissociation in collisions of metal clusters with atoms

We present a combined theoretical and experimental study of charge transfer and dissociation in collisions of slow Li31(2+) clusters with Cs atoms. We provide a direct quantitative comparison between theory and experiment and show that good agreement is found only when the exact experimental time of flight and initial cluster temperature are taken into account in the theoretical modeling. We demonstrate the validity of the simple physical image that consists in explaining evaporation as resulting from a collisional energy deposit due to cluster electronic excitation during charge transfer.     

Self-diffusion rates in Al from combined first-principles and model-potential calculations

Monovacancy diffusion alone dominates over diffusion due to divacancies and interstitials in Al for all temperatures up to the melting point. Deviations from a single Arrhenius dependence are due to anharmonicity. The conclusion is based on a combination of theoretical methods, from density functional theory to thermodynamic integration, without fitting to experimental data. The calculated diffusion rate agrees with experimental data over 11 orders of magnitude.