Exponential averaging for traveling wave solutions in rapidly varying periodic media

Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH3 on Pt(1 0 0) coupled by diffusion

The Lombardo–Imbihl–Fink (LFI) ODE model of the NO+NH₃ reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH₃ and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH₃ and H.     

Interferometrische Messung der Mikrostruktur von synthetischen Fasern

Zusammenfassung Bei den optisch anisotropen Fasern stellen der Brechungsindex bzw. die Doppelbrechung kennzeichnende Größen für die Struktur des Materials dar. Anhand von Beispielen wird die interferenzmikroskopische Messung der Brechungszahlen erläutert und insbesondere eine bisher noch nicht praktizierte Methode zur detaillierten Erfassung der Inhomogenitäten über den Faserquerschnitt vorgestellt. Einige Meßergebnisse für Polyamidfasern werden mitgeteilt. Es wird ein quantitativer Zusammenhang zwischen den Brechungsindizes und der Kristallinität der Faser angegeben. Aufgrund der vorliegenden Brechzahlmessungen ist z. B. ein Unterschied im Kristallinitätsgrad zwischen Mitte und Rand der Faser von 1–2% noch deutlich nachweisbar.

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Summary For optically anisotropic fibres the refractive index and the double refraction are parameters characterizing the structure of the material. Examples are used to explain the measurement of refractive indices by interference microscopy and especially to introduce a method, not yet applied so far, for the detailed determination of the inhomogeneities over the cross-section of the fibre. Some test readings for polyamide fibres are communicated. A quantitative relationship is given between the refractive indices and the crystallinity of the fibre. In accordance with the refractive index measurements available, it is still possible to distinctly prove, e.g., a difference in the degree of crystallinity between the centre and the rim of the fibre of 1–2%.

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Herrn Prof. Dr.Otto Bayer zu seinem 70. Geburtstag gewidmet.

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Für die umsichtige und sorgfältige Ausführung der interferenzmikroskopischen Messungen und der Auswertungen sei an dieser Stelle FrauAntje Mazzucco herzlich gedankt.     

E-1,2-Dichlorovinyl ethers as irreversible protease inhibitors

The synthesis of a novel motif for threonine protease inhibition is described. The desired E-1,2-dichlorovinyl ethers are obtained from alcohols and trichloroethylene as single diastereomers. Aqueous treatment at pH 11 unmasks the hidden α-chloroacetate, which is required for the reaction with the active site of the protease.     

Robust Identification of Parametric Radiation Force Models via Impulse Response Fitting

This paper presents a new identification method for obtaining parametric state-space models for radiation force computation. These state-space models can substitute the convolution integral in the equations of motion based on the impulse response function method. Thus, the method converts the integro-differential equation to an ordinary differential equation which reduces the computational effort of radiation force computation significantly. The identification is performed in time-domain which means that the retardation function is subject to fit. The method is verified by the application to a floating cylinder. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Copper-Catalyzed Highly Stereoselective Synthesis of Unprotected C-Acyl Manno-, Rhamno- and Lyxopyranosides

Due to their high stability towards enzymatic hydrolysis C-acyl glycosidic compounds are useful synthetic intermediates for potential candidates in drug discovery. Syntheses for C-acyl mannosides have remained scarce and usually employ donors obtained from lengthy syntheses. Furthermore, syntheses of unprotected C-acyl mannosides have not been reported so far, due to the incapability of the C-acyl mannoside motif with deprotection conditions for protective groups commonly used in carbohydrate chemistry. Herein, we report an efficient and highly α-selective four-step one-pot method for the synthesis of C-acyl α-d -manno-, l -rhamno- and d -lyxopyranosides from easily accessible persilylated monosaccharides and dithianes requiring only trace amounts of a copper source as catalyst and explain the crucial role of the catalyst by mechanistic studies. Furthermore, the C-acyl α-glycosides were easily isomerized to give rapid access to their β-anomers.     

Directed Design of a AuI Complex with a Reduced Mesoionic Carbene Radical Ligand: Insights from 1,2,3-Triazolylidene Selenium Adducts and Extensive Electrochemical Investigations

Carbene-based radicals are important for both fundamental and applied chemical research. Herein, extensive electrochemical investigations of nine different 1,2,3-triazolylidene selenium adducts are reported. It is found that the half-wave potentials of the first reduction of the selones correlate with their calculated LUMO levels and the LUMO levels of the corresponding triazolylidene-based mesoionic carbenes (MICs). Furthermore, unexpected quasi-reversibility of the reduction of two triazoline selones, exhibiting comparable reduction potentials, was discovered. Through UV/Vis/NIR and EPR spectroelectrochemical investigations supported by DFT calculations, the radical anion was unambiguously assigned to be triazoline centered. This electrochemical behavior was transferred to a triazolylidene-type MIC-gold phenyl complex resulting in a MIC-radical coordinated Au^I species. Apart from UV-Vis-NIR and EPR spectroelectrochemical investigations of the reduction, the reduced gold-coordinated MIC radical complex was also formed in situ in the bulk through chemical reduction. This is the first report of a monodentate triazolylidene-based MIC ligand that can be reduced to its anion radical in a metal complex. The results presented here provide design principles for stabilizing radicals based on MICs.     

Live Monitoring of Strain-Promoted Azide Alkyne Cycloadditions in Complex Reaction Environments by Inline ATR-IR Spectroscopy

The strain-promoted azide alkyne cycloaddition (SPAAC) is a powerful tool for forming covalent bonds between molecules even under physiological conditions, and therefore found broad application in fields ranging from biological chemistry and biomedical research to materials sciences. For many applications, knowledge about reaction kinetics of these ligations is of utmost importance. Kinetics are commonly assessed and studied by NMR measurements. However, these experiments are limited in terms of temperature and restricted to deuterated solvents. By using an inline ATR-IR probe we show that the cycloaddition of azides and alkynes can be monitored in aqueous and even complex biological fluids enabling the investigation of reaction kinetics in various solvents and even human blood plasma under controlled conditions in low reaction volumes.     

Approaching the Integer‐Charge Transfer Regime in Molecularly Doped Oligothiophenes by Efficient Decarboxylative Cross‐Coupling

A library of symmetrical linear oligothiophene was prepared employing decarboxylative cross‐coupling reaction as the key transformation. Thiophene potassium carboxylate salts were used as cross‐coupling partners without the need of co‐catalyst, base, or additives. This method demonstrates complete chemoselectivity and is a comprehensive greener approach compared to the existing methods. The modularity of this approach is demonstrated with the preparation of discreet oligothiophenes with up to 10 thiophene repeat units. Symmetrical oligothiophenes are prototypical organic semiconductors where their molecular electrical doping as a function of the chain length can be assessed spectroscopically. An oligothiophene critical length for integer charge transfer was observed to be 10 thiophene units, highlighting the potential use of discrete oligothiophenes as doped conduction or injection layers in organic electronics applications.