Two linearized models for a hyperbolic free boundary value problem

We consider two linearized models which describe the motion of a gas in a cylinder with a piston at one end whose motion is determined by the pressure of the gas within the cylinder and by external forces. In the first model all second and higher order terms are neglected, whereas in the second model a quadratic correction term is added to the equation of motion of the piston so that energy arguments become applicable. For both models existence and uniqueness theorems are given.

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Zusammenfassung Wir betrachten zwei linearisierte Modelle, die die Bewegung eines Gases in einem Zylinder beschreiben, an dessen einem Ende sich ein Kolben befindet, dessen Bewegung durch den Druck des Gases innerhalb des Zylinders und durch äußere Kräfte bestimmt wird. Im ersten Modell werden alle Ausdrücke zweiter und höherer Ordnung vernachlässigt, während im zweiten Modell ein quadratischer Korrekturterm eingefügt wird, sodaß Energieargumente anwendbar werden. Für beide Modelle werden Existenz- und Eindeutigkeitssätze angegeben.

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This work was partially supported by a Summer Research Fellowship granted by the University of Missouri-Columbia.     

Bunched laser cooling of a stored weak 7Li+ ion beam in a pure triplet state

A preparation scheme for a 7Li+ ion beam in a storage ring is presented which provides ions in the metastable triplet states with well controlled longitudinal phase space properties. For both state selective preparation and beam cooling, laser- and electron-cooler forces are applied. The spatial- and momentum distributions of the ions are directly detected by a time resolved measurement of the fluorescence light. At low beam intensities, the remaining heating rate of such a beam is completely determined by residual gas scattering. This revised version was published online in July 2006 with corrections to the Cover Date.     

Energy of optical polarons in systems with anisotropic energy bands

We consider a (band) electron-LO phonon system described by an anisotropic Fröhlich Hamiltonian. By means of functional integration techniques, the phonon terms can be eliminated exactly, leading to an effective one-particle problem. The (formal) free energy of this effective system is investigated. We clarify its asymptotic behaviour (that is the small- and large-coupling regime) and present Monte-Carlo results for the ground-state energy in the intermediate region. Finally, a comparison is drawn with previous work.     

The DMAP-catalyzed acetylation of alcohols--a mechanistic study (DMAP = 4-(dimethylamino)pyridine)

The acetylation of tert-butanol with acetic anhydride catalyzed by 4-(dimethylamino)pyridine (DMAP) has been studied at the Becke3 LYP/6-311 + G(d,p)//Becke3 LYP/6-31G(d) level of theory. Solvent effects have been estimated through single-point calculations with the PCM/UAHF solvation model. The energetically most favorable pathway proceeds through nucleophilic attack of DMAP at the anhydride carbonyl group and subsequent formation of the corresponding acetylpyridinium/acetate ion pair. Reaction of this ion pair with the alcohol substrate yields the final product, tert-butylacetate. The competing base-catalyzed reaction pathway can either proceed in a concerted or in a stepwise manner. In both cases the reaction barrier far exceeds that of the nucleophilic catalysis mechanism. The reaction mechanism has also been studied experimentally in dichloromethane through analysis of the reaction kinetics for the acetylation of cyclohexanol with acetic anhydride, in the presence of DMAP as catalyst and triethylamine as the auxiliary base. The reaction is found to be first-order with respect to acetic anhydride, cyclohexanol, and DMAP, and zero-order with respect to triethyl amine. Both the theoretical as well as the experimental studies strongly support the nucleophilic catalysis pathway.     

Die Konfiguration der stereoisomeren Tris(glycinato)-Kobalt(III)-Komplexe

It is shown that the stereoisomeric tris(glycinato)cobalt(III) complexes, first prepared by Ley & Winkler, differ in their molecular symmetry. Based on this difference it is possible to assign by ¹³C-NMR. spectroscopy the facial configuration to the red β-complex and the peripheral configuration to the violet α-isomer.     

Die Deutung des Energie-Impuls-Tensors des Dirac-Feldes

By comparing the structure of the particle current and of the energy and momentum density, the meaning of the various tensor components is clarified. We decompose the energy momentum tensor into two parts. The one describes orbital, the other spin properties.     

Real-time observation of structural and orientational transitions during growth of organic thin films

We study kinetically controlled orientational and structural transitions of molecular thin films during growth in situ and in real time, using diindenoperylene (DIP) as an example. By time-resolved surface-sensitive x-ray scattering (out of plane and in plane), we follow the organic molecular beam deposition of DIP on silicon oxide, on stepped sapphire, and on rubrene as an organic model surface. We identify transitions for the few-monolayer (ML) regime, as well as for thick (several 10's of ML) films. We show that the differences in the interaction of DIP with the substrate change the thickness as well as temperature range of the transitions, which include (transient) strain, subtle changes of the orientation, as well as complete reorientation. These effects should be considered rather general features of the growth of organics, which, with its orientational degrees of freedom, is qualitatively different from growth of inorganics.     

Falling and explosive,dormant, and rising markets via multiple‐regime financial time series models

A multiple‐regime threshold nonlinear financial time series model, with a fat‐tailed error distribution, is discussed and Bayesian estimation and inference are considered. Furthermore, approximate Bayesian posterior model comparison among competing models with different numbers of regimes is considered which is effectively a test for the number of required regimes. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme is designed, while importance sampling is employed to estimate Bayesian residuals for model diagnostic testing. Our modeling framework provides a parsimonious representation of well‐known stylized features of financial time series and facilitates statistical inference in the presence of high or explosive persistence and dynamic conditional volatility. We focus on the three‐regime case where the main feature of the model is to capturing of mean and volatility asymmetries in financial markets, while allowing an explosive volatility regime. A simulation study highlights the properties of our MCMC estimators and the accuracy and favourable performance as a model selection tool, compared with a deviance criterion, of the posterior model probability approximation method. An empirical study of eight international oil and gas markets provides strong support for the three‐regime model over its competitors, in most markets, in terms of model posterior probability and in showing three distinct regime behaviours: falling/explosive, dormant and rising markets. Copyright © 2009 John Wiley & Sons, Ltd.     

Impact of molecular tilt angle on the absorption spectra of pentacene:perfluoropentacene blends

We investigate the relation between the optical properties and the average molecular tilt angle for blends of pentacene and perfluoropentacene, which can be considered as a prototypical donor–acceptor complex. Combining near‐edge X‐ray absorption fine‐structure spectroscopy and optical spectroscopy we study thin films of these compounds prepared at three different substrate temperatures T_sub. For T_sub =180 K we observe a larger average tilt angle than for blends prepared at higher substrate temperatures. This orientational change has significant impact on the uniaxial anisotropic optical properties of the mixed films which we measure post growth as well as in real‐time during growth. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)