Morse�CSmale theory for flows on covering spaces of compact manifolds

For a dynamical system X on a compact differentiable manifold M and for the dynamical system X(ρ) induced from X by a covering map r :  [(M)\tilde] ?  M{\rho \, : \, \widetilde{M}\, \rightarrow \, M}, we develop algebraic topology methods for estimating the lower bounds on the number of codimension-1 surfaces (i.e., on the number of index-1 equilibria of flows and their stable manifolds) on the boundary of regions of stability on [(M)\tilde]{\widetilde{M}}. We also develop methods for estimating the number of equilibria on the boundaries of stability regions of noncompact manifolds with very general assumptions. Our methods allow us to obtain results for noncompact manifolds in cases when Morse–Smale approach does not work.     

Formation of simple organic molecules in the interstellar medium

In this work we present a methodology for the synthesis of simple molecules from basic formaldehyde (H₂CO) precursors. We have approached this challenging problem by considering a basic dimerization scheme that eventually leads to diose and methyl formate, using an HCO⁺ proton source. This species was chosen due to its ample abundance in the atmosphere. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A rapid method for the sampling of atmospheric water vapour for isotopic analysis

Analysis of the stable isotopic composition of atmospheric moisture is widely applied in the environmental sciences. Traditional methods for obtaining isotopic compositional data from ambient moisture have required complicated sampling procedures, expensive and sophisticated distillation lines, hazardous consumables, and lengthy treatments prior to analysis. Newer laser‐based techniques are expensive and usually not suitable for large‐scale field campaigns, especially in cases where access to mains power is not feasible or high spatial coverage is required. Here we outline the construction and usage of a novel vapour‐sampling system based on a battery‐operated Stirling cycle cooler, which is simple to operate, does not require any consumables, or post‐collection distillation, and is light‐weight and highly portable. We demonstrate the ability of this system to reproduce δ¹⁸O isotopic compositions of ambient water vapour, with samples taken simultaneously by a traditional cryogenic collection technique. Samples were collected over 1 h directly into autosampler vials and were analysed by mass spectrometry after pyrolysis of 1 µL aliquots to CO. This yielded an average error of < ±0.5‰, approximately equal to the signal‐to‐noise ratio of traditional approaches. This new system provides a rapid and reliable alternative to conventional cryogenic techniques, particularly in cases requiring high sample throughput or where access to distillation lines, slurry maintenance or mains power is not feasible. Copyright © 2009 John Wiley & Sons, Ltd.     

Über die Einwirkung von Chlor auf den Äthylenalkohol (1, 2-Äthandiol)

Ohne Zusammenfassung     

Morphology study of Nafion membranes prepared by solutions casting

The structures of Nafion membranes prepared by solutions casting from low aliphatic alcohols/water mixture solvents and N,N′‐dimethyl formamide (DMF) solvent were investigated using differential scanning calorimeter and small angle X‐ray scattering. The aggregation behavior of Nafion molecules in the casting solutions was also investigated using dynamic light scattering. We show that the morphology of membranes was strongly influenced by the conformations of Nafion molecules in the solutions. In aliphatic alcohol/water mixture solvents, which have a worse compatibility with Nafion backbones, the Nafion molecules aggregate and form fringed rod‐like structures. These primary rod‐like structures then aggregate again through fringed side chains to form secondary ionic aggregations. In DMF solvent, owing to its better compatibility with Nafion backbones, less Nafion molecules aggregate. The high degree of Nafion molecular aggregations in aliphatic alcohol/water mixture solvents leads to a high degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/aliphatic alcohol/water solutions. However, the lower degree of molecular aggregations in DMF solvent results in a lower degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/DMF solution. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3044–3057, 2005     

Als zweckm?fsigste Form der Ar?ometer

Ohne Zusammenfassung     

Chaotic Dynamics in an Electronic Model of a Genetic Network

We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low (i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics, like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods for characterizing dynamics in these networks.     

Muon-catalyzed fusion theory

Some topics in muon-catalyzed fusion theory are discussed: Resonant formation ofddμ molecules appears to be well understood, with good agreement so far between theory and experiment. The situation for resonantdtμ formation is much less clear, because of the more complicated kinetics, the apparent three-body effect, and the evident need to treat thermalization and molecular formation together to compare theory and experiment. Recent theoretical progress inpdμ fusion by Friar et al. has resolved a serious discrepancy in the Wolfenstein-Gershtein effect, i.e., the increase inpdμ fusion yield with increased deuterium fraction.