Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization.     

High finesse opto-mechanical cavity with a movable thirty-micron-size mirror

We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic force microscope cantilever. Cavity ring-down measurements performed on a 25 mm long Fabry-Pérot cavity with the 30 microm mirror at one end show an optical finesse of 2100. Numerical calculations show that the finesse is not diffraction limited and that orders of magnitude higher finesse should be possible. A mechanical quality factor of more than 10(5) at pressures below 10(-3) mbar is demonstrated for the cantilever with a mirror attached.     

A few remarks on the Generalized Vanishing Conjecture

We show that the Generalized Vanishing Conjecture $$\forall_{m \ge 1} [\Lambda^m f^m = 0] \Longrightarrow \forall_{m \gg 0}[\Lambda^m (g f^m) = 0]$$ for a fixed differential operator ${\Lambda \in k[\partial]}$ follows from a special case of it, namely that the additional factor g is a power of the radical polynomial f. Next we show that in order to prove the Generalized Vanishing Conjecture (up to some bound on the degree of Λ), we may assume that Λ is a linear combination of powers of distinct partial derivatives. At last, we show that the Generalized Vanishing Conjecture holds for products of linear forms in ?, in particular homogeneous differential operators ${\Lambda \in k[\partial_1,\partial_2]}$ .     

Catalytic Adventures in Space and Time Using High Energy X-rays

Very high energy X-rays (ca. >40 keV) have long offered great promise in providing great insight into the inner workings of catalysts; insights that may complement the battery of techniques available to researchers in catalysis either in the laboratory or at more conventional X-ray wavelengths. This contribution aims to critically assess the diverse possibilities now available in the high energy domain as a result of the maturation of third generation synchrotron facilities and to look forward to the potential that forthcoming developments in synchrotron source technology may offer the world of catalysis in the near future.     

Catalytic Gas‐Phase Production of Lactide from Renewable Alkyl Lactates

A new route to lactide, which is a key building block of the bioplastic polylactic acid, is proposed involving a continuous catalytic gas‐phase transesterification of renewable alkyl lactates in a scalable fixed‐bed setup. Supported TiO₂/SiO₂ catalysts are highly selective to lactide, with only minimal lactide racemization. The solvent‐free process allows for easy product separation and recycling of unconverted alkyl lactates and recyclable lactyl intermediates. The catalytic activity of TiO₂/SiO₂ catalysts was strongly correlated to their optical properties by DR UV/Vis spectroscopy. Catalysts with high band‐gap energy of the supported TiO₂ phase, indicative of a high surface spreading of isolated Ti centers, show the highest turnover frequency per Ti site.     

An easy and versatile synthesis of ureas from 2-benzylaminopyrimidine

A general procedure for the easy and versatile synthesis of ureas from 2-benzylaminopyrimidine is described. This methodology involves the preparation of a highly reactive carbamoyl chloride intermediate that can be further reacted with a high variety of different amines, including highly hindered secondary amines and deactivated anilines with excellent yields. Furthermore, this smooth procedure is compatible with a second functionality on the amine.     

Ultrafast vibrational dynamics of interfacial water

We report investigations of the vibrational dynamics of water molecules at the water–air and at the water–lipid interface. Following vibrational excitation with an intense femtosecond infrared pulse resonant with the O–H stretch vibration of water, we follow the subsequent relaxation processes using the surface-specific spectroscopic technique of sum frequency generation. This allows us to selectively follow the vibrational relaxation of the approximately one monolayer of water molecules at the interface. Although the surface vibrational spectra of water at the interface with air and lipids are very similar, we find dramatic variations in both the rates and mechanisms of vibrational relaxation. For water at the water–air interface, very rapid exchange of vibrational energy occurs with water molecules in the bulk, and this intermolecular energy transfer process dominates the response. For membrane-bound water at the lipid interface, intermolecular energy transfer is suppressed, and intramolecular relaxation dominates. The difference in relaxation mechanism can be understood from differences in the local environments experienced by the interfacial water molecules in the two different systems.     

Dynamic kinetic resolution of racemic beta-haloalcohols: direct access to enantioenriched epoxides

The direct chemo-enzymatic DKR of racemic beta-haloalcohols is reported, yielding the corresponding optically active epoxides in a single step. The mutant haloalcohol dehalogenase HheC Cys153Ser Trp249Phe is used for the asymmetric ring closure, whereas racemization of the remaining enantiomer of the haloalcohol is achieved using the new iridacycle 3, one of the most effective racemization catalysts to date for beta-haloalcohols.