When Do Tracer Particles Dominate the Lyapunov Spectrum?

Dynamical instability is studied in a deterministic dynamical system of Hamiltonian type composed of a tracer particle in a fluid of many particles. The tracer and fluid particles are hard balls (disks, in two dimensions, or spheres, in three dimensions) undergoing elastic collisions. The dynamical instability is characterized by the spectrum of Lyapunov exponents. The tracer particle is shown to dominate the Lyapunov spectrum in the neighborhoods of two limiting cases: the Lorentz-gas limit in which the tracer particle is much lighter than the fluid particles and the Rayleigh-flight limit in which the fluid particles have a vanishing radius and form an ideal gas. In both limits, a gap appears in the Lyapunov spectrum between the few largest Lyapunov exponents associated with the tracer and the rest of the Lyapunov spectrum.     

Ring‐Closing and Cross‐Metathesis with Artificial Metalloenzymes Created by Covalent Active Site‐Directed Hybridization of a Lipase

A series of Grubbs‐type catalysts that contain lipase‐inhibiting phosphoester functionalities have been synthesized and reacted with the lipase cutinase, which leads to artificial metalloenzymes for olefin metathesis. The resulting hybrids comprise the organometallic fragment that is covalently bound to the active amino acid residue of the enzyme host in an orthogonal orientation. Differences in reactivity as well as accessibility of the active site by the functionalized inhibitor became evident through variation of the anchoring motif and substituents on the N‐heterocyclic carbene ligand. Such observations led to the design of a hybrid that is active in the ring‐closing metathesis and the cross‐metathesis of N,N‐diallyl‐p‐toluenesulfonamide and allylbenzene, respectively, the latter being the first example of its kind in the field of artificial metalloenzymes.     

How thermal curing of an organic paper coating changes topography, chemistry, and wettability

Celluloses are preferred renewable substrates, but hydrophilicity and porosity disfavor their water resistance. We present here an ecofriendly application of imidized nanoparticles and a method to flexibly tune the surface wettability of papers. The soft nanostructured coating is sensitive to thermal curing, which affects both the surface chemistry and morphology. The thermal stability of the coating is first investigated with conventional and modulated differential scanning calorimetry, revealing influences of the imide content and an endotherm reaction below the glass transition temperature at 120-150 °C. The latter is studied in detail for an appropriate selection of the copolymer precursors. According to diffuse reflection infrared spectroscopy, Raman spectroscopy, and UV/vis spectroscopy, the endotherm corresponds to an imidization reaction. The morphology of the coatings is followed at various scale levels by contactless roughness measurements and atomic force microscopy. Finally, the experimental values are fitted to the parameters of the Wenzel wetting model, and so-called calibration curves for the relation between contact angles, surface roughness, and surface chemistry are presented. They allow the prediction of the water contact angle of coated papers from the hydrophilic to the hydrophobic range, with a maximum in hydrophobicity after increasing the imide content at 120-150 °C curing.     

Large Eddy Simulation of the vortex end in reverse-flow centrifugal separators

The present work is a study of the gas-flow phenomenon known as the “end of the vortex” (EoV), which spontaneously occurs at the lower end, or under, reverse-flow centrifugal separators such as cyclones or swirl tubes. Different CFD models of swirl tubes have been built to study and analyse this phenomenon in detail. The present numerical work is based on—and compared with—previous experimental observations of this phenomenon. The numerical models were built in complete agreement with the geometrical configurations and operating conditions used in these earlier experimental studies [1]. Two different configurations of swirl tubes were analyzed. One configuration was an in principle long tube with variable length in which the dependence on the vessel length of the behaviour of the vortex core in a simple, well-defined geometry was studied. The other configuration was equipped with a wide “dust collection vessel” at the bottom, the depth of which was varied, to study the behaviour of the vortex core in a widely-used geometry. 3-D LES simulations were carried out using the commercial CFD package Star-CD. The bending of the vortex core to the wall of the vessel and its precessional motion, constituting the phenomenon of the EoV, was seen in both configurations, and the obtained results are in very good agreement, both qualitatively and to an extent quantitatively, with previous experimental results [1].     

Inequalities between successive minima and intrinsic volumes of a convex body

The second theorem of Minkowski establishes a relation between the successive minima and the volume of a 0-symmetric convex body. Based on this theorem we will prove a series of inequalities connecting the product of certain successive minima with certain intrinsic volumes.     

Existence of unique SRB-measures is typical for real unicritical polynomial families

We show that for a one-parameter family of unicritical polynomials {fc} with even critical order ??2, for almost all parameters c, fc admits a unique SRB-measure, being either absolutely continuous, or supported on the postcritical set. As a byproduct we prove that if fc has a Cantor attractor, then it is uniquely ergodic on its postcritical set.     

On-line single column capillary gas chromatographic analysis of all reactants and products in the synthesis of fuel methanol from hydrogen and oxides of carbon

The main problems with complete analysis of the components of fuel methanol, or in Fischer-Tropsch studies, are the several classes of compound present in the sample (permanent gases, water, alcohols, hydrocarbons), its wide range of components, its boiling point range, and the wide range of component concentrations. A flexible on-line GC method has been developed for kinetic study of catalyzed chemical reactions of hydrogen and oxides of carbon. The single capillary column, temperature programmed method was designed for complete analysis of reactants and products (hydrogen, carbon monoxide, carbon dioxide, water, C₁-C₁₀ hydrocarbons, and C₁-C₆ alcohols): a sample selection valve is used to switch between either the heated line used for input of the synthesis gases or the heated line used to transport reaction products from the reactor. Sample is introduced to the capillary column by means of a 10-port heated gas sampling valve with two external injection loops (0.07 and 1.95 cm³); this results in the determination of components over a wide range of concentrations in the sample (ppm to percentage levels). Helium from a pressure-controlled supply is used as carrier gas and detection of the components is performed by serial connection of thermal conductivity and flame ionization detectors. Peak identification is performed by mass spectrometry and by comparison of component retention times. The automated analytical equipment is integrated with a process control computer and delivers repeatable analytical results for the individual components (RSDs varying between 0.3 and 10% depending strongly on the concentration of the component and the accuracy of the determination of its peak area).     

Simultaneous analysis of 13C‐glutathione as its dimeric form GSSG and its precursor [1‐13C]glycine using liquid chromatography/isotope ratio mass spectrometry

Determination of glutathione kinetics using stable isotopes requires accurate measurement of the tracers and tracees. Previously, the precursor and synthesized product were measured with two separate techniques, liquid chromatography/isotope ratio mass spectrometry (LC/IRMS) and gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS). In order to reduce sample volume and minimize analytical effort we developed a method to simultaneously determine ¹³C‐glutathione as its dimeric form (GSSG) and its precursor [1‐¹³C]glycine in a small volume of erythrocytes in one single analysis. After having transformed ¹³C‐glutathione into its dimeric form GSSG, we determined both the intra‐erythrocytic concentrations and the ¹³C‐isotopic enrichment of GSSG and glycine in 150 µL of whole blood using liquid chromatography coupled to LC/IRMS. The results show that the concentration (range of µmol/mL) was reliably measured using cycloleucine as internal standard, i.e. with a precision better than 0.1 µmol/mL. The ¹³C‐isotopic enrichment of GSSG and glycine measured in the same run gave reliable values with excellent precision (standard deviation (sd) <0.3‰) and accuracy (measured between 0 and 5 APE). This novel method opens up a variety of kinetic studies with relatively low dose administration of tracers, reducing the total cost of the study design. In addition, only a minimal sample volume is required, enabling studies even in very small subjects, such as preterm infants. Copyright © 2009 John Wiley & Sons, Ltd.