On the genericity of loxodromic actions

Suppose that a finitely generated group G acts by isometries on a δ-hyperbolic space, with at least one element acting loxodromically. Suppose that the elements of G have a normal form such that the language of normal forms can be recognized by a finite state automaton. Suppose also that a certain compatibility condition linking the automatic and the δ-hyperbolic structures is satisfied. Then we prove that in the “ball” consisting of elements of G whose normal form is of length at most l, the proportion of elements which act loxodromically is bounded away from zero, as l tends to infinity. We present several applications of this result, including the genericity of pseudo-Anosov braids.     

Curve graphs and Garside groups

We present a simple construction which associates to every Garside group a metric space, called the additional length graph, on which the group acts. These spaces share important features with curve graphs: they are \(\delta \)-hyperbolic, infinite, and typically locally infinite graphs. We conjecture that, apart from obvious counterexamples, additional length graphs have always infinite diameter. We prove this conjecture for the classical example of braid groups \((B_n,B_n^{+},\varDelta )\); moreover, in this framework, reducible and periodic braids act elliptically, and at least some pseudo-Anosov braids act loxodromically. We conjecture that for \(B_n\), the additional length graph is actually quasi-isometric to the curve graph of the n times punctured disk.     

Subgrid-modelling in LES of compressible flow

Subgrid-models for Large Eddy Simulation (LES) of compressible turbulent flow are tested for the three-dimensional mixing layer. For the turbulent stress tensor the recently developed dynamic mixed model yields reasonable results.A priori estimates of the subgrid-terms in the filtered energy equation show that the usually neglected pressure-dilatation and turbulent dissipation rate are as large as the commonly retained pressure-velocity subgrid-term. Models for all these terms are proposed: a similarity model for the pressure-dilatation, similarity andk-dependent models for the turbulent dissipation rate and a dynamic mixed model for the pressure-velocity subgrid-term. Actual LES demonstrates that for a low Mach number all subgrid-terms in the energy equation can be neglected, while for a moderate Mach number the effect of the modelled turbulent dissipation rate is larger than the combined effect of the other modelled subgrid-terms in the filtered energy equation.     

Pickering emulsions: wetting and colloidal stability of hairy particles--a self-consistent field theory

The assembly of sterically stabilized colloids at liquid-liquid interfaces is studied with the self-consistent field (SCF) theory using the discretization scheme that was developed by Scheutjens, Fleer, and co-workers. The model is based on a poly(methyl methacrylate) (pMMA) particle with poly(isobutylene) (pIB) grafted to the surface. The stabilizing groups on the particle surface have a significant effect on the interfacial assembly and, therefore, also on the formation and properties of Pickering emulsions. The wetting behavior of the particle is altered by the presence of the stabilizing groups, which affects the equilibrium position of the particles at the interface. The stabilizing groups can also lead to an activation barrier before interfacial adsorption, analogous to the steric repulsion between two particles. These effects are numerically solved with the SCF theory. It is commonly known that flocculating conditions enhance the interfacial adsorption and yield stable Pickering emulsions, which is confirmed in this work. Additionally, it is concluded that those conditions are not an absolute requirement. There is a window of stabilizer concentrations Γ(pIB), 2.2-3.3 mg/m(2) pIB, that shows both partial wetting and colloidal stability. The activation barrier for interfacial assembly is 140-550 k(B)T and is an order of magnitude higher than the colloidal stability. The difference can be attributed to the unfavorable interaction of pIB with water and a difference in geometry (plate-sphere vs sphere-sphere). This study demonstrates the interplay and provides a quantitative comparison between the wetting behavior and the colloidal stability, and it gives a better understanding of the colloidal assembly at soft interfaces and formation of Pickering emulsions in general.     

Coke formation during the methanol-to-olefin conversion: in situ microspectroscopy on individual H-ZSM-5 crystals with different Brønsted acidity

Coke formation during the methanol‐to‐olefin (MTO) conversion has been studied at the single‐particle level with in situ UV/Vis and confocal fluorescence microscopy. For this purpose, large H‐ZSM‐5 crystals differing in their Si/Al molar ratio have been investigated. During MTO, performed at 623 and 773 K, three major UV/Vis bands assigned to different carbonaceous deposits and their precursors are observed. The absorption at 420 nm, assigned to methyl‐substituted aromatic compounds, initiates the buildup of the optically active coke species. With time‐on‐stream, these carbonaceous compounds expand in size, resulting in the gradual development of a second absorption band at around 500 nm. An additional broad absorption band in the 600 nm region indicates the enhanced formation of extended carbonaceous compounds that form as the reaction temperature is raised. Overall, the rate of coke formation decreases with decreasing aluminum content. Analysis of the reaction kinetics indicates that an increased Brønsted acid site density facilitates the formation of larger coke species and enhances their formation rate. The use of multiple excitation wavelengths in confocal fluorescence microscopy enables the localization of coke compounds with different molecular dimensions in an individual H‐ZSM‐5 crystal. It demonstrates that small coke species evenly spread throughout the entire H‐ZSM‐5 crystal, whereas extended coke deposits primarily form near the crystal edges and surfaces. Polarization‐dependent UV/Vis spectroscopy measurements illustrate that extended coke species are predominantly formed in the straight channels of H‐ZSM‐5. In addition, at higher temperatures, fast deactivation leads to the formation of large aromatic compounds within channel intersections and at the external zeolite surface, where the lack of spatial restrictions allows the formation of graphite‐like coke.     

The porosity, acidity, and reactivity of dealuminated zeolite ZSM-5 at the single particle level: the influence of the zeolite architecture

A combination of atomic force microscopy (AFM), high‐resolution scanning electron microscopy (HR‐SEM), focused‐ion‐beam scanning electron microscopy (FIB‐SEM), X‐ray photoelectron spectroscopy (XPS), confocal fluorescence microscopy (CFM), and UV/Vis and synchrotron‐based IR microspectroscopy was used to investigate the dealumination processes of zeolite ZSM‐5 at the individual crystal level. It was shown that steaming has a significant impact on the porosity, acidity, and reactivity of the zeolite materials. The catalytic performance, tested by the styrene oligomerization and methanol‐to‐olefin reactions, led to the conclusion that mild steaming conditions resulted in greatly enhanced acidity and reactivity of dealuminated zeolite ZSM‐5. Interestingly, only residual surface mesoporosity was generated in the mildly steamed ZSM‐5 zeolite, leading to rapid crystal coloration and coking upon catalytic testing and indicating an enhanced deactivation of the zeolites. In contrast, harsh steaming conditions generated 5–50 nm mesopores, extensively improving the accessibility of the zeolites. However, severe dealumination decreased the strength of the Brønsted acid sites, causing a depletion of the overall acidity, which resulted in a major drop in catalytic activity.     

Stability and structure of mixed-ligand metal ion complexes that contain Ni2+, Cu2+, or Zn2+, and Histamine, as well as adenosine 5'-triphosphate (ATP4-) or uridine 5'-triphosphate (UTP(4-): an intricate network of equilibria

With a view on protein–nucleic acid interactions in the presence of metal ions we studied the “simple” mixed‐ligand model systems containing histamine (Ha), the metal ions Ni²⁺, Cu²⁺, or Zn²⁺ (M²⁺), and the nucleotides adenosine 5′‐triphosphate (ATP^4?) or uridine 5′‐triphosphate (UTP^4?), which will both be referred to as nucleoside 5′‐triphosphate (NTP^4?) . The stability constants of the ternary M(NTP)(Ha)^2? complexes were determined in aqueous solution by potentiometric pH titrations. We show for both ternary‐complex types, M(ATP)(Ha)^2? and M(UTP)(Ha)^2?, that intramolecular stacking between the nucleobase and the imidazole residue occurs and that the stacking intensity is approximately the same for a given M²⁺ in both types of complexes: The formation degree of the intramolecular stacks is estimated to be 20 to 50 %. Consequently, in protein–nucleic acid interactions imidazole–nucleobase stacks may well be of relevance. Furthermore, the well‐known formation of macrochelates in binary M²⁺ complexes of purine nucleotides, that is, the phosphate‐coordinated M²⁺ interacts with N7, is confirmed for the M(ATP)^2? complexes. It is concluded that upon formation of the mixed‐ligand complexes the M²⁺? N7 bond is broken and the energy needed for this process corresponds to the stability differences determined for the M(UTP)(Ha)^2? and M(ATP)(Ha)^2? complexes. It is, therefore, possible to calculate from these stability differences of the ternary complexes the formation degrees of the binary macrochelates: The closed forms amount to (65±10) %, (75±8) %, and (31±14) % for Ni(ATP)^2?, Cu(ATP)^2?, and Zn(ATP)^2?, respectively, and these percentages agree excellently with previous results obtained by different methods, confirming thus the internal validity of the data and the arguments used in the evaluation processes. Based on the overall results it is suggested that M(ATP)^2? species, when bound to an enzyme, may exist in a closed macrochelated form only, if no enzyme groups coordinate directly to the metal ion.     

Identification of Nitrotyrosine Containing Peptides using Combined Fractional Diagonal Chromatography (COFRADIC) and Off-Line Nano-LC-MALDI

Protein nitration take place on tyrosine residues under oxidative stress conditions and may influence a number of processes including enzyme activity, protein-protein interactions and phospho-tyrosine signalling pathways. Nitrated proteins have been identified in a number of diseases, however, the study of these proteins has been compromised by the lack of good methods for identifying nitrated proteins, their nitration sites and the level of nitration. Here, we present a method for identification of nitrated peptides that allows the site specific assignment of nitration, is easy to use and reproducible, and opens up for the possibility to quantify the level of nitration of specific peptides as function of different oxidative conditions, namely combined fractional diagonal chromatography (COFRADIC) in combination with off-line nano-LC-MALDI. We identify six nitrated peptides from in vitro nitrated bovine serum albumin and propose that automated COFRADIC using nano-LC and off-line MALDI-MS might be a possibility for identification of tyrosine nitrated proteins and the nitration sites in complex samples.     

QTAIM analysis of the HF, HCl, HBr, and HOH elimination reactions of halohydrocarbons and halohydroalcohols

The 1,2-HX elimination reaction (where X = F, Cl, Br, OH) has been established as an important reaction in the degradation of compounds introduced into the upper atmosphere, including common CFC replacement compounds. By analyzing the electron densities of the transition state geometries of these reactions using QTAIM, we see that we can divide these reactions into two types. For HF and HOH elimination, the transition state is a complete ring of bonds, and neither the C-H nor the C-X bonds have been broken at the maximum of energy. There is very little accumulation of electron density on the X atom, with the majority of charge being lost by the hydrogen atom undergoing elimination, being transferred on to the two carbon atoms. In HCl and HBr elimination, a similar loss of electron density of the hydrogen atom is accompanied by significant accumulation of electron density on the X atom and a smaller change in electron density on the carbon atoms. The C-X bond is broken in the transition state geometry, with no ring critical point being present. This may explain the relative stabilities of halohydrocarbons and haloalcohols with respect to loss of H-X.