An inhomogeneous,anisotropic, elastically modified Gibbs­Thomson law as singular limit of a diffuse interface model

We consider the sharp interface limit of a diffuse phase-field model with prescribed total mass taking into account a spatially inhomogeneous, anisotropic interfacial energy and an elastic energy. The main aim is to establish a weak formulation of an inhomogeneous, anisotropic, elastically modified Gibbs-Thomson law in the sharp interface limit. To this end we pass to the limit in the weak formulation of the Euler-Lagrange equation of the diffuse phase-field energy. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Azetidine‐Containing Alkaloids Produced by a Quorum‐Sensing Regulated Nonribosomal Peptide Synthetase Pathway in Pseudomonas aeruginosa

Pseudomonas aeruginosa displays an impressive metabolic versatility, which ensures its survival in diverse environments. Reported herein is the identification of rare azetidine‐containing alkaloids from P. aeruginosa PAO1, termed azetidomonamides, which are derived from a conserved, quorum‐sensing regulated nonribosomal peptide synthetase (NRPS) pathway. Biosynthesis of the azetidine motif has been elucidated by gene inactivation, feeding experiments, and biochemical characterization in vitro, which involves a new S‐adenosylmethionine‐dependent enzyme to produce azetidine 2‐carboxylic acid as an unusual building block of NRPS. The mutants of P. aeruginosa unable to produce azetidomonamides had an advantage in growth at high cell density in vitro and displayed rapid virulence in Galleria mellonella model, inferring functional roles of azetidomonamides in the host adaptation. This work opens the avenue to study the biological functions of azetidomonamides and related compounds in pathogenic and environmental bacteria.     

Atomic‐Scale Observation of the Metal–Promoter Interaction in Rh‐Based Syngas‐Upgrading Catalysts

The direct conversion of syngas to ethanol, typically using promoted Rh catalysts, is a cornerstone reaction in CO₂ utilization and hydrogen storage technologies. A rational catalyst development requires a detailed structural understanding of the activated catalyst and the role of promoters in driving chemoselectivity. Herein, we report a comprehensive atomic‐scale study of metal–promoter interactions in silica‐supported Rh, Rh–Mn, and Rh–Mn–Fe catalysts by aberration‐corrected (AC) TEM. While the catalytic reaction leads to the formation of a Rh carbide phase in the Rh–Mn/SiO₂ catalyst, the addition of Fe results in the formation of bimetallic Rh–Fe alloys, which further improves the selectivity and prevents the carbide formation. In all promoted catalysts, Mn is present as an oxide decorating the metal particles. Based on the atomic insight obtained, structural and electronic modifications induced by promoters are revealed and a basis for refined theoretical models is provided.     

In Situ Investigations of Mechanochemical One‐Pot Syntheses

We present an in situ triple coupling of synchrotron X‐ray diffraction with Raman spectroscopy, and thermography to study milling reactions in real time. This combination of methods allows a correlation of the structural evolution with temperature information. The temperature information is crucial for understanding both the thermodynamics and reaction kinetics. The reaction mechanisms of three prototypical mechanochemical syntheses, a cocrystal formation, a C?C bond formation (Knoevenagel condensation), and the formation of a manganese‐phosphonate, were elucidated. Trends in the temperature development during milling are identified. The heat of reaction and latent heat of crystallization of the product contribute to the overall temperature increase. A decrease in temperature occurs via release of, for example, water as a by‐product. Solid and liquid intermediates are detected. The influence of the mechanical impact could be separated from temperature effects caused by the reaction.     

Array of electrodeposited Ru-decorated TiO<Subscript>2</Subscript> nanotubes with enhanced photoresponse

Although TiO₂ anatase phase has been widely chosen as the main photocatalyst, it presents high electron/hole recombination rate. However, today, what is sought is a semiconductor material with enhanced photocatalytic activity with higher photon to electron conversion efficiency by introduction of electrons trap dopants. In this paper, TiO₂ nanotubes arrays obtained by anodization of Ti substrates were decorated with Ru via electrodeposition, and their photo-response was investigated. First, voltammetric experiments were performed to elucidate the route of Ru reduction on the TiO₂ surface and to select the range of potentials for Ru deposition. The reduction potentials were used for controlling the amount of Ru distributed all over the surface. Although Ru was electrodeposited at potentials over the range from ??0.025 to ??0.188 V vs. Ag/AgCl, the deposition of 3.7 mC cm^?2 at ??0.100 V for 30 min resulted in a tenfold greater photocurrent when compared to the recorded photocurrent for the undecorated TiO₂ nanotubes array. Next, Ru-decorated TiO₂ nanotubes with a length of 323?±?18 nm and inner and outer diameters of 91 and 104 nm, respectively, were characterized using SEM-WDS, SEM-FEG, XRD, and XPS. UV-Vis-NIR diffuse reflectance spectroscopy and photoluminescence (PL) measurements, which revealed a maximum PL emission at 445 nm, showed that for the array of Ru-decorated TiO₂ nanotubes, the electron-hole recombination may be effectively inhibited by the presence of ruthenium electrodeposited, which can make this photocatalyst even more attractive for environmental applications. The performances of the TiO₂ and Ru-decorated TiO₂ catalysts were compared in heterogeneous photocatalysis experiments for color removal of an azo-dye, which presented a pseudo-first-order rate constant more than twofold greater for the Ru-decorated TiO₂ catalysts.     

Representation theory of generalized deformed oscillator algebras

The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators {1, a, a , N}. Their commutators and Hermiticity properties are those of the boson oscillator algebra, except for [a, a ] _q = G(N), where [a, b] _q = ab – q ba and G(N) is a Hermitian, analytic function. The unitary irreductible representations are obtained by means of a Casimir operator C and the semi-positive operator a a. They may belong to one out of four classes: bounded from below (BFB), bounded from above (BFA), finite-dimentional (FD), unbounded (UB). Some examples of these different types of unirreps are given.     

Random Walks on Trees and an Inequality of Means

We define trees generated by bi-infinite sequences, calculate their walk-invariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-infinite sequence with a simple random walk on an augmented Galton-Watson tree. We find that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree generated by a bi-infinite sequence. This is due to an inequality for random variables with values in [1, [ involving harmonic, geometric and arithmetic mean.