Random walks on Baumslag–Solitar groups

We consider random walks on non-amenable Baumslag–Solitar groups BS(p, q) and describe their Poisson–Furstenberg boundary. The latter is a probabilistic model for the long-time behaviour of the random walk. In our situation, we identify it in terms of the space of ends of the Bass–Serre tree and the real line using Kaimanovich’s strip criterion.     

Approximations and solution estimates in optimization

Approximation is central to many optimization problems and the supporting theory provides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing finite- and infinite-dimensional constrained minimization problems as instances of extended real-valued lower semicontinuous functions defined on a general metric space. Since the Attouch-Wets distance between such functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through bounds of that distance. In particular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with modulus one in this distance. Under additional assumptions on the underlying metric space, we construct approximating functions involving only a finite number of parameters that still are close to an arbitrary extended real-valued lower semicontinuous functions.     

Thermal Residual Stresses and Triaxiality Measures

High performance ceramics have found their way into many highly challenging engineering tasks. For example silicon nitride is one of the best choices, if a material for demanding applications like metal forming and cutting is required. Due to the brittle nature of these hard and strong materials it is useful to know about thermal residual stresses, which can arise during the sintering process. In order to gain insight into the material behaviour, a single grain inclusion is exposed to thermal loads. Due to thermal mismatch, it undergoes a residual stress and strain field. The geometry of the model and the material data are motivated by the properties of silicon nitride. The stress fields are analyzed by three different measures for stress triaxiality. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discriminative response of surface-confined metalloporphyrin molecules to carbon and nitrogen monoxide

The binding of small gas molecules to metalloporphyrins is of both fundamental scientific and technological interest. It plays a key role in the transport of respiratory gases, catalytic processes in biological systems, and artificial nanostructures for sensing. Here, we present a detailed molecular-level investigation regarding the interaction of nitrogen monoxide (NO) and carbon monoxide (CO) with metallo-tetraphenylporphyrin (M-TPP, M = Co, Fe) arrays, anchored on a noble metal Ag(111) surface, providing M-TPP species with a distinct saddle-shape conformation. Scanning tunneling microscopy and spectroscopy experiments reveal that the impact of CO and NO is strikingly different on both species. In the case of CO, the M-TPP core can be dressed by either one or two carbon monoxide ligands, whereby the porphyrin geometric and electronic structure remains nearly unaffected. In contrast, following NO exposure exclusively a mononitrosyl species evolves. The NO axial ligation induces a relaxation of the adsorption-induced molecular deformation and markedly modifies the electronic structure of the porphyrin.     

The glass transition and crystallization of ball milled cellulose

Samples of ball milled cellulose were prepared by ball milling pulps from eucalyptus and softwood (spruce/pine). Water sorption isotherms were obtained by both dynamic vapor sorption and equilibration over saturated salt solutions, in the water content range of 5–42% db (db = dry basis; water as a % age of total solids). Dynamic mechanical analysis using a pocket technique showed a water content dependent thermal transition occurring at the same temperature for the two pulp samples, which was interpreted as a glass transition. Fitting the data to a Couchman–Karasz relationship predicted a value for T _g of the dry cellulose of approximately 478 K, which was similar to values previously reported for other dry polysaccharides. No clear glass transition could be observed calorimetrically, although an endotherm at approximately 333 K was measured, which in polymers is normally attributed to enthalpic relaxation, however the lack of dependence of this endotherm on water content suggests that the melting of some weak associations, such as residual hydrogen bonds, could be a more credible explanation. An exotherm was also observed on heating, which was dependent on water content and which was attributed to partial crystallization of the cellulose. This was confirmed by Wide angle X-ray diffraction and cross polarization magic angle spinning ¹³C NMR (CPMAS NMR). The recrystallisation was predominantly to form I of cellulose. This was thought to be caused by a small amount of residual form I (probably less than 5%) acting as a template for the crystallizing material. Differential scanning calorimetry reheat curves showed the appearance of freezable water for water contents higher than 20%, as a result of a transfer of water to the amorphous phase following crystallization. The increase in cellulose rigidity following crystallization was also confirmed by CPMAS NMR relaxation. Low resolution proton NMR T ₂ relaxation suggested the presence of proton water/cellulose exchange, which was active at water contents of 20% and above.     

On the trapping of SOx on CaO-Al2O3-based novel high capacity sorbents

Calcium-aluminum mixed oxide based materials doped with Na and Mn were explored as sulfur trapping materials. The materials showed a three times higher total storage capacity and a higher time on stream with complete SO2 removal compared to a second generation SOx trapping material which was mesoporous with calcium mainly present in oxidic form. Combining in situ XANES at the S K-edge and IR spectroscopy the key properties of the storage materials and the affiliated storage processes were identified. CaO-Al2O3 acts as the primary support and storage component, while Na+ cations adjust the base strength and enhances the storage capacity. Manganese cations provide the appropriate oxidation capacity in absence and presence of up to 10% water. The transport into the bulk phase, which is markedly influenced by a layer of sorbed water, is the rate-limiting step in presence of Mn cations. In the absence of manganese cations the oxidation step appears controlling the rate. The overall reaction network, identified by in situ IR spectroscopy and the 2D Correlation Analysis, is similar on all materials.     

A unifying mechanism for all high-temperature Heck reactions. The role of palladium colloids and anionic species

The Heck reaction has been the subject of intense investigation in the past decade. Many new types of catalysts have been developed in addition to the existing palladium/phosphine complexes. Prominent among these are palladacycles, pincers, several types of heterogeneous palladium catalysts, colloids and ligand-free palladium, usually in the form of Pd(OAc)2. Most of the newer types function only at higher temperatures, typically between 120 and 160 degrees C. It has been shown that irrespective of the catalyst precursor, none of these catalysts are stable at these high temperatures. They all have a tendency to form soluble palladium(0) colloids or nanoparticles, certainly with less reactive substrates such as aryl bromides or chlorides. The Heck reaction takes place by attack of the arylating agent on the palladium atoms in the outer rim of the nanoparticles. This leads to formation of monomeric or dimeric anionic palladium complexes that undergo the usual steps of the Heck mechanism as described by Amatore and Jutand.