An ALE approach to mechano‐chemical processes in fluid–structure interactions

Mathematical modeling and simulation of fluid–structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano‐chemical fluid–structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long‐time effect. The time scale of the formation is in the simulation of comparable order as in reality. Copyright © 2016 John Wiley & Sons, Ltd.     

Différentiabilité de la composition et complétitude de certains espaces fonctionnels

Sans résumé Ce travail a été partiellement subventionné par le Fonds National Suisse pour la Recherche scientifique.     

A general hilbert space approach to wavelets and its application in geopotential determination

A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling functions and wavelet are defined in terms of H-product kernels. Wavelts are shown to be ‘building blocks’ that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organzied as an example of wavelet approximation in Hilbert space structure.     

Crown ethers as building blocks for carbohydrate receptors

[STRUCTURE: SEE TEXT] Acyclic receptors containing neutral hydrogen bonding sites, such as amino-pyridine groups and a crown unit, perform effective recognition of neutral sugar molecules through multiple interactions. Receptor 1 has been shown to be a particularly effective and highly selective receptor for beta-glucopyranoside.     

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.     

Hydroxid-halogenid-verbindungen des di-t-butyl-substituierten zinns

The di-t-butyltin hydroxide halides t-Bu₂Sn(OH)X (X = F, Cl or Br) have been prepared starting from the dihalides t-Bu₂SnX₂ or the oxide (t-Bu₂SnO)₃. X-Ray analysis of the three compounds shows dimeric molecules: two 5-coordinated tin atoms and the oxygen atoms of the hydroxyl groups are linked to a four-membered ring. As confirmed by the IR spectra, the molecules in the crystal are held together by OH?X hydrogen bonds. These are strong in the hydroxide fluoride but are weak in the analogous chloride and bromide.     

Chlorthionitrenkomplexe des Rheniums Die Kristallstruktur von AsPh4[ReCl4(NSCl)2] · CH2Cl2

Chlorothionitrene Complexes of Rhenium. Crystal Structure of AsPh₄[ReCl₄(NSCl)₂] · CH₂Cl₂ Rhenium pentachloride reacts in POCl₃ solution with (NSCl)₃ forming the chlorothionitrene complexes [(Cl₃PO)ReCl₄(NSCl)] ( I ) and [(Cl₃PO)ReCl₃(NSCl)₂] ( II ). I reacts with AsPh₄Cl in CH₂Cl₂ solution under abstraction of SCl₂ and POCl₃, yielding AsPh₄[ReNCl₄], while II forms the complex AsPh₄[ReCl₄(NSCl)₂] · CH₂Cl₂. The i.r. spectra of the compounds are discussed and assigned. The crystal structure of AsPh₄[ReCl₄(NSCl)₂] · CH₂Cl₂ was determined and refined with X-ray diffraction data (R = 0.031 for 2785 reflexions). It crystallizes in the space group Pī with two formula units per unit cell; the lattice constants are a = 1119, b = 1144, c = 1473 pm, α = 77.6, β = 70.8 and γ = 71.2°. The two NSCl ligands have cis arrangement with nearly linear Re?N?S groups, with interatomic distances corresponding to double bonds. The Re? Cl bonds are somewhat longer than usual and show no trans-effect; this is possibly due to Cl…?H? C bridges.     

Darstellung und strukturen diorganylsubstituierter Silicium-Germanium-Sauerstoff-achtringe

Diphenylgermanium diphenylsilicon oxide and dimethylgermanium diphenylsilicon oxide [(R₂Ge)O(Ph₂Si)O]₂ (R = Ph, Me) have been synthesized by treatment of diorganogermanium dihalides with diphenyldihydroxysilane. The X-ray analysis showed nonplanar eight-membered silicon-germanium-oxygen rings which are more puckered than those of cyclotetrasiloxanes. In the compound with R = phenyl the silicon and germanium atoms are disordered.