Riddled basins of coupled elastic arches

Riddled basins are shown to occur in a simple mechanical device consisting of masses and springs. Convergence probabilities versus deviations in the initial conditions are quantified by three independent methods, all leading to scale-invariance over many decades. Conditions exist for the occurrence of two-state on-off intermittency involving switching between predictable and unpredictable oscillations.     

Numerical aspects of the eXtended Finite Element Method

The eXtended Finite Element Method (XFEM) is a very efficient way to reduce mesh dependencies when analysing crack growth. Displacements and stresses around the crack tip are calculated using additional shape functions which span the analytical displacement field around a crack tip. In this paper the following numerical aspects of the XFEM are discussed: • The integration of the stiffness matrix has to be done accurately. Therefore singular functions have to be integrated and an error estimator must be available. We will compare the estimated error and the necessary number of integration points when using different routines. • In case a crack truncates a very small part of a finite element the global stiffness matrix may become singular. One possibility to overcome this problem is to delete some of the enhanced degrees of freedom in the finite element analysis. Another way is to remove zero eigenvalues in the global stiffness matrix algebraically by a stabilization term. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DMAP/Cr(III) Catalyst Ratio: The Decisive Factor for Poly(propylene carbonate) Formation in the Coupling of CO2 and Propylene Oxide

Highly efficient formation of poly(propylene carbonate) can be achieved in the coupling of CO₂ and propylene oxide assisted by 4‐(N,N‐dimethylamino)pyridine (DMAP) and catalyzed with salen chromium(III) chloride by using DMAP/Cr ratios of less than 2. Under these conditions a possible backbiting mechanism is suppressed, leading to only minor amounts of cyclic carbonate as a side product.

     

Stereoselectivity in the Oligomerization of Racemic Tryptophan N‐Carboxyanhydride (NCA‐Trp) as Determined by Isotope Labeling and Mass Spectrometry

The polycondensation of tryptophan N‐carboxyanhydride (NCA‐Trp) is investigated in the presence and in the absence of POPC (1‐O‐palmitoyl‐2‐O‐oleoyl‐sn‐glycerol‐3‐O‐phosphocholine) liposomes with the aim to study and to quantify possible stereoselective effects of the process. A novel technique, based on isotope labeling of one enantiomer, and high performance liquid chromatography mass spectrometry (LC‐MS) allow determination of the individual stereoisomer distribution of oligomers up to n=10. For the first time, the preferential homochiral growth and the relative stereoisomer distributions for each oligomer length are directly demonstrated.     

Synthese und Kristallstruktur des Goldclusters [Au16(AsPh3)8Cl6]

Synthesis and Structures of the Gold Cluster [Au₁₆(AsPh₃)₈Cl₆] Reduction of Ph₃AsAuCl with NaBH₄ in ethanol yields the gold cluster [Au₁₆(AsPh₃)₈Cl₆]. It can be crystallized from dichloromethane/diisopropyl ether in form of dark red, light sensitive crystals with the space group P2₁/n and a = 1777.68(8), b = 3372.7(1), c = 2696.2(1)pm, β = 94.166(6)°, Z = 4). The inner skeleton of the 16 Au atoms consists of a centered icosahedron of which one of the corners binds to three additional Au atoms forming a tetrahedron pendent. The shortest Au–Au distances of 264.3 to 266.6 pm correspond to the bonds to the three external Au atoms. Within the icosahedron the distances between the central atom and the peripheral atoms (273.0–279.1 pm) are distinctly shorter than the distances between the peripheral atoms (283.6–299.0 pm).     

Hexakis(2,4,6‐triisopropylphenyl)cyclotristannoxane – a Molecular Diorganotin Oxide with Kinetically Inert Sn–O Bonds

The single‐crystal X‐ray structure analysis of hexakis(2,4,6‐triisopropylphenyl)cyclotristannoxane, cyclo‐[(2,4,6‐i‐Pr₃‐C₆H₂)₂SnO]₃ ( 1 ), is reported and reveals this compound to contain an almost planar six‐membered ring. Redistribution reactions of 1 with cyclo‐(t‐Bu₂SnO)₃ and t‐Bu₂SiCl₂, respectively, failed and indicate an unusual kinetic inertness of the Sn–O bonds in 1 as compared to related molecular diorganotin oxides containing less bulkier substituents. The redistribution reaction of cyclo‐(t‐Bu₂SnO)₃ with cyclo‐(t‐Bu₂SnS)₂ leads to an equilibrium involving the trimeric diorganotin oxysulphides cyclo‐t‐Bu₂Sn(OSnt‐Bu₂)₂S ( 2 a ) and cyclo‐t‐Bu₂Sn(SSnt‐Bu₂)₂O ( 2 b ).