Asymptotic Analysis of Free-Edge and Free-Corner Effects in Laminate Structures

Stress fields in the vicinity of free edges and corners of composite laminates exhibit singular characteristics and may lead to premature interlaminar failure modes like delamination fracture. It is of practical interest to investigate the nature of the arising free-edge and free-corner stress singularities - i.e. the singularity orders and modes - closely. The present investigations are performed using the Boundary Finite Element Method (BFEM) which in essence is a fundamental-solution-less boundary element method employing standard finite element formulations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boltzmann's Formulation of the Helmholtz Vorticity Theorem

A dual form of the general relativistic and covariant generalization of the first vorticity theorem of Helmholtz is proven. This dual form is the generalization of Boltzmann's formulation of the Helmholtz theorem.     

Evaluation of light scattering data from bimodal turbid suspensions: a simple fit procedure

Whereas correlation spectroscopy gives reliable information on the size of immersed particles in those cases where the size distribution is narrow, large problems arise for more complex particle distributions. For instance, samples containing distinctly different particles of rather similar size lead to correlation functions which are very close to those of monodisperse samples. We present a measurement technique which is based on angle dependent measurements of 3D cross correlation functions and an evaluation scheme which uses the results of the Mie theory. The experimental technique warrants applications to strongly scattering samples. Having tested this procedure with mixtures containing standard latex particles we applied it to a sample of skimmed, homogenized milk.     

Synthesis and Silica‐Based Immobilization of Monofunctionalized Heptakis(2,6‐di‐O‐methyl‐3‐O‐pentyl)‐β‐cyclodextrin for Enantioselective Capillary‐HPLC

Heptakis(2,6‐di‐O‐methyl‐3‐O‐pentyl)‐β‐cyclodextrin was monofunctionalized by the regioselective introduction of exactly one ω‐epoxyoctyl group at the primary site of the cyclodextrin. The site‐specifically substituted cyclodextrin was immobilized to commercially available aminopropyl silica by nucleophilic opening of the epoxy function of the spacer substituent resulting in a lipophilic chiral stationary phase with broad applicability for enantiomer separations in capillary‐HPLC under reversed‐phase conditions.     

Quantitation of major elements with secondary ion mass spectrometry by using M 2 + -molecular ions

A new quantitation method, based on the detection of M ₂ ⁺ molecular ions, is presented. It has been shown that M ₂ ⁺ molecular ions are formed by a recombination process between independently sputtered M and M⁺ particles. Based on this formation mechanism, it will be demonstrated that M ₂ ⁺ molecular ions can be used to quantitate major elements. The method will be used for quantitation of an Al _x Ga_1?x As multilayer. Furthermore, it will be shown that some matrix effects can be explained by the energy dependence of instrument transmission.     

On the product distribution of degradable polymers

We present a simplified model for calculating the product distribution of degradable polymers which is based on a grand canonical approach. The distribution depends on two physical parameters, the energy of a bond formation and the initial concentration of monomers. Due to its simplicity this model covers the two limiting cases, namely a polymerization process (no degradation) and micellar association (dominant degradation), and allows for straightforward extension to branched chain topologies or flow fields. In shear flow, a flow rate dependent length distribution leads to shear thinning.     

Influences of stoichiometry on steadily propagating triple flames in counterflows

Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is 1/2. There then exist lean and rich premixed flames of roughly equal strengths, with a diffusion flame trailing behind from the stoichiometric point at which they meet. In the majority of realistic situations, however, the stoichiometric mixture fraction departs appreciably from unity, typically being quite small. With the objective of clarifying the influences of stoichiometry, attention is focused on one of the simplest possible models, addressed here mainly by numerical integration. When the stoichiometric mixture fraction departs appreciably from 1/2, one of the premixed wings is found to be dominant to such an extent that the diffusion flame and the other premixed flame are very weak by comparison. These curved, partially premixed flames are expected to be relevant in realistic configurations. In addition, a simple kinematic balance is shown to predict the shape of the front and the propagation velocity reasonably well in the limit of low stretch and low curvature.     

Enhanced effective mass in doped SrTiO3 and related perovskites

The effective mass is one of the main factors determining the Seebeck coefficient and electrical conductivity of thermo-electrics. In this ab-initio LDA-GGA study the effective mass is estimated from the curvature of electronic bands by one-band-approximation and is in excellent agreement with experimental data of Nb- and La-doped SrTiO₃. It is clarified that the deformation of SrTiO₃ crystals has a significant influence on the bandgap, effective electronic DOS-mass and band-mass, but the electronic effect due to the e_g-band flattening near the Γ-point due to Nb-doping up to 0.2 at% is the main factor for the effective mass increase. Doping of La shows a linear decrease of the effective mass; this can be explained by the different surroundings of A- and B-sites in perovskite. Substitution with other elements such as Ba on the A-site and V on the B-site in SrTiO₃ increases the effective mass as well.     

RERhZn (RE = Y,Sm, Gd–Lu) compounds with TiNiSi type structure – Synthesis and magnetic properties

The TiNiSi type intermetallic compounds RERhZn (RE = Y, Sm, Gd–Lu) were synthesized by induction melting of the elements in sealed tantalum ampoules. They were characterized by X-ray powder diffraction. Five structures were refined from single crystal X-ray diffractometer data: Pnma, Z = 4, a = 699.7(2), b = 405.6(2), c = 816.9(2) pm, wR2 = 0.038, 628 F² values for SmRhZn, a = 696.1(2), b = 405.6(1), c = 811.9(3) pm, wR2 = 0.028, 886 F² values for GdRhZn, a = 692.8(1), b = 403.0(1), c = 809.5(2) pm, wR2 = 0.039, 562 F² values, for TbRhZn, a = 690.6(3), b = 401.50(9), c = 808.2(2) pm, wR2 = 0.036, 763 F² values, for DyRhZn, and a = 688.6(5), b = 399.6(4), c = 808.3(7) pm, wR2 = 0.048, 546 F² values for HoRhZn with 20 variables for each refinement. The rhodium atoms have coordination number 9 (5 RE + 4 Zn atoms) in the form of a tricapped trigonal prism. Together the rhodium and zinc atoms build up three-dimensional [RhZn] networks with short Rh–Zn (263–269 pm in GdRhZn) and Zn–Zn (296 pm in GdRhZn) distances. The gadolinium atoms bind to the [RhZn] network by Gd–Rh bonds (292–294 pm). Magnetic susceptibility measurements show Pauli paramagnetism for YRhZn and van Vleck paramagnetism for SmRhZn. The remaining RERhZn compounds are Curie–Weiss paramagnets which show magnetic ordering at low temperatures.     

Analysis of crack formation in bonded lap joints using finite fracture mechanics on the basis of linear elasticity solutions.

In this work, crack formation and the corresponding failure load of bonded lap joints is analyzed. The analysis is based on linear elasticity solutions for bonded lap joints and makes use of the finite fracture mechanics. A hybrid criterion is applied that states the spontaneous formation of a crack of finite size if a stress and an energy criterion are fulfilled simultaneously. The stress distribution of a linear elasticity solution is used for the stress criterion and for the calculation of the incremental energy release rate which is necessary for definition of the energy criterion. The resulting fracture criterion is compared to literature results and shows a good agreement. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)