A Phase Field Approach for Dynamic Fracture

In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Configurational Forces in Crystal Plasticity

The surface morphology of micro machined surfaces depends on the heterogeneous microstructure. A crystal plasticity model is used to describe the plastic deformation in cp-titanium with its hcp crystal structure. Therefore the basal and prismatic slip systems are taken into account. Furthermore, self and latent hardening are considered. The rate dependency is motivated by a visco plastic evolution law. The cutting process of cp-titanium is modeled within the concept of configurational forces for a standard dissipative media. This framework is implemented into the finite element method. An example illustrates the effects of the microstructure on plastic deformation and configurational forces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Steiner connectivity problem

The Steiner connectivity problem has the same significance for line planning in public transport as the Steiner tree problem for telecommunication network design. It consists in finding a minimum cost set of elementary paths to connect a subset of nodes in an undirected graph and is, therefore, a generalization of the Steiner tree problem. We propose an extended directed cut formulation for the problem which is, in comparison to the canonical undirected cut formulation, provably strong, implying, e.g., a class of facet defining Steiner partition inequalities. Since a direct application of this formulation is computationally intractable for large instances, we develop a partial projection method to produce a strong relaxation in the space of canonical variables that approximates the extended formulation. We also investigate the separation of Steiner partition inequalities and give computational evidence that these inequalities essentially close the gap between undirected and extended directed cut formulation. Using these techniques, large Steiner connectivity problems with up to 900 nodes can be solved within reasonable optimality gaps of typically less than five percent.     

Symbolic Differential Elimination for Symmetry Analysis

Differential problems are ubiquitous in mathematical modeling of physical and scientific problems. Algebraic analysis of differential systems can help in determining qualitative and quantitative properties of solutions of such systems. In this tutorial paper we describe several algebraic methods for investigating differential systems.     

Semisynthetic, site-specific ubiquitin modification of α-synuclein reveals differential effects on aggregation

The process of neurodegeneration in Parkinson's Disease is intimately associated with the aggregation of the protein α-synuclein into toxic oligomers and fibrils. Interestingly, many of these protein aggregates are found to be post-translationally modified by ubiquitin at several different lysine residues. However, the inability to generate homogeneously ubiquitin modified α-synuclein at each site has prevented the understanding of the specific biochemical consequences. We have used protein semisynthesis to generate nine site-specifically ubiquitin modified α-synuclein derivatives and have demonstrated that different ubiquitination sites have differential effects on α-synuclein aggregation.     

Neutron bound beta-decay: BOB

Frozen solution samples were made from gold chloride and KAu(CN)₂ solvated with TBP/xylene. The ¹⁹⁷Au M?ssbauer parameters were similar to those same species as frozen solutions or adsorbed onto activated carbon. Solvated samples from EuO dissolved in HCl or H₂SO₄ and frozen gave characteristic Eu(III) spectra. All the spectra were consistent with bonding to the TBP being through hydronium ions or water molecules.     

CPT-symmetry studies with antihydrogen

Various approaches to physics beyond the Standard Model can lead to small violations of CPT invariance. Since CPT symmetry can be measured with ultra-high precision, CPT tests offer an interesting phenomenological avenue to search for underlying physics. We discuss this reasoning in more detail, comment on the connection between CPT and Lorentz invariance, and review how CPT breaking would affect the (anti)hydrogen spectrum.     

On the direct connection of rheological elements in nonlinear continuum mechanics

The structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exploring between the extremes: conversion-dependent kinetics of phosphite-modified hydroformylation catalysis

The kinetics of the hydroformylation of 3,3-dimethyl-1-butene with a rhodium monophosphite catalyst has been studied in detail. Time-dependent concentration profiles covering the entire olefin conversion range were derived from in situ high-pressure FTIR spectroscopic data for both, pure organic components and catalytic intermediates. These profiles fit to Michaelis-Menten-type kinetics with competitive and uncompetitive side reactions involved. The characteristics found for the influence of the hydrogen concentration verify that the pre-equilibrium towards the catalyst substrate complex is not established. It has been proven experimentally that the hydrogenolysis of the intermediate acyl complex remains rate limiting even at high conversions when the rhodium hydride is the predominant resting state and the reaction is nearly of first order with respect to the olefin. Results from in situ FTIR and high-pressure (HP) NMR spectroscopy and from DFT calculations support the coordination of only one phosphite ligand in the dominating intermediates and a preferred axial position of the phosphite in the electronically saturated, trigonal bipyramidal (tbp)-structured acyl rhodium complex.     

Temperature analysis of laser heated polymers on microsecond time scales

To investigate the temperature profiles on laser heated polymer films, we track the thermal radiation with 1 μs time and 1 μm spatial resolution. The resulting two-dimensional temperature graphs are compared to finite element simulations in order to understand the heat conversion and flow. The temperature measurement setup consists of a NIR laser and an optical detection system, which includes high performance optics and a microsecond gated camera, equipped with several interference filters. In this way the thermal radiation is detected in the visible range with spectral resolution. Fitting the spectrum with Planck’s law, two-dimensional micrographs of the temperature distribution are obtained. For polystyrene surfaces we were able to analyze the heating and the ablation behavior. Good agreement was found between experimental results and finite element simulations, when ablation is limited to a few tens of nanometers of the film thickness. Ablation of polystyrene starts at 150°C, 50 K above the glass transition temperature. We suggest a photomechanical ablation mechanism at that threshold fluence. For ablation at higher fluence and peak temperature, experiments indicate a thermal decomposition reaction. The temperature range of spinodal decomposition is not reached and can in our case be ruled out as ablation mechanism.