Free dense subgroups of holomorphic automorphisms

We show the existence of free dense subgroups, generated by two elements, in the holomorphic shear and overshear group of complex-Euclidean space and extend this result to the group of holomorphic automorphisms of Stein manifolds with the density property, provided there exists a generalized translation. The conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms.

Positron bunching and electrostatic transport system for the production and emission of dense positronium clouds into vacuum

We describe a system designed to re-bunch positron pulses delivered by an accumulator supplied by a positron source and a Surko-trap. Positron pulses from the accumulator are magnetically guided in a 0.085 T field and are injected into a region free of magnetic fields through a μ -metal field terminator. Here positrons are temporally compressed, electrostatically guided and accelerated towards a porous silicon target for the production and emission of positronium into vacuum. Positrons are focused in a spot of less than 4 mm FWTM in bunches of ∼8 ns FWHM. Emission of positronium into the vacuum is shown by single shot positron annihilation lifetime spectroscopy.

On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Deformation mechanisms in second-phase affected microstructures and their energy balance

Based on the relationship Zener parameter (Z=second-phase size/second-phase volume fraction) vs. calcite grain size (dg), second-phase controlled aggregates and microstructures that are weakly affected by second-phases are discriminated. The latter are characterized by large but constant grain sizes, high calcite grain boundary fractions and crystallographic preferred orientations (CPO), while calcite grain size and calcite grain boundary fraction decrease continuously and CPO weakens with decreasing Z in second-phase controlled microstructures. These observations suggest that second-phase controlled microstructures predominantly deform via granular flow because pinning of calcite grain boundaries reduces the efficiency of dynamic recrystallization favoring mass transfer processes and grain boundary sliding. In contrast, the balance of grain size reduction and growth by dynamic recrystallization maintains a steady state grain size in microstructures that are only weakly affected by second-phases promoting a predominance of dislocation creep. With increasing temperature, the relationship between Z and dg persists but the calcite grain size increases continuously. Based on microstructures, the energy of each modifying process is calculated and its relative contribution is compared with energies of the competing processes (surface energy, dragging energy, dynamic recrystallization energy). The steady state microstructures result from a temperature-dependent energy minimization procedure of the system.

A new technique to automatically quantify microstructures of fine grained carbonate mylonites: two-step etching combined with SEM imaging and image analysis

A two-step etching technique for fine-grained calcite mylonites using 0.37% hydrochloric and 0.1% acetic acid produces a topographic relief which reflects the grain boundary geometry. With this technique, calcite grain boundaries become more intensely dissolved than their grain interiors but second phase minerals like dolomite, quartz, feldspars, apatite, hematite and pyrite are not affected by the acid and therefore form topographic peaks. Based on digital backscatter electron images and element distribution maps acquired on a scanning electron microscope, the geometry of calcite and the second phase minerals can be automatically quantified using image analysis software. For research on fine-grained carbonate rocks (e.g. dolomite calcite mixtures), this low-cost approach is an attractive alternative to the generation of manual grain boundary maps based on photographs from ultra-thin sections or orientation contrast images.