Über topologische Lösungssysteme

Zusammenfassung Die topologischen — Systeme haben durchweg die selben Eingenschaften wie toeologische Gruppeu oder Quasigruppen. In dieser Arbeit untersuchen wir hauptsaechlich in welchen Punkten Abweichungen in den Resultaten oder Beweismethoden vorhanden sind. Enrico Bompiani zu seinem wissenschaftlichen Jubil?um     

A Note on the Null Surface Formulation of GR

The purpose of this work is to study the structure and nature of the singularities of wavefronts in flat space-time. We computed the behavior at the singularities of important objects that take place in the null surface formulation of general relativity. As a secondary result we show that the Minkowski space-time with non-trivial null surfaces is a solution of the null surface approach to general relativity.     

In situ TEM study of mechanical behaviour of twinned nanoparticles

There is strong interest in studying changes in mechanical properties with reducing grain size. The rational is that consequent dislocation glide cannot be sustained, resulting in an increase in material strength. However, this comes with the cost of a reduction in ductility. It has been shown that coherent twin boundaries in nanostructured Cu improve the ductility to 14% [Lu et al., Science 324 (2009) p. 349]. In this paper, we report for the first time the compression of individual nanoparticles using an in situ force probing holder in the transmission electron microscope. Four types of nanoparticles were tested, three with twin boundaries (decahedra, icosahedra and a single twin) and one free of defects (octahedral). Our results indicate the yield strength of the twinned nanoparticles is between 0.5 and 2.0 GPa. The total malleability for the twinned particles range from 80 to 100%. In addition, experimental results were reproduced by MD simulations of the compression phenomena and suggest that the outstanding mechanical properties are related with partial dislocation multiplication at twin boundaries.     

Wavelength-dependent selective loss for wavelength switching operation of an erbium-doped fiber ring laser

A wavelength-switchable erbium-doped fiber ring laser based on a wavelength-dependent selective loss fiber filter is demonstrated and reported. The filter is based on a long-period fiber grating and bending loss. The operating wavelength of the fiber laser can be switched from a single-wavelength operation at 1565 to 1527 nm.     

Berry phase magnification in optical microcoil resonators

We have studied the effects of the Berry phase on the linear transmission properties of optical microcoil resonators and analyzed the resonant behavior for different input polarizations and coil geometries. Contrary to previous expectations, we find that on resonance the size of the Berry phase shift can be magnified significantly, leading to a measurable polarization rotation for some geometries. Our model also considers other polarization effects including elasto-optic bend birefringence and the polarization dependent coupling coefficients, which were also previously neglected, and we still find that observable Berry phase effects persist. For example, in a three turn microcoil with a diameter of 0.2 mm, close to 100% of an initially x polarized light will be coupled into the orthogonal y polarization, due to the optical activity arising from the cumulative effects of Berry phase on resonance. More generally, the cross-polarization coupling also significantly influences the resonance extinction ratio and quality factor.     

Surface modification of SnO2 nanoparticles containing Mg or Fe: Effects on sintering

Controlling the surface chemistry of oxide systems has emerged an effective tool to obtain desirable nanostructures and macro properties. A relatively simple way to achieve this is by using dopants that are prone to segregate to the surfaces of the powders. In this work, we delineate the effect of Mg and Fe on SnO₂ nanopowders focusing on the surface modifications caused by surface segregation. The effects of increasing the temperature of calcinations are particularly addressed to evaluate the surface modifications at high temperatures. The powders were studied by infrared spectroscopy, zeta potential measurements, X-ray diffraction, and specific surface area measurements. Since sintering is a high-temperature process strongly dependent on surface characteristics, we drawn a relationship between the final densities after sintering and the surface chemistry of the doped powders. Doped SnO₂ pellets were sintered to over 95% of the theoretical density within a few seconds (fast firing) when significant surface modifications were observed.