Stellare Magnetfelder spielen eine wichtige Rolle bei der Entstehung und Entwicklung von Sternen. Leider entziehen sie sich aber, aufgrund ihrer großen Entfernung zur Erde, einer direkten Beobachtung. Dies gilt zumindest für derzeitige und in naher Zukunft zur Verfügung stehende Instrumente. Um aber beispielsweise zu verstehen, ob Magnetfelder durch einen Dynamoprozess generiert werden oder Überbleibsel der Sternentstehung sind, ist es zwingend erforderlich, die Oberflächenstruktur und die zeitliche Entwicklung von stellaren Feldern zu untersuchen. Glücklicherweise haben wir mit der Dopplerverschiebung sowie der Polarisation von Licht Mittel zur Verfügung, um indirekt die Magnetfeldtopologie entfernter Sternen zu rekonstruieren, wenn auch nur die schnell rotierender. Die auf den beiden genannten Effekten basierende Rekonstruktionsmethode ist unter dem Namen Zeeman-Doppler Imaging (ZDI) bekannt. Sie stellt eine leistungsfähige Methode dar, um aus rotationsverbreiterten Stokes Profilen schnell rotierender Sterne Oberflächenkartierungen der Temperatur und Magnetfeldverteilung zu erstellen. Durch das ZDI konnten in den vergangenen Jahren die Magnetfeldverteilungen zahlreicher Sterne rekonstruiert werden. Diese Methode stellt allerdings sehr hohe Anforderungen sowohl an die Instrumentierung als auch an die Rechenleistung und ist deshalb häufig mit zahlreichen Annahmen und Näherungen verbunden. Ziel dieser Arbeit war es, Methoden für ein ZDI zu entwickeln, das darauf ausgelegt ist, zeitaufgelöste spektropolarimetrische Daten von aktiven späten Sternen zu invertieren. Es sollte also insbesondere den komplexen und lokalen Magnetfeldstrukturen dieser Sterne Rechnung getragen werden. Um die Orientierung und Stärke solcher Felder zuverlässig rekonstruieren zu können, sollte die Inversion im Stande sein, alle vier Stokes-Komponenten einzubeziehen. Ferner war vorgesehen auf vollständigen polarisierten Strahlungstransportmodellierungen aufzubauen. Dies ermöglicht eine simultane und selbstkonsistente Temperatur- und Magnetfeld-Inversion, die damit dem komplexen Zusammenspiel zwischen Temperatur und Magnetfeld gerecht wird. Schließlich sollte die Anwendung eines neu zu entwickelnden ZDI Programms auf Stokes I und V Beobachtungen von II Pegasi (kurz: II Peg) erste Magnefeldkarten dieses sehr aktiven Sterns liefern. Um den hohen Rechenaufwand, der mit der Inversionsmethode einhergeht, besser bewältigen zu können, wurde zunächst eine schnelle Approximationsmethode für den polarisierten Strahlungstransport entwickelt. Sie basiert auf einer Hauptkomponentenanalyse (PCA) sowie auf künstlichen Neuronalen Netzen. Letztere approximieren den funktionalen Zusammenhang zwischen atmosphärischen Parametern und den zugehörigen lokalen Stokes Profilen. Inverse Probleme sind potentiell schlecht gestellt und erfordern in der Regel eine Regularisierung. Der entwickelte Ansatz verwendet eine lokale Entropie, die auf die Besonderheiten bei der Rekonstruktion lokalisierter Magnetfeder eingeht. Ein weiterer neuartiger Ansatz befasst sich mit der Rauschreduktion polarimetrischer Beobachtungsdaten. Er macht sich die Hauptkomponentenanalyse zu Nutze, um mit Hilfe einer Vielzahl beobachteter Spektrallinien, einzelne Linien mit drastisch vergrößertem Signal-zu-Rausch-Verhältnis wieder zu geben. Diese Methode hat gegenüber anderen Multi-Spektrallinien-Verfahren den Vorteil, nach wie vor eine Inversion auf der Basis einzelner Spektrallinien durchführen zu können. Schließlich wurde das Inversionsprogramm iMap entwickelt, das die zuvor genannten Methoden implementiert. Detaillierte Testrechnungen demonstrieren die Funktionsfähigkeit und Genauigkeit der schnellen Synthese-Methode und weisen einen Zeitgewinn von nahezu drei Größenordnungen gegenüber der konventionellen Strahlungstransportberechnung auf. Desweiteren untersuchen wir den Einfluss der verschiedenen Stokes Komponenten (IV bzw. IVQU) auf die Zuverlässigkeit, ein bekanntes Magnetfeld zu rekonstruieren. Damit belegen wir die Zuverlässigkeit unseres Inversionsprogrammes und zeigen darüber hinaus auch Einschränkungen von Magnetfeldinversionen im allgemeinen auf. Eine erste Inversion von Stokes I und V Profilen von II Peg liefert zum ersten Mal für diesen Stern simultan Temperatur- und Magnetfeldverteilungen. / Stellar magnetic fields, as a crucial component of star formation and evolution, evade direct observation at least with current and near future instruments. However investigating whether magnetic fields are generated by a dynamo process or represent relics from the formation process, or whether they show a behavior similar to the sun or something very different, it is essential to investigate their structure and temporal evolution. Fortunately nature provides us with the possibility to indirectly observe surface topologies on distant stars by means of Doppler shift and polarization of light, though not without its challenges. Based on the mentioned effects, the so called Zeeman-Doppler Imaging technique is a powerful method to retrieve magnetic fields from rapid rotating stars based on measurements of spectropolarimetric observations in terms of Stokes profiles. In recent years, a large number of stellar magnetic field distributions could be reconstructed by Zeeman-Doppler Imaging (ZDI). However, the implementation of this method often relies on many approximations because, as an inversion method, it entails enormous computational requirements. The aim of this thesis is to develop methods for a ZDI, designed to invert time-resolved spectropolarimetric data of active late type stars, and to account for the expected complex and small scale magnetic fields on these stars. In order to reliably reconstruct the detailed field orientation and strength, the inversion method is employed to be able to use of all four Stokes components. Furthermore it is based on fully polarized radiative transfer calculations to account for the intricate interplay between temperature and magnetic field. Finally, the application of a newly developed ZDI code to Stokes I and V observations of II Pegasi (short: II Peg) was supposed to deliver the first magnetic surface maps for this highly active star. To accomplish the high computational burden of a radiative transfer based ZDI, we developed a novel approximation method to speed up the inversion process. It is based on Principal Component Analysis and Artificial Neural Networks. The latter approximate the functional mapping between atmospheric parameters and the corresponding local Stokes profiles. Inverse problems, as we are dealing with, are potentially ill-posed and require a regularization method. We propose a new regularization scheme, which implements a local entropy function that accounts for the peculiarities of the reconstruction of localized magnetic fields. To deal with the relatively large noise that is always present in polarimetric data, we developed a multi-line denoising technique based on Principal Component Analysis. In contrast to other multi-line techniques that extract from a large number of spectral lines a sort of mean profile, this method allows to extract individual spectral lines and thus allows for an inversion on the basis of specific lines. All these methods are incorporated in our newly developed ZDI code iMap, which is based on a conjugated gradient method. An in depth validation of our new synthesis method demonstrates the reliability and accuracy of this approach as well as a gain in computation time by almost three orders of magnitude relative to the conventional radiative transfer calculations. We investigated the influence of the different Stokes components (IV / IVQU) on the ability to reconstruct a known synthetic field configuration. In doing so we validate the capability of our inversion code, and we also assess limitations of magnetic field inversions in general. In a first application to II Peg, a K2 IV subgiant, we derived temperature and magnetic field surface distributions from spectropolarimetric data obtained in 2004 and 2007. It gives for the first time simultaneously the temporal evolution of the surface temperature and magnetic field distribution on II Peg.

This thesis reports on the controlled formation of surface rippling structures induced by tip scanning processes on compliant and brittle materials. Periodic surface structures were generated on polymeric and vitreous materials and with different length scales. Two aspects were focused on: the controlling of orientation and periodicity of the resulting structures via proper tuning the scan conditions and the physical mechanisms ruling the early stages of plowing wear causing the rippling effect. Specifically the influence of the scanned area geometric shape on the orientation of the rippling structure was investigated on a polystyrene surface. Nanoripples were induced by scanning the surface with a silicon tip using atomic force microscopy and dedicated scripts. Inside a structured area two ripple orientations can be observed: near boundaries the ripple orientation is determined by boundary orientation and regions away from the boundaries the ripples are aligned in a steady orientation. This steady orientation can be tuned by the distance between the scan lines. In the boundary regions the orientation of the ripples is different from steady orientation. The orientation of the boundaries clearly affected the orientation of the ripples and the tendency of the ripples to align in a steady angle defined by the scan parameters could be significantly modified. Geometric shapes like squares, circles, stars, pentagons and hearts allowed to distinguish the influence of curved and straight boundaries. Straight boundaries with different orientations allowed a detailed analysis of the influence of the angle on the rippling process. Straight boundaries inclined in the direction of the steady state angle of ripple orientation previously defined generate a uniform ripple pattern covering the entire scan area. The aspect of wear originating from the rippled surface was also investigated on similar polystyrene surfaces. As a result of repetitive scan passes spherical particles with diameters up to 250 nm were nucleated and detached from the surface. The particles originate from the crests of the ripples formed in the first scan pass. As proven by the lateral force signal the detachment occurs smoothly without a static friction peak suggesting a crazing mechanism induced by the scanning tip. Once detached from the surface the particles are displaced and piled up along the edges of scanned area. The formation of periodic surface structures was also investigated on a brittle silica glass. By a combination of scratch tests performed with a diamond microtip mounted in a nanoindenter and imaging with atomic force microscopy the existence of a periodic herringbone pattern inside scratch grooves on silica glass was proven. The rippled pattern was induced in the scratch process when the indenter was pulled laterally along the surface resulting in a microscopic scratch groove. The load was varied up to 30 nN and the scan velocity up to 500 µm/s. The resulting periodicity of the structures was found to increase linearly with increasing scratch velocity. The repetition distance was in the range of sub-µm and the corrugation in the range of a few hundred nm, which was well below indentation depth. In both cases, the surface rippling on a polymeric surfaces and the formation of a periodic pattern inside microscratches on a glass surface, the results were found to be consistent with minimalistic theoretical models for stick-slip.:Contents i Abstract iii Zusammenfassung v 1. Introduction 1 1.1. Periodic surface structures – relevance and formation 1 1.2. Surface rippling created by scanning probe lithography 2 1.3. Wear and nanoparticle release 4 1.4. Aim and outline 4 2. Experimental methods and fundamental concepts 6 2.1. Nanolithography 6 2.2. Atomic force microscopy 7 2.3. Nanoindentation and -scratching 10 2.4. Wear 11 2.5. Stick-slip motion 12 2.6. Spin coating 14 3. Surface rippling on polystyrene 15 3.1. Background and motivation 15 3.2. Methods 20 3.2.1. Sample preparation 20 3.2.2. Scanning probe lithography process 20 3.2.3. Imaging of structures and nanoparticles 21 3.3. Effect of boundaries on the orientation of surface rippling 22 3.4. Particle release as a result of surface rippling 31 4. Periodic structures inside scratches on silica glass 37 4.1. Background and motivation 37 4.2. Methods 38 4.2.1. Sample preparation 39 4.2.2. Scratch tests 39 4.2.3. AFM imaging and analysis 39 4.3. Surface rippling induces by scraping with a sharp indenter 40 5. Conclusion and outlook 49 A. Appendix surface rippling on polymers I B. Appendix surface rippling on glass IV Acknowledgements VII References IX

Surfaces equipped with periodic patterns with feature sizes in the micrometer, submicrometer and nanometer range present outstanding surface properties. Many of these surfaces can be found on different plants and animals. However, there are few methods capable to produce such patterns in a one-step process on relevant technological materials. Direct laser interference patterning (DLIP) provides both high resolution as well as high throughput. Recently, fabrication rates up to 1 m²·min-1 could be achieved. However, resolution was limited to a few micrometers due to typical thermal effects that arise when nanosecond pulsed laser systems are used. Therefore, this study introduces an alternative to ns-DLIP for the fabrication of multi-scaled micrometer and submicrometer structures on nickel surfaces using picosecond pulses (10 ps at a wavelength of 1064 nm). Due to the nature of the interaction process of the metallic surfaces with the ultrashort laser pulses, it was not only possible to directly transfer the shape of the interference pattern intensity distribution to the material (with spatial periods ranging from 1.5 μm to 5.7 μm), but also to selectively obtain laser induce periodic surface structures with feature sizes in the submicrometer and nanometer range. Finally, the structured nickel sleeves are utilized in a roll-to-roll hot embossing unit for structuring of polymer foils. Processing speeds up to 25 m·min-1 are reported.