The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber.

Leichtbau zählt als eines der Zukunftstechnologien des 21. Jahrhunderts, um sowohl die Mobilitätsfragen von morgen zu beantworten als auch die klima- und energiepolitischen Ziele zu erreichen. Ein wesentlicher Fokus wird dabei auf Multi-Material-Systeme gelegt. Insbesondere die Kombination von faserverstärkten Kunststoffen und metallischen Legierungen zu sog. hybriden Laminaten zeigt ein hohes Substitutions- und Leichtbaupotential gegenüber klassischen monolithischen Konstruktionswerkstoffen. Vorrangig werden derartige hybride Schichtverbunde mit einer duroplastischen Matrix hergestellt, wodurch allerdings Restriktionen, bspw. gegenüber Produktivität, Recycling- und Lagerfähigkeit, resultieren. Eine besondere Alternative dazu bieten hybride Laminate auf Thermoplastbasis. Im Rahmen dieser Arbeit wurden die am Bundesexzellenzcluster MERGE entwickelten neuartigen thermoplastbasierten Schichtverbunde Carbon Fibre-Reinforced Polyamid/Aluminium Laminate (CAPAAL®) und Carbon Fibre-Reinforced Thermoplastic Polyurethane/Aluminium Laminate (CATPUAL) erforscht und im optimierten variothermen Pressprozess hergestellt. Um die Werkstoffverbunde über die Grundlagenforschung hinaus, etwa in der industriellen Nutzung, zu etablieren, wurden umfangreiche Charakterisierungen und Fertigungsstudien durchgeführt. Zum einen erfolgten mikrostrukturell-analytische Untersuchungen u. a. zu der Imprägniergüte, der Oberflächenbehandlung der Aluminiumlegierung und des Versagensverhaltens. Zum anderen fanden mechanisch-technologische Charakterisierungen bezüglich quasi-statischer Versuche unter Zug- und Biegebelastung sowie Ermüdungsversuche unter Biegebelastung im Niedrig-Frequenzbereich statt. Die quasi-statischen Untersuchungen der Subkomponenten (Aluminiumlegierung, Verbundwerkstoff) und der hybriden Laminate wurden sowohl unter Raumtemperatur als auch unter definierten Temperaturbelastungen und Konditionierungszuständen durchgeführt, um deren Sensitivität zu analysieren sowie zu bewerten. Ebenfalls erfolgten analytische Berechnungen zur Auslegung der hybriden Schichtverbunde basierend auf der klassischen Laminattheorie und der Mischungsregel unter Einbeziehung des Metallvolumengehalts. Darüber hinaus wurden die thermisch induzierten Eigenspannungen analytisch ermittelt und in die Berechnungen der quasi-statischen Kennwerte inkludiert. Anhand der Untersuchungen konnte nachgewiesen werden, dass CAPAAL® und CATPUAL als „maßgeschneiderte“ Halbzeuge oder Strukturbauteile mit einem hohen Leichtbaupotential für großseriennahe Anwendungen prädestiniert sind. Diese weisen in Abhängigkeit der medialen Belastungen eine höhere Performance und ein weniger katastrophales Versagensverhalten als die entsprechenden Faser-Kunststoff-Verbunde auf. Zudem wurde konstatiert, dass eine hervorragende Ermüdungsfestigkeit unter Biegebelastung vorliegt. Die theoretischen Vorhersagen weisen vor allem über den Ansatz der Mischungsregel eine gute Korrelation zu den experimentell ermittelten Kennwerten auf.:1 Einleitung 2 Stand der Wissenschaft und Technik 3 Materialien und experimentelle Untersuchungen 4 Versuchsergebnisse und Diskussion 5 Bewertung der erzielten Ergebnisse 6 Ausgewählte Leichtbaulösungen 7 Zusammenfassung und Ausblick / Lightweight construction is considered one of the future technologies of the 21st century, both to answer tomorrow's mobility questions and to achieve climate and energy policy goals. A major focus is placed on multi-material systems. In particular, the combination of fibre-reinforced plastics and metal alloys to form so-called hybrid laminates shows a high substitution and lightweight construction potential compared to classic monolithic construction materials. Such hybrid laminates are primarily produced with a thermoset matrix, which results in restrictions, e. g. with regard to productivity, recyclability and storability. Hybrid laminates based on thermoplastics offer a special alternative. In the context of this work, the novel thermoplastic-based laminates Carbon Fibre-Reinforced Polyamid/Aluminium Laminate (CAPAAL®) and Carbon Fibre-Reinforced Thermoplastic Polyurethane/Aluminium Laminate (CATPUAL) were researched and produced in an optimised vario-heat pressing process. In order to establish the material composites beyond basic research, for example in industrial use, extensive characterization and manufacturing studies were carried out. On the one hand, microstructural-analytical characterisations were conducted, for example, on the impregnation quality, the surface treatment of the aluminium alloy and the failure behaviour. On the other hand, mechanical-technological investigations were carried out with regard to quasi-static tests under tensile and bending load as well as fatigue tests under bending load in the low-frequency range. The quasi-static tests of the subcomponents (aluminium alloy, composite material) and hybrid laminates were carried out both at room temperature and under defined temperature loads and conditioning conditions in order to analyse and evaluate their sensitivity. Analytical calculations for the design of the hybrid laminates based on the classical laminate theory and the rule of mixtures including the metal volume content were also considered. Furthermore, the thermally induced residual stresses were determined analytically and included in the calculations of the quasi-static characteristic values. Based on the investigations, it was possible to prove that CAPAAL® and CATPUAL are predestined as 'tailor-made' semi-finished products or structural components with a high lightweight construction potential for applications close to large-scale production. Depending on the medial loads, these exhibit higher performance and less catastrophic failure behaviour than the corresponding fibre-plastic composites. In addition, it was stated that there is an excellent fatigue strength under bending load. The theoretical predictions show a good correlation to the experimentally determined characteristic values, especially via the rule of mixtures approach.:1 Einleitung 2 Stand der Wissenschaft und Technik 3 Materialien und experimentelle Untersuchungen 4 Versuchsergebnisse und Diskussion 5 Bewertung der erzielten Ergebnisse 6 Ausgewählte Leichtbaulösungen 7 Zusammenfassung und Ausblick

The Antimatter Experiment: Gravity, Interferometry, Spectroscopy (AEGIS) at the European Organization for Nuclear Research (CERN) is an experiment investigating the influence of earth’s gravitational force upon antimatter. To perform precise measurements the antimatter needs to be cooled to a temperature of 100 mK. This will be done in a Penning trap, formed by several electrodes, which are charged with several kV and have to be individually electrically insulated. The trap is thermally linked to a mixing chamber of a 3He-4He dilution refrigerator. Two link designs are examined, the Rod design and the Sandwich design. The Rod design electrically connects a single electrode with a heat exchanger, immersed in the helium of the mixing chamber, by a copper pin. An alumina ring and the helium electrically insulate the Rod design. The Sandwich uses an electrically insulating sapphire plate sandwiched between the electrode and the mixing chamber. Indium layers on the sapphire plate are applied to improve the thermal contact. Four differently prepared test Sandwiches are investigated. They differ in the sapphire surface roughness and in the application method of the indium layers. Measurements with static and sinusoidal heat loads are performed to uncover the behavior of the thermal boundary resistances. The thermal total resistance of the best Sandwich shows a temperature dependency of T-2,64 and is significantly lower, with roughly 30 cm2K4/W at 50 mK, than experimental data found in the literature. The estimated thermal boundary resistance between indium and sapphire agrees very well with the value of the acoustic mismatch theory at low temperatures. In both designs, homemade heat exchangers are integrated to transfer the heat to the cold helium. These heat exchangers are based on sintered structures to increase the heat transferring surface and to overcome the significant influence of the thermal resistance (Kapitza resistance). The heat exchangers are optimized concerning the adherence of the sinter to the substrate and its sinter height, e.g. its thermal penetration length. Ruthenium oxide metallic resistors (RuO2) are used as temperature sensors for the investigations. They consist of various materials, which affect the reproducibility. The sensor conditioning and the resulting good reproducibility is discussed as well.

The Antimatter Experiment: Gravity, Interferometry, Spectroscopy (AEGIS) at the European Organization for Nuclear Research (CERN) is an experiment investigating the influence of earth’s gravitational force upon antimatter. To perform precise measurements the antimatter needs to be cooled to a temperature of 100 mK. This will be done in a Penning trap, formed by several electrodes, which are charged with several kV and have to be individually electrically insulated. The trap is thermally linked to a mixing chamber of a 3He-4He dilution refrigerator. Two link designs are examined, the Rod design and the Sandwich design. The Rod design electrically connects a single electrode with a heat exchanger, immersed in the helium of the mixing chamber, by a copper pin. An alumina ring and the helium electrically insulate the Rod design. The Sandwich uses an electrically insulating sapphire plate sandwiched between the electrode and the mixing chamber. Indium layers on the sapphire plate are applied to improve the thermal contact. Four differently prepared test Sandwiches are investigated. They differ in the sapphire surface roughness and in the application method of the indium layers. Measurements with static and sinusoidal heat loads are performed to uncover the behavior of the thermal boundary resistances. The thermal total resistance of the best Sandwich shows a temperature dependency of T-2,64 and is significantly lower, with roughly 30 cm2K4/W at 50 mK, than experimental data found in the literature. The estimated thermal boundary resistance between indium and sapphire agrees very well with the value of the acoustic mismatch theory at low temperatures. In both designs, homemade heat exchangers are integrated to transfer the heat to the cold helium. These heat exchangers are based on sintered structures to increase the heat transferring surface and to overcome the significant influence of the thermal resistance (Kapitza resistance). The heat exchangers are optimized concerning the adherence of the sinter to the substrate and its sinter height, e.g. its thermal penetration length. Ruthenium oxide metallic resistors (RuO2) are used as temperature sensors for the investigations. They consist of various materials, which affect the reproducibility. The sensor conditioning and the resulting good reproducibility is discussed as well.