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The subject of this thesis is the development and test of silicon strip detectors for the high luminosity upgrade of the tracking detector of the ATLAS experiment at the Large Hadron Collider. Special emphasis is devoted to the understanding of the impact of mechanical stress on the electrical properties and the particle detection performance of detector modules.
First simulations were done to estimate the maximum expected stress on a sensor when operated at -30 °C within the future silicon strip tracking detector ITk, at ATLAS. The maximum stress in a worst case scenario is expected to be 27 MPa. Tensile strength tests were done to estimate the maximum stress which can be applied to a silicon strip sensor. Silicon shards, with a thickness and dopand concentration corresponding to the ITk sensor specifications break at >23 MPa, wafers at >700 MPa and sensors at ~ 400 MPa. The huge variations lead to the assumption, that the tensile stregth, which is highly dependent on the quality of the crystal lattice, is due to different cutting technology. Wafers, irradiated with a fluence equivalent of a lifetime dose of an ITk sensor, show no stress dependency of the youngs modulus. The tensile strength of irradiated wafers is decreased by ~ 6,6 %. No damage on silicon sensors from mechanical stress is expected for sensor modules installed it the ITk.
The electrical properties of silicon strip sensors were studied for applied mechanical stress on ATLAS07 sensors up to 60 MPa. The specifications of the sensors are similar to the specification of strip sensors in the future silicon strip tracker barrel region of the ATLAS detector. The leakage current changes at 50 MPa by -1.7 %, the bias resistance by +0.8 % and the interstrip resistance by -25 %. The depletion voltage and the implant resistance are not affected by mechanical stress. Except for the interstrip resistance the results can be explained by piezoresistive effects.
Silicon strip modules were build and studied in particle test beams. These modules consists of an ATLAS07 or an ATLAS12 sensor and an analogue readout to study the influence of stress on the module performance. The sensor module noise is independent from the applied stress. An effect of stress on the signal strength was seen. The ATLAS07 sensor module signal strength was decreased and the ATLAS12 sensor module signal strength was increased with a slope of ~0,6 MPa^-1. The average cluster size of the ATLAS07 sensor module was increased by 0,25 % MPa^-1 and the average cluster size of the ATLAS12 sensor module was decreased by 0,06 % MPa^-1 with applied stress.
In this thesis we study efficient time integration methods for linear parabolic PDEs to solve practical problems that arise in a variety of real-world applications. The classical construction of numerical methods for solving PDEs is based on the method of lines, which leads to a large sparse semi-discretised system of ODEs to which any numerical method for initial value ODE problems can be applied. When dealing with parabolic-type problems, the underlying ODE systems are known to be stiff. Therefore, in the context of linear model problems, the use of implicit schemes is usually considered to be the best choice in practice.
However, this statement is not correct for some relevant real-world applications. In particular, implicit schemes can cause high computational costs that are equipped with certain model conditions. The model problems considered here are coupled with various settings, ranging from many different initial conditions over long-term simulation with relatively frequent model updates, to dealing with very large-scale problems for which the matrix size can exceed several millions. For this reason, we are interested in sophisticated and computationally efficient numerical methods that bring the aspects of approximation accuracy as well as computational and storage complexity into balance.
Even nowadays it is still a challenging task to devise a numerical method that combines high accuracy, robustness and computational efficiency for the model problem to be solved. Therefore, the main objective is to find an easy and efficient ODE integration scheme for each individual model problem. On this basis, we first give a comprehensive introduction to the state-of-the-art methods that are often used for practical purposes. In this framework, we will investigate very detailed the theoretical and numerical foundations of two popular techniques, namely the fast explicit methods and the model order reduction techniques. This is primarily important in order to fully understand the numerical methods, and also absolutely essential in finding the best numerical method that is specifically suitable for the intended purpose.
Our second goal is then to efficiently solve the practical problems that arise in connection with shape correspondence, geothermal energy storage and image osmosis filtering. For each application we specify a complete setup, and in order to provide an efficient and accurate numerical approximation, we give a thorough discussion of the various numerical solvers along with many technical details and own adaptations. We validate our numerical findings through many experiments using synthetic and real-world data. In addition, the thesis provides a complete and detailed description of the powerful methods that can be very useful for tackling similar problems that are the subject of interest in many applications.
Das deutsche Energieversorgungssystem soll bis zum Jahr 2050 umfassend transformiert werden. Auch wenn es auf dem Pfad zur vollständigen Dekarbonisierung der Energieversorgung noch eine Vielzahl technischer Herausforderungen gibt, ist davon auszugehen, dass an der politischen Ambition einer treibhausgasneutralen Energieversorgung bis spätestens zum Jahr 2045 festgehalten wird. Klimaschutz ist jedoch nur eine Dimension im Spannungsfeld Energiewende. Es gilt, Ökologie, Wirtschaftlichkeit, technische Realisierbarkeit und Versorgungssicherheit sowie gesellschaftliche Aspekte in Einklang zu bringen. Das Ziel dieser Arbeit ist es, einen wissenschaftlichen Beitrag zur Untersuchung eines durch erneuerbare Energieanlagen dominierten Energieversorgungssystems im Jahr 2050 zu leisten. Die Einspeisung elektrischer Energie aus Wind- und Photovoltaikanlagen unterliegt jedoch hohen Fluktuationen. Aus diesem Grund sind im zukünftigen Energieversorgungssystem hohe temporäre Energieüberschüsse und -defizite zu erwarten.
Eine mögliche Lösung könnte hierfür die Sektorenkopplung darstellen. Die vollständige Kopplung dieser Sektoren würde es ermöglichen, hohe Energieüberschüsse sinnvoll zu verwenden oder auftretende Energiedefizite auszugleichen. Bedingt durch die fluktuierende EE-Einspeisung sind die Potenziale zur Nutzung von überschüssiger elektrischer Energie in anderen Energie- und Wirtschaftssektoren im Zeitverlauf jedoch nicht konstant. Aus diesem Grund erscheint es sinnvoll, die Diskussion über Sektorenkopplungspotenziale auf zeitlich und räumlich aufgelöste Untersuchungen zu stützen. Ohne die Prognose und Modellierung von zeitlich und räumlich hoch aufgelösten Einspeise- und Lastzeitreihen ist es nicht möglich, zielführende Aussagen über Sektorenkopplungspotenziale und eine bedarfsgerechte Energiebereitstellung im zukünftigen Energieversorgungssystem zu treffen.
Zur Quantifizierung und Prognose zukünftiger Sektorenkopplungspotenziale wurde im Rahmen dieser Dissertation ein vielseitig einsetzbares Energiemodell entwickelt und detailliert vorgestellt. Hierbei handelt es sich um eine modular aufgebaute, Microsoft Excel-basierte Lösung in Verbindung mit Visual Basic for Applications. So ist es möglich, das Modell auf jedem modernen Windowssystem ohne weitere Software zu verwenden. Das Energiemodell wurde anschließend auf eine geeignete Modellregion für das Jahr 2050 angewendet. Im Energiemodell werden elektrische Erzeugungs- und Lastzeitreihen in stündlicher Auflösung für bis zu 200 Modellknoten (räumliche Auflösung) ermittelt, miteinander verrechnet und auf mehreren Modellebenen aggregiert. Am Beispiel der gewählten Modellregion konnten so die Sektorenkopplungspotenziale im Rahmen einer Sensitivitätsanalyse umfangreich diskutiert werden. Damit war es möglich, die Forschungsfragen dieser Dissertation detailliert zu beantworten.
In 2012 a group of researchers proposed a basic research initiative to the German Research Foundation (DFG) as a special priority project (SPP) with the name: Wireless 100 Gbps and beyond. The main goal of this initiative was the investigation of architectures, technologies and methods to go well beyond the state of the art. The target of 100 Gbps was set far away from the (at that time) achievable 1 Gbps such that it was not possible to achieve promising results just by tuning some parameters. We wanted to find breakthrough solutions. When we started the work on the proposal we discussed the challenges to be addressed in order to advancing the wireless communication speed significantly. Having the fundamental Shannon boundary in mind we discussed how to achieve the 100 Gbps speed.