No description available.

No description available.

Today in the scientific and technological world, physical and artificial processes are often described by mathematical models which can be used for simulation, optimization or control. As the mathematical models get more detailed and different coupling effects are required to include, usually the dimension of these models become very large. Such large-scale systems lead to large memory requirements and computational complexity. To handle these large models efficiently in simulation, control or optimization model order reduction (MOR) is essential. The fundamental idea of model order reduction is to approximate a large-scale model by a reduced model of lower state space dimension that has the same (to the largest possible extent) input-output behavior as the original system. Recently, the system-theoretic method Balanced Truncation (BT) which was believed to be applicable only to moderately sized problems, has been adapted to really large-scale problems. Moreover, it also has been extended to so-called descriptor systems, i.e., systems whose dynamics obey differential-algebraic equations. In this thesis, a BT algorithm is developed for MOR of index-1 descriptor systems based on several papers from the literature. It is then applied to the setting of a piezo-mechanical system. The algorithm is verified by real-world data describing micro-mechanical piezo-actuators. The whole algorithm works for sparse descriptor form of the system. The piezo-mechanical original system is a second order index-1 descriptor system, where mass, damping, stiffness, input and output matrices are highly sparse. Several techniques are introduced to reduce the system into a first order index-1 descriptor system by preserving the sparsity pattern of the original models. Several numerical experiments are used to illustrate the efficiency of the algorithm.

The dynamics of Hamiltonian systems (e.g. planetary motion, electron dynamics in nano-structures, molecular dynamics) can be investigated by symplectic maps. While a lot of work has been done for 2D maps, much less is known for higher dimensions. For a generic 4D map regular 2D-tori are organized around a skeleton of families of elliptic 1D-tori, which can be visualized by 3D phase-space slices. An analysis of the different bifurcations of the families of 1D-tori in phase space and in frequency space by computing the involved hyperbolic and elliptic 1D-tori is presented. Applying known results of normal form analysis, both the local and the global structure can be understood: Close to a bifurcation of a 1D-torus, the phase-space structures are surprisingly similar to bifurcations of periodic orbits in 2D maps. Far away the phase-space structures can be explained by remnants of broken resonant 2D-tori. / Die Dynamik Hamilton'scher Syteme (z.B. Planetenbewegung, Elektronenbewegung in Nanostrukturen, Moleküldynamik) kann mit Hilfe symplektischer Abbildungen untersucht werden. Bezüglich 2D Abbildungen wurde bereits umfassende Forschungsarbeit geleistet, doch für Systeme höherer Dimension ist noch vieles unverstanden. In einer generischen 4D Abbildung sind reguläre 2D-Tori um ein Skelett aus Familien von elliptischen 1D-Tori organisiert, was in 3D Phasenraumschnitten visualisiert werden kann. Durch die Berechnung der beteiligten hyperbolischen und elliptischen 1D-Tori werden die verschiedenen Bifurkationen der Familien von 1D-Tori im Phasenraum und im Frequenzraum analysiert. Die Anwendung bekannter Ergebnisse aus Normalformanalysen ermöglicht das Verständnis sowohl des lokalen, als auch des globalen Regimes. Nahe an der Bifurkation eines 1D-Torus sind die Phasenraumstrukturen denen von Bifurkationen periodischer Orbits in 2D Abbildungen überraschend ähnlich. Weit entfernt können die Phasenraumstrukturen als Überreste eines zerplatzten resonanten 2D-Torus erklärt werden.

Audience Response Systems (ARSs) provide a promising opportunity to address issues occurring in traditional higher education, e.g., the lack of interaction, by allowing students to participate anonymously in lectures using their mobile devices. This can promote the students' attention, increase the interaction between the lecturer and the students and foster active thinking during class. In order to choose an appropriate ARS, numerous surveys list and classify these systems according to different criteria, e.g., supported features and platforms. [From the introduction]

The dynamics of Hamiltonian systems (e.g. planetary motion, electron dynamics in nano-structures, molecular dynamics) can be investigated by symplectic maps. While a lot of work has been done for 2D maps, much less is known for higher dimensions. For a generic 4D map regular 2D-tori are organized around a skeleton of families of elliptic 1D-tori, which can be visualized by 3D phase-space slices. An analysis of the different bifurcations of the families of 1D-tori in phase space and in frequency space by computing the involved hyperbolic and elliptic 1D-tori is presented. Applying known results of normal form analysis, both the local and the global structure can be understood: Close to a bifurcation of a 1D-torus, the phase-space structures are surprisingly similar to bifurcations of periodic orbits in 2D maps. Far away the phase-space structures can be explained by remnants of broken resonant 2D-tori. / Die Dynamik Hamilton'scher Syteme (z.B. Planetenbewegung, Elektronenbewegung in Nanostrukturen, Moleküldynamik) kann mit Hilfe symplektischer Abbildungen untersucht werden. Bezüglich 2D Abbildungen wurde bereits umfassende Forschungsarbeit geleistet, doch für Systeme höherer Dimension ist noch vieles unverstanden. In einer generischen 4D Abbildung sind reguläre 2D-Tori um ein Skelett aus Familien von elliptischen 1D-Tori organisiert, was in 3D Phasenraumschnitten visualisiert werden kann. Durch die Berechnung der beteiligten hyperbolischen und elliptischen 1D-Tori werden die verschiedenen Bifurkationen der Familien von 1D-Tori im Phasenraum und im Frequenzraum analysiert. Die Anwendung bekannter Ergebnisse aus Normalformanalysen ermöglicht das Verständnis sowohl des lokalen, als auch des globalen Regimes. Nahe an der Bifurkation eines 1D-Torus sind die Phasenraumstrukturen denen von Bifurkationen periodischer Orbits in 2D Abbildungen überraschend ähnlich. Weit entfernt können die Phasenraumstrukturen als Überreste eines zerplatzten resonanten 2D-Torus erklärt werden.

In algorithmic computing, the program follows a predefined set of rules – the algorithm. The analyst/designer of the program analyzes the intended tasks of the program, defines the rules for its expected behaviour and programs the implementation. The creators of algorithmic software must therefore foresee, identify and implement all possible cases for its behaviour in the future application! However, what if the problem is not fully defined? Or the environment is uncertain? What if situations are too complex to be predicted? Or the environment is changing dynamically? In many such cases algorithmic computing fails. In such situations, the software needs an additional degree of freedom: Autonomy! Autonomy allows software to adapt to partially defined problems, to uncertain or dynamically changing environments and to situations that are too complex to be predicted. As more and more applications – such as autonomous cars and planes, adaptive power grid management, survivable networks, and many more – fall into this category, a gradual switch from algorithmic computing to autonomic computing takes place. Autonomic computing has become an important software engineering discipline with a rich literature, an active research community, and a growing number of applications.:Introduction 5 1 A Process Data Based Autonomic Optimization of Energy Efficiency in Manufacturing Processes, Daniel Höschele 9 2 Eine autonome Optimierung der Stabilität von Produktionsprozessen auf Basis von Prozessdaten, Richard Horn 25 3 Assuring Safety in Autonomous Systems, Christian Rose 41 4 MAPE-K in der Praxis - Grundlage für eine mögliche automatische Ressourcenzuweisung, in der Cloud Michael Schneider 59

CeCu_2Si_2 was the first heavy-fermion compound showing signatures of bulk superconductivity (T_c = 0.5 K). Further observations have put in evidence the correlations between superconductivity, magnetic order, Kondo physics, and quantum critical phenomena. In spite of the interest generated, a systematic study of such correlations was hampered by strong sample dependences. Fortunately, the inherent complexity associated to the stoichiometric composition has been recently understood. The availability of single-crystals with well-defined properties has thus reignited the interest in CeCu_2Si_2 as a window to novel phenomena, such as unconventional superconductivity. The present work summarizes the results of my doctoral research. It exemplifies the importance not only of high-quality materials, but also of suitable experimental techniques. A first step in this project involved the design of angle-dependent techniques in the milli-kelvin range, namely: electrical resistivity and thermal conductivity. It comprised the development of a rotational stage, the construction of sample holders, and the implementation of controlling and measuring components. In the second part of the project, electrical- and thermal-transport measurements on CeCu_2Si_2 were performed. Power-law behavior below T_c in the thermal conductivity suggests the presence of lines of nodes in the gap function. Also, the non-vanishing extrapolated residual terms (k_00/T ) support the presence of a residual density of states. The nodes are broadened by potential scattering, which appears to be significant in CeCu_2Si_2. The scattering hinders the determination of the symmetry of the order parameter and might be responsible for the observed isotropic angle dependence of the thermal conductivity. In contrast, angle-dependent measurements of the upper critical field exhibit a four-folded behavior, which also points towards the presence of nodes. By comparing with a weak-coupling model including the effects of Pauli limiting and anisotropic Fermi velocity, the results point towards a d_xy-wave symmetry of the order parameter. Such results represent the first angle-dependent measurements supporting a d-wave symmetry in CeCu_2Si_2.

Future applications will run in a highly heterogeneous and dynamic execution environment that forces them to adapt their behavior and offered functionality depending on the user's or the system's current situation. Since application components in such heterogeneous multi-device systems will be distributed over multiple interconnected devices and cooperate to achieve a common goal, a coordinated adaptation is required to ensure a consistent system behavior. In this paper we present a decentralized adaptation middleware to adapt a distributed software system. Our approach supports the reliable execution of multiple adaptation operations that depend on each other and are performed transactionally even in unsteady environments coined by message loss or node failures. We implemented our approach in a search-and-rescue robot scenario to show its feasibility and conduct first performance evaluations.

Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical reactions. While the transport in lower-dimensional systems with two degrees of freedom is well understood, much less is known for the higher-dimensional case. A central new feature in higher-dimensional systems are transport phenomena due to resonance channels. In this thesis, we clarify the complex geometry of resonance channels in phase space and identify a turnstile mechanism that dominates the transport out of such channels. To this end, we consider the coupled standard map for numerical investigations as it is a generic example for 4D symplectic maps. At first, we visualize resonance channels in phase space revealing their highly non-trivial geometry. Secondly, we study the transport away from such channels. This is governed by families of hyperbolic 1D-tori and their stable and unstable manifolds. We provide an approach to measure the volume of a turnstile in higher dimensions as well as the corresponding transport. From the very good agreement of the two measurements we conclude that these structures are a suitable generalization of the well-known 2D turnstile mechanism to higher dimensions. / Viele Systeme in der Natur, z.B. Atome, Moleküle und Planetenbewegungen, können als Hamilton'sche Systeme beschrieben werden. In solchen Systemen bestimmt der Transport zwischen verschiedenen Regionen des Phasenraums einige ihrer wichtigsten Eigenschaften wie die Stabilität des Sonnensystems und die Geschwindigkeit chemischer Reaktionen. Während der Transport in niedrigdimensionalen Systemen mit zwei Freiheitsgraden gut verstanden ist, ist für den höherdimensionalen Fall deutlich weniger bekannt. Eine zentrales neues Merkmal von höherdimensionalen Systemen sind Transportphänomene aufgrund von Resonanzkanälen. In dieser Arbeit verdeutlichen wir die komplexe Geometrie von Resonanzkanälen im Phasenraum und identifizieren einen Drehkreuzmechanismus, der den Transport aus einem solchen Kanal heraus dominiert. Zu diesem Zweck betrachten wir die gekoppelte Standardabbildung für numerische Untersuchungen, da sie ein generisches Beispiel für 4D symplektische Abbildungen ist. Zuerst visualisieren wir Resonanzkanäle im Phasenraum und zeigen ihre höchst nicht-triviale Geometrie. Zweitens untersuchen wir den Transport weg von solchen Kanälen. Dieser wird durch Familien von hyperbolischen 1D-Tori sowie deren stabile und instabile Mannigfaltigkeiten bestimmt. Wir stellen einen Ansatz zur Messung sowohl des eingeschlossenen Volumens in höheren Dimensionen als auch des entsprechenden Transports vor. Aus der sehr guten Übereinstimmung der beiden Messungen schließen wir, dass diese Strukturen eine geeignete Verallgemeinerung des bekannten 2D Drehkreuzmechanismus in höheren Dimensionen sind.