Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden. / This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader.

Basic resonator structures for frequency-selective capacitive vibration sensors which exploit their mechanical resonance peak for spectral selectivity are developed and analyzed. As an important capability, the stuctures offer voltage-controlled frequency tuning realized by electrostatic principles. Direct electrostatic tuning based on displacement-dependent electrostatic forces as well as tuning by stress-stiffening based on constant electrostatic forces are discussed. The sensor structures are designed for fabrication using common silicon surface microtechnologies. Experimental tests of both mentioned tuning principles are carried out at structures fabricated using a surface technology known as SCREAM. A considerable part of the work focusses on nonlinear oscillations of the mechanical resonator at large amplitudes arising in resonance. Dimensioning rules for minimum nonlinear disturbance are derived from a detailed analysis of the Duffing oscillator. Various capacitive principles for signal detection and electrostatic frequency tuning are evaluated in terms of nonlinearity. A novel type of specially shaped electrode systems offering linear properties within an amplitude range of 10 micrometers, so-called curved comb capacitors, is developed for fabrication in SCREAM technology. / In der vorliegenden Arbeit werden Grundstrukturen frequenzselektiver kapazitiver Vibrationssensoren entwickelt und analysiert, deren spektrale Selektionswirkung durch Ausnutzung ihrer mechanischen Resonanzüberhöhung entsteht. Wesentliches Merkmal der Strukturen ist ihre spannungsgesteuerte Abstimmbarkeit, die auf elektrostatischen Prinzipien beruht. Es werden die direkte elektrostatische Frequenzabstimmung, basierend auf positionsabhängigen Feldkräften, sowie das Prinzip des Stress-Stiffening, basierend auf einer konstanten elektrostatischen Kraft, diskutiert. Die Entwicklung konzentriert sich auf Sensorstrukturen, die in klassischen Oberflächentechnologien gefertigt werden können. Experimentelle Tests der beiden genannten Abstimmprinzipien werden anhand von Strukturen in oberflächennaher Silizium-bulk-Mikromechanik (SCREAM) durchgeführt. Schwerpunkt der Arbeit sind nichtlineare Schwingungen der mechanischen Resonatorkomponente bei großen Amplituden, die durch die Resonanzüberhöhung entstehen. Für den Sonderfall des Duffing-Schwingers werden Dimensionierungsregeln zur Minimierung der Nichtlinearitäten entwickelt. Kapazitive Prinzipien zur Detektion bzw. elektrostatischen Abstimmung werden hinsichtlich ihrer Linearität geprüft. Es werden neuartige Elektrodensysteme für die SCREAM-Technologie, sogenannte Kurvenkammsysteme entwickelt, die bei Schwingamplituden bis zu 10 Mikrometer linear arbeiten.

Radio frequency oscillations up to several hundreds of MHz were observed during turn-off the high-current conducting IGBTs. They are described in this work as Transient Avalanche oscillations. Other than PETT oscillations that happen in the tail current phase, this oscillation appears during the rise of collector-emitter voltage VCE and during the fall of the collectoremitter current ICE. The turn-off process of IGBTs are investigated with the help of measurements, the circuit- and device-simulations to reveal the working mechanisms of transient high-frequency oscillations. For the first time the Transient Avalanche Oscillation is successfully reproduced with computer simulation, which allows the further investigation on the influences of individual parameters. The participation of IMPATT mechanism in Transient Avalanche oscillation is demonstrated. The interaction between IMPATT mechanism und PETT mechanism during the setting up of depletion region in IGBTs was investigated. Measures to suppress such oscillation are discussed on the levels of chip design, module design and the driver concept. Supplying electron current during critical phase is found to be an effctive method to avoid the dynamic avalanche and the TA-oscillation. / Radio Frequenz Oszillationen bis zu mehreren hundert MHz wurden während des Abschaltens von Hochstrom leitenden IGBTs beobachtet. Sie werden in dieser Arbeit als Transient Avalanche Oscillationen beschrieben. Anders als PETT Oszillationen, die in der Tail-Strom Phase vorkommen, erscheint diese Oszillation während des Anstiegs der Kollektor-Emitter-Spannung VCE und des Fallens des Kollektor-Emitter Stroms ICE. In dieser Arbeit werden die Abschaltvorgänge von IGBTs mit Hilfe von Messungen, Schaltungs- bzw. Device-Simulationen untersucht, um die Wirkungsmechanismen der transient erscheinenden hochfrequenten Oszillationen zu erklären. Es ist erstmals gelungen solche Transient Avalanche Oszillationen mit der Simulation zu reproduzieren und anschließend die Einflüsse einzelner Parameter zu untersuchen. Die Beteiligung des IMPATT Mechanismus an der Transient Avalanche Oszillation wurde nachgewiesen. Die Interaktion von IMPATT und PETT während Aufbau der Raumladungszone im IGBT wurde untersucht. Maßnahmen zur Unterdrückung der Oszillation werden auf den Ebenen von Chip-Design, Modulauslegung und der Treiberschaltung diskutiert. Das Zuführen des Elektrostromes während der kritischen Phase wird als ein effective Methode zur Vermeidung der TA-Oscillation nachgewiesen.

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Due to recent progress in theory and the growing number of physical realizations, low-dimensional quantum magnets continue to receive a considerable amount of attention. They serve as model systems for investigating numerous physical phenomena in spin systems with cooperative ground states, including the field-induced evolution of the ground-state properties and the corresponding rearrangement of their low-energy excitation spectra. This work is devoted to systematic studies of recently synthesized low-dimensional quantum spin systems by means of multi-frequency high-field electron spin resonance (ESR) investigations. In the spin- 1/2 chain compound (C6H9N2)CuCl3 [known as (6MAP)CuCl3] the striking incompatibility with a simple uniform S = 1/2 Heisenberg chain model employed previously is revealed. The observed ESR mode is explained in terms of a recently developed theory, revealing the important role of the alternation and next-nearest-neighbor interactions in this compound. The excitations spectrum in copper pyrimidine dinitrate [PM·Cu(NO3)2(H2O)2]n, an S = 1/2 antiferromagnetic chain material with alternating g-tensor and Dzyaloshinskii-Moriya interaction, is probed in magnetic fields up to 63 T. To study the high field behavior of the field-induced energy gap in this material, a multi-frequency pulsed-field ESR spectrometer is built. Pronounced changes in the frequency-field dependence of the magnetic excitations are observed in the vicinity of the saturation field, B ∼ Bs = 48.5 T. ESR results clearly indicate a transition from the soliton-breather to a spin-polarized state with magnons as elementary excitations. Experimental data are compared with results of density matrix renormalization group calculations; excellent agreement is found. ESR studies of the spin-ladder material (C5H12N)2CuBr4 (known as BPCB) completes the determination of the full spin Hamiltonian of this compound. ESR results provide a direct evidence for a pronounced anisotropy in this compound, that is in contrast to fully isotropic spin-ladder model employed previously for BPCB. Our observations can be of particular importance for describing the rich temperature-field phase diagram of this material. The frequency-field diagram of magnetic excitations in the quasi-two dimensional S = 1/2 compound [Cu(C4H4N2)2(HF2)]PF6 in the AFM-ordered state is studied. The AFM gap is observed directly. Using high-field magnetization and ESR results, parameters of the effective spin-Hamiltonian (exchange interaction, anisotropy and g-factor) are obtained and compared with those estimated from thermodynamic properties of this compound.

We have investigated processes of ionization, energy absorption and subsequent explosion of atomic and molecular clusters under intense laser illumination using numerical as well as analytical methods. In particular, we focused on the response of composite clusters, those consisting of different atomic elements, to intense light pulses. Another major theme is the effect of the molecular structure of clusters on their Coulomb explosion. The action of intense laser pulses on clusters leads to fundamental, irreversible changes: they turn almost instantaneously into nanoplasmas and subsequently disintegrate into separate ions and electrons. Due to this radical transformation, remarkable new features arise. Transient cluster nanoplasmas are capable of absorbing enormous amounts of laser energy. In some cases more than 90 % of incident laser energy is absorbed by a gas of clusters with a density much smaller than that of a solid. After the efficient absorption, the energy is transformed into production of energetic ions, electrons, photons, and even neutrons. Composite clusters show especially interesting behavior when they interact with intense laser pulses. Nanoplasmas formed in composite clusters may absorb even more laser energy, than those formed in homogeneous clusters, as we demonstrate in this work. One of the most important results of this thesis is the identification of a novel type of plasma resonance. This resonance is enabled by an unusual ellipsoidal shape of the nanoplasma created during the ionization process in a helium droplet doped with just a few xenon atoms. In contrast to the conventional plasma resonance, which requires significant ion motion, here, the resonant energy absorption occurs at a remarkably fast rate, within a few laser cycles. Therefore, this resonance is not only the most efficient (like the conventional resonance), but also, perhaps, the fastest way to transfer laser energy to clusters. Recently, dedicated experimental studies of this effect were performed at the Max Planck Institute in Heidelberg. Their preliminary results confirm our prediction of a strong, avalanche-like ionization of the helium droplet with a small xenon cluster inside. A conventional plasma resonance, which relies on the cluster explosion, also exhibits interesting new properties when it occurs in a composite xenon-helium cluster with a core-shell geometry. We have revealed an intriguing double plasma resonance in this system. This was the first theoretical study of the influence of the helium embedding on the laser- driven nanoplasma dynamics. Our results demonstrate the important role of the interaction between xenon and helium parts of the cluster. Understanding this interaction is necessary in order to correctly interpret the experimental results. We have elucidated several important properties of Coulomb explosion in atomic and molecular clusters. Specifically, it was found that the kinetic energy distribution of ions after the Coulomb explosion of an atomic cluster is quite similar to the initial potential energy distribution of ions and is only weakly influenced by ion overtake effects, as was believed before. For the case of molecular hydrogen clusters, we have shown that the alignment of molecules inside the cluster affects its Coulomb explosion. Investigation of the dynamical processes in composite and molecular clusters induced by intense laser pulses is a step towards understanding them in more complex nano-objects, such as biomolecules or viruses. This is of great interest in the context of x-ray diffractive imaging of biomolecules with atomic resolution, which is one of the main goals of new x-ray free electron laser facilities.

Basic resonator structures for frequency-selective capacitive vibration sensors which exploit their mechanical resonance peak for spectral selectivity are developed and analyzed. As an important capability, the stuctures offer voltage-controlled frequency tuning realized by electrostatic principles. Direct electrostatic tuning based on displacement-dependent electrostatic forces as well as tuning by stress-stiffening based on constant electrostatic forces are discussed. The sensor structures are designed for fabrication using common silicon surface microtechnologies. Experimental tests of both mentioned tuning principles are carried out at structures fabricated using a surface technology known as SCREAM. A considerable part of the work focusses on nonlinear oscillations of the mechanical resonator at large amplitudes arising in resonance. Dimensioning rules for minimum nonlinear disturbance are derived from a detailed analysis of the Duffing oscillator. Various capacitive principles for signal detection and electrostatic frequency tuning are evaluated in terms of nonlinearity. A novel type of specially shaped electrode systems offering linear properties within an amplitude range of 10 micrometers, so-called curved comb capacitors, is developed for fabrication in SCREAM technology. / In der vorliegenden Arbeit werden Grundstrukturen frequenzselektiver kapazitiver Vibrationssensoren entwickelt und analysiert, deren spektrale Selektionswirkung durch Ausnutzung ihrer mechanischen Resonanzüberhöhung entsteht. Wesentliches Merkmal der Strukturen ist ihre spannungsgesteuerte Abstimmbarkeit, die auf elektrostatischen Prinzipien beruht. Es werden die direkte elektrostatische Frequenzabstimmung, basierend auf positionsabhängigen Feldkräften, sowie das Prinzip des Stress-Stiffening, basierend auf einer konstanten elektrostatischen Kraft, diskutiert. Die Entwicklung konzentriert sich auf Sensorstrukturen, die in klassischen Oberflächentechnologien gefertigt werden können. Experimentelle Tests der beiden genannten Abstimmprinzipien werden anhand von Strukturen in oberflächennaher Silizium-bulk-Mikromechanik (SCREAM) durchgeführt. Schwerpunkt der Arbeit sind nichtlineare Schwingungen der mechanischen Resonatorkomponente bei großen Amplituden, die durch die Resonanzüberhöhung entstehen. Für den Sonderfall des Duffing-Schwingers werden Dimensionierungsregeln zur Minimierung der Nichtlinearitäten entwickelt. Kapazitive Prinzipien zur Detektion bzw. elektrostatischen Abstimmung werden hinsichtlich ihrer Linearität geprüft. Es werden neuartige Elektrodensysteme für die SCREAM-Technologie, sogenannte Kurvenkammsysteme entwickelt, die bei Schwingamplituden bis zu 10 Mikrometer linear arbeiten.