In this thesis novel motion models have been developed and incorporated into an extended parameter estimation framework that allows to accurately estimate the parameters and regularize them if needed. The performance of this framework has been increased to real time and implemented on inexpensive graphics hardware. Confidence and situation measures have been designed to discard inaccurate estimates. A phase field approach was developed to estimate piecewise smooth motion while detecting object boundaries at the same time. These algorithmic improvements have been successfully applied to three areas of fluid dynamics: air-sea interaction, microfluidics and plant physiology. At the ocean surface, the fluxes of heat and momentum have been measured with thermographic techniques, both spatially and temporally highly resolved. These measurement techniques present milestones for research in air-sea interaction, where point measurements and particle based laboratory measurements represent the state-of-the art. Calculations were done with two models, both making complement assumptions. Still, results derived from both models agree remarkably well. Measurements were conducted in laboratory settings as well as in the field. Microfluidic flow was measured with a new approach to molecular tagging velocimetry that explicitly models Taylor dispersion. This has lead to an increase in accuracy and applicability. Inaccuracies and problems of previous approaches due to Taylor dispersion were successfully evaded. Ground truth test measurements have been conducted, proving the accuracy of this novel technique. For the first time, flow velocities were measured in the xylem of plant leaves with active thermography. This represents a technique for measuring these flows on extended leaf areas on free standing plants, minimizing the impact caused by the measurement. Ground truth measurements on perfused leafs were performed. Measurements were also conducted on free standing plants in a climatic chamber, to measure xylem flows and relate flow velocities to environmental parameter. With a cuvette, environmental factors were varied locally. These measurements underlined the sensitivity of the new approach. A linear relationship in between flow rates and xylem diameter was found.
Probleme der Optimalen Steuerung, die zeitabhaengige diskrete Entscheidungen beinhalten, haben in letzter Zeit zunehmend Beachtung gefunden, da sie in praktischen Anwendungen mit hohem Potential fuer Optimierung auftreten. Typische Beispiele sind die Wahl von Gaengen in Transport-Problemen oder Prozesse, in denen Ventile verwendet werden. Wir praesentieren Rundungsstrategien fuer direkte Methoden der optimalen Steuerung, die zu einer Approximation der Zielfunktion und Nebenbedingungen fuehren, deren Guete durch die Feinheit des Kontrolldiskretisierungsgitters abgeschaetzt werden kann. Erstmals wird gezeigt, dass eine endliche Anzahl von Umschaltungen sowohl im linearen wie im nichtlinearen Fall ausreicht, und dies bei Existenz von Pfad- und Kontrollbeschraenkungen. Ein numerisches Beispiel wird angegeben um die Methodik zu illustrieren.
In the present work a chemical kinetic mechanism was developed, suitable for modeling combustion and partial oxidation processes of C1 – C4 alkanes. The gas-phase kinetic mechanism describes intermediate and high temperature chemistry. Accordingly, the formation and evolution of important intermediate gas-phase species: Olefins and oxygenates were described in terms of different pathways typical at those temperature regimes. A previously developed mechanism suitable for high temperature conditions was extended by including reactions which described the chemistry of total and partial oxidation of methane, ethane, propane, butane, lower alkenes and formation and consumption of their characteristic organic hydro-peroxide radicals and cyclical compounds. The kinetic mechanism was validated by comparing calculated results of ignition delay times, against experimental data obtained in shock tubes, for various hydrocarbons and their mixtures, over a wide range of reaction conditions (temperature, pressure and mixture composition). Further, the kinetic mechanism was evaluated by comparing numerical simulations against experimentally obtained concentration profiles of the main gas-phase species, measured in jet stirred reactors for different hydrocarbons and their mixtures during partial oxidation. Next, the mechanism was applied to get a better understanding of the interactions between flow, mass transfer and homogeneous-heterogeneous chemistries during the catalytic partial oxidation of methane in a short contact time reactor, which has recently attracted strong scientific and technological interest. The detailed study of the catalytic partial oxidation of methane to syngas in a single gauze reactor was based on three-dimensional numerical simulations of the flow field coupled with heat transport and multi-step gas-phase and surface reaction mechanisms, including the computation of the surface coverage. Results from the model were compared with experimental data reported in the literature. The gas-phase mechanism was modeled using a reduced mechanism, and for the surface a previously developed mechanism was adapted. The results from the simulation of the partial oxidation of methane in a short contact time reactor were carried out using the commercial computational fluid dynamics code Fluent, which was coupled with external subroutines to model the detailed gas-phase and surface chemistry. Today, the production of synthesis gas (carbon monoxide + hydrogen) is currently carried out via steam reforming. In that process steam passes over a carbon source, often methane or coal, and is heated to produce the synthesis gas. Synthesis gas is extremely valuable commercially for the production of methanol, hydrocarbons, higher alcohols for use in detergents, and ammonia to use in fertilizers. There is also a significant interest in the production of hydrogen for fuel cells. However, steam reforming has the major disadvantage of being endothermic and hence requires a large amount of wasted energy to drive the reaction. An alternative to steam reforming is the partial oxidation of the hydrocarbons, especially methane in short contact time reactors. This promising route for natural gas conversion into more useful chemicals has the advantage of being auto thermal.
This thesis investigates Time-of-Flight (TOF) 3D imaging systems. A mathematical model is developed to predict the systematic errors and statistical uncertainties of such cameras. In order to determine the errors experimentally and to test the model, a custom experimental setup has been built for this work. Chapter 2 provides a detailed discussion of this experimental setup. Three camera systems are investigated experimentally: the PMD[vision] 19k, the SwissRanger SR-3000) and the Effector O3D. All cameras have a maximum measurement range of 7.5 m. This thesis discusses the experiments, the results and the implication of this tests and concludes with a critical discussion of the results. Possible ways to correct the revealed systematic errors is presented in the discussion. This work reveals three common systematic errors: the variation due to the anharmonic LED modulation provokes a periodic depth error of around 80-200 mm (depending on camera), the inhomogeneity of the pixels accounts for around 20 mm and the constant offset depending on the integration time was found to vary between 35-100 mm. The statistical variances at 30% of the maximum amplitude was found to be between 9 mm and 23 mm. Moreover, a technique to detect and remove overexposed pixels whenever possible is presented. With the proposed calibration, the absolute systematic error could be reduced in a sample calibration for the SwissRanger SR-3000 from maximal 300 mm (standard deviation: 40.81 mm) to below 16 mm (standard deviation: 3.16 mm) for all well exposed pixels. This work has been done within the framework of the Lynkeus-3D project (http://www.lynkeus-3d.de) supported by the BMBF (Bundesministerium für Bildung und Forschung) and in close cooperation with industry partners. The investigations of this work led to the detection and the mending of a construction error in one of the camera systems.
The film Seljuk Muqarnas along the Silk Road gives an overview of muqarnas, stalactite vaults, in Seljuk style architecture (1038-1194). The muqarnas are located in portals and niches of caravansaraies, madrassas and mosques. Starting with the Sultan Han near Kayseri we follow the Silk Road westward till Konya and finally show the Arslanhane Camii in Ankara. Video recordings alternate with computer reconstructions and animations, explaining the assembly of a caravansaray and the composition of muqarnas. The timeline of the video is contained in this paper. Muqarnas reconstructions follow mathematical rules and stylistic specialties. Possible combinations of elements in tiers can be expressed in their 2D plane projection by means of a directed graph. On the other hand, given a 2D plan we are able to determine the directed graphs which correspond to a muqarnas. After adjusting some free directions manually, the 3D models can be generated automatically.
The mechanisms through which proteins achieve their functional three-dimensional structure starting from a string of amino acids, as well as the manner in which the interactions between different structural elements are orchestrated to mediate function are largely unknown, despite the large amount of data accumulating from theoretical and experimental studies. One clear view emerging from all these studies is that function is a result of the intrinsic protein dynamics and flexibility, namely the motions of its well-defined structural elements and their ability to change their position and shape in space to allow large conformational transitions necessary for the function. Simulation techniques have been increasingly used over the past years in the endeavour to solve the structure-function puzzle as they have proven to be powerful tools to investigate the dynamics of proteins. However, extracting useful dynamical information from trajectories thus generated in order to draw functionally relevant conclusions is not always straight forward, especially when the protein function involves concerted movements of entire protein domains. This is due to the high dimensionality of the energy surface the proteins can explore. Therefore, a decrease in complexity is to be desired and can be achieved in principle by reducing the number of dimensions to the ones capturing only the dominant motions of the protein. To this purpose, in this thesis two different dimensionality reducing techniques, namely Principal Component Analysis and Sammon Mapping are applied and compared on four proteins that undergo conformational changes with different amplitudes and mechanisms. In particular, the present thesis tackles the large conformational change occurring during the recovery stroke of myosin, using these methods and rigidity analysis algorithms in the attempt to elucidate in atomic detail the structural mechanism underlying the function of this protein that couples ATP hydrolysis to the mechanical force needed to achieve muscle contraction. The results presented in this thesis show the successful applicability of certain dimensionality reducing methods to large conformational changes and their suitability in analyzing and dissecting dynamical transitions in computationally generated trajectories. The findings regarding the recovery stroke step in the myosin cycle are consistent with experimental data coming from mutational studies and confirm the previously postulated communication mechanism between the active sites of the protein, thus representing a major contribution to the field of molecular motors and a strong evidence of the importance of theoretical studies in complementing the experimental investigations.
Pollutant reduction of internal combustion engines plays an essential role in automotive industry research and development. Exhaust-gas after-treatment using catalytic converters is of key importance to this goal. Storage catalytic converters based on barium oxide are a technology with promising potential to meet current and future emission standards for nitric oxides (NOx) abatement of lean-burning gasoline and Diesel engines. The aim of this work was to develop elementary reaction steps and determine kinetic parameters for the NOx storage reaction mechanism by means of density functional theory (DFT). DFT has proven a powerful tool in investigating microscopic aspects of heterogeneous reactions. Electronic structure calculations were performed for adsorption of different molecules on two surfaces relevant in automotive exhaust gas purification: barium oxide and platinum.
In dieser Dissertation wird eine Methode zur simultanen, optischen Objektvermessung basierend auf Weißlicht-Interferometrie vorgestellt. Das Verfahren beruht auf dem Prinzip des räumlichen Phasenschiebens und profitiert gegenüber herkömmlichen sequentiellen Techniken vom Verzicht beweglicher mechanischer Komponenten. Als statischer optischer Aufbau zeichnet es sich durch seine Robustheit aus und eignet sich somit für Anwendungsgebiete außerhalb des Labors. Auf Grund der simultanen Signalerfassung ist es nicht nur für die berührungslose Qualitätskontrolle interessant, sondern auch für medizinische Applikationen und zur quantitativen Beobachtung dynamischer Oberflächenprozesse. Im ersten Teil der Arbeit wird die Entwicklung des Systems im Kontext physikalischer Voraus-setzungen und technischer Randbedingungen diskutiert. Darauf folgt die Untersuchung einzelner Komponenten und deren Einflusses auf das Gesamtsystem. Ein weiterer Schwerpunkt der Arbeit liegt in den statistischen Eigenschaften der Speckle-Felder, die sich durch Reflexion diffus streuender Medien ausbilden. Bereits existierende Theorien, die den Einfluss von Speckle auf die longitudinale Auflösung der Weißlicht-Interferometrie beschreiben, werden mit dieser Arbeit vervollständigt. Mit Hilfe der entwickelten Methoden zur Simulation und experi-mentellen Überprüfung lassen sich die theoretischen Vorhersagen verdeutlichen und veri-fizieren. Sowohl für simultane als auch sequentielle Verfahren sind diese Ergebnisse insbe-sondere bei der Entwicklung hochaperturiger Systeme entscheidend.
In this thesis, fast and highly accurate interferometric metrology systems for both smooth and rough surfaces are presented. First, high-speed algorithms for white-light interferometry (WLI) and line scanning WLI are developed and their performance is compared. For large height differences, multiple wavelength interferometry is significantly faster, though, as in this approach the number of frames required for a surface estimate does not increase with surface height range. A system based on a tunable diode laser is discussed in detail, and new sampling schemes and estimation algorithms for the device are derived. An approximation to the theoretically optimal sampling pattern is given and a corresponding fast estimation algorithm is presented. As a building block for that algorithm, accurate and fast phase and frequency estimation from a low number of samples is discussed, and a new approach based on an interpolated FFT is presented. The influence of laser speckle on rough surfaces is investigated. A robust, adaptive filtering algorithm is developed. It takes spatial relationships into account — without imposing strong smoothness constraints — and uses additional knowledge on the signal from the raw data to improve performance significantly, especially on rough surfaces.
In this thesis the use of state-space models for analysis and classification of time series data, gathered from industrial manufacturing processes and the life sciences, is investigated. To overcome hitherto unsolved problems in both application domains the temporal behavior of the data is captured using state-space models. Industrial laser welding processes are monitored with a high speed camera and the appearance of unusual events in the image sequences correlates with errors on the produced part. Thus, novel classification frameworks are developed to robustly detect these unusual events with a small false positive rate. For classifier learning, class labels are by default only available for the complete image sequence, since scanning the sequences for anomalies is expensive. The first framework combines appearance based features and state-space models for the unusual event detection in image sequences. For the first time, ideas adapted from face recognition are used for the automatic dimension reduction of images recorded from laser welding processes. The state-space model is trained incrementally and can learn from erroneous sequences without the need of manually labeling the position of the error event within sequences. %The limitation to weakly labeled data helps to reduce the labeling effort. In addition, a second framework for the object-based detection of sputter events in laser welding processes is developed. The framework successfully combines for the first time temporal change detection, object tracking and trajectory classification for the detection of weak sputter events. %This is the first time that object tracking is successfully applied to automatic sputter detection. For the application in the life sciences the improvement and further development of data analysis methods for Single Molecule Fluorescence Spectroscopy (SMFS) is considered. SMFS experiments allow to study biochemical processes on a single molecule basis. The single molecule is excited with a laser and the photons which are emitted thereon by fluorescence contain important information about conformational changes of the molecule. Advanced statistical analysis techniques are necessary to infer state changes of the molecule from changes in the photon emissions. By using state-space models, it is possible to extract information from recorded photon streams which would be lost with traditional analysis techniques.
Similarly to funnel equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. A distribution-like approach leads to so-called right-hand forward solutions. This concept is applied to a type of geometric evolution having motivated the definitions : compact subsets of the Euclidean space evolve according to nonlocal properties of both the set and their limiting normal cones at the boundary. The existence of a solution is based on Euler method using reachable sets of differential inclusions as "elementary deformations" (called forward transitions). Thus, the regularity of these reachable sets at the topological boundaries is studied extensively in the appendix.
We study the asymptotic behaviour of some mesoscopic stochastic models for systems of reacting and diffusing particles (also known as density-dependent population processes) as the number of particles goes to infinity. Our approach is related to the variational approach to solving the parabolic partial differential equations that arise as limit dynamics. We first present a result for a model that converges to a classical system of reaction-diffusion equations. In addition, we discuss two models with nonlinear diffusion that give rise to quasilinear parabolic equations in the limit.
Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear “reduction equations” particularly difficult in many cases where the gap in intrinsic time scales is not large enough. We demonstrate that trajectory optimization approaches can avoid such severe restrictions by computing numerical solutions that correspond to “maximally relaxed” dynamical modes in a suitable sense. We present a framework of trajectory-based optimization for model reduction in chemical kinetics and a general class of reduction criteria characterizing the relaxation of chemical forces along reaction trajectories. These criteria can be motivated geometrically exploiting ideas from differential geometry and fundamental physics and turn out to be highly successful in example applications. Within this framework, we provide results for the computational approximation of slow attracting low-dimensional manifolds in terms of families of optimal trajectories for a six-component hydrogen combustion mechanism.
The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well-known assumptions of Filippov's existence theorem (about differential inclusions), every epi-Lipschitzian initial compact set (of the Euclidean space) preserves this regularity for a (possibly short) time, i.e. its reachable set is also epi-Lipschitzian for all small times. The proof is based on Rockafellar's geometric characterization of epi-Lipschitzian sets and uses a new result about the "inner semicontinuity" of Clarke tangent cone (to reachable sets) with respect to both time and base point.
The focus of interest is the Cauchy problem of the nonlinear transport equation d_t u + div (f(u, ·) u) = g(u, ·) u together with its distributional solutions u(·) whose values are positive Radon measures on the Euclidean space with compact support. The coefficients f(u, t), g(u, t) are assumed to be uniformly bounded and Lipschitz continuous vector fields on the Euclidean space. Sufficient conditions on the coefficients for existence, uniqueness and even for stability of these distributional solutions are presented. Starting from the well-known results about the corresponding linear problem, the step towards the nonlinear problem here relies on Aubin's mutational equations, i.e. dynamical systems in a metric space (with a new slight modification).
In many types of media, and in particular within living cells or within their membranes, diffusing species do not follow Fick's laws, but instead show transient subdiffusive behavior. Formulating spatiotemporal models that take this behavior into account is a delicate matter, as one is faced with the choice of resorting either to fractional calculus or to microscopic descriptions. In this article, we provide an alternative designed to be easier to tackle analytically and numerically than the existing approaches. Specifically, starting from the Continuous Time Random Walk model, we construct linear reaction diffusion systems that can be used as components within such a model, and which capture the defining properties of subdiffusion. We show how to impose physically relevant parameters, and prove stability and mass conservation. While applications to cellular biology are our main motivation, our approach is abstract, and should thus be applicable to any situation where anomalous subdiffusion is observed.
Das molekulare Motorprotein Myosin wandelt chemische Energie aus der ATP Hydolyse in mechanische Arbeit um, die dazu genutzt wird um Myosin- und Aktin-Filamente gegeneinander zu verschieben und so z.B. die Muskelkontraktion zu ermoeglichen. Der Mechanismus dieser chemisch-mechanischen Kopplung, der fuer die Funktion von Myosin essenziell ist, ist nur in Ansaetzen verstanden. In dieser Arbeit wird ein rechnergesttzter Ansatz verwendet um den Mechanismus des recovery stroke'' zu verstehen. Der recovery stroke'' ist einer der fundamentalen Prozesse bei der Muskelkontraktion in lebenen Organismen. Waehrend des recovery stroke'' wird der Myosin Motor fuer den naechsten Kraftschlag vorbereited indem der Myosin-Kopf um 60 degree relativ zur Konverter-Domaene und dem Hebelarm gedreht wird. Der Drehpunkt ist mit der Bindetasche, in der die ATP Hydrolyse stattfindet, durch die sogenannte Relais-Helix verbunden. Waehrend des "recovery stroke" finden eine eine Reihe von strukturellen Aenderungen laengs dieser Helix statt. In der vorliegenden Arbeit wird der Kopplungsmechanismus zwischen der ATP Hydrolyse und der Drehbewegung mit Hilfe eines Minimum-Energie Pfades (MEP) simuliert. Der MEP verbindet die Roentgenkristallographischen End-Zustaende des Prozesses durch eine Kette von geometrieoptimierten intermediren Strukturen. Der "recovery stroke" beruht auf der Bildung zweier Wasserstoffbrueckenbindungen durch die "switch-2" Schleife, in Korrelation mit der Bewegung zweier Helices welche die Konverter-Domaene halten: der Relais-Helix und der SH1-Helix. Der MEP zeigt dass dieser Prozess aus zwei Phasen besteht. In der ersten Phase bildet sich eine Wasserstoffbrueckenbindung zwischen Gly457 am N-terminalen Ende der Relais-Helix und dem gamma-Phosphat des ATP, was eine Kipp-Bewegung der Relais-Helix zur Folge hat. Die zweite Phase wird durch die Bildung einer Wasserstoffbrueckenbindung zwischen der "switch-2" Schleife und Ser181 der P-Schleife initiiert. Dadurch wird eine weitere Schleifeaehnlich einem Keil gegen das N-terminale Ende der SH1-Helix geschoben, wodurch letztere parallel zur Relais-Helix verschoben wird. Die Kippbewegung der ersten Phase bewirkt eine Drehung der Konverter-Domäne um 30 degree, wahrend die Verschiebung der SH1-Helix eine Drehung um weitere 40 degree zur Folge hat. Der hier vorgeschlagene Kopplungsmechanismus ist konsistent mit verfuegbaren Mutations-Experimenten und erklaert zum ersten Mal die Rolle der hochgradig Sequenz-konservierten Schleife, die hier "Keil"-Schleife genannt wird. In einem weiteren Teil der Arbeit werden Molekulardynamik-Simulationen von Myosin II des Organismus Dictyostelium Discoideum in beiden End-Zustaenden des "recovery stroke" mit verschiedenen Nukleotid-Zustaenden (ATP, ADP.Pi, ADP) durchgefuehrt. Diese Simulationen zeigen dass die Seitenkette von Asn475 (welche die erste Phase des "recovery stroke" initiiert") sich durch die ATP-Hydrolyse von "switch-2" wegbewegt und eine Wasserstoffbrueckenbindung mit Tyr573 auf der Keilschleife bildet. Diese Abhaengigkeit vom Nukleotid-Zustand wird erklaert durch eine kleine Verschiebung des abgespaltenen beta-Phosphats hin zu Gly457 welches seinerseits Asn475 verschiebt. Die Sensitivitaet bezueglich des Nukleotid-Zustandes ist wichtig fuer (i) die Vermeidung einer unproduktiven Umkehrung des "recovery strokes" waehrend des ADP.Pi Zustandes, und (ii) die Entkopplung der Relais-Helix vom "switch-2", wodurch erreicht wird, dass der Kraftschlag nach der initialen Bindung an Aktin ausgelast wird, wobei Gly457 von "switch-2" weiterhin mit dem Pi interagiert,welches bekanntermass en erst nach der Bindung an Aktin freigelassen wird. Es wird beobachtet dass die katalytisch wichtige Salzbruecke zwischen Arg238 (in "switch-1") und Glu459 (in "switch-2"), welche die Bindetasche and der Hydrolysestelle bedeckt, durch die Bindung von ATP an die Struktur vor dem "recovery stroke" schnell gebildet wird. Diese Salzbrucke bleibt auch nach dem "recovery stroke" stabil, was darauf hindeuted dass sie die Rolle hat die ATP Bindetasche durch "induced fit" zu formen.