Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Phosphorus placement an acid arenosols of the West African Sahel

Phosphorus (P) deficiency is a major constraint to pearl millet (Pennisetum glaucum L.) growth on acid sandy soils of the West African Sahel. To develop cost-effective fertilization strategies for cash poor farmers, experiments with pearl millet were conducted in southwestern Niger. Treatments comprised single superphosphate hill-placed at rates of 1, 3, 5 or 7 kg P ha^−1 factorially combined with broadcast P at a rate of 13 kg ha^−1. Nitrogen was applied as calcium ammonium nitrate at rates of 30 and 45 kg ha^−1. At low soil moisture, placement of single superphosphate in immediate proximity to the seed reduced seedling emergence. Despite these negative effects on germination, P placement resulted in much faster growth of millet seedlings than did broadcast P. With P application, potassium nutrition of millet was improved and seedling nitrogen uptake increased two- to three-fold, indicating that nitrogen was not limiting early millet growth. Averaged over the 1995 and 1996 cropping seasons, placed applications of 3, 5 and 7 kg P ha^−1 led to 72%, 81% and 88% respectively, of the grain yield produced by broadcasting 13 kg P ha^−1. Nitrogen application did not show major effects on grain yield unless P requirements were met. A simple economic analysis revealed that the profitability of P application, defined as additional income per unit of fertilizer, was highest for P placement at 3 and 5 kg ha^−1.

Development of thermo-analytical prediction and classification models for food in thermal devices using a multi sensor system and artificial neural networks

Die thermische Verarbeitung von Lebensmitteln beeinflusst deren Qualität und ernährungsphysiologischen Eigenschaften. Im Haushalt ist die Überwachung der Temperatur innerhalb des Lebensmittels sehr schwierig. Zudem ist das Wissen über optimale Temperatur- und Zeitparameter für die verschiedenen Speisen oft unzureichend. Die optimale Steuerung der thermischen Zubereitung ist maßgeblich abhängig von der Art des Lebensmittels und der äußeren und inneren Temperatureinwirkung während des Garvorgangs. Das Ziel der Arbeiten war die Entwicklung eines automatischen Backofens, der in der Lage ist, die Art des Lebensmittels zu erkennen und die Temperatur im Inneren des Lebensmittels während des Backens zu errechnen. Die für die Temperaturberechnung benötigten Daten wurden mit mehreren Sensoren erfasst. Hierzu kam ein Infrarotthermometer, ein Infrarotabstandssensor, eine Kamera, ein Temperatursensor und ein Lambdasonde innerhalb des Ofens zum Einsatz. Ferner wurden eine Wägezelle, ein Strom- sowie Spannungs-Sensor und ein Temperatursensor außerhalb des Ofens genutzt. Die während der Aufheizphase aufgenommen Datensätze ermöglichten das Training mehrerer künstlicher neuronaler Netze, die die verschiedenen Lebensmittel in die entsprechenden Kategorien einordnen konnten, um so das optimale Backprogram auszuwählen. Zur Abschätzung der thermische Diffusivität der Nahrung, die von der Zusammensetzung (Kohlenhydrate, Fett, Protein, Wasser) abhängt, wurden mehrere künstliche neuronale Netze trainiert. Mit Ausnahme des Fettanteils der Lebensmittel konnten alle Komponenten durch verschiedene KNNs mit einem Maximum von 8 versteckten Neuronen ausreichend genau abgeschätzt werden um auf deren Grundlage die Temperatur im inneren des Lebensmittels zu berechnen. Die durchgeführte Arbeit zeigt, dass mit Hilfe verschiedenster Sensoren zur direkten beziehungsweise indirekten Messung der äußeren Eigenschaften der Lebensmittel sowie KNNs für die Kategorisierung und Abschätzung der Lebensmittelzusammensetzung die automatische Erkennung und Berechnung der inneren Temperatur von verschiedensten Lebensmitteln möglich ist.

Multi-site time-trend analysis of soil fertility management effects on crop production in sub-Saharan West Africa

Soil fertility constraints to crop production have been recognized widely as a major obstacle to food security and agro-ecosystem sustainability in sub-Saharan West Africa. As such, they have led to a multitude of research projects and policy debates on how best they should be overcome. Conclusions, based on long-term multi-site experiments, are lacking with respect to a regional assessment of phosphorus and nitrogen fertilizer effects, surface mulched crop residues, and legume rotations on total dry matter of cereals in this region. A mixed model time-trend analysis was used to investigate the effects of four nitrogen and phosphorus rates, annually applied crop residue dry matter at 500 and 2000 kg ha^-1, and cereal-legume rotation versus continuous cereal cropping on the total dry matter of cereals and legumes. The multi-factorial experiment was conducted over four years at eight locations, with annual rainfall ranging from 510 to 1300 mm, in Niger, Burkina Faso, and Togo. With the exception of phosphorus, treatment effects on legume growth were marginal. At most locations, except for typical Sudanian sites with very low base saturation and high rainfall, phosphorus effects on cereal total dry matter were much lower with rock phosphate than with soluble phosphorus, unless the rock phosphate was combined with an annual seed-placement of 4 kg ha^-1 phosphorus. Across all other treatments, nitrogen effects were negligible at 500 mm annual rainfall but at 900 mm, the highest nitrogen rate led to total dry matter increases of up to 77% and, at 1300 mm, to 183%. Mulch-induced increases in cereal total dry matter were larger with lower base saturation, reaching 45% on typical acid sandy Sahelian soils. Legume rotation effects tended to increase over time but were strongly species-dependent.

3D Simultaneous Inversion for Seismic Structure and Local Hypocenters in Germany under Consideration of Seismic Anisotropy in the Upper Mantel

The main task of this work has been to investigate the effects of anisotropy onto the propagation of seismic waves along the Upper Mantle below Germany and adjacent areas. Refraction- and reflexion seismic experiments proved the existence of Upper Mantle anisotropy and its influence onto the propagation of Pn-waves. By the 3D tomographic investigations that have been done here for the crust and the upper mantle, considering the influence of anisotropy, a gap for the investigations in Europe has been closed. These investigations have been done with the SSH-Inversionprogram of Prof. Dr. M. Koch, which is able to compute simultaneously the seismic structure and hypocenters. For the investigation, a dataset has been available with recordings between the years 1975 to 2003 with a total of 60249 P- and 54212 S-phase records of 10028 seismic events. At the beginning, a precise analysis of the residuals (RES, the difference between calculated and observed arrivaltime) has been done which confirmed the existence of anisotropy for Pn-phases. The recognized sinusoidal distribution has been compensated by an extension of the SSH-program by an ellipse with a slow and rectangular fast axis with azimuth to correct the Pn-velocities. The azimuth of the fast axis has been fixed by the application of the simultaneous inversion at 25° - 27° with a variation of the velocities at +- 2.5 about an average value at 8 km/s. This new value differs from the old one at 35°, recognized in the initial residual analysis. This depends on the new computed hypocenters together with the structure. The application of the elliptical correction has resulted in a better fit of the vertical layered 1D-Model, compared to the results of preceding seismological experiments and 1D and 2D investigations. The optimal result of the 1D-inversion has been used as initial starting model for the 3D-inversions to compute the three dimensional picture of the seismic structure of the Crust and Upper Mantle. The simultaneous inversion has showed an optimization of the relocalization of the hypocenters and the reconstruction of the seismic structure in comparison to the geology and tectonic, as described by other investigations. The investigations for the seismic structure and the relocalization have been confirmed by several different tests. First, synthetic traveltime data are computed with an anisotropic variation and inverted with and without anisotropic correction. Further, tests with randomly disturbed hypocenters and traveltime data have been proceeded to verify the influence of the initial values onto the relocalization accuracy and onto the seismic structure and to test for a further improvement by the application of the anisotropic correction. Finally, the results of the work have been applied onto the Waldkirch earthquake in 2004 to compare the isotropic and the anisotropic relocalization with the initial optimal one to verify whether there is some improvement.

Nutrient cycling and nutrient use efficiency in urban and peri-urban agriculture of Kabul, Afghanistan

Like elsewhere also in Kabul, Afghanistan urban and peri-urban agriculture (UPA) has often been accused of being resource inefficient and unsustainable causing negatives externalities to community health and to the surroundings. These arise from the inappropriate management and use of agricultural inputs, including often pesticides and inter-city wastes containing heavy metal residues and pathogens. To address these concerns, parallel studies with the aims of quantification of carbon (C), nitrogen (N), phosphorus (P) and potassium (K) horizontal and vertical fluxes; the assessment of heavy metal and pathogen contaminations of UPA produce, and an economic analysis of cereal, vegetable and grape production systems conducted for two years in UPA of Kabul from April 2008 to October 2009. The results of the studies from these three UPA diverse production systems can be abridged as follows: Biennial net balances in vegetable production systems were positive for N (80 kg ha-1 ), P (75 kg ha-1) and C (3,927 kg ha-1), negative for K (-205 kg ha-1), whereas in cereal production systems biennial horizontal balances were positive for P (20 kg ha-1 ) and C (4,900 kg ha-1) negative for N (-155 kg ha-1) and K (-355 kg ha-1) and in vineyards corresponding values were highly positive for N (295 kg ha-1), P (235 kg ha-1), C (3,362 kg ha-1) and slightly positive for K (5 kg ha-1). Regardless of N and C gaseous emissions, yearly leaching losses of N and P in selected vegetable gardens varied from 70 - 205 kg N ha-1 and 5 - 10 kg P ha-1. Manure and irrigation water contributed on average 12 - 79% to total Inputs of N, P, K and C, 10 - 53% to total inputs of C in the gardens and fields. The elevated levels of heavy metal and pathogen loads on fresh UPA vegetables reflected contamination from increasing traffic in the city, deposits of the past decades of war, lacking collection and treatment of raw inter-city wastes which call for solutions to protect consumer and producer health and increase reliability of UPA productions. A cost-revenue analysis of all inputs and outputs of cereal, vegetable and grapes production systems over two years showed substantial differences in net UPA household income. To confirm these results, more detailed studies are needed, but tailoring and managing the optimal application of inputs to crop needs will significantly enhance farmer’s better revenues as will as environmental and produce quality.

Biochar improves fertility of a clay soil in the Brazilian Savannah: short term effects and impact on rice yield

The objective of this study was to report single season effects of wood biochar (char) application coupled with N fertilization on soil chemical properties, aerobic rice growth and grain yield in a clayey Rhodic Ferralsol in the Brazilian Savannah. Char application effected an increase in soil pH, K, Ca, Mg, CEC, Mn and nitrate while decreasing Al content and potential acidity of soils. No distinct effect of char application on grain yield of aerobic rice was observed. We believe that soil properties impacted by char application were inconsequential for rice yields because neither water, low pH, nor the availability of K or P were limiting factors for rice production. Rate of char above 16 Mg ha^(−1) reduced leaf area index and total shoot dry matter by 72 days after sowing. The number of panicles infected by rice blast decreased with increasing char rate. Increased dry matter beyond the remobilization capacity of the crop, and high number of panicles infected by rice blast were the likely cause of the lower grain yield observed when more than 60 kg N ha^(−1) was applied. The optimal rate of N was 46 kg ha^(−1) and resulted in a rice grain yield above 3 Mg ha^(−1).

Optimierung von Betriebsstrategien für elektrifizierte Antriebskonzepte

Im Rahmen dieser Arbeit wird eine gemeinsame Optimierung der Hybrid-Betriebsstrategie und des Verhaltens des Verbrennungsmotors vorgestellt. Die Übernahme von den im Steuergerät verwendeten Funktionsmodulen in die Simulationsumgebung für Fahrzeuglängsdynamik stellt eine effiziente Applikationsmöglichkeit der Originalparametrierung dar. Gleichzeitig ist es notwendig, das Verhalten des Verbrennungsmotors derart nachzubilden, dass das stationäre und das dynamische Verhalten, inklusive aller relevanten Einflussmöglichkeiten, wiedergegeben werden kann. Das entwickelte Werkzeug zur Übertragung der in Ascet definierten Steurgerätefunktionen in die Simulink-Simulationsumgebung ermöglicht nicht nur die Simulation der relevanten Funktionsmodule, sondern es erfüllt auch weitere wichtige Eigenschaften. Eine erhöhte Flexibilität bezüglich der Daten- und Funktionsstandänderungen, sowie die Parametrierbarkeit der Funktionsmodule sind Verbesserungen die an dieser Stelle zu nennen sind. Bei der Modellierung des stationären Systemverhaltens des Verbrennungsmotors erfolgt der Einsatz von künstlichen neuronalen Netzen. Die Auswahl der optimalen Neuronenanzahl erfolgt durch die Betrachtung des SSE für die Trainings- und die Verifikationsdaten. Falls notwendig, wird zur Sicherstellung der angestrebten Modellqualität, das Interpolationsverhalten durch Hinzunahme von Gauß-Prozess-Modellen verbessert. Mit den Gauß-Prozess-Modellen werden hierbei zusätzliche Stützpunkte erzeugt und mit einer verminderten Priorität in die Modellierung eingebunden. Für die Modellierung des dynamischen Systemverhaltens werden lineare Übertragungsfunktionen verwendet. Bei der Minimierung der Abweichung zwischen dem Modellausgang und den Messergebnissen wird zusätzlich zum SSE das 2σ-Intervall der relativen Fehlerverteilung betrachtet. Die Implementierung der Steuergerätefunktionsmodule und der erstellten Steller-Sensor-Streckenmodelle in der Simulationsumgebung für Fahrzeuglängsdynamik führt zum Anstieg der Simulationszeit und einer Vergrößerung des Parameterraums. Das aus Regelungstechnik bekannte Verfahren der Gütevektoroptimierung trägt entscheidend zu einer systematischen Betrachtung und Optimierung der Zielgrößen bei. Das Ergebnis des Verfahrens ist durch das Optimum der Paretofront der einzelnen Entwurfsspezifikationen gekennzeichnet. Die steigenden Simulationszeiten benachteiligen Minimumsuchverfahren, die eine Vielzahl an Iterationen benötigen. Um die Verwendung einer Zufallsvariablen, die maßgeblich zur Steigerung der Iterationanzahl beiträgt, zu vermeiden und gleichzeitig eine Globalisierung der Suche im Parameterraum zu ermöglichen wird die entwickelte Methode DelaunaySearch eingesetzt. Im Gegensatz zu den bekannten Algorithmen, wie die Partikelschwarmoptimierung oder die evolutionären Algorithmen, setzt die neu entwickelte Methode bei der Suche nach dem Minimum einer Kostenfunktion auf eine systematische Analyse der durchgeführten Simulationsergebnisse. Mit Hilfe der bei der Analyse gewonnenen Informationen werden Bereiche mit den bestmöglichen Voraussetzungen für ein Minimum identifiziert. Somit verzichtet das iterative Verfahren bei der Bestimmung des nächsten Iterationsschrittes auf die Verwendung einer Zufallsvariable. Als Ergebnis der Berechnungen steht ein gut gewählter Startwert für eine lokale Optimierung zur Verfügung. Aufbauend auf der Simulation der Fahrzeuglängsdynamik, der Steuergerätefunktionen und der Steller-Sensor-Streckenmodelle in einer Simulationsumgebung wird die Hybrid-Betriebsstrategie gemeinsam mit der Steuerung des Verbrennungsmotors optimiert. Mit der Entwicklung und Implementierung einer neuen Funktion wird weiterhin die Verbindung zwischen der Betriebsstrategie und der Motorsteuerung erweitert. Die vorgestellten Werkzeuge ermöglichten hierbei nicht nur einen Test der neuen Funktionalitäten, sondern auch eine Abschätzung der Verbesserungspotentiale beim Verbrauch und Abgasemissionen. Insgesamt konnte eine effiziente Testumgebung für eine gemeinsame Optimierung der Betriebsstrategie und des Verbrennungsmotorverhaltens eines Hybridfahrzeugs realisiert werden.