Studies on High- Tc Superconductors with Inequivalent Conducting Layers

The thesis deals with the study of super conducting properties of layered cuprates within the frame work of a modified Lawrence-Doniach (LD) model. The thesis is organized in seven chapters. Chapter I is a survey of the phenomena and theories of conventional superconductivity which can serve as a springboard for launching the study of the new class of oxide superconductors and it also includes a chronological description of the efforts made to overcome the temperature barrier. Chapter II deals with the structure and properties of the copper oxide superconductors and also the experimental constraints on the theories of high te:::nperature superconductivity. A modified Lawrence-Doniach type of phenomenological model which forms the basis of the presnt study is also discussed. In chapter III~ the temperature dependence of the upper critical field both parallel and perpendicular to the layers is determined and the results are compared with d.c. magnetization measurements on different superconducting compoilllds. The temperature and angular dependence of the lower critical field both parallel and perpendicular to the layers is also discussed. Chapters IV, V and VI deal with thermal fluctuation effects on superconducting properties. Fluctuation specific heat is studied in chapter IV. Paraconductivity both parallel and perpendicular to the layers is discussed in chapter V. Fluctuation diamagnetism is dealt with in chapter VI. Dimensional cross over in the fluctuation regime of all these quantities is also discussed. Chapter VII gives a summary of the results and the conclusions arrived at.

Finite size effects on the electrical properties of sol–gel synthesized CoFe2O4 powders: deviation from Maxwell–Wagner theory and evidence of surface polarization effects

Fine particles of cobalt ferrite were synthesized by the sol–gel method. Subsequent heat treatment at different temperatures yielded cobalt ferrites having different grain sizes. X-ray diffraction studies were carried out to elucidate the structure of all the samples. Dielectric permittivity and ac conductivity of all the samples were evaluated as a function of frequency, temperature and grain size. The variation of permittivity and ac conductivity with frequency reveals that the dispersion is due to Maxwell–Wagner type interfacial polarization in general, with a noted variation from the expected behaviour for the cold synthesized samples. High permittivity and conductivity for small grains were explained on the basis of the correlated barrier-hopping model

Enhanced shape anisotropy and magneto-optical birefringence by high energy ball milling in NixFe1 xFe2O4 ferrofluids

Ferrofluids belonging to the series NixFe1 xFe2O4 were synthesised by two different procedures—one by standard co-precipitation techniques, the other by co-precipitation for synthesis of particles and dispersion aided by high-energy ball milling with a view to understand the effect of strain and size anisotropy on the magneto-optical properties of ferrofluids. The birefringence measurements were carried out using a standard ellipsometer. The birefringence signal obtained for chemically synthesised samples was satisfactorily fitted to the standard second Langevin function. The ball-milled ferrofluids showed a deviation and their birefringence was enhanced by an order. This large enhancement in the birefringence value cannot be attributed to the increase in grain size of the samples, considering that the grain sizes of sample synthesised by both modes are comparable; instead, it can be attributed to the lattice strain-induced shape anisotropy(oblation) arising from the high-energy ball-milling process. Thus magnetic-optical (MO) signals can be tuned by ball-milling process, which can find potential applications

GA-based Optimization of a Fourth-order Sigma-delta Modulator for WLAN

Over-sampling sigma-delta analogue-to-digital converters (ADCs) are one of the key building blocks of state of the art wireless transceivers. In the sigma-delta modulator design the scaling coefficients determine the overall signal-to-noise ratio. Therefore, selecting the optimum value of the coefficient is very important. To this end, this paper addresses the design of a fourthorder multi-bit sigma-delta modulator for Wireless Local Area Networks (WLAN) receiver with feed-forward path and the optimum coefficients are selected using genetic algorithm (GA)- based search method. In particular, the proposed converter makes use of low-distortion swing suppression SDM architecture which is highly suitable for low oversampling ratios to attain high linearity over a wide bandwidth. The focus of this paper is the identification of the best coefficients suitable for the proposed topology as well as the optimization of a set of system parameters in order to achieve the desired signal-to-noise ratio. GA-based search engine is a stochastic search method which can find the optimum solution within the given constraints.

Texture Description of low grade and high grade Glioma using Statistical features in Brain MRIs

Low grade and High grade Gliomas are tumors that originate in the glial cells. The main challenge in brain tumor diagnosis is whether a tumor is benign or malignant, primary or metastatic and low or high grade. Based on the patient's MRI, a radiologist could not differentiate whether it is a low grade Glioma or a high grade Glioma. Because both of these are almost visually similar, autopsy confirms the diagnosis of low grade with high-grade and infiltrative features. In this paper, textural description of Grade I and grade III Glioma are extracted using First order statistics and Gray Level Co-occurance Matrix Method (GLCM). Textural features are extracted from 16X16 sub image of the segmented Region of Interest(ROI) .In the proposed method, first order statistical features such as contrast, Intensity , Entropy, Kurtosis and spectral energy and GLCM features extracted were showed promising results. The ranges of these first order statistics and GLCM based features extracted are highly discriminant between grade I and Grade III. In this study which gives statistical textural information of grade I and grade III Glioma which is very useful for further classification and analysis and thus assisting Radiologist in greater extent.

Vertikale Integrationsstrukturen kommunaler Verkehrsunternehmen : eine transaktionskostentheoretische Evaluation

Der Markt für öffentlichen Personennahverkehr (ÖPNV) wird liberalisiert, in die gewachsenen Monopolstrukturen werden Marktmechanismen implementiert. Ziel der neuen ordnungspolitischen Rahmenbedingungen ist die Steigerung der Effizienz des defizitären Verkehrsbereichs, der von kommunalen Verkehrsunternehmen dominiert wird. Diese erbringen als Quasi-Monopolisten traditionell die Verkehrsdurchführung, regelmäßig anfallende Defizite werden von der öffentlichen Hand ausgeglichen. Bedingt durch ihre Leistungsstrukturen sind kommunale Verkehrsunternehmen in einem Wettbewerbsmarkt kaum konkurrenzfähig. Charakteristisch für diesen Unternehmenstyp ist der hohe Grad an vertikal integrierten Wertschöpfungsstufen. Im Gegensatz zu anderen Branchen erbringen kommunale Verkehrsunternehmen die wesentlichen Teile der gesamten ÖPNV-Wertschöpfungskette innerhalb der eigenen Unternehmensgrenzen. An dem hohen vertikalen Integrationsgrad setzt die Untersuchung an. Mit dem von Williamson entwickelten Instrumentarium der Transaktionskostentheorie werden die Leistungsbereiche einer transaktionskostentheoretischen Bewertung unterzogen. Als Alternativen zum institutionellen Arrangement der vertikalen Integration – das als Hierarchie bezeichnet wird – stehen die Arrangements Kooperation und Markt zur Verfügung. Die Bewertung zeigt, welche Leistungsbereiche unter transaktionskostentheoretischen Gesichtspunkten hierarchisch institutionalisiert werden sollten und welche alternativ erbracht werden können. Aus den Ergebnissen werden Strategieempfehlungen abgeleitet, die als Arbeitshypothesen einer anschließenden empirischen Überprüfung unterzogen werden. Die befragten ÖPNV-Experten bewerten somit die Marktfähigkeit der Strategieempfehlungen. Die Untersuchungsergebnisse werden für die Erarbeitung eines alternativen Koordinierungsarrangements für kommunale Verkehrsunternehmen herangezogen. Das Modell basiert auf der Grundlage Strategischer Netzwerke. Kommunale Verkehrsunternehmen nehmen in dem Modell die Rolle des Nukleus ein, der eine Vielzahl von Netzwerkpartnern steuert und für die Erbringung der ÖPNV-Leistungen mit diesen kooperiert.

Degrees of Free Word-Order and Freely Rewriting Restarting Automata

In natural languages with a high degree of word-order freedom syntactic phenomena like dependencies (subordinations) or valencies do not depend on the word-order (or on the individual positions of the individual words). This means that some permutations of sentences of these languages are in some (important) sense syntactically equivalent. Here we study this phenomenon in a formal way. Various types of j-monotonicity for restarting automata can serve as parameters for the degree of word-order freedom and for the complexity of word-order in sentences (languages). Here we combine two types of parameters on computations of restarting automata: 1. the degree of j-monotonicity, and 2. the number of rewrites per cycle. We study these notions formally in order to obtain an adequate tool for modelling and comparing formal descriptions of (natural) languages with different degrees of word-order freedom and word-order complexity.

Computeralgebraische Herleitung und Auswertung atomarer Störungsreihen und deren Anwendung auf geschlossenschalige und einfache offenschalige Systeme

In der vorliegenden Arbeit wurde gezeigt, wie mit Hilfe der atomaren Vielteilchenstörungstheorie totale Energien und auch Anregungsenergien von Atomen und Ionen berechnet werden können. Dabei war es zunächst erforderlich, die Störungsreihen mit Hilfe computeralgebraischer Methoden herzuleiten. Mit Hilfe des hierbei entwickelten Maple-Programmpaketes APEX wurde dies für geschlossenschalige Systeme und Systeme mit einem aktiven Elektron bzw. Loch bis zur vierten Ordnung durchgeführt, wobei die entsprechenden Terme aufgrund ihrer großen Anzahl hier nicht wiedergegeben werden konnten. Als nächster Schritt erfolgte die analytische Winkelreduktion unter Anwendung des Maple-Programmpaketes RACAH, was zu diesem Zwecke entsprechend angepasst und weiterentwickelt wurde. Erst hier wurde von der Kugelsymmetrie des atomaren Referenzzustandes Gebrauch gemacht. Eine erhebliche Vereinfachung der Störungsterme war die Folge. Der zweite Teil dieser Arbeit befasst sich mit der numerischen Auswertung der bisher rein analytisch behandelten Störungsreihen. Dazu wurde, aufbauend auf dem Fortran-Programmpaket Ratip, ein Dirac-Fock-Programm für geschlossenschalige Systeme entwickelt, welches auf der in Kapitel 3 dargestellen Matrix-Dirac-Fock-Methode beruht. Innerhalb dieser Umgebung war es nun möglich, die Störungsterme numerisch auszuwerten. Dabei zeigte sich schnell, dass dies nur dann in einem angemessenen Zeitrahmen stattfinden kann, wenn die entsprechenden Radialintegrale im Hauptspeicher des Computers gehalten werden. Wegen der sehr hohen Anzahl dieser Integrale stellte dies auch hohe Ansprüche an die verwendete Hardware. Das war auch insbesondere der Grund dafür, dass die Korrekturen dritter Ordnung nur teilweise und die vierter Ordnung gar nicht berechnet werden konnten. Schließlich wurden die Korrelationsenergien He-artiger Systeme sowie von Neon, Argon und Quecksilber berechnet und mit Literaturwerten verglichen. Außerdem wurden noch Li-artige Systeme, Natrium, Kalium und Thallium untersucht, wobei hier die niedrigsten Zustände des Valenzelektrons betrachtet wurden. Die Ionisierungsenergien der superschweren Elemente 113 und 119 bilden den Abschluss dieser Arbeit.

Optimal Sub-Pixel arrangements and coding for ultra-high resolution three-dimensional OLED displays

Information display technology is a rapidly growing research and development field. Using state-of-the-art technology, optical resolution can be increased dramatically by organic light-emitting diode - since the light emitting layer is very thin, under 100nm. The main question is what pixel size is achievable technologically? The next generation of display will considers three-dimensional image display. In 2D , one is considering vertical and horizontal resolutions. In 3D or holographic images, there is another dimension – depth. The major requirement is the high resolution horizontal dimension in order to sustain the third dimension using special lenticular glass or barrier masks, separate views for each eye. The high-resolution 3D display offers hundreds of more different views of objects or landscape. OLEDs have potential to be a key technology for information displays in the future. The display technology presented in this work promises to bring into use bright colour 3D flat panel displays in a unique way. Unlike the conventional TFT matrix, OLED displays have constant brightness and colour, independent from the viewing angle i.e. the observer's position in front of the screen. A sandwich (just 0.1 micron thick) of organic thin films between two conductors makes an OLE Display device. These special materials are named electroluminescent organic semi-conductors (or organic photoconductors (OPC )). When electrical current is applied, a bright light is emitted (electrophosphorescence) from the formed Organic Light-Emitting Diode. Usually for OLED an ITO layer is used as a transparent electrode. Such types of displays were the first for volume manufacture and only a few products are available in the market at present. The key challenges that OLED technology faces in the application areas are: producing high-quality white light achieving low manufacturing costs increasing efficiency and lifetime at high brightness. Looking towards the future, by combining OLED with specially constructed surface lenses and proper image management software it will be possible to achieve 3D images.

Further investigations on doubly excited four-electron ions: beam-foil experiment and MCDF theory

In continuation of our previous work on the quintet transitions 1s2s2p^2 ^5 P-1s2s2p3d ^5 P^0, ^5 D^0, results on other n = 2 - n' = 3 quintet transitions for elements N, 0 and F are presented. Assignments have been established by comparison with Multi-Configuration Dirac-Fock calculations. High spectral resolution on beam-foil spectroscopy was essential for the identification of most of the lines. For some of the quintet lines decay curves were measured, and the lifetimes extracted were found to be in reasonable agreement with MCDF calculations.

Information Exchange and Fusion in Dynamic and Heterogeneous Distributed Environments

Context awareness, dynamic reconfiguration at runtime and heterogeneity are key characteristics of future distributed systems, particularly in ubiquitous and mobile computing scenarios. The main contributions of this dissertation are theoretical as well as architectural concepts facilitating information exchange and fusion in heterogeneous and dynamic distributed environments. Our main focus is on bridging the heterogeneity issues and, at the same time, considering uncertain, imprecise and unreliable sensor information in information fusion and reasoning approaches. A domain ontology is used to establish a common vocabulary for the exchanged information. We thereby explicitly support different representations for the same kind of information and provide Inter-Representation Operations that convert between them. Special account is taken of the conversion of associated meta-data that express uncertainty and impreciseness. The Unscented Transformation, for example, is applied to propagate Gaussian normal distributions across highly non-linear Inter-Representation Operations. Uncertain sensor information is fused using the Dempster-Shafer Theory of Evidence as it allows explicit modelling of partial and complete ignorance. We also show how to incorporate the Dempster-Shafer Theory of Evidence into probabilistic reasoning schemes such as Hidden Markov Models in order to be able to consider the uncertainty of sensor information when deriving high-level information from low-level data. For all these concepts we provide architectural support as a guideline for developers of innovative information exchange and fusion infrastructures that are particularly targeted at heterogeneous dynamic environments. Two case studies serve as proof of concept. The first case study focuses on heterogeneous autonomous robots that have to spontaneously form a cooperative team in order to achieve a common goal. The second case study is concerned with an approach for user activity recognition which serves as baseline for a context-aware adaptive application. Both case studies demonstrate the viability and strengths of the proposed solution and emphasize that the Dempster-Shafer Theory of Evidence should be preferred to pure probability theory in applications involving non-linear Inter-Representation Operations.

Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

Regional Labor Market Disparities

Regionale Arbeitsmärkte unterscheiden sich erheblich hinsichtlich wesentlicher Kennzahlen wie der Arbeitslosenquote, des Lohnniveaus oder der Beschäftigungsentwicklung. Wegen ihrer Persistenz sind diese Unterschiede von hoher Relevanz für die Politik. Die wirtschaftswissenschaftliche Literatur liefert bereits theoretische Modelle für die Analyse regionaler Arbeitsmärkte. In der Regel sind diese Modelle aber nicht dazu geeignet, regionale Arbeitsmarktunterschiede endogen zu erklären. Das bedeutet, dass sich die Unterschiede regionaler Arbeitsmärkte in der Regel nicht aus den Modellzusammenhängen selbst ergeben, sondern „von außen“ eingebracht werden müssen. Die empirische Literatur liefert Hinweise, dass die Unterschiede zwischen regionalen Arbeitsmärkten auf die Höhe der regionalen Arbeitsnachfrage zurückzuführen sind. Die Arbeitsnachfrage wiederum leitet sich aus den Gütermärkten ab: Es hängt von der Entwicklung der regionalen Gütermärkte ab, wie viele Arbeitskräfte benötigt werden. Daraus folgt, dass die Ursachen für Unterschiede regionaler Arbeitsmärkte in den Unterschieden zwischen den regionalen Gütermärkten zu suchen sind. Letztere werden durch die Literatur zur Neuen Ökonomischen Geographie (NÖG) untersucht. Die Literatur zur NÖG erklärt Unterschiede regionaler Gütermärkte, indem sie zentripetale und zentrifugale Kräfte gegenüberstellt. Zentripetale Kräfte sind solche, welche hin zur Agglomeration ökonomischer Aktivität wirken. Im Zentrum dieser Diskussion steht vor allem das Marktpotenzial: Unternehmen siedeln sich bevorzugt an solchen Standorten an, welche nahe an großen Märkten liegen. Erwerbspersonen wiederum bevorzugen solche Regionen, welche ihnen entsprechende Erwerbsaussichten bieten. Beides zusammen bildet einen sich selbst verstärkenden Prozess, der zur Agglomeration ökonomischer Aktivität führt. Dem stehen jedoch zentrifugale Kräfte gegenüber, welche eine gleichmäßigere Verteilung ökonomischer Aktivität bewirken. Diese entstehen beispielsweise durch immobile Produktionsfaktoren oder Ballungskosten wie etwa Umweltverschmutzung, Staus oder hohe Mietpreise. Sind die zentripetalen Kräfte hinreichend stark, so bilden sich Zentren heraus, in denen sich die ökonomische Aktivität konzentriert, während die Peripherie ausdünnt. In welchem Ausmaß dies geschieht, hängt von dem Verhältnis beider Kräfte ab. Üblicherweise konzentriert sich die Literatur zur NÖG auf Unterschiede zwischen regionalen Gütermärkten und geht von der Annahme perfekter Arbeitsmärkte ohne Arbeitslosigkeit aus. Die Entstehung und Persistenz regionaler Arbeitsmarktunterschiede kann die NÖG daher üblicherweise nicht erklären. An dieser Stelle setzt die Dissertation an. Sie erweitert die NÖG um Friktionen auf dem Arbeitsmarkt, um die Entstehung und Persistenz regionaler Arbeitsmarktunterschiede zu erklären. Sie greift dazu auf eine empirische Regelmäßigkeit zurück: Zahlreiche Studien belegen einen negativen Zusammenhang zwischen Lohn und Arbeitslosigkeit. In Regionen, in denen die Arbeitslosigkeit hoch ist, ist das Lohnniveau gering und umgekehrt. Dieser Zusammenhang wird als Lohnkurve bezeichnet. Auf regionaler Ebene lässt sich die Lohnkurve mithilfe der Effizienzlohntheorie erklären, die als theoretische Grundlage in der Dissertation Anwendung findet. Konzentriert sich nun die ökonomische Aktivität aufgrund der zentripetalen Kräfte in einer Region, so ist in diesem Zentrum die Arbeitsnachfrage höher. Damit befindet sich das Zentrum auf einer günstigen Position der Lohnkurve mit geringer Arbeitslosigkeit und hohem Lohnniveau. Umgekehrt findet sich die Peripherie auf einer ungünstigen Position mit hoher Arbeitslosigkeit und geringem Lohnniveau wieder. Allerdings kann sich die Lohnkurve in Abhängigkeit des Agglomerationsgrades verschieben. Das komplexe Zusammenspiel der endogenen Agglomeration mit den Arbeitsmarktfriktionen kann dann unterschiedliche Muster regionaler Arbeitsmarktdisparitäten hervorrufen. Die Dissertation zeigt auf, wie im Zusammenspiel der NÖG mit Effizienzlöhnen regionale Arbeitsmarktdisparitäten hervorgerufen werden. Es werden theoretische Modelle formuliert, die diese Interaktionen erklären und welche die bestehende Literatur durch spezifische Beiträge erweitern. Darüber hinaus werden die zentralen Argumente der Theorie einem empirischen Test unterworfen. Es kann gezeigt werden, dass das zentrale Argument – der positive Effekt des Marktpotentials auf die Arbeitsnachfrage – relevant ist. Außerdem werden Politikimplikationen abgeleitet und der weitere Forschungsbedarf aufgezeigt.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

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.