Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Entwicklung kohärenter Lichtquellen im XUV-Regime

Plasmabasierte Röntgenlaser sind aufgrund ihrer kurzen Wellenlänge und schma-rnlen spektralen Bandbreite attraktive Diagnose-Instrumente in einer Vielzahl potentieller Anwendungen, beispielsweise in den Bereichen Spektroskopie, Mikroskopie und EUV-Lithografie. Dennoch sind Röntgenlaser zum heutigen Stand noch nicht sehr weit verbreitet, was vorwiegend auf eine zu geringe Pulsenergie und für manche Anwendungen nicht hinreichende Strahlqualität zurückzuführen ist. In diesem Zusammenhang wurden in den letzten Jahren bedeutende Fortschritte erzielt. Die gleichzeitige Weiterentwicklung von Pumplasersystemen und Pumpmechanismen ermöglichte es, kompakte Röntgenlaserquellen mit bis zu 100 Hz zu betreiben. Um gleichzeitig höhere Pulsenergien, höhere Strahlqualität und volle räumliche Kohärenz zu erhalten, wurden intensive Studien theoretischer und experimenteller Natur durchgeführt. In diesem Kontext wurde in der vorliegenden Arbeit ein experimenteller Aufbau zur Kombination von zwei Röntgenlaser-Targets entwickelt, die sogenannte Butterfly-Konfiguration. Der erste Röntgenlaser wird dabei als sogenannter Seed für das zweite, als Verstärker dienende Röntgenlasermedium verwendet (injection-seeding). Aufrndiese Weise werden störende Effekte vermieden, welche beim Entstehungsprozessrndes Röntgenlasers durch die Verstärkung von spontaner Emission zustande kom-rnmen. Unter Verwendung des ebenfalls an der GSI entwickelten Double-Pulse Gra-rnzing Incidence Pumpschemas ermöglicht das hier vorgestellte Konzept, erstmaligrnbeide Röntgenlasertargets effizient und inklusive Wanderwellenanregung zu pum-rnpen.rnBei einer ersten experimentellen Umsetzung gelang die Erzeugung verstärkter Silber-Röntgenlaserpulse von 1 µJ bei 13.9 nm Wellenlänge. Anhand der gewonnenen Daten erfolgte neben dem Nachweis der Verstärkung die Bestimmung der Lebensdauer der Besetzungsinversion zu 3 ps. In einem Nachfolgeexperiment wurden die Eigenschaften eines Molybdän-Röntgenlaserplasmas näher untersucht. Neben dem bisher an der GSI angewandten Pumpschema kam in dieser Strahlzeit noch eine weitere Technik zum Einsatz, welche auf einem zusätzlichen Pumppuls basierte. In beiden Schemata gelang neben dem Nachweis der Verstärkung die zeitliche und räumliche Charakterisierung des Verstärkermediums. Röntgenlaserpulse mit bis zu 240 nJ bei einer Wellenlänge von 18.9 nm wurden nachgewiesen. Die erreichte Brillanz der verstärkten Pulse lag ca. zwei Größenordnungen über der des ursprünglichen Seeds und mehr als eine Größenordnung über der Brillanz eines Röntgenlasers, dessen Erzeugung auf der Verwendung eines einzelnen Targets basierte. Das in dieser Arbeitrnentwickelte und experimentell verifizierte Konzept birgt somit das Potential, extrem brillante plasmabasierte Röntgenlaser mit vollständiger räumlicher und zeitlicher Kohärenz zu erzeugen.rnDie in dieser Arbeit diskutierten Ergebnisse sind ein wesentlicher Beitrag zu der Entwicklung eines Röntgenlasers, der bei spektroskopischen Untersuchungen von hochgeladenen Schwerionen eingesetzt werden soll. Diese Experimente sind amrnExperimentierspeicherring der GSI und zukünftig auch am High-Energy StoragernRing der FAIR-Anlage vorgesehen.rn

Variational Monte Carlo study of the hydrogen electronic structure at ultra-high pressure

Die causa finalis der vorliegenden Arbeit ist das Verständnis des Phasendiagramms von Wasserstoff bei ultrahohen Drücken, welche von nichtleitendem H2 bis hin zu metallischem H reichen. Da die Voraussetzungen für ultrahohen Druck im Labor schwer zu schaffen sind, bilden Computersimulationen ein wichtiges alternatives Untersuchungsinstrument. Allerdings sind solche Berechnungen eine große Herausforderung. Eines der größten Probleme ist die genaue Auswertung des Born-Oppenheimer Potentials, welches sowohl für die nichtleitende als auch für die metallische Phase geeignet sein muss. Außerdem muss es die starken Korrelationen berücksichtigen, die durch die kovalenten H2 Bindungen und die eventuellen Phasenübergänge hervorgerufen werden. Auf dieses Problem haben unsere Anstrengungen abgezielt. Im Kontext von Variationellem Monte Carlo (VMC) ist die Shadow Wave Function (SWF) eine sehr vielversprechende Option. Aufgrund ihrer Flexibilität sowohl lokalisierte als auch delokalisierte Systeme zu beschreiben sowie ihrer Fähigkeit Korrelationen hoher Ordnung zu berücksichtigen, ist sie ein idealer Kandidat für unsere Zwecke. Unglücklicherweise bringt ihre Formulierung ein Vorzeichenproblem mit sich, was die Anwendbarkeit limitiert. Nichtsdestotrotz ist es möglich diese Schwierigkeit zu umgehen indem man die Knotenstruktur a priori festlegt. Durch diesen Formalismus waren wir in der Lage die Beschreibung der Elektronenstruktur von Wasserstoff signifikant zu verbessern, was eine sehr vielversprechende Perspektive bietet. Während dieser Forschung haben wir also die Natur des Vorzeichenproblems untersucht, das sich auf die SWF auswirkt, und dabei ein tieferes Verständnis seines Ursprungs erlangt. Die vorliegende Arbeit ist in vier Kapitel unterteilt. Das erste Kapitel führt VMC und die SWF mit besonderer Ausrichtung auf fermionische Systeme ein. Kapitel 2 skizziert die Literatur über das Phasendiagramm von Wasserstoff bei ultrahohem Druck. Das dritte Kapitel präsentiert die Implementierungen unseres VMC Programms und die erhaltenen Ergebnisse. Zum Abschluss fasst Kapitel 4 unsere Bestrebungen zur Lösung des zur SWF zugehörigen Vorzeichenproblems zusammen.

Diskontinuierliche Galerkin-Verfahren für die operationelle Wettervorhersage

In dieser Arbeit wird ein neuer Dynamikkern entwickelt und in das bestehendernnumerische Wettervorhersagesystem COSMO integriert. Für die räumlichernDiskretisierung werden diskontinuierliche Galerkin-Verfahren (DG-Verfahren)rnverwendet, für die zeitliche Runge-Kutta-Verfahren. Hierdurch ist ein Verfahrenrnhoher Ordnung einfach zu realisieren und es sind lokale Erhaltungseigenschaftenrnder prognostischen Variablen gegeben. Der hier entwickelte Dynamikkern verwendetrngeländefolgende Koordinaten in Erhaltungsform für die Orographiemodellierung undrnkoppelt das DG-Verfahren mit einem Kessler-Schema für warmen Niederschlag. Dabeirnwird die Fallgeschwindigkeit des Regens, nicht wie üblich implizit imrnKessler-Schema diskretisiert, sondern explizit im Dynamikkern. Hierdurch sindrndie Zeitschritte der Parametrisierung für die Phasenumwandlung des Wassers undrnfür die Dynamik vollständig entkoppelt, wodurch auch sehr große Zeitschritte fürrndie Parametrisierung verwendet werden können. Die Kopplung ist sowohl fürrnOperatoraufteilung, als auch für Prozessaufteilung realisiert.rnrnAnhand idealisierter Testfälle werden die Konvergenz und die globalenrnErhaltungseigenschaften des neu entwickelten Dynamikkerns validiert. Die Massernwird bis auf Maschinengenauigkeit global erhalten. Mittels Bergüberströmungenrnwird die Orographiemodellierung validiert. Die verwendete Kombination ausrnDG-Verfahren und geländefolgenden Koordinaten ermöglicht die Behandlung vonrnsteileren Bergen, als dies mit dem auf Finite-Differenzenverfahren-basierendenrnDynamikkern von COSMO möglich ist. Es wird gezeigt, wann die vollernTensorproduktbasis und wann die Minimalbasis vorteilhaft ist. Die Größe desrnEinflusses auf das Simulationsergebnis der Verfahrensordnung, desrnParametrisierungszeitschritts und der Aufteilungsstrategie wirdrnuntersucht. Zuletzt wird gezeigt dass bei gleichem Zeitschritt die DG-Verfahrenrnaufgrund der besseren Skalierbarkeit in der Laufzeit konkurrenzfähig zurnFinite-Differenzenverfahren sind.

Supramolecular order and dynamics of discotic materials studied by solid-state NMR recoupling methods

The topic of this thesis is the investigation of structure,order and dynamics in discotic mesogens by advancedsolid-state NMR spectroscopy. Most of the discotic mesogensunder investigation are hexa-peri-hexabenzocoronene (HBC)derivatives which are of particular interest for potentialdevice applications due to their high one-dimensional chargecarrier mobilities. The supramolecular stacking arrangement of the discoticcores was investigated by 2D 1H-1H double-quantum (DQ)methods, which were modified by incorporating the WATERGATEsuppression technique into the experiments in order toovercome severe phase problems arising from the strongsignal of the long alkyl sidechains. Molecular dynamics and sample orientation was probed throughthe generation of sideband patterns by reconversion rotorencoding in 2D recoupling experiments. These experimentswere extended by new recoupling schemes to enable thedistinction of motion and orientation effects. The solid-state NMR studies presented in this work aim tothe understanding of structure-property relationships in theinvestigated discotic materials, while the experimentsapplied to these materials include new recoupling schemeswhich make the desired information on molecular orientationand dynamics accessible without isotope labelling.

Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.

Development of a comprehensive on-line multidimensional high performance column liquid chromatography system for protein and peptide mapping with integrated size selective sample fractionation

Aufbau einer kontinuierlichen, mehrdimensionalen Hochleistungs-flüssigchromatographie-Anlage für die Trennung von Proteinen und Peptiden mit integrierter größenselektiver ProbenfraktionierungEs wurde eine mehrdimensionale HPLC-Trennmethode für Proteine und Peptide mit einem Molekulargewicht von <15 kDa entwickelt.Im ersten Schritt werden die Zielanalyte von höhermolekularen sowie nicht ionischen Bestandteilen mit Hilfe von 'Restricted Access Materialien' (RAM) mit Ionenaustauscher-Funktionalität getrennt. Anschließend werden die Proteine auf einer analytischen Ionenaustauscher-Säule sowie auf Reversed-Phase-Säulen getrennt. Zur Vermeidung von Probenverlusten wurde ein kontinuierlich arbeitendes, voll automatisiertes System auf Basis unterschiedlicher Trenngeschwindigkeiten und vier parallelen RP-Säulen aufgebaut.Es werden jeweils zwei RP-Säulen gleichzeitig, jedoch mit zeitlich versetztem Beginn eluiert, um durch flache Gradienten ausreichende Trennleistungen zu erhalten. Während die dritte Säule regeneriert wird, erfolgt das Beladen der vierte Säule durch Anreicherung der Proteine und Peptide am Säulenkopf. Während der Gesamtanalysenzeit von 96 Minuten werden in Intervallen von 4 Minuten Fraktionen aus der 1. Dimension auf die RP-Säulen überführt und innerhalb von 8 Minuten getrennt, wobei 24 RP-Chromatogramme resultieren.Als Testsubstanzen wurden u.a. Standardproteine, Proteine und Peptide aus humanem Hämofiltrat sowie aus Lungenfibroblast-Zellkulturüberständen eingesetzt. Weiterhin wurden Fraktionen gesammelt und mittels MALDI-TOF Massenspektrometrie untersucht. Bei einer Injektion wurden in den 24 RP-Chromatogrammen mehr als 1000 Peaks aufgelöst. Der theoretische Wert der Peakkapazität liegt bei ungefähr 3000.

Doppelresonanzmessungen an in einer Penningfalle gespeicherten Europium-Ionen zur Bestimmung des Kern-g-Faktors

Die differentielle Hyperfeinanomalie beschreibt den Isotopieeffekt der magnetischen Hyperfeinwechselwirkung und stellt eine Testmöglichkeit für Kernmodelle dar. Nachdem in einer Reihe von Messungen die A-Faktoren der Hyperfeinwechselwirkung im Grundzustand von zwei stabilen und fünf instabilen Europium-Isotopen bestimmt wurden, sollen nun die Kern-g-Faktoren der gleichen Isotope bestimmt werden.Um die Kern-g-Faktoren zu bestimmen, wurden zunächst die Termschemata des Grundzustandesder stabilen Isotope 151,153Eu+ simuliert. Wegen der hohen Kern- und Hüllenspins I=5/2, J=4 ergeben sich 54 Zeemanzustände und ein komplexes optisches Spektrum.Etwa 10^6 Ionen der beiden stabilen Isotope 151,153Eu+ werden in einer Penningfalle beieinem Magnetfeld von ca. 1.5T gespeichert. Durch Puffergas und Anregung einer Seitenbandfrequenzder Ionenbewegung wird optisches Pumpen in metastabile D-Zustände bei gleichzeitiger Kühlung der Ionenwolke verhindert.Bei Verstimmung eines frequenzverdoppelten Ti:Sa-Lasers wurde die Ionenfluoreszenz aufgenommen. Durch die Simulation der optischen Spektren gelang es, einzelne Übergänge des Isotopes 151Eu+ zu identifizieren. Mit Laser/Mikrowellen-Doppelresonanzmessungen erhält man ein in erster Ordnung dopplerfreies Mikrowellenspektren eines Überganges zwischen zwei Zeemanzuständen im Grundzustand.Durch Messung der Übergangsfrequenzen von insgesamt fünf Delta mI=+1 Übergängen und Bestimmung des Magnetfeldes durch Messung der Zyklotronfrequenz gespeicherter Elektronen konnte der gI-Faktor des Isotopes151Eu zu 151gI = 1.37734(6) bestimmt werden.

A structural and metamorphic study of the southern Menderes Massif (Western Turkey)

P-T conditions, paragenetic studies and the relation between mineral growth, deformation and - when possible- isograd minerals have been used to describe the type of metamorphism involved within lower units of the southern Menderes Massif of the Anatolide Belt in western Turkey. The study areas mainly consist of Proterozoic orthogneiss and surrounding schists of presumed Paleozoic age. Both units are seen as nappes in the southern study area, the Çine and the Selimiye nappe, on the whole corresponding to Proterozoic orthogneiss and surrounding schists, respectively. The Çine and Selimiye nappes are part of a complex geological structure within the core series of the Menderes Massif. Their emplacement under lower greenschist facies conditions, would result from closure of the northern Neo-Thethys branch during the Eocene. These two nappes are separated by a major tectonic structure, the Selimiye shear zone, which records top-to-the-S shearing under greenschist facies conditions. Amphibolite to upper amphibolite facies metamorphism is widely developed within the metasedimentary rocks of the Çine nappe whereas no metamorphism exceeding lower amphibolite facies has been observed in the Selimiye nappe. In the southern margin of the Çine Massif, around Selimiye and Millas villages, detailed sampling has been undertaken in order to map mineral isograds within the Selimiye nappe and to specify P-T conditions in this area. The data collected in this area reveals a global prograde normal erosion field gradient from south to north and toward the orthogneiss. The mineralogical parageneses and P-T estimates are correlated with Barrovian-type metamorphism. A jump of P-T conditions across the Selimiye shear zone has been identified and estimated c. 2 kbar and 100 °C which evidences the presence of amphibolite facies metasedimentary rocks near the orthogneiss. Metasedimentary rocks from the overlying Selimiye nappe have maximum P-T conditions of c. 4-5 kbar and c. 525 °C near the base of the nappe. Metasedimentary rocks from the Çine nappe underneath the Selimiye shear zone record maximum P-T conditions of about 7 kbar and >550 °C. Kinematic indicators in both nappes consistently show a top-S shear sense. Metamorphic grade in the Selimiye nappe decreases structurally upwards as indicated by mineral isograds defining the garnet-chlorite zone at the base, the chloritoid-biotite zone and the biotite-chlorite zone at the top of the nappe. The mineral isograds in the Selimiye nappe run parallel to the regional SR foliation. 40Ar/39Ar mica ages indicate an Eocene age of metamorphism in the Selimiye nappe and underneath the Çine nappe in this area. Metasedimentary rocks of the Çine nappe 20-30 km north of the Selimiye shear zone record maximum P-T conditions of 8-11 kbar and 600-650 °C. Kinematic indicators show mainly top-N shear sense associated with prograde amphibolite facies metamorphism. An age of about 550 Ma could be indicated for amphibolite facies metamorphism and associated top-N shear in the orthogneiss and metasedimentary rocks of the Çine nappe. However, there is no evidence for polymetamorphism in the 6 metasedimentary rocks of the Çine nappe, making tectonic interpretations about late Neoproterozoic to Cambrian and Tertiary metamorphic events speculative. In the western margin of the Çine Massif metamorphic mineral parageneses and pressure– temperature conditions lead to similar conclusion regarding the erosion field gradient, prograde normal toward the orthogneiss. The contact between orthogneiss and surrounding metasedimentary rocks is mylonitic and syn-metamorphism. P-T estimates are those already observed within the Selimiye nappe and correlated with lower amphibolite facies parageneses. Finally additional data in the eastern part and a general paragenetic study within the Menderes Massif lower units, the Çine and the Selimiye nappes, strongly suggest a single Barrovian-type metamorphism predating Eocene emplacement of the high pressure–low temperature Lycean and Cycladic blueschist nappes. Metamorphic mineral parageneses and pressure–temperature conditions do not support the recently proposed model of high pressure–low temperature metamorphic overprinting, which implies burial of the lower units of the Menderes Massif up to depth of 30 km, as a result of closure of the Neo-Tethys. According to the geochronological problem outlined during this thesis, there are two possible schemes: either Barrovian-type metamorphism is Proterozoic in age and part of the sediments from Selimiye nappe (lower amphibolite facies) has to be proterozoic of age too, or Barrovian-type metamorphism in Eocene of age. In the first case the structure observed now in the core series would correspond to simple exhumation of Proterozoic basement. In the latter case a possible correlation with closure of Neo-Tethys (sensu stricto, southern branch) is envisaged.

High quality colloidal crystals with different architectures and their optical properties

In this present work high quality PMMA opals with different sphere sizes, silica opals from large size spheres, multilayer opals, and inverse opals were fabricated. Highly monodisperse PMMA spheres were synthesized by surfactant-free emulsion polymerization (polydispersity ~2%). Large-area and well-ordered PMMA crystalline films with a homogenous thickness were produced by the vertical deposition method using a drawing device. Optical experiments have confirmed the high quality of these PMMA photonic crystals, e.g., well resolved high-energy bands of the transmission and reflectance spectra of the opaline films were observed. For fabrication of high quality opaline photonic crystals from large silica spheres (diameter of 890 nm), self-assembled in patterned Si-substrates a novel technique has been developed, in which the crystallization was performed by using a drawing apparatus in combination with stirring. The achievements comprise a spatial selectivity of opal crystallization without special treatment of the wafer surface, the opal lattice was found to match the pattern precisely in width as well as depth, particularly an absence of cracks within the size of the trenches, and finally a good three-dimensional order of the opal lattice even in trenches with a complex confined geometry. Multilayer opals from opaline films with different sphere sizes or different materials were produced by sequential crystallization procedure. Studies of the transmission in triple-layer hetero-opal revealed that its optical properties cannot only be considered as the linear superposition of two independent photonic bandgaps. The remarkable interface effect is the narrowing of the transmission minima. Large-area, high-quality, and robust photonic opal replicas from silicate-based inorganic-organic hybrid polymers (ORMOCER® s) were prepared by using the template-directed method, in which a high quality PMMA opal template was infiltrated with a neat inorganic-organic ORMOCER® oligomer, which can be photopolymerized within the opaline voids leading to a fully-developed replica structure with a filling factor of nearly 100%. This opal replica is structurally homogeneous, thermally and mechanically stable and the large scale (cm2 size) replica films can be handled easily as free films with a pair of tweezers.

Ophiolites of the eastern Vardar Zone, N. Greece

In the present thesis, the geochemistry, petrology and geochronology of ophiolite complexes from central northern Greece were studied in detail in order to gain insights on the petrogenetic pathways and geodynamic processes that lead to their formation and evolution. The major- and trace-element content of minerals and whole rocks from all four ophiolite complexes was determined using high-precision analytical equipment. These results were then coupled with Nd and Sr isotopic measurements. In order to precisely place the evolution of these ophiolites in time, U-Pb geochronology on zircons was conducted using a SHRIMP-II. The data obtained suggest that the ophiolites studied invariably show typical characteristics of subduction-zone magmatism (e.g. negative Nb anomalies, Th enrichment). In N-MORB-normalised multielement profiles the high field-strength elements display patterns that vary from depleted to N-MORB-like. Chondrite-normalised rare-earth element (REE) profiles show flat heavy-REE patterns suggesting a shallow regime of source melting for all the ophiolites, well within the stability field of spinel lherzolite. The majority of the samples have light-REE depleted patterns. 87Sr/86Sr isotopic ratios range from 0.703184 to 0.715853 and are in cases influenced by alteration. The εNd values are positive (the majority of the mafic samples is typically 7.1-3.1) but lower than N-MORB and depleted mantle. With the exception of the Thessaloniki ophiolite that has uniform island-arc tholeiitic chemical characteristics, the rest of the ophiolites show dual chemistry consisting of rocks with minor subduction-zone characteristics that resemble chemically back-arc basin basalts (BABB) and rocks with more pronounced subduction-zone characteristics. Tectonomagmatic discrimination schemes classify the samples as island-arc tholeiites and back-arc basin basalts or N-MORB. Melting modelling carried out to evaluate source properties and degree of melting verifies the dual nature of the ophiolites. The samples that resemble back-arc basin basalts require very small degrees of melting (<10%) of fertile sources, whereas the rest of the samples require higher degrees (25-15%) of melting. As deduced from the present geochemical and petrological investigation, the ophiolites from Guevguely, Oraeokastro, Thessaloniki, and Chalkidiki represent relics of supra-subduction zone crust that formed in succeeding stages of island-arc rifting and back-arc spreading as well as in a fore arc setting. The geochronological results have provided precise determination of the timing of formation of these complexes. The age of the Guevguely ophiolite has been determined as 167±1.2 Ma, that of Thessaloniki as 169±1.4 Ma, that of Kassandra as 167±2.2 Ma and that of Sithonia as 160±1.2 Ma.

Supramolecular order and dynamics of functional materials studied by solid state NMR

The goal of this thesis was the investigation of the structure, conformation, supramolecular order and molecular dynamics of different classes of functional materials (phthalocyanine, perylene and hexa-peri-hexabenzocoronene derivatives and mixtures of those), all having planar aromatic cores modified with various types of alkyl chains. The planar aromatic systems are known to stack in the solid and the liquid-crystalline state due to p-p interactions forming columnar superstructures with high one-dimensional charge carrier mobility and potential application in photovoltaic devices. The different functionalities attached to the aromatic cores significantly influence the behavior of these systems allowing the experimentalists to modify the structures to fine-tune the desired thermotropic properties or charge carrier mobility. The aim of the presented studies was to understand the interplay between the driving forces causing self-assembly by relating the structural and dynamic information about the investigated systems. The supramolecular organization is investigated by applying 1H solid state NMR recoupling techniques. The results are related with DSC and X-ray scattering data. Detailed information about the site-specific molecular dynamics is gained by recording spinning sideband patterns using 1H-1H and 13C-1H solid state NMR recoupling techniques. The determined dipole-dipole coupling constants are then related with the coupling constants of the respective rigid pairs, thus providing local dynamic order parameters for the respective moieties. The investigations presented reveal that in the crystalline state the preferred arrangement in the columnar stack of discotic molecules modified with alkyl chains is tilted. This leads to characteristic differences in the 1H chemical shifts of otherwise chemically equivalent protons. Introducing branches and increasing the length of the alkyl chains results in lower mesophase transitions and disordered columnar stacks. In the liquid-crystalline state some of the discs lose the tilted orientation, others do not, but all start a rapid rotation about the columnar axis.

Pore structure and column efficiency of silica monoliths in high performance liquid chromatography (HPLC)

Five different methods were critically examined to characterize the pore structure of the silica monoliths. The mesopore characterization was performed using: a) the classical BJH method of nitrogen sorption data, which showed overestimated values in the mesopore distribution and was improved by using the NLDFT method, b) the ISEC method implementing the PPM and PNM models, which were especially developed for monolithic silicas, that contrary to the particulate supports, demonstrate the two inflection points in the ISEC curve, enabling the calculation of pore connectivity, a measure for the mass transfer kinetics in the mesopore network, c) the mercury porosimetry using a new recommended mercury contact angle values. rnThe results of the characterization of mesopores of monolithic silica columns by the three methods indicated that all methods were useful with respect to the pore size distribution by volume, but only the ISEC method with implemented PPM and PNM models gave the average pore size and distribution based on the number average and the pore connectivity values.rnThe characterization of the flow-through pore was performed by two different methods: a) the mercury porosimetry, which was used not only for average flow-through pore value estimation, but also the assessment of entrapment. It was found that the mass transfer from the flow-through pores to mesopores was not hindered in case of small sized flow-through pores with a narrow distribution, b) the liquid penetration where the average flow-through pore values were obtained via existing equations and improved by the additional methods developed according to Hagen-Poiseuille rules. The result was that not the flow-through pore size influences the column bock pressure, but the surface area to volume ratio of silica skeleton is most decisive. Thus the monolith with lowest ratio values will be the most permeable. rnThe flow-through pore characterization results obtained by mercury porosimetry and liquid permeability were compared with the ones from imaging and image analysis. All named methods enable a reliable characterization of the flow-through pore diameters for the monolithic silica columns, but special care should be taken about the chosen theoretical model.rnThe measured pore characterization parameters were then linked with the mass transfer properties of monolithic silica columns. As indicated by the ISEC results, no restrictions in mass transfer resistance were noticed in mesopores due to their high connectivity. The mercury porosimetry results also gave evidence that no restrictions occur for mass transfer from flow-through pores to mesopores in the small scaled silica monoliths with narrow distribution. rnThe prediction of the optimum regimes of the pore structural parameters for the given target parameters in HPLC separations was performed. It was found that a low mass transfer resistance in the mesopore volume is achieved when the nominal diameter of the number average size distribution of the mesopores is appr. an order of magnitude larger that the molecular radius of the analyte. The effective diffusion coefficient of an analyte molecule in the mesopore volume is strongly dependent on the value of the nominal pore diameter of the number averaged pore size distribution. The mesopore size has to be adapted to the molecular size of the analyte, in particular for peptides and proteins. rnThe study on flow-through pores of silica monoliths demonstrated that the surface to volume of the skeletons ratio and external porosity are decisive for the column efficiency. The latter is independent from the flow-through pore diameter. The flow-through pore characteristics by direct and indirect approaches were assessed and theoretical column efficiency curves were derived. The study showed that next to the surface to volume ratio, the total porosity and its distribution of the flow-through pores and mesopores have a substantial effect on the column plate number, especially as the extent of adsorption increases. The column efficiency is increasing with decreasing flow through pore diameter, decreasing with external porosity, and increasing with total porosity. Though this tendency has a limit due to heterogeneity of the studied monolithic samples. We found that the maximum efficiency of the studied monolithic research columns could be reached at a skeleton diameter of ~ 0.5 µm. Furthermore when the intention is to maximize the column efficiency, more homogeneous monoliths should be prepared.rn

Magnetization dynamics in spin valves

Key technology applications like magnetoresistive sensors or the Magnetic Random Access Memory (MRAM) require reproducible magnetic switching mechanisms. i.e. predefined remanent states. At the same time advanced magnetic recording schemes push the magnetic switching time into the gyromagnetic regime. According to the Landau-Lifschitz-Gilbert formalism, relevant questions herein are associated with magnetic excitations (eigenmodes) and damping processes in confined magnetic thin film structures.rnObjects of study in this thesis are antiparallel pinned synthetic spin valves as they are extensively used as read heads in today’s magnetic storage devices. In such devices a ferromagnetic layer of high coercivity is stabilized via an exchange bias field by an antiferromagnet. A second hard magnetic layer, separated by a non-magnetic spacer of defined thickness, aligns antiparallel to the first. The orientation of the magnetization vector in the third ferromagnetic NiFe layer of low coercivity - the freelayer - is then sensed by the Giant MagnetoResistance (GMR) effect. This thesis reports results of element specific Time Resolved Photo-Emission Electron Microscopy (TR-PEEM) to image the magnetization dynamics of the free layer alone via X-ray Circular Dichroism (XMCD) at the Ni-L3 X-ray absorption edge.rnThe ferromagnetic systems, i.e. micron-sized spin valve stacks of typically deltaR/R = 15% and Permalloy single layers, were deposited onto the pulse leading centre stripe of coplanar wave guides, built in thin film wafer technology. The ferromagnetic platelets have been applied with varying geometry (rectangles, ellipses and squares), lateral dimension (in the range of several micrometers) and orientation to the magnetic field pulse to study the magnetization behaviour in dependence of these magnitudes. The observation of magnetic switching processes in the gigahertz range became only possible due to the joined effort of producing ultra-short X-ray pulses at the synchrotron source BESSY II (operated in the so-called low-alpha mode) and optimizing the wave guide design of the samples for high frequency electromagnetic excitation (FWHM typically several 100 ps). Space and time resolution of the experiment could be reduced to d = 100 nm and deltat = 15 ps, respectively.rnIn conclusion, it could be shown that the magnetization dynamics of the free layer of a synthetic GMR spin valve stack deviates significantly from a simple phase coherent rotation. In fact, the dynamic response of the free layer is a superposition of an averaged critically damped precessional motion and localized higher order spin wave modes. In a square platelet a standing spin wave with a period of 600 ps (1.7 GHz) was observed. At a first glance, the damping coefficient was found to be independent of the shape of the spin-valve element, thus favouring the model of homogeneous rotation and damping. Only by building the difference in the magnetic rotation between the central region and the outer rim of the platelet, the spin wave becomes visible. As they provide an additional efficient channel for energy dissipation, spin waves contribute to a higher effective damping coefficient (alpha = 0.01). Damping and magnetic switching behaviour in spin valves thus depend on the geometry of the element. Micromagnetic simulations reproduce the observed higher-order spin wave mode.rnBesides the short-run behaviour of the magnetization of spin valves Permalloy single layers with thicknesses ranging from 3 to 40 nm have been studied. The phase velocity of a spin wave in a 3 nm thick ellipse could be determined to 8.100 m/s. In a rectangular structure exhibiting a Landau-Lifschitz like domain pattern, the speed of the field pulse induced displacement of a 90°-Néel wall has been determined to 15.000 m/s.rn

Between the scales: Water from different perspectives

In der vorliegenden Arbeit werden verschiedene Wassermodelle in sogenannten Multiskalen-Computersimulationen mit zwei Auflösungen untersucht, in atomistischer Auflösung und in einer vergröberten Auflösung, die als "coarse-grained" bezeichnet wird. In der atomistischen Auflösung wird ein Wassermolekül, entsprechend seiner chemischen Struktur, durch drei Atome beschrieben, im Gegensatz dazu wird ein Molekül in der coarse-grained Auflösung durch eine Kugel dargestellt.rnrnDie coarse-grained Modelle, die in dieser Arbeit vorgestellt werden, werden mit verschiedenen coarse-graining Methoden entwickelt. Hierbei kommen hauptsächlich die "iterative Boltzmann Inversion" und die "iterative Monte Carlo Inversion" zum Einsatz. Beides sind struktur-basierte Ansätze, die darauf abzielen bestimmte strukturelle Eigenschaften, wie etwa die Paarverteilungsfunktionen, des zugrundeliegenden atomistischen Systems zu reproduzieren. Zur automatisierten Anwendung dieser Methoden wurde das Softwarepaket "Versatile Object-oriented Toolkit for Coarse-Graining Applications" (VOTCA) entwickelt.rnrnEs wird untersucht, in welchem Maße coarse-grained Modelle mehrere Eigenschaftenrndes zugrundeliegenden atomistischen Modells gleichzeitig reproduzieren können, z.B. thermodynamische Eigenschaften wie Druck und Kompressibilität oder strukturelle Eigenschaften, die nicht zur Modellbildung verwendet wurden, z.B. das tetraedrische Packungsverhalten, welches für viele spezielle Eigenschaft von Wasser verantwortlich ist.rnrnMit Hilfe des "Adaptive Resolution Schemes" werden beide Auflösungen in einer Simulation kombiniert. Dabei profitiert man von den Vorteilen beider Modelle:rnVon der detaillierten Darstellung eines räumlich kleinen Bereichs in atomistischer Auflösung und von der rechnerischen Effizienz des coarse-grained Modells, die den Bereich simulierbarer Zeit- und Längenskalen vergrössert.rnrnIn diesen Simulationen kann der Einfluss des Wasserstoffbrückenbindungsnetzwerks auf die Hydration von Fullerenen untersucht werden. Es zeigt sich, dass die Struktur der Wassermoleküle an der Oberfläche hauptsächlich von der Art der Wechselwirkung zwischen dem Fulleren und Wasser und weniger von dem Wasserstoffbrückenbindungsnetzwerk dominiert wird.rn