Time-delayed actions appear as an essential component of numerous systems especially in evolution processes, natural phenomena, and particular technical applications and are associated with the existence of a memory. Under common conditions, external forces or state dependent parameters modify the length of the delay with time. Consequently, an altered dynamical behavior emerges, whose characterization is compulsory for a deeper understanding of these processes. In this thesis, the well-investigated class of time-homogeneous finite-state Markov processes is utilized to establish a variation of memory length by combining a first-order Markov chain with a memoryless Markov chain of order zero. The fluctuations induce a non-stationary process, which is accomplished for two special cases: a periodic and a random selection of the available Markov chains. For both cases, the Kolmogorov-Sinai entropy as a characteristic property is deduced analytically and compared to numerical approximations to the entropy rate of related symbolic dynamics. The convergences of per-symbol and conditional entropies are examined in order to recognize their behavior when identifying unknown processes. Additionally, the connection from Markov processes with varying memory length to hidden Markov models is illustrated enabling further analysis. Hence, the Kolmogorov-Sinai entropy of hidden Markov chains is calculated by means of Blackwell’s entropy rate involving Blackwell’s measure. These results are used to verify the previous computations.

In der vorliegenden Arbeit werden mithilfe von Methoden zur numerischen Behandlung schwach besetzter Matrizen O(n³)- und O(n)-Berechnungsalgorithmen für Mehrkörpersysteme aus deren Bewegungsgleichungen abgeleitet. Durch Verwendung von Dualen Basen kann gezeigt werden, dass sich die bezüglich der Berechnungszeit effizienten Algorithmen sowohl auf Systeme mit explizit als auch implizit formulierten Bindungsgleichungen anwenden lassen. Mit diesen gewonnen Erkenntnissen wird die derzeitige Implementierung der vorgestellten Algorithmen im Sprachstandard Modelica untersucht. Es werden Ansatzmöglichkeiten aufgezeigt, mit denen ausgewählte Modelica Compiler große Mehrkörpersysteme effizienter lösen können. Zum einen wird durch eine graphentheoretische Verallgemeinerung des O(n)-Algorithmus dieser direkt in dem freien Modelica Werkzeug OpenModelica umgesetzt. Zum anderen wird die Methode der Subsysteme für den O(n)-Algorithmus vorgestellt. Sie ermöglicht es, beliebig komplexe Teilsysteme als eigenständige Modellelemente zu erstellen. Die Berechnung von kinematischen Schleifen kann auf diese Weise wesentlich beschleunigt werden. Ferner wird gezeigt, dass sich mit der Methode der Subsysteme Modellgleichungen eines idealen homokinetischen Gelenks ableiten lassen, die frei von Zwangsbedingungen sind. Dies führt ebenfalls zu einer schnelleren und robusteren Berechnung.:1. Einleitung 1.1. Motivation 1.2. Präzisierung der Aufgabe 1.3. Aufbau der Arbeit 2. Mechanik der Mehrkörpersysteme 2.1. Bewegungsgleichung des starren Körpers 2.2. Beschreibung einer Bindung 2.3. Bewegungsgleichung eines Mehrkörpersystems 2.4. Zusammenfassung zur Mechanik der Mehrkörpersysteme 3. Lösungsalgorithmen für Mehrkörpersysteme 3.1. Die Graphen eines Mehrkörpersystems 3.2. Lösungsalgorithmen für Systeme mit Baumstruktur 3.3. Lösungsalgorithmen am Beispiel einer ebenen Pendelkette 3.4. Berücksichtigung kinematischer Schleifen 3.5. Zusammenfassung der Lösungsalgorithmen eines Mehrkörpersystems 4. Effiziente Berechnung von Mehrkörpersystemen 4.1. Berechnung von Mehrkörpersystemen basierend auf Modelica 4.2. O(n)-Algorithmus für Modelica Compiler 4.3. O(n)-Algorithmus für Bibliothekselemente 5. Zusammenfassung und Ausblick A. Anhang A.1. Grundlagen der Tensorrechnung A.2. Duale Basis einer Bindung A.3. Herleitung des Subsystems des Viergelenks A.4. Homokinetisches Gelenk als Subsystem / Using methods from sparse matrice theory, O(n³)- and O(n)-algorithms for multibody systems are derived from the equations of motion. The concept of Dual Bases reveals that efficient algorithms for explicit joint descriptions, regarding calculation time, may also be applied to systems which use implicit joint constraints. Consequently, the feasibility of implementing these results in Modelica is examined. This leads to new approaches which enable selected Modelica compilers to solve large multibody systems more efficiently. On the one hand side a graph-theoretic generalization of the O(n)-algorithm has been implemented into the OpenModelica compiler. On the other hand, a method of subsystems for the O(n)-algorithm has been devised. It allows to derive the model equations for arbitrary complex sub-systems which can be implemented as new model elements for an O(n)-algorithm library. This has been carried out for recurring kinematic loops of Mobile Machinery improving simulation speed considerably. Furthermore, it is shown that a fast and robust model of an ideal constant velocity joint can be derived that way.:1. Einleitung 1.1. Motivation 1.2. Präzisierung der Aufgabe 1.3. Aufbau der Arbeit 2. Mechanik der Mehrkörpersysteme 2.1. Bewegungsgleichung des starren Körpers 2.2. Beschreibung einer Bindung 2.3. Bewegungsgleichung eines Mehrkörpersystems 2.4. Zusammenfassung zur Mechanik der Mehrkörpersysteme 3. Lösungsalgorithmen für Mehrkörpersysteme 3.1. Die Graphen eines Mehrkörpersystems 3.2. Lösungsalgorithmen für Systeme mit Baumstruktur 3.3. Lösungsalgorithmen am Beispiel einer ebenen Pendelkette 3.4. Berücksichtigung kinematischer Schleifen 3.5. Zusammenfassung der Lösungsalgorithmen eines Mehrkörpersystems 4. Effiziente Berechnung von Mehrkörpersystemen 4.1. Berechnung von Mehrkörpersystemen basierend auf Modelica 4.2. O(n)-Algorithmus für Modelica Compiler 4.3. O(n)-Algorithmus für Bibliothekselemente 5. Zusammenfassung und Ausblick A. Anhang A.1. Grundlagen der Tensorrechnung A.2. Duale Basis einer Bindung A.3. Herleitung des Subsystems des Viergelenks A.4. Homokinetisches Gelenk als Subsystem

For many centuries, the study of the Sun has been an important testbed for understanding stars that are further away. One of the first astronomical observations Galileo Galilei made in 1612 with the newly invented telescope concerned the sunspots, and in 1814, Joseph von Fraunhofer employed his new spectroscope to discover the absorption lines in the solar spectrum that are now named after him. Even though more refined and new modes of observation are now available than in the days of Galileo and Fraunhofer, the study of the Sun is still high on the agenda of contemporary science, due to three guiding interests. The first is connected to the ages-old human striving to understand the structure of the larger world surrounding us. Modern telescopes, some of them even based outside the Earth’s atmosphere in space, have succeeded in observing astronomical objects that are billions of light- years away. However, for practical reasons precision data that are important for understanding stars can still only be gained from the Sun. In a sense, the observations of far-away astronomical objects thus call for a more precise study of the closeby, of the Sun, for their interpretation. The second interest stems from the human desire to understand the essence of the world, in particular the elementary particles of which it consists. Large accelerators have been constructed to produce and collide these particles. However, man-made machines can never be as luminous as the Sun when it comes to producing particles. Solar neutrinos have thus served not only as an astronomical tool to understand the Sun’s inner workings, but their behavior on the way from the Sun to the Earth is also being studied with the aim to understand their nature and interactions. The third interest is strictly connected to life on Earth. A multitude of research has shown that even relatively slight changes in the Earth’s climate may strongly affect the living conditions in a number of densely populated areas, mainly near the ocean shore and in arid regions. Thus, great effort is expended on the study of greenhouse gases in the Earth’s atmosphere. Also the Sun, via the solar irradiance and via the effects of the so-called solar wind of magnetic particles on the Earth’s atmosphere, may affect the climate. There is no proof linking solar effects to short-term changes in the Earth’s climate. However, such effects cannot be excluded, either, making it necessary to study the Sun. The experiments summarized in the present work contribute to the present-day study of our Sun by repeating, in the laboratory, some of the nuclear processes that take place in the core of the Sun. They aim to improve the precision of the nuclear cross section data that lay the foundation of the model of the nuclear reactions generating energy and producing neutrinos in the Sun. In order to reach this goal, low-energy nuclear physics experiments are performed. Wherever possible, the data are taken in a low-background, underground environment. There is only one underground accelerator facility in the world, the Laboratory Underground for Nuclear Astro- physics (LUNA) 0.4 MV accelerator in the Gran Sasso laboratory in Italy. Much of the research described here is based on experiments at LUNA. Background and feasibility studies shown here lay the base for future, higher-energy underground accelerators. Finally, it is shown that such a device can even be placed in a shallow-underground facility such as the Dresden Felsenkeller without great loss of sensitivity.

Die vorliegende Arbeit beschäftigt sich mit der theoretischen Beschreibung der komplexen physikalischen Eigenschaften von Netzwerken semiflexibler Polymere. Ausgehend vom mathematischen Modell eines semiflexiblen Polymers, der \"wurmartigen Kette\" (wormlike chain), werden zwei wesentlich neue Konzepte zur Beschreibung dieses ungeordneten Materialzustands eingeführt. Einerseits wird das experimentell beobachtete, glasähnliche Fließen solcher Materialien durch das phänomenologische Modell eines semiflexiblen Polymers mit verallgemeinerter Reibung beschrieben, welche den Gesamteffekt der physikalischen oder auch chemischen Wechselwirkungen der Polymere untereinander widerspiegelt. Andererseits wird das bestehende Konzept der durch seine Nachbarfilamente erzeugten röhrenförmigen Einsperrung eines Filaments erweitert und die experimentell nachgewiesene, räumlich veränderliche Struktur der Röhre erklärt. Die erzielten Ergebnisse werden durch Rechnersimulationen sowie durch experimentelle Daten gestützt.

Reliability of low-level operating-system (OS) code is an indispensable requirement. This includes functional properties from the safety-liveness spectrum, but also quantitative properties stating, e.g., that the average waiting time on locks is sufficiently small or that the energy requirement of a certain system call is below a given threshold with a high probability. This paper reports on our experiences made in a running project where the goal is to apply probabilistic model checking techniques and to align the results of the model checker with measurements to predict quantitative properties of low-level OS code.

In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.

In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.:List of Figures List of Tables List of Abbreviations 1. Introduction 2. Magnetism of cuprates 3. Experimental methods 4. DFT-based microscopic modeling 5. Simulations of a magnetic model 6. Model spin systems: challenging the computational approach 7. Kagome lattice compounds 8. Summary and outlook Appendix Bibliography List of publications Acknowledgments

Um die Kontraktion einer Herzmuskelzelle durch den Kalziumeinstrom zu ermöglichen, ist die Kopplung von Erregung und Kontraktion (ECC) von zentraler Bedeutung. Durch das elektrische Signal einer Nachbarzelle wird die Depolarisation des Sarkolemmas verursacht, wodurch sich die L-Typ-Kalziumkanäale (LKK) öffnen und der Amplifizierungsprozess eingeleitet wird. Letzterer ist bekannt als Kalzium induzierte Kalzium Freisetzung (CICR). Durch die LKK wird ein Kalziumeinstrom in die Zelle ermöglicht, welcher zur Öffnung der Ryanodinrezeptoren (RyR) des Sarkoplasmatischen Retikulums (SR) führt. Durch die Kalziumfreisetzung des SR wird dieses im Cytoplasma akkumuliert. Modelle für diese Prozesse werden seit mehreren Jahrzenten entwickelt. Bisher fehlte jedoch die Kombination aus räumlich aufgelösten Kalziumkonzentrationen der dyadischen Spalte mit stochastischen Simulationen der einzelnen Kalziumkanäle und die Kalziumdynamiken in der ganzen Zelle mit einem Elektrophysiologiemodell einer ganzen Herzmuskelzelle. In dieser Arbeit entwickleten wir ein neues Modell, in welchem die Konzentrationsgradienten von einzelnen Kanälen bis zum Ganzzelllevel räumlich aufgelöst werden. Es wurde der quasistatische Ansatz und die Finite-Elemente-Methode zur Integration partieller Differentialgleichungen verwendet. Es wurden Simulationen mit unterschiedlichen RyR Markow-Kette-Modellen, verschiedenen Parametern für die Bestandteile des SR, verschiedenen Konditionen des Natrium-Kalzium-Austauschers und unter Einbindung der Mitochondrien durchgeführt. Ziel war es, das physiologische Verhalten einer Kaninchen-Herzmuskelzelle zu simulieren. In dem neu entwickelten Multiskalenmodell wurden Hochleistungsrechner verwendet, um detaillierte Informationen über die Verteilung, die Regulation und die Relevanz von den im ECC involvierten Komponenten aufzuzeigen. Zukünftig soll das entwickelte Modell Anwendung bei der Untersuchung von Herzkontraktionen und Herzmuskelversagen finden. / Excitation contraction coupling (ECC) is of central importance to enable the contraction of the cardiac myocyte via calcium in ux. The electrical signal of a neighbouring cell causes the membrane depolarization of the sarcolemma and L-type Ca2+ channels (LCCs) open. The amplifcation process is initiated. This process is known as calcium-induced calcium release (CICR). The calcium in ux through the LCCs activates the ryanodine receptors (RyRs) of the sarcoplasmic reticulum (SR). The Ca2+ release of the SR accumulates calcium in the cytoplasm. For many decades models for these processes were developed. However, previous models have not combined the spatially resolved concentration dynamics of the dyadic cleft including the stochastic simulation of individual calcium channels and the whole cell calcium dynamics with a whole cardiac myocyte electrophysiology model. In this study, we developed a novel approach to resolve concentration gradients from single channel to whole cell level by using quasistatic approximation and finite element method for integrating partial differential equations. We ran a series of simulations with different RyR Markov chain models, different parameters for the SR components, sodium-calcium exchanger conditions, and included mitochondria to approximate physiological behaviour of a rabbit ventricular cardiac myocyte. The new multi-scale simulation tool which we developed makes use of high performance computing to reveal detailed information about the distribution, regulation, and importance of components involved in ECC. This tool will find application in investigation of heart contraction and heart failure.

The aim of the present work was to screen the main methods for the synthesis of conjugated polymers for their suitability in the preparation of conductive polymer brushes. The main focus was put on the grafting of intrinsically soluble substituted regioregular polyalkylthiophenes because of their excellent optoelectronic properties. The resulting polymer films were characterized and their optoelectrical properties studied. For the first time, a synthesis of conductive polymer brushes on solid substrates using “grafting-from” method was performed. The most important, from my opinion, finding of this work is that regioregular head-to-tail poly-3-alkylthiophenes – benchmark materials for organic electronics - can be now selectively grafted from appropriately-terminated surfaces to produce polymer brushes of otherwise soluble polymers - the architecture earlier accessible only in the case of non-conductive polymers. In particular, we developed a new method to grow P3ATs via Kumada Catalyst Transfer Polymerization (KCTP) of 2-bromo-5-chloromagnesio-3-alkylthiophene. Exposure of the initiator layers to monomer solutions leads to selective chain-growth polycondensation of the monomers from the surface, resulting into P3AT brushes in a very economical way. The grafting process was investigated in detail and the structure of the resulting composite films was elucidated using several methods. The obtained data suggests that the grafting process occurs not only at the poly(4-bromstyrene) (PS-Br)/polymerization solution interface, but also deeply inside the swollen PS-Br films, penetrable for the catalyst and for the monomer The grafting process was investigated in detail and the structure of the resulting composite film was elucidated using ellipsometry, X-ray Photoelectron Spectroscopy (XPS), Rutherford backscattering spectroscopy (RBS), and Conductive atomic force microscopy (C-AFM). The obtained data suggests that the grafting process occurs not only at the poly(4-bromostyrene), PS-Br/polymerization solution interface, but also deeply inside the swollen PS-Br film, which is penetrable for the catalyst and the monomer. The process results in an interpenetrated PS-Br/P3HT network, in which relatively short poly(3-hexylthiophene), P3HT grafts emanate from long, cross-linked PS-Br chains. A further method investigated during our work was to covalently graft regioirregular P3HT to substrates modified by macromolecular anchors using oxidative polymerization of 3HT with FeCl3. P3HT layers with variable thicknesses from 30 nm up to 200 nm were produced using two steps of polymerization reaction. The P3HT obtained by oxidative polymerization had always an irregular structure, which was a result of the starting monomer being asymmetric, which is undesired for electronic applications. The third method for the production of conductive polymer brushes was to graft regioregular poly(3,3''-dioctyl-[2,2';5',2'']terthiophene) (PDOTT) by electrochemical oxidative polycondensation of symmetrically substituted 3,3''-dioctyl-[2,2';5',2'']terthiophene (DOTT). A modification of the supporting ITO electrode by the self-assembled monolayers (SAMs) of compounds having polymerizable head-groups with properly adjusted oxidative potentials was found to be essential to achieve a covalent attachment of PDOTT chains. The polymer films produced show solvatochromism and electrochromism, as well as the previous two methods. After polymerization, the next step towards building organic electronic devices is applying the methods obtained in nano- and microscale production. Block copolymers constitute an attractive option for such surface-engineering, due to their ability to form a variety of nanoscale ordered phase-separated structures. However, block copolymers containing conjugated blocks are less abundant compared to their non-conjugated counterparts. Additionally, their phase behaviour at surfaces is not always predictable. We demonstrated in this work, how surface structures of non-conductive block copolymers, such as P4VP-b-PS-I, can be converted into (semi)conductive P4VP-b-PS-graft-P3HT chains via a surface-initiated polymerization of P3HT (Kumada Catalyst Transfer Polymerization (KCTP) from reactive surface-grafted block copolymers. This proves that our method is applicable to develop structured brushes of conductive polymers. We believe that it can be further exploited for novel, stimuli-responsive materials, for the construction of sensors, or for building various opto-electronic devices. The methods developed here can in principle be adapted for the preparation of any conductive block copolymers and conductive polymers, including other interesting architectures of conductive polymers, such as block copolymers, cylindrical brushes, star-like polymers, etc. To this end, one needs to synthesize properly-designed and multi-functional Ni-initiators before performing the polycondensation.

Die Effizienz einer Tumortherapie durch einen Transfer von ex vivo aktivierten Tumor-spezifischen zytotoxischen T-Lymphozyten wird durch zahlreiche Faktoren wie geringe Anzahl der isolierten spezifischen T-Zellen, schnelles Abklingen der Aktivität und kurzzeitige Persistenz der transferierten Effektorzellen im Empfängerorganismus stark limitiert. Eine Möglichkeit zur Überwindung dieser Einschränkungen bietet die Entwicklung einer neuen Strategie zur Armierung der zytotoxischen T-Lymphozyten mit Tumor-spezifischen chimären Rezeptoren. Ziel dieser Arbeit war es, die Grundlagen für eine solche immuntherapeutische Strategie zu erarbeiten. Da das Prostatakarzinom die am meisten diagnostizierte maligne Erkrankung und die dritt häufigste Todesursache des Mannes ist, wurde das auf der Oberfläche von Prostatakarzinomzellen exprimierte PSCA (prostataspezifisches Stammzellantigen) als Zielantigen gewählt. Neben der therapierefraktären Spätstadien des Prostatakarzinoms bedürfen die früh entstehenden Mikrometastasen (minimale Resterkrankung) einer neuen adjuvanten Behandlungsoption. Das PSCA ist ein membranständiges Tumor-assoziiertes Antigen, das in mehr als 80 % der primären Prostatakarzinome überexprimiert wird. PSCA wird als besonders aussichtsreiches Zielantigen einer Immuntherapie bei fortgeschrittenen Prostatakarzinomen angesehen, weil sein Expressionsniveau mit der Tumorprogression und der Entwicklung zum androgenunabhängigen Wachstum ansteigt. In der vorgelegten Arbeit wurde zunächst ein neuer monoklonaler PSCA-spezifischer Antikörper generiert, der als Grundlage für die Konstruktion eines Einzelkettenantikörpers (scFv) verwendet wurde. Aus einem Hybridomklon, der sich durch sehr hohe Bindungsstärke auszeichnete, wurden mittels degenerierter Primer die kodierenden Sequenzen für die variablen VH und VL Domänen des Antikörpers amplifiziert. Durch die Verbindung der beiden VH und VL Domänen mittels eines Linkers wurde der PSCA-spezifische Einzelkettenantikörper generiert. Die mit gereinigtem scFv durchgeführten Bindungsanalysen bestätigten die Funktionalität des rekombinanten Proteins und seine Anwendbarkeit zur Chimerisierung eines membranständigen Rezeptors. Nach dem ?Zwei-Signal-Modell? benötigen T-Zellen für eine effiziente Antigen-spezifische Aktivierung neben dem T-Zell-Rezeptorsignal ein zusätzliches kostimulatorisches Signal. Daher wurden chimäre Rezeptoren auf der Basis der Beta-Kette des T-Zell-Rezeptors und des CD28-Moleküls generiert. Bei der Konstruktion des chimären T-Zell-Rezeptors wurde die konstante Domäne der Beta-Kette mit der CD3 -Kette fusioniert. Neben einer starken Oberflächenexpression des Rezeptors wurde auch die effiziente Bindung von löslichem PSCA nachgewiesen. Die Bindung des Rezeptors an das PSCA führte zur Phosphorylierung der ITAM-Sequenzen der heterodimeren -Kette, was die Funktionalität des chimären Rezeptors bestätigte. Die Stimulation der Zellen über den anti-CD3 Antikörper resultierte ebenfalls in der Phosphorylierung der heterodimeren -Kette, was ein Hinweis auf eine mögliche Interaktion der chimären Kette mit dem endogenen CD3-Komplex lieferte. Um die kostimulatorische Wirkung über das selbe Antigen zu erzielen, wurde das CD28 Molekül N-terminal ebenfalls mit dem Einzelkettenantikörper modifiziert. Die durch Bindung des löslichen Proteins induzierte Phosphorylierung der Akt-Kinase bewies die Funktionalität der chimären CD28 Kette als PSCA-spezifischer Rezeptor. Diese Arbeit demonstriert die Generierung eines hochaffinen PSCA-spezifischen Einzelkettenantikörpers als eine Antigen-erkennende Struktur eines chimären Rezeptors. Die Armierung polyklonaler zytotoxischer T-Lymphozyten mit den funktionsfähigen chimären Rezeptoren stellt den ersten Schritt einer neuen Strategie zur Eliminierung hormon-refrektärer und metastasierender Prostatakarzinomzellen dar.