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In nature, society and technology many disordered systems exist, that show emergent behaviour, where the interactions of numerous microscopic agents result in macroscopic, systemic properties, that may not be present on the microscopic scale. Examples include phase transitions in magnetism and percolation, for example in porous unordered media, biological, and social systems. Also technological systems that are explicitly designed to function without central control instances, like their prime example the Internet, or virtual networks, like the World Wide Web, which is defined by the hyperlinks from one web page to another, exhibit emergent properties. The study of the common network characteristics found in previously seemingly unrelated fields of science and the urge to explain their emergence, form a scientific field in its own right, the science of complex networks. In this field, methodologies from physics, leading to simplification and generalization by abstraction, help to shift the focus from the implementation's details on the microscopic level to the macroscopic, coarse grained system level. By describing the macroscopic properties that emerge from microscopic interactions, statistical physics, in particular stochastic and computational methods, has proven to be a valuable tool in the investigation of such systems. The mathematical framework for the description of networks is graph theory, in hindsight founded by Euler in 1736 and an active area of research since then. In recent years, applied graph theory flourished through the advent of large scale data sets, made accessible by the use of computers. A paradigm for microscopic interactions among entities that locally optimize their behaviour to increase their own benefit is game theory, the mathematical framework of decision finding. With first applications in economics e.g. Neumann (1944), game theory is an approved field of mathematics. However, game theoretic behaviour is also found in natural systems, e.g. populations of the bacterium Escherichia coli, as described by Kerr (2002). In the present work, a combination of graph theory and game theory is used to model the interactions of selfish agents that form networks. Following brief introductions to graph theory and game theory, the present work approaches the interplay of local self-organizing rules with network properties and topology from three perspectives. To investigate the dynamics of topology reshaping, coupling of the so called iterated prisoners' dilemma (IPD) to the network structure is proposed and studied in Chapter 4. In dependence of a free parameter in the payoff matrix, the reorganization dynamics result in various emergent network structures. The resulting topologies exhibit an increase in performance, measured by a variance of closeness, of a factor 1.2 to 1.9, depending in the chosen free parameter. Presented in Chapter 5, the second approach puts the focus on a static network structure and studies the cooperativity of the system, measured by the fixation probability. Heterogeneous strategies to distribute incentives for cooperation among the players are proposed. These strategies allow to enhance the cooperative behaviour, while requiring fewer total investments. Putting the emphasis on communication networks in Chapters 6 and 7, the third approach investigates the use of routing metrics to increase the performance of data packet transport networks. Algorithms for the iterative determination of such metrics are demonstrated and investigated. The most successful of these algorithms, the hybrid metric, is able to increase the throughput capacity of a network by a factor of 7. During the investigation of the iterative weight assignments a simple, static weight assignment, the so called logKiKj metric, is found. In contrast to the algorithmic metrics, it results in vanishing computational costs, yet it is able to increase the performance by a factor of 5.
After a brief introduction on QCD and effective models in the first chapter, I analyze the dependence of the QCD transition temperature on the quark (or pion) mass in the second chapter. I found that a linear sigma model, which links the transition to chiral symmetry restoration, predicts a much stronger dependence of T_c on m_pi than seen in present lattice data for m_pi >~ 0.4 GeV. On the other hand, an effective Lagrangian for the Polyakov loop requires only small explicit symmetry breaking to describe T_c(m_pi) in the above mass range. In the third and fourth chapter, I study the linear sigma model with O(N) symmetry at nonzero temperature in the framework of the Cornwall-Jackiw-Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual Hartree-Fock (or Hartree) contributions, I derive a new approximation scheme which extends the standard Hartree-Fock (or Hartree) approximation by the inclusion of nonzero decay widths.
Die Dissertation ist in den Bereichen der semiklassischen Quantengravitation und der pseudokomplexen Allgemeinen Relativitätstheorie (pk-ART) anzusiedeln. Dabei wird unter semiklassischer Quantengravitation die Untersuchung quantenmechanischer Phänomene in einem durch eine klassische Gravitationstheorie gegebenen gravitativen Hintergrundfeld verstanden und bei der pk-ART handelt es sich um eine Alternative zu der aktuell anerkannten klassischen Gravitationstheorie, der Allgemeinen Relativitätstheorie (ART), die die reellen Raumzeitkoordinaten der ART pseudokomplex erweitert. Dies führt zusammen mit einer Veränderung des Variationsprinzips in führender Ordnung auf eine Korrektur der Einstein- Gleichung der ART mit einem zusätzlichen Quellterm (Energie-Impuls-Tensor), dessen exakte Form jedoch bisher nicht bekannt ist.
Die Beschreibung der Gravitation als Hintergrundfeld ergibt sich zwangsläufig daraus, dass auf Basis der ART bisher keine quantisierte Beschreibung für sie gefunden werden konnte. Jedoch wird erhofft, dass die Untersuchung semiklassischer Phänomene Hinweise auf die korrekte Theorie der Quantengravitation gibt. Zudem motiviert der Mangel einer quantisierten Gravitationstheorie die Verwendung alternativer Theorien, da sich dadurch die Frage stellt, ob die ART die korrekte Beschreibung klassischer Felder ist.
Das Ziel der vorliegenden Dissertation war die grundlegenden Unterschiede zwischen der ART und der pk-ART für gebundene sphärisch symmetrische Zustände der Klein-Gordon- und der Dirac-Gleichung zu identifizieren und ein qualitatives Modell der Vakuumfluktuationen in sphärisch symmetrischen Materieverteilungen zu bestimmen, wobei der Zusammenhang der pk-ART mit den Vakuumfluktuationen in der Annahme besteht, dass ein Zusammenhang zwischen ihnen und dem zusätzlichen Quellterm der pk-ART existiert. Dafür wurden die gebundenen Zustände der Klein-Gordon- und der Dirac-Gleichung für drei verschiedene Metrikmodelle (zwei ART-Modelle und ein pk-ART-Modell) mit konstanter Dichte systematisch numerisch berechnet, einige repräsentative Grafiken erstellt, anhand derer die grundlegenden Unterschiede der Ergebnisse der ART-Modelle und des pk-ART-Modells erörtert wurden, und die ART Ergebnisse der Dirac-Gleichung soweit wie möglich mit Ergebnissen der Literatur verglichen. Insbesondere wurde dabei festgestellt, dass die Energieeigenwerte in der pk-ART im Gegensatz zu denen in der ART in Abhängigkeit der Ausdehnung des Zentralobjekts ein Minimum aufweisen. Zudem wurden die Energieeigenwerte der Klein-Gordon-Gleichung teilweise sowohl über das Eigenwertproblem einer Matrix als auch über ein Anfangswertproblem berechnet und es wurde festgestellt, dass die Beschreibung als Eigenwertproblem deutlich uneffektiver ist, wenn dafür die Basis des dreidimensionalen harmonischen Oszillators genutzt wird. Für die Entwicklung des qualitativen Vakuumfluktuationsmodells wurden zwei Näherungen für den Erwartungswert des Energie-Impuls-Tensors in führender Ordnung für die Schwarzschildmetrik (ART) verglichen und die Verwendung eines qualitativen Modells durch die dabei auftretende Diskrepanz gerechtfertigt. Danach wurden die Vakuumfluktuationen für Metriken konstanter Materiedichte mit Hilfe einer der Näherungen in führender Ordnung berechnet und ein Modell gesucht, das den gleichen qualitativen Verlauf aufweist. Im Anschluss wurde dieses Modell noch für einfache Metriken mit variabler Materiedichte verifiziert.
Die Dissertation leistet mit der Analyse der gebundenen Zustände einen Beitrag in der Identifikation der Unterschiede zwischen der pk-ART und der ART und führt somit auf weitere mögliche Messgrößen, die der Unterscheidung der beiden Theorien dienen könnten. Weiterhin ermöglicht das abgeleitete Modell eine Verfeinerung der schon publizierten Ergebnisse über Neutronensterne und die für die Erstellung nötigen Vorarbeiten leisten einen Beitrag zur Identifikation des
pk-ART Quellterms.
Detailed knowledge of reaction mechanisms is key to understanding chemical, biological, and biophysical processes. For many reasons, it is desirable to comprehend how a reaction proceeds and what influences the reaction rate and its products.
In biophysics, reaction mechanisms provide insight into enzyme and protein function, the reason why they are so efficient, and what determines their reaction rates. They also reveal the relationship between the function of a protein and its structure and dynamics.
In chemistry, reaction mechanisms are able to explain side products, solvent effects, and the stereochemistry of a product. They are also the basis for potentially optimizing reactions with respect to yield, enhancing the stereoselectivity, or for modifying reactions in order to obtain other related products.
A key step to investigate reaction mechanisms is the identification and characterization of intermediates, which may be reactive, short-lived, and therefore only weakly populated. Nowadays, the structures of those can in most cases only be hypothesized based on products, side products, and isolable intermediates, because intermediates with a life time of less than a few microseconds are not accessible with the commonly used techniques for structure determination such as X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy.
In this thesis, two-dimensional infrared (2D-IR) spectroscopy is shown to be a powerful complement to the existing techniques for structure determination in solution. 2D-IR spectroscopy uses a femtosecond laser setup to investigate interactions between vibrations - analogous to 2D-NMR, which investigates the interactions between spins. Its ultrafast time resolution makes 2D-IR spectroscopy particularly well suited for the two topics investigated in this thesis: Structure Determination of Reactive Intermediates and Conformational Dynamics of Proteins.
Structure Determination of Reactive Intermediates: The focus of this thesis is using polarization-dependent 2D-IR (P2D-IR) spectroscopy for structure determination of N-crotonyloxazolidinone (referred to as 1), a small organic compound with a chiral oxazolidinone, known as Evans auxiliary, and its reactive complexes with the Lewis acids SnCl4 and Mg(ClO4)2. Chiral oxazolidinones in combination with Lewis acids have frequently been used in stereoselective synthesis for over 30 years. Nevertheless, the detailed mechanisms are in many cases xvi ABSTRACT still mere hypotheses and have not yet been experimentally proven. By accurately measuring the angles between the transition dipole moments in the molecules using an optimized P2D-IR setup and comparing the results to DFT calculations, the conformation of 1 and the conformation and coordination of the main complexes with SnCl4 and Mg(ClO4)2 are unequivocally identified and analyzed in depth. Structural details, such as a slight twist in the solution structure of 1, are detected using P2D-IR spectroscopy; these cannot be inferred from NMR spectroscopy or DFT calculations. In addition to the main Lewis acid complexes, complexes in low concentration are detected and tentatively assigned to different conformations and complexation geometries. The knowledge of those structures is essential for rationalizing the observed stereoselectivities. Additionally, a method is introduced that enables structure determination of molecules in complex mixtures and even in the presence of molecules with similar spectral properties and in high concentration. This work sets the stage for future studies of other substrate-catalyst complexes and reaction intermediates for which the structure determination has not been possible to date.
Conformational Dynamics of Proteins: Exchange 2D-IR spectroscopy allows the investigation of fast dynamics without disturbing the equilibrium of the exchanging species. It is therefore well suited to investigate fast dynamics of proteins and to reveal the speed limit of those. The temperature dependence of the conformational dynamics between the myoglobin substates A1 and A3 in equilibrium is analyzed. The various substates of myoglobin can be detected with FTIR spectroscopy, if carbon monoxide is bound to the heme. From previous studies it is known that the exchange rates at room temperature are in the picosecond time range, well suited to be investigated by 2D-IR spectroscopy. In the temperature range between 0 °C and 40 °C only a weak temperature dependence of the exchange rate in the myoglobin mutant L29I is observed in the present study. The exchange rate approximately doubles from 15 ns-1 at 0 °C to 31 ns-1 at 40 °C. It turned out that the conformational dynamics correlates linearly with the solvent viscosity, which itself is temperature dependent. Comparing our results to measurements at cryogenic temperatures, the linear relation between exchange time constant for this process and the viscosity is shown for the temperature range between -100 °C and 40 °C (corresponding to a viscosity change of 14 orders of magnitude). Thus, it is proven that the dynamics of the conformational switching are mainly determined by solvent dynamics, i.e., the protein dynamics are slaved to the solvent dynamics. This is the first time slaving is observed for such fast processes (in the picosecond time range). The observation implies a long-range structural rearrangement between the myoglobin substates A1 and A3. In addition, the exchange for other mutants and wild type myoglobin is analyzed qualitatively and found to agree with the conclusions drawn from L29I myoglobin.
In the present paper we develop the essential theoretical tools for the treatment of the dynamics of High Energy Heavy Ion Collisions. We study the influence of the nuclear equation of state and discuss the new phenomena connected with phase transitions in nuclear matter (pion condensation). Furthermore we investigate the possibility of a transition from nuclear to quark matter in High Energy Heavy Ion Collisions. In this context we discuss exotic phenomena like strongly bound pionic states, limiting temperatures, and exotic nuclei.
The requirement of the versatile signal generator has always been evident in modern RF and communication systems. The most conventional technique, voltage control oscillator (VCO), has inferior phase noise and narrow bandwidth despite its operating frequency can be up to the sub-THz regime. Its phase noise influenced by a various parameter associated with the oscillator circuit e.g. transistor size \& noise, bias current, noise leaking from the bias supply etc. The bandwidth is limited because the input voltage \& the output frequency of the VCO is not strictly linear over the tuning range. The phase noise and SFDR of the VCO output are enhanced by using the phase-lock technique. The phase-locked loop (PLL) uses the feedback system locking the reference frequency set by the VCO. However, the settling time of the PLL is higher due to a feedback control loop. The higher settling time increases the frequency switching time between PLL outputs. IG-oscillators is suitable for multi-GHz range and wide bandwidth application. Signal generation can alos be achieved by the free-electron radiation, optical lasers, Gunn diodes as well and they can operate even at the THz domain. All these signal generators suffer from slow frequency switching, lack of digital controllability, and advance modulation capability even though their frequency of operation is THz regime. Alternatively, the AWG (arbitrary wave generator) can produce a wide range of frequencies with low phase noise, including digital controllability. One of the vital components of the AWG is the direct digital synthesiser (DDS). Generally, it is composed of a phase accumulator, digital to analogue converter, sine mapping circuits and low pass filter. It needs a reference clock that acts as samples of the DDS outputs. Its output frequency can be varied by applying an appropriate digital input code. But high-speed DDS has several limitations; such as low number of output frequency points, lack of phase control unit, high power consumptions etc. This work addresses such limitations.
The goal of this project is to develop a framework for a cell that takes in consideration its internal structure, using an agent-based approach. In this framework, a cell was simulated as many sub-particles interacting to each other. This sub-particles can, in principle, represent any internal structure from the cell (organelles, etc). In the model discussed here, two types of sub-particles were used: membrane sub-particles and cytosolic elements. A kinetic and dynamic Delaunay triangulation was used in order to define the neighborhood relations between the sub-particles. However, it was soon noted that the relations defined by the Delaunay triangulation were not suitable to define the interactions between membrane sub-particles. The cell membrane is a lipid bilayer, and does not present any long range interactions between their sub-particles. This means that the membrane particles should not be able to interact in a long range. Instead, their interactions should be confined to the two-dimensional surface supposedly formed by the membrane. A method to select, from the original three-dimensional triangulations, connections restricted to the two-dimensional surface formed by the cell membrane was then developed. The algorithm uses as starting point the three-dimensional Delaunay triangulation involving both internal and membrane sub-particles. From this triangulation, only the subset of connections between membrane sub-particles was considered. Since the cell is full of internal particles, the collection of the membrane particles' connections will resemble the surface to be obtained, even though it will still have many connections that do not belong to the restricted triangulation on the surface. This "thick surface" was called a quasi-surface. The following step was to refine the quasi-surface, cutting out some of the connections so that the ones left made a proper surface triangulation with the membrane points. For that, the quasi-surface was separated in clusters. Clusters are defined as areas on the quasi-surface that are not yet properly triangulated on a two-dimensional surface. Each of the clusters was then re-triangulated independently, using re-triangulation methods also developed during this work. The interactions between cytosolic elements was given by a Lennard-Jones potential, as well as the interactions between cytosolic elements and membrane particles. Between only membrane particles, the interactions were given by an elastic interaction. For each particle, the equation of motion was written. The algorithm chosen to solve the equations of motion was the Verlet algorithm. Since the cytosol can be approximated as a gel, it is reasonable to suppose that the sub-cellular particles are moving in an overdamped environment. Therefore, an overdamped approximation was used for all interactions. Additionally, an adaptive algorithm was used in order to define the size of the time step used in each interaction. After the method to re-triangulate the membrane points was implemented, the time needed to re-triangulate a single cluster was studied, followed by an analysis on how the time needed to re-triangulate each point in a cluster varied with the cluster size. The frequency of appearance for each cluster size was also compared, as this information is necessary to guarantee that the total time needed by to re-triangulate a cell is convergent. At last, the total time spent re-triangulating a surface was plotted, as well as a scaling for the total re-triangulation time with the variation. Even though there is still a lot to be done, the work presented here is an important step on the way to the main goal of this project: to create an agent-based framework that not only allows the simulation of any sub-cellular structure of interest but also provides meaningful interaction relations to particles belonging to the cell membrane.
This thesis deals with the simulation, optimization and realization of quasi-optical scanning systems for active THz cameras. Active THz cameras are sensitive in the THz regime of the electromagnetic spectrum and are suitable for the detection of metal objects such as weapons behind clothing or fabrics (maybe for security applications) or material investigation. An advantage of active THz-systems is the possibility to measure the phase of the THz-radiation and thus to reconstruct the surface topography of the objects under test. Due to the coherent illumination and the required system parameters (like image field size, working distance and lateral resolution) the optical systems (in the THz region often called quasi-optical systems) must be optimized. Specifically, the active illumination systems require highly optimized quasioptical systems to achieve a good image quality. Since currently no suitable multi-pixel detectors are available, the object has to be scanned in one or two dimensions in order to cover a full field of view. This further reinforces the occurring aberrations. The dissertation covers, alongside the underlying theory, the simulation, optimisation and realisation of three different active THz systems. The subdivision of the chapters is as follows: Chapter 1 deals with a motivation. Chapter 2 develops the underlying theory and it is demonstrated that the geometrical optics is an adequate and powerful description of the image field optimization. It also addresses the developed analytic on-axis and the off-axis image field optimization routine. Chapter 3, 4 and 5 are about the basis of various active THz cameras, each presented a major system aspect. Chapter 3 shows how active THz-cameras with very high system dynamics range can be realised. Within this chapter it could although be demonstrated how very high depth resolution can be achieved due to the coherent and active illumination and how high refresh rate can be implemented. Chapter 4 shows how absolute distance data of the objects under test can be obtained. Therefore it is possible to reconstruct the entire object topography up to a fraction of the wavelength. Chapter 5 shows how off-axis quasi-optical systems must be optimized. It is also shown how the illumination geometry of the active THz systems must be changed to allow for real-time frame rates. The developed widened multi-directional lighting approach also fixes the still existing problem of phase ambiguity of the single phase measurement. Within this chapter, the world’s first active real-time camera with very high frame rates around 10 Hz is presented. This could be only realized with the highly optimised quasioptical system and the multi-directional lighting approach. The paper concludes with a summary and an outlook for future work. Within the outlook some results regarding the simulation of synthetic aperture radar systems and metamaterials are shown.
The PANDA experiment at FAIR will study fundamental questions of strong interaction with high precision. Effcient particle identification for a wide momentum range and the full solid angle is required for successful reconstruction of the benchmark channels of the broad PANDA physics program. For this purpose a compact ring imaging Cherenkov detector is being developed for the barrel region of the PANDA detector. The concept and the baseline design of the PANDA Barrel DIRC were inspired by the BABAR DIRC and improved with important modifications, like fast photon timing, a compact expansion volume, and focusing optics. The required detector resolution was defined based on the PANDA PID specifications using the phase space distributions of the final state kaons produced in selected benchmark channels. To optimize the PANDA Barrel DIRC design in terms of performance and cost the baseline detector geometry and a number of design options were implemented in the simulation. The key options include the radiator dimensions, two types of expansion volume shapes, and a variety of focusing systems. The performance of the detector designs was quantified in terms of single photon Cherenkov angle resolution and photon yield. It was found that the number of radiators can be reduced by about 40% without loss in performance. A compound spherical lens without air gap was found to be a promising focusing system. An optimized Barrel DIRC design meeting the PID requirements includes three radiator bars per at section, the compound lens without air gap, a compact prism-shaped EV, and a total of 192 Microchannel-Plate PMTs as photosensors. The number of electronic channels can be halved without loss in performance by combining two neighbouring pixels. For such a detector design the total cost will be significantly reduced compared to the baseline version while still meeting or exceeding the PANDA PID performance goals.