Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

Herstellung und physikochemische Charakterisierung von planaren gestützten Lipid-Modellmembran-Systemen

Es wurden funktionalisierte polymerunterstützte planare Phospholipid-Modellmembran-Systeme hergestellt und auf jeder Präparationsstufe eingehend charakterisiert. Dünne Polysaccharidfilme wurden in der Form von quellbaren Gelen auf oxidische Oberflächen aufgebracht und bezüglich ihres Quellungsverhaltens und der Oberflächeneigenschaften in Abhängigkeit vom Wassergehalt untersucht. Lipidmonoschichten unterschiedlicher Zusammensetzung wurden mittels Langmuir-Blodgett-Tranfer auf Polymersubstrate übertragen und bezüglich der Stärke der Lipid/Polymer Wechselwirkung, der lateralen Selbstdiffusion in Abhängigkeit von der Wasseraktivität, dem Spreitverhalten der monomolekularen Membran auf dem Substrat in Abhängigkeit von der Wasseraktivität und dem Lateraldruck der Monoschicht, sowie des Ausmaßes der Hydratation im Kopfgruppenbereich der Lipidmembran in Abhängigkeit von der Wasseraktivität mittels Fluoreszensondenmethoden (Fluoreszenzerholung nach Photobleichung (FRAP), Fluoreszenzmikroskopie und Fluoreszenzspektroskopie) untersucht. Diffusions- und Spreitverhalten von amphiphilen Monoschichten auf Polymersubstraten wurden auf der Basis von in dieser Arbeit entwickelten physikalischen Modellen diskutiert. Mittels Langmuir-Schäfer Transfer wurde auf polymerunterstützte Lipidmonoschichten eine zweite Monoschicht übertragen. Die somit erhaltenen Lipid-Doppelschichtmembranen wurden bezüglich ihrer Stabilität, der lateralen Struktur, der lateralen Selbstdiffusion, des Spreitverhaltens auf unbedeckte Bereiche sowie der Stärke der Membran/Substrat Wechselwirkung vermittels Fluoreszenzmikroskopie, FRAP und Interferenz-Kontrast-Mikroskopie (RICM) untersucht. Schließlich wurden substratgestützte Doppelschicht-Lipidmembranen mit als Protonenpumpen fungierenden integralen Membranproteinen versehen. Die laterale Selbstdiffusion der rekonstituierten Proteinmoleküle wurde mittels FRAP, die funktionale Aktivität der Protonenpumpen mit einem Ionen-sensitiven Feldeffekttransistor-Array analysiert.

Charge transport in amorphous organic semiconductors

Organic semiconductors with the unique combination of electronic and mechanical properties may offer cost-effective ways of realizing many electronic applications, e.g. large-area flexible displays, printed integrated circuits and plastic solar cells. In order to facilitate the rational compound design of organic semiconductors, it is essential to understand relevant physical properties e.g. charge transport. This, however, is not straightforward, since physical models operating on different time and length scales need to be combined. First, the material morphology has to be known at an atomistic scale. For this atomistic molecular dynamics simulations can be employed, provided that an atomistic force field is available. Otherwise it has to be developed based on the existing force fields and first principle calculations. However, atomistic simulations are typically limited to the nanometer length- and nanosecond time-scales. To overcome these limitations, systematic coarse-graining techniques can be used. In the first part of this thesis, it is demonstrated how a force field can be parameterized for a typical organic molecule. Then different coarse-graining approaches are introduced together with the analysis of their advantages and problems. When atomistic morphology is available, charge transport can be studied by combining the high-temperature Marcus theory with kinetic Monte Carlo simulations. The approach is applied to the hole transport in amorphous films of tris(8-hydroxyquinoline)aluminium (Alq3). First the influence of the force field parameters and the corresponding morphological changes on charge transport is studied. It is shown that the energetic disorder plays an important role for amorphous Alq3, defining charge carrier dynamics. Its spatial correlations govern the Poole-Frenkel behavior of the charge carrier mobility. It is found that hole transport is dispersive for system sizes accessible to simulations, meaning that calculated mobilities depend strongly on the system size. A method for extrapolating calculated mobilities to the infinite system size is proposed, allowing direct comparison of simulation results and time-of-flight experiments. The extracted value of the nondispersive hole mobility and its electric field dependence for amorphous Alq3 agree well with the experimental results.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Quantum hydrodynamic models for semiconductors with and without collisions

In dieser Arbeit werden Quantum-Hydrodynamische (QHD) Modelle betrachtet, die ihren Einsatz besonders in der Modellierung von Halbleiterbauteilen finden. Das QHD Modell besteht aus den Erhaltungsgleichungen für die Teilchendichte, das Momentum und die Energiedichte, inklusive der Quanten-Korrekturen durch das Bohmsche Potential. Zu Beginn wird eine Übersicht über die bekannten Ergebnisse der QHD Modelle unter Vernachlässigung von Kollisionseffekten gegeben, die aus ein­em Schrödinger-System für den gemischten-Zustand oder aus der Wigner-Glei­chung hergeleitet werden können. Nach der Reformulierung der eindimensionalen QHD Gleichungen mit linearem Potential als stationäre Schrö­din­ger-Gleichung werden die semianalytischen Fassungen der QHD Gleichungen für die Gleichspannungs-Kurve betrachtet. Weiterhin werden die viskosen Stabilisierungen des QHD Modells be­rück­sich­tigt, sowie die von Gardner vorgeschlagene numerische Viskosität für das {sf upwind} Finite-Differenzen Schema berechnet. Im Weiteren wird das viskose QHD Modell aus der Wigner-Glei­chung mit Fokker-Planck Kollisions-Ope­ra­tor hergeleitet. Dieses Modell enthält die physikalische Viskosität, die durch den Kollision-Operator eingeführt wird. Die Existenz der Lösungen (mit strikt positiver Teilchendichte) für das isotherme, stationäre, eindimensionale, viskose Modell für allgemeine Daten und nichthomogene Randbedingungen wird gezeigt. Die dafür notwendigen Abschätzungen hängen von der Viskosität ab und erlauben daher den Grenzübergang zum nicht-viskosen Fall nicht. Numerische Simulationen der Resonanz-Tunneldiode modelliert mit dem nichtisothermen, stationären, eindimensionalen, viskosen QHD Modell zeigen den Einfluss der Viskosität auf die Lösung. Unter Verwendung des von Degond und Ringhofer entwickelten Quanten-Entropie-Minimierungs-Verfahren werden die allgemeinen QHD-Gleichungen aus der Wigner-Boltzmann-Gleichung mit dem BGK-Kollisions-Operator hergeleitet. Die Herleitung basiert auf der vorsichtige Entwicklung des Quanten-Max­well­ians in Potenzen der skalierten Plankschen Konstante. Das so erhaltene Modell enthält auch vertex-Terme und dispersive Terme für die Ge­schwin­dig­keit. Dadurch bleibt die Gleichspannungs-Kurve für die Re­so­nanz-Tunnel­diode unter Verwendung des allgemeinen QHD Modells in einer Dimension numerisch erhalten. Die Ergebnisse zeigen, dass der dispersive Ge­schwin­dig­keits-Term die Lösung des Systems stabilisiert.

Global simulated soil biogenic nitric oxide (NO) emissions: Impact, improvement and innovation

rnNitric oxide (NO) is important for several chemical processes in the atmosphere. Together with nitrogen dioxide (NO2 ) it is better known as nitrogen oxide (NOx ). NOx is crucial for the production and destruction of ozone. In several reactions it catalyzes the oxidation of methane and volatile organic compounds (VOCs) and in this context it is involved in the cycling of the hydroxyl radical (OH). OH is a reactive radical, capable of oxidizing most organic species. Therefore, OH is also called the “detergent” of the atmosphere. Nitric oxide originates from several sources: fossil fuel combustion, biomass burning, lightning and soils. Fossil fuel combustion is the largest source. The others are, depending on the reviewed literature, generally comparable to each other. The individual sources show a different temporal and spatial pattern in their magnitude of emission. Fossil fuel combustion is important in densely populated places, where NO from other sources is less important. In contrast NO emissions from soils (hereafter SNOx) or biomass burning are the dominant source of NOx in remote regions.rnBy applying an atmospheric chemistry global climate model (AC-GCM) I demonstrate that SNOx is responsible for a significant part of NOx in the atmosphere. Furthermore, it increases the O3 and OH mixing ratio substantially, leading to a ∼10% increase in the oxidizing efficiency of the atmosphere. Interestingly, through reduced O3 and OH mixing ratios in simulations without SNOx, the lifetime of NOx increases in regions with other dominating sources of NOx

Blood-CNS barriers in neurodegenerative diseases

The blood-brain barrier (BBB) and the blood-spinal cord barrier (BSCB) separate the brain and the spinal cord from the circulating blood and are important for the maintenance of the CNS homeostasis. They build a physical barrier thereby protecting the CNS from pathogens and toxic agents, and their disruption plays a crucial role in the pathogenesis of several CNS disorders. In this thesis, the blood-CNS-barriers were studied via in vitro models in two case studies for neurodegenerative disorders, in particular Alzheimer’s disease (AD) and amyotrophic lateral sclerosis (ALS). The first model evaluates treatment possibilities of AD using nanotechnology-based strategies. Since the toxic amyloid-β42 (Aβ42) peptide plays a crucial role in the pathogenesis of AD, reduced generation or enhanced clearance of Aβ42 peptides are expected to modify the disease course in AD. Therefore, several Aβ42-lowering drugs like flurbiprofen had been tested in clinical trials, but most of them failed due to their low brain penetration. Here, flurbiprofen was embedded in polylactide (PLA) nanoparticles and its transport was examined in an in vitro BBB model. The embedding of flurbiprofen into the nanoparticles disguised its cytotoxic potential and enabled the administration of higher drug concentrations which resulted in a sufficient transport of the drug across an endothelial cell monolayer. These results demonstrate that non-permeable drugs can be transported efficiently via nanoparticles and that these nanotechnology-based strategies are a promising tool to generate novel therapeutic options for AD and other CNS diseases. rnThe focus of the second project was to investigate the impaired integrity of the BSCB in a mouse model for ALS. About 20% of all familial ALS cases are associated with missense mutations or small deletions in the gene that encodes Cu/Zn-superoxide dismutase 1 (SOD1). To date, the molecular mechanisms resulting in ALS are still unknown, but there is evidence that the disruption of the BSCB is one of the primary pathological events. In both familial and sporadic ALS patients, loss of endothelial integrity and endothelial cell damage was observed, and studies with SOD1 transgenic mice demonstrated that the BSCB disruption was found prior to motor neuron degeneration and neurovascular inflammation. Thus, an in vitro model for ALS endothelial cells was generated which exhibited comparable integrity characteristics and tight junction (TJ) protein expression profiles as isolated primary endothelial cells of the BSCB of SOD1 transgenic mice. In this, an alteration of the βcat/AKT/FoxO1 pathway, which regulates the expression of the TJ protein claudin-5, could be observed. These data furthermore indicate that ALS is a neurovascular disease, and understanding of the primary events in ALS pathogenesis will hopefully provide ideas for the development of new therapeutic strategies. rn

Synthesis and application of stimuli responsive tunable systems based on physical interactions

Novel single step synthetic procedure for hydrophobically modified alkali soluble latexes (HASE) via a miniemulsion-analogous method is presented. This facile method simplifies the copolymerization of the monomers with basically “opposite” character in terms of their hydrophilic/hydrophobic nature, which represent one of the main challenges in water based systems. Considered systems do not represent classical miniemulsions due to a high content of water soluble monomers. However, the polymerization mechanism was found to be rather similar to miniemulsion polymerization process.rnThe influence of the different factors on the system stability has been investigated. The copolymerization behavior studies typically showed strong composition drifts during copolymerization. It was found that the copolymer composition drift can be suppressed via changing the initial monomer ratio.rnThe neutralization behavior of the obtained HASE systems was investigated via potentiometric titration. The rheological behavior of the obtained systems as a function of the different parameters, such as pH, composition (ultrahydrophobe content) and additive type and content has also been investigated.rnDetailed investigation of the storage and loss moduli, damping factor and the crossover frequencies of the samples showed that at the initial stages of the neutralization the systems show microgel-like behavior.rnThe dependence of the rheological properties on the content and the type of the ultrahydrophobe showed that the tuning of the mechanical properties can be easily achieved via minor (few percent) but significant changes in the content of the latter. Besides, changing the hydrophobicity of the ultrahydrophobe via increasing the carbon chain length represents another simple method for achieving the same results.rnThe influence of amphiphilic additives (especially alcohols) on the rheological behavior of the obtained systems has been studied. An analogy was made between micellation of surfactants and the formation of hydrophobic domains between hydrophobic groups of the polymer side chain.rnDilution induced viscosity reduction was investigated in different systems, without or with different amounts or types of the amphiphilic additive. Possibility of the controlled response to dilution was explored. It was concluded that the sensitivity towards dilution can be reduced, and in extreme cases even the increase of the dynamic modulus can be observed, which is of high importance for the setting behavior of the adhesive material.rnIn the last part of this work, the adhesive behavior of the obtained HASE systems was investigated on different substrates (polypropylene and glass) for the standard labeling paper. Wet tack and setting behavior was studied and the trends for possible applications have been evaluated.rnThe novel synthetic procedure, investigation of rheological properties and the possibility of the tuning via additives, investigated in this work create a firm background for the development of the HASE based adhesives as well as rheology modifiers with vast variety of possible applications due to ease of tuning the mechanical and rheological properties of the systems.