Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

Ionenleitfähigkeit in polymeren Matrizes – Synthese, Charakterisierung und Untersuchung dynamischer Prozesse von neuen Lithium- und Protonenleitern

Die vorliegende Dissertation befasst sich mit der Synthese, physikochemischen und polymerspezifischen Charakterisierung und insbesondere der impedanzspektroskopischen Untersuchung von sowohl neuartigen, solvensfreien lithiumionen- als auch protonenleitfähigen Polymermaterialien für potentielle Anwendungen in sekundären Lithiumionenbatterien bzw. in Hochtemperatur-Protonenaustauschmembran-Brennstoffzellen (engl.: proton exchange membrane fuel cell, auch: polymer electrolyte membrane fuel cell, PEMFC). Beiden Typen von ionenleitfähigen Membranen liegt das gängige Prinzip der chemischen Anbindung einer für den Ionentransport verantwortlichen Seitengruppe an eine geeignete Polymerhauptkette zugrunde („Entkopplung“; auch Immobilisierung), welcher hinsichtlich Glasübergangstemperatur (Tg), elektrochemischer und thermischer Stabilität (Td) eine dynamisch entkoppelte, aber nicht minder bedeutsame Rolle zukommt. Die Transportaktivierung erfolgt in beiden Fällen thermisch. Im Falle der Protonenleiter liegt die zusätzliche Intention darin, eine Alternative aufzuzeigen, in der die Polymerhauptkette gekoppelt direkt am Protonentransportmechanismus beteiligt ist, d.h., dass der translatorisch diffusive Ionentransport entlang der Hauptkette stattfindet und nicht zwischen benachbarten Seitenketten. Ein Hauptaugenmerk der Untersuchungen liegt sowohl bei den lithiumionen- als auch den protonenleitfähigen Polymermembranen auf temperaturabhängigen dynamischen Prozessen der jeweiligen Ionenspezies in der polymeren Matrix, was die Ionenleitfähigkeit selbst, Relaxationsphänomene, die translatorische Ionendiffusion und im Falle der Protonenleiter etwaige mesomere Grenzstrukturübergänge umfasst. Lithiumionenleiter: Poly(meth)acrylate mit (2-Oxo-1,3-dioxolan)resten (Cyclocarbonat-) in der Seitenkette unterschiedlicher Spacerlänge wurden synthetisiert und charakterisiert. Die Leitfähigkeit s(,T) erreicht bei Poly(2-oxo-[1,3]dioxolan-4-yl)methylacrylat (PDOA): Lithium-bis-trifluormethansulfonimid (LiTFSI) (10:3) ca. 10^-3,5 S cm^-1 bei 150 °C. Weichmachen (Dotieren) mit äquimolaren Mengen an Propylencarbonat (PC) bewirkt in allen Fällen einen enormen Anstieg der Leitfähigkeit. Die höchsten Leitfähigkeiten von Mischungen dieser Polymere mit LiTFSI (und LiBOB) werden nicht beim System mit der niedrigsten Tg gefunden. Auch dient Tg nicht als Referenztemperatur (Tref) nach Williams-Landel-Ferry (WLF), so dass eine WLF-Anpassung der Leitfähigkeitsdaten nur über einen modifizierten WLF-Algorithmus gelingt. Die ermittelten Tref liegen deutlich unterhalb von Tg bei Temperaturen, die charakteristisch für die Seitenkettenrelaxation sind („Einfrieren“). Dies legt nahe, dass der Relaxation der Seitenketten eine entscheidende Rolle im Li^+-Leitfähigkeitsmechanismus zukommt. Die Li^+-Überführungszahlen tLi^+ in diesen Systemen schwanken zwischen 0,13 (40 °C) und 0,55 (160 °C). Protonenleiter: Polymere mit Barbitursäure- bzw. Hypoxanthinresten in der Seitenkette und Polyalkylenbiguanide unterschiedlicher Spacerlänge wurden synthetisiert und charakterisiert. Die Leitfähigkeit s(,T) erreicht bei Poly(2,4,6(1H,3H,5H)-trioxopyrimidin-5-yl)methacrylat (PTPMA) maximal ca. 10^-4,4 S cm^-1 bei 140 °C. Höhere Leitfähigkeiten sind nur durch Mischen mit aprotischen Lösungsmitteln erreichbar. Die höchste Leitfähigkeit wird im Falle der Polyalkylenbiguanide bei Polyethylenbiguanid (PEB) erzielt. Sie erreicht 10^-2,4 S cm^-1 bei 190 °C. Die Aktivierungsenergien EA der Polyalkylenbiguanide liegen (jeweils unterhalb von Tg) zwischen ca. 3 – 6 kJ mol^-1. In allen beobachteten Fällen dient Tg als Tref, so dass eine konventionelle WLF-Behandlung möglich ist und davon auszugehen ist, dass die Leitfähigkeit mit dem freien Volumen Vf korreliert.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Hunting for warped extra dimensions via loop-induced processes

This thesis is on loop-induced processes in theories with warped extra dimensions where the fermions and gauge bosons are allowed to propagate in the bulk, while the Higgs sector is localized on or near the infra-red brane. These so-called Randall-Sundrum (RS) models have the potential to simultaneously explain the hierarchy problem and address the question of what causes the large hierarchies in the fermion sector of the Standard Model (SM). The Kaluza-Klein (KK) excitations of the bulk fields can significantly affect the loop-level processes considered in this thesis and, hence, could indirectly indicate the existence of warped extra dimensions. The analytical part of this thesis deals with the detailed calculation of three loop-induced processes in the RS models in question: the Higgs production process via gluon fusion, the Higgs decay into two photons, and the flavor-changing neutral current b → sγ. A comprehensive, five-dimensional (5D) analysis will show that the amplitudes of the Higgs processes can be expressed in terms of integrals over 5D propagators with the Higgs-boson profile along the extra dimension, which can be used for arbitrary models with a compact extra dimension. To this end, both the boson and fermion propagators in a warped 5D background are derived. It will be shown that the seemingly contradictory results for the gluon fusion amplitude in the literature can be traced back to two distinguishable, not smoothly-connected incarnations of the RS model. The investigation of the b → sγ transition is performed in the KK decomposed theory. It will be argued that summing up the entire KK tower leads to a finite result, which can be well approximated by a closed, analytical expression.rnIn the phenomenological part of this thesis, the analytic results of all relevant Higgs couplings in the RS models in question are compared with current and in particular future sensitivities of the Large Hadron Collider (LHC) and the planned International Linear Collider. The latest LHC Higgs data is then used to exclude significant portions of the parameter space of each RS scenario. The analysis will demonstrate that especially the loop-induced Higgs couplings are sensitive to KK particles of the custodial RS model with masses in the multi tera-electronvolt range. Finally, the effect of the RS model on three flavor observables associated with the b → sγ transition are examined. In particular, we study the branching ratio of the inclusive decay B → X_s γ

A molecular dynamics study of the influence of chain branching on the properties of polymer systems

Die vorliegende Arbeit beschäftigt sich mit dem Einfluß von Kettenverzweigungen unterschiedlicher Topologien auf die statischen Eigenschaften von Polymeren. Diese Untersuchungen werden mit Hilfe von Monte-Carlo- und Molekular-Dynamik-Simulationen durchgeführt.Zunächst werden einige theoretische Konzepte und Modelle eingeführt, welche die Beschreibung von Polymerketten auf mesoskopischen Längenskalen gestatten. Es werden wichtige Bestimmungsgrößen eingeführt und erläutert, welche zur quantitativen Charakterisierung von Verzweigungsstrukturen bei Polymeren geeignet sind. Es wird ebenso auf die verwendeten Optimierungstechniken eingegangen, die bei der Implementierung des Computerprogrammes Verwendung fanden. Untersucht werden neben linearen Polymerketten unterschiedliche Topolgien -Sternpolymere mit variabler Armzahl, Übergang von Sternpolymeren zu linearen Polymeren, Ketten mit variabler Zahl von Seitenketten, reguläre Dendrimere und hyperverzweigte Strukturen - in Abhängigkeit von der Lösungsmittelqualität. Es wird zunächst eine gründliche Analyse des verwendeten Simulationsmodells an sehr langen linearen Einzelketten vorgenommen. Die Skalierungseigenschaften der linearen Ketten werden untersucht in dem gesamten Lösungsmittelbereich vom guten Lösungsmittel bis hin zu weitgehend kollabierten Ketten im schlechten Lösungsmittel. Ein wichtiges Ergebnis dieser Arbeit ist die Bestätigung der Korrekturen zum Skalenverhalten des hydrodynamischen Radius Rh. Dieses Ergebnis war möglich aufgrund der großen gewählten Kettenlängen und der hohen Qualität der erhaltenen Daten in dieser Arbeit, insbesondere bei den linearen ketten, und es steht im Widerspruch zu vielen bisherigen Simulations-Studien und experimentellen Arbeiten. Diese Korrekturen zum Skalenverhalten wurden nicht nur für die linearen Ketten, sondern auch für Sternpolymere mit unterchiedlicher Armzahl gezeigt. Für lineare Ketten wird der Einfluß von Polydispersität untersucht.Es wird gezeigt, daß eine eindeutige Abbildung von Längenskalen zwischen Simulationsmodell und Experiment nicht möglich ist, da die zu diesem Zweck verwendete dimensionslose Größe eine zu schwache Abhängigkeit von der Polymerisation der Ketten besitzt. Ein Vergleich von Simulationsdaten mit industriellem Low-Density-Polyäthylen(LDPE) zeigt, daß LDPE in Form von stark verzweigten Ketten vorliegt.Für reguläre Dendrimere konnte ein hochgradiges Zurückfalten der Arme in die innere Kernregion nachgewiesen werden.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Electronic energy transfer processes and charge carrier transport in pi-conjugated polymers

Conjugated polymers have attracted tremendous academical and industrial research interest over the past decades due to the appealing advantages that organic / polymeric materials offer for electronic applications and devices such as organic light emitting diodes (OLED), organic field effect transistors (OFET), organic solar cells (OSC), photodiodes and plastic lasers. The optimization of organic materials for applications in optoelectronic devices requires detailed knowledge of their photophysical properties, for instance energy levels of excited singlet and triplet states, excited state decay mechanisms and charge carrier mobilities. In the present work a variety of different conjugated (co)polymers, mainly polyspirobifluorene- and polyfluorene-type materials, was investigated using time-resolved photoluminescence spectroscopy in the picosecond to second time domain to study their elementary photophysical properties and to get a deeper insight into structure-property relationships. The experiments cover fluorescence spectroscopy using Streak Camera techniques as well as time-delayed gated detection techniques for the investigation of delayed fluorescence and phosphorescence. All measurements were performed on the solid state, i.e. thin polymer films and on diluted solutions. Starting from the elementary photophysical properties of conjugated polymers the experiments were extended to studies of singlet and triplet energy transfer processes in polymer blends, polymer-triplet emitter blends and copolymers. The phenomenon of photonenergy upconversion was investigated in blue light-emitting polymer matrices doped with metallated porphyrin derivatives supposing an bimolecular annihilation upconversion mechanism which could be experimentally verified on a series of copolymers. This mechanism allows for more efficient photonenergy upconversion than previously reported for polyfluorene derivatives. In addition to the above described spectroscopical experiments, amplified spontaneous emission (ASE) in thin film polymer waveguides was studied employing a fully-arylated poly(indenofluorene) as the gain medium. It was found that the material exhibits a very low threshold value for amplification of blue light combined with an excellent oxidative stability, which makes it interesting as active material for organic solid state lasers. Apart from spectroscopical experiments, transient photocurrent measurements on conjugated polymers were performed as well to elucidate the charge carrier mobility in the solid state, which is an important material parameter for device applications. A modified time-of-flight (TOF) technique using a charge carrier generation layer allowed to study hole transport in a series of spirobifluorene copolymers to unravel the structure-mobility relationship by comparison with the homopolymer. Not only the charge carrier mobility could be determined for the series of polymers but also field- and temperature-dependent measurements analyzed in the framework of the Gaussian disorder model showed that results coincide very well with the predictions of the model. Thus, the validity of the disorder concept for charge carrier transport in amorphous glassy materials could be verified for the investigated series of copolymers.

Context-dependent interpretation of the conjunction 'und' in different age-groups

In contrast to formal semantics, the conjunction and is nonsymmetrical in pragmatics. The events in Marc went to bed and fell asleep seem to have occurred chronologically although no explicit time reference is given. As the temporal interpretation appears to be weaker in Mia ate chocolate and drank milk, it seems that the kind and nature of events presented in a context influences the interpretation of the conjunction. This work focuses on contextual influences on the interpretation of the German conjunction und (‘and’). A variety of theoretic approaches are concerned with whether and contributes to the establishment of discourse coherence via pragmatic processes or whether the conjunction has complex semantic meaning. These approaches are discussed with respect to how they explain the temporal and additive interpretation of the conjunction and the role of context in the interpre-tation process. It turned out that most theoretic approaches do not consider the importance of different kinds of context in the interpretation process.rnIn experimental pragmatics there are currently only very few studies that investigate the inter-pretation of the conjunction. As there are no studies that investigate contextual influences on the interpretation of und systematically or investigate preschoolers interpretation of the con-junction, research questions such as How do (preschool) children interpret ‘und’? and Does the kind of events conjoined influence children’s and adults’ interpretation? are yet to be answered. Therefore, this dissertation systematically investigates how different types of context influence children’s interpretation of und. Three auditory comprehension studies were conducted in German. Of special interest was whether and how the order of events introduced in a context contributes to the temporal read-ing of the conjunction und. Results indicate that the interpretation of und is – at least in Ger-man – context-dependent: The conjunction is interpreted temporally more often when events that typical occur in a certain order are connected (typical contexts) compared to events with-out typical event order (neutral contexts). This suggests that the type of events conjoined in-fluences the interpretation process. Moreover, older children and adults interpret the conjunc-tion temporally more often than the younger cohorts if the conjoined events typically occur in a certain order. In neutral contexts, additive interpretations increase with age. 5-year-olds reject reversed order statements more often in typical contexts compared to neutral contexts. However, they have more difficulties with reversed order statements in typical contexts where they perform at chance level. This suggests that not only the type of event but also other age-dependent factors such as knowledge about scripts influence children’s performance. The type of event conjoined influences children’s and adults’ interpretation of the conjunction. There-fore, the influence of different event types and script knowledge on the interpretation process does not only have to be considered in future experimental studies on language acquisition and pragmatics but also in experimental pragmatics in general. In linguistic theories, context has to be given a central role and a commonly agreed definition of context that considers the consequences arising from different event types has to be agreed upon.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

The role of indigenous people in national development processes: Participation and marginalisation of indigenous Bedouin in South Sinai tourism development

The Bedouin of South Sinai have been significantly affected by the politics of external powers for a long time. However, never had the interest of external powers in Sinai been so strong as since the Israeli-Egyptian wars in the second half of the 20th century when Bedouin interests started to collide with Egypt’s plans for a development of luxury tourism in South Sinai. rnrnThe tourism boom that has started in the 1980s has brought economic and infrastructure development to the Bedouin and tourism has become the most important source of income for the Bedouin. However, while the absolute increase of tourists to Sinai has trickled down to the Bedouin to some extent, the participation of Bedouin in the overall tourism development is under-proportionate. Moreover, the Bedouin have become increasingly dependent on monetary income and consequently from tourism as the only significant source of income while at the same time they have lost much of their land as well as their self-determination.rnrnIn this context, the Bedouin livelihoods have become very vulnerable due to repeated depressions in the tourism industry as well as marginalization. Major marginalization processes the Bedouin are facing are the loss of land, barriers to market entry, especially increasingly strict rules and regulations in the tourism industry, as well as discrimination by the authorities. Social differentiation and Bedouin preferences are identified as further factors in Bedouin marginalization.rnrnThe strategies Bedouin have developed in response to all these problems are coping strategies, which try to deal with the present problem at the individual level. Basically no strategies have been developed at the collective level that would aim to actively shape the Bedouin’s present and future. Collective action has been hampered by a variety of factors, such as the speed of the developments, the distribution of power or the decay of tribal structures.rnWhile some Bedouin might be able to continue their tourism activities, a large number of informal jobs will not be feasible anymore. The majority of the previously mostly self-employed Bedouin will probably be forced to work as day-laborers who will have lost much of their pride, dignity, sovereignty and freedom. Moreover, with a return to subsistence being impossible for the majority of the Bedouin, it is likely that an increasing number of marginalized Bedouin will turn to illegal income generating activities such as smuggling or drug cultivation. This in turn will lead to further repression and discrimination and could escalate in a serious violent conflict between the Bedouin and the government.rnrnDevelopment plans and projects should address the general lack of civil rights, local participation and protection of minorities in Egypt and promote Bedouin community development and the consideration of Bedouin interests in tourism development.rnrnWether the political upheavals and the resignation of president Mubarak at the beginning of 2011 will have a positive effect on the situation of the Bedouin remains to be seen.rn