Numerical and analytical approaches to strongly correlated electron systems

In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2. In the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT algorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy. The main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined Falicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase. In the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory. This model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The renormalization factor q can be evaluated as a function of the filling n for 00, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.

Reliability and consistency affect the integration of visual depth cues

Abstract Originalsprache (englisch) Visual perception relies on a two-dimensional projection of the viewed scene on the retinas of both eyes. Thus, visual depth has to be reconstructed from a number of different cues that are subsequently integrated to obtain robust depth percepts. Existing models of sensory integration are mainly based on the reliabilities of individual cues and disregard potential cue interactions. In the current study, an extended Bayesian model is proposed that takes into account both cue reliability and consistency. Four experiments were carried out to test this model's predictions. Observers had to judge visual displays of hemi-cylinders with an elliptical cross section, which were constructed to allow for an orthogonal variation of several competing depth cues. In Experiment 1 and 2, observers estimated the cylinder's depth as defined by shading, texture, and motion gradients. The degree of consistency among these cues was systematically varied. It turned out that the extended Bayesian model provided a better fit to the empirical data compared to the traditional model which disregards covariations among cues. To circumvent the potentially problematic assessment of single-cue reliabilities, Experiment 3 used a multiple-observation task, which allowed for estimating perceptual weights from multiple-cue stimuli. Using the same multiple-observation task, the integration of stereoscopic disparity, shading, and texture gradients was examined in Experiment 4. It turned out that less reliable cues were downweighted in the combined percept. Moreover, a specific influence of cue consistency was revealed. Shading and disparity seemed to be processed interactively while other cue combinations could be well described by additive integration rules. These results suggest that cue combination in visual depth perception is highly flexible and depends on single-cue properties as well as on interrelations among cues. The extension of the traditional cue combination model is defended in terms of the necessity for robust perception in ecologically valid environments and the current findings are discussed in the light of emerging computational theories and neuroscientific approaches.

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

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

In vitro characterization of human AML-reactive CTL clones generated from the naive subset of healthy donors and adoptive transfer into leukemia-engrafted NSG mice

Acute myeloid leukemia (AML) is a very aggressive cancer of the hematopoietic system. Chemotherapy and immunotherapeutical approaches including hematopoietic stem cell transplantation (HSCT) and donor lymphocyte infusion (DLI) are the only curative options available. The beneficial graft-versus-leukemia (GVL) effect of cellular immunotherapy is mostly mediated by donor-derived CD8+ T lymphocytes that recognize minor histocompatibility antigens (mHags) and leukemia-associated antigens (LAAs) presented on the surface of AML blasts (Falkenburg et al. 2008; Kolb 2008). A main complication is graft-versus-host disease (GVHD) that can be induced when cytotoxic T lymphocytes (CTLs) recognize broadly expressed antigens. To reduce the risk of GVHD, specific allogeneic T-cell therapy inducing selective GVL responses could be an option (Barrett & Le Blanc 2010; Parmar et al. 2011; Smits et al. 2011). This requires efficient in vitro strategies to generate AML-reactive T cells with an early differentiation phenotype as well as vigorous effector functions and humanized mouse models to analyze the anti-leukemic potential of adoptively transferred T cells in vivo. In this study, AML-reactive CTL clones and oligoclonal T-cell lines could be reliably generated from the naive subset of healthy HLA-class I-identical donors by stimulation with primary AML blasts in mini-mixed-lymphocyte / leukemia cultures (MLLCs) in eight different patient / donor pairs. These CTLs were promising candidates for cellular immunotherapy because of their relatively early differentiation phenotype and strong proliferative and lytic capabilities. The addition of the common γ-chain cytokine IL-21 to the stimulation protocol enabled more precursors to develop into potent leukemia-reactive CTLs, presumably by its beneficial effects on cell survival and antigen-specific proliferation during the first weeks of cultures. It also strengthened the early-stage phenotype. Three long-term cultured CTLs exemplarily transferred into leukemia-engrafted immunodeficient NSG mice mediated a significant reduction of the leukemic burden after a single transfusion. These results demonstrate that CTL clones with reactivity to patient-derived AML blasts can be isolated from the naive compartment of healthy donors and show potent anti-leukemic effects in vivo. The herein described allo-MLLC approach with in vitro “programmed” naive CTL precursors independent of a HSCT setting is a valuable alternative to the conventional method of isolating in vivo primed donor CTLs out of patients after transplantation (Kloosterboer et al. 2004; Warren et al. 2010). This would make leukemia-reactive CTLs already available at the time point of HSCT, when residual leukemia disease is minimal and the chances for complete leukemia eradication are high. Furthermore, leukemia-reactive CTLs effectively expanded by this in vitro protocol can be used as screening populations to identify novel candidate LAAs and mHags for antigen-specific immunotherapy.

Phenothiazine based polymers for energy and data storage application

Die vorliegende Arbeit befasst sich mit der Synthese und Charakterisierung von Polymeren mit redox-funktionalen Phenothiazin-Seitenketten. Phenothiazin und seine Derivate sind kleine Redoxeinheiten, deren reversibles Redoxverhalten mit electrochromen Eigenschaften verbunden ist. Das besondere an Phenothiazine ist die Bildung von stabilen Radikalkationen im oxidierten Zustand. Daher können Phenothiazine als bistabile Moleküle agieren und zwischen zwei stabilen Redoxzuständen wechseln. Dieser Schaltprozess geht gleichzeitig mit einer Farbveränderung an her.rnrnIm Rahmen dieser Arbeit wird die Synthese neuartiger Phenothiazin-Polymere mittels radikalischer Polymerisation beschrieben. Phenothiazin-Derivate wurden kovalent an aliphatischen und aromatischen Polymerketten gebunden. Dies erfolgte über zwei unterschiedlichen synthetischen Routen. Die erste Route beinhaltet den Einsatz von Vinyl-Monomeren mit Phenothiazin Funktionalität zur direkten Polymerisation. Die zweite Route verwendet Amin modifizierte Phenothiazin-Derivate zur Funktionalisierung von Polymeren mit Aktivester-Seitenketten in einer polymeranalogen Reaktion. rnrnPolymere mit redox-funktionalen Phenothiazin-Seitenketten sind aufgrund ihrer Elektron-Donor-Eigenschaften geeignete Kandidaten für die Verwendung als Kathodenmaterialien. Zur Überprüfung ihrer Eignung wurden Phenothiazin-Polymere als Elektrodenmaterialien in Lithium-Batteriezellen eingesetzt. Die verwendeten Polymere wiesen gute Kapazitätswerte von circa 50-90 Ah/kg sowie schnelle Aufladezeiten in der Batteriezelle auf. Besonders die Aufladezeiten sind 5-10 mal höher als konventionelle Lithium-Batterien. Im Hinblick auf Anzahl der Lade- und Entladezyklen, erzielten die Polymere gute Werte in den Langzeit-Stabilitätstests. Insgesamt überstehen die Polymere 500 Ladezyklen mit geringen Veränderungen der Anfangswerte bezüglich Ladezeiten und -kapazitäten. Die Langzeit-Stabilität hängt unmittelbar mit der Radikalstabilität zusammen. Eine Stabilisierung der Radikalkationen gelang durch die Verlängerung der Seitenkette am Stickstoffatom des Phenothiazins und der Polymerhauptkette. Eine derartige Alkyl-Substitution erhöht die Radikalstabilität durch verstärkte Wechselwirkung mit dem aromatischen Ring und verbessert somit die Batterieleistung hinsichtlich der Stabilität gegenüber Lade- und Entladezyklen. rnrnDes Weiteren wurde die praktische Anwendung von bistabilen Phenothiazin-Polymeren als Speichermedium für hohe Datendichten untersucht. Dazu wurden dünne Filme des Polymers auf leitfähigen Substraten elektrochemisch oxidiert. Die elektrochemische Oxidation erfolgte mittels Rasterkraftmikroskopie in Kombination mit leitfähigen Mikroskopspitzen. Mittels dieser Technik gelang es, die Oberfläche des Polymers im nanoskaligen Bereich zu oxidieren und somit die lokale Leitfähigkeit zu verändern. Damit konnten unterschiedlich große Muster lithographisch beschrieben und aufgrund der Veränderung ihrer Leitfähigkeit detektiert werden. Der Schreibprozess führte nur zu einer Veränderung der lokalen Leitfähigkeit ohne die topographische Beschaffenheit des Polymerfilms zu beeinflussen. Außerdem erwiesen sich die Muster als besonders stabil sowohl mechanisch als auch über die Zeit.rnrnZum Schluss wurden neue Synthesestrategien entwickelt um mechanisch stabile als auch redox-funktionale Oberflächen zu produzieren. Mit Hilfe der oberflächen-initiierten Atomtransfer-Radikalpolymerisation wurden gepfropfte Polymerbürsten mit redox-funktionalen Phenothiazin-Seitenketten hergestellt und mittels Röntgenmethoden und Rasterkraftmikroskopie analysiert. Eine der Synthesestrategien geht von gepfropften Aktivesterbürsten aus, die anschließend in einem nachfolgenden Schritt mit redox-funktionalen Gruppen modifiziert werden können. Diese Vorgehensweise ist besonders vielversprechend und erlaubt es unterschiedliche funktionelle Gruppen an den Aktivesterbürsten zu verankern. Damit können durch Verwendung von vernetzenden Gruppen neben den Redoxeigenschaften, die mechanische Stabilität solcher Polymerfilme optimiert werden. rn rn

Systematics, phylogeny and biogeography of Juncaginaceae

I investigated the systematics, phylogeny and biogeographical history of Juncaginaceae, a small family of the early-diverging monocot order Alismatales which comprises about 30 species of annual and perennial herbs. A wide range of methods from classical taxonomy to molecular systematic and biogeographic approaches was used. rnrnIn Chapter 1, a phylogenetic analysis of the family and members of Alismatales was conducted to clarify the circumscription of Juncaginaceae and intrafamilial relationships. For the first time, all accepted genera and those associated with the family in the past were analysed together. Phylogenetic analysis of three molecular markers (rbcL, matK, and atpA) showed that Juncaginaceae are not monophyletic. As a consequence the family is re-circumscribed to exclude Maundia which is pro-posed to belong to a separate family Maundiaceae, reducing Juncaginaceae to include Tetroncium, Cycnogeton and Triglochin. Tetroncium is weakly supported as sister to the rest of the family. The reinstated Cycnogeton (formerly included in Triglochin) is highly supported as sister to Triglochin s.str. Lilaea is nested within Triglochin s. str. and highly supported as sister to the T. bulbosa complex. The results of the molecular analysis are discussed in combination with morphological characters, a key to the genera of the family is given, and several new combinations are made.rnrnIn Chapter 2, phylogenetic relationships in Triglochin were investigated. A species-level phylogeny was constructed based on molecular data obtained from nuclear (ITS, internal transcribed spacer) and chloroplast sequence data (psbA-trnH, matK). Based on the phylogeny of the group, divergence times were estimated and ancestral distribution areas reconstructed. The monophyly of Triglochin is confirmed and relationships between the major lineages of the genus were resolved. A clade comprising the Mediterranean/African T. bulbosa complex and the American T. scilloides (= Lilaea s.) is sister to the rest of the genus which contains two main clades. In the first, the widespread T. striata is sister to a clade comprising annual Triglochin species from Australia. The second clade comprises T. palustris as sister to the T. maritima complex, of which the latter is further divided into a Eurasian and an American subclade. Diversification in Triglochin began in the Miocene or Oligocene, and most disjunctions in Triglochin were dated to the Miocene. Taxonomic diversity in some clades is strongly linked to habitat shifts and can not be observed in old but ecologically invariable lineages such as the non-monophyletic T. maritima.rnrnChapter 3 is a collaborative revision of the Triglochin bulbosa complex, a monophyletic group from the Mediterranean region and Africa. One new species, Triglochin buchenaui, and two new subspecies, T. bulbosa subsp. calcicola and subsp. quarcicola, from South Africa were described. Furthermore, two taxa were elevated to species rank and two reinstated. Altogether, seven species and four subspecies are recognised. An identification key, detailed descriptions and accounts of the ecology and distribution of the taxa are provided. An IUCN conservation status is proposed for each taxon.rnrnChapter 4 deals with the monotypic Tetroncium from southern South America. Tetroncium magellanicum is the only dioecious species in the family. The taxonomic history of the species is described, type material is traced, and a lectotype for the name is designated. Based on an extensive study of herbarium specimens and literature, a detailed description of the species and notes on its ecology and conservation status are provided. A detailed map showing the known distribution area of T. magellanicum is presented. rnrnIn Chapter 5, the flower structure of the rare Australian endemic Maundia triglochinoides (Maundiaceae, see Chapter 1) was studied in a collaborative project. As the morphology of Maundia is poorly known and some characters were described differently in the literature, inflorescences, flowers and fruits were studied using serial mictrotome sections and scanning electron microscopy. The phylogenetic placement, affinities to other taxa, and the evolution of certain characters are discussed. As Maundia exhibits a mosaic of characters of other families of tepaloid core Alismatales, its segregation as a separate family seems plausible.