Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

optomotor-blind and the horizontal and vertical system cells of the drosophila optic lobes

The horizontal and vertical system neurons (HS and VS cells) are part of a conserved set of lobula plate giant neurons (LPGNs) in the optic lobes of the adult brain. Structure and physiology of these cells are well known, predominantly from studies in larger Dipteran flies. Our knowledge about the ontogeny of these cells is limited and stems predominantly from laser ablation studies in larvae of the house fly Musca domestica. These studies suggested that the HS and VS cells stem from a single precursor, which, at least in Musca, has not yet divided in the second larval instar. A regulatory mutation (In(1)omb[H31]) in the Drosophila gene optomotor-blind (omb) leads to the selective loss of the adult HS and VS cells. This mutation causes a transient reduction in omb expression in what appears to be the entire optic lobe anlage (OLA) late in embryogenesis. Here, I have reinitiated the laser approach with the goal of identifying the presumptive embryonic HS/VS precursor cell in Drosophila. The usefulness of the laser ablation approach which has not been applied, so far, to cells lying deep within the Drosophila embryo, was first tested on two well defined embryonic sensory structures, the olfactory antenno-maxillary complex (AMC) and the light-sensitive Bolwing´s organ (BO). In the case of the AMC, the efficiency of the ablation procedure was demonstrated with a behavioral assay. When both AMCs were ablated, the response to an attractive odour (n-butanol) was clearly reduced. Interestingly, the larvae were not completely unresponsive but had a delayed response kinetics, indicating the existence of a second odour system. BO will be a useful test system for the selectivity of laser ablation when used at higher spatial resolution. An omb-Gal4 enhancer trap line was used to visualize the embryonic OLA by GFP fluorescence. This fluorescence allowed to guide the laser beam to the relevant structure within the embryo. The success of the ablations was monitored in the adult brain via the enhancer trap insertion A122 which selectively visualizes the HS and VS cell bodies. Due to their tight clustering, individual cells could not be identified in the embryonic OLA by conventional fluorescence microscopy. Nonetheless, systematic ablation of subdomains of the OLA allowed to localize the presumptive HS/VS precursor to a small area within the OLA, encompassing around 10 cells. Future studies at higher resolution should be able to identify the precursor as (an) individual cell(s). Most known lethal omb alleles do not complement the HS/VS phenotype of the In(1)omb[H31] allele. This is the expected behaviour of null alleles. Two lethal omb alleles that had been isolated previously by non-complementation of the omb hypomorphic allele bifid, have been reported, however, to complement In(1)omb[H31]. This report was based on low resolution paraffin histology of adult heads. Four mutations from this mutagenesis were characterized here in more detail (l(1)omb[11], l(1)omb[12], l(1)omb[13], and l(1)omb[15]). Using A122 as marker for the adult HS and VS cells, I could show, that only l(1)omb[11] can partly complement the HS/VS cell phenotype of In(1)omb[H31]. In order to identify the molecular lesions in these mutants, the exons and exon/intron junctions were sequenced in PCR-amplified material from heterozygous flies. Only in two mutants could the molecular cause for loss of omb function be identified: in l(1)omb[13]), a missense mutation causes the exchange of a highly conserved residue within the DNA-binding T-domain; in l(1)omb[15]), a nonsense mutation causes a C-terminal truncation. In the other two mutants apparently regulatory regions or not yet identified alternative exons are affected. To see whether mutant OMB protein in the missense mutant l(1)omb[13] is affected in DNA binding, electrophoretic shift assays on wildtype and mutant T-domains were performed. They revealed that the mutant no longer is able to bind the consensus palindromic T-box element.

Mediterranean-type climate in the South Aegean (Eastern Mediterranean) during the Late Miocene: Evidence from isotope and element proxies

The present-day climate in the Mediterranean region is characterized by mild, wet winters and hot, dry summers. There is contradictory evidence as to whether the present-day conditions (“Mediterranean climate”) already existed in the Late Miocene. This thesis presents seasonally-resolved isotope and element proxy data obtained from Late Miocene reef corals from Crete (Southern Aegean, Eastern Mediterranean) in order to illustrate climate conditions in the Mediterranean region during this time. There was a transition from greenhouse to icehouse conditions without a Greenland ice sheet during the Late Miocene. Since the Greenland ice sheet is predicted to melt fully within the next millennia, Late Miocene climate mechanisms can be considered as useful analogues in evaluating models of Northern Hemispheric climate conditions in the future. So far, high resolution chemical proxy data on Late Miocene environments are limited. In order to enlarge the proxy database for this time span, coral genus Tarbellastraea was evaluated as a new proxy archive, and proved reliable based on consistent oxygen isotope records of Tarbellastraea and the established paleoenvironmental archive of coral genus Porites. In combination with lithostratigraphic data, global 87Sr/86Sr seawater chronostratigraphy was used to constrain the numerical age of the coral sites, assuming the Mediterranean Sea to be equilibrated with global open ocean water. 87Sr/86Sr ratios of Tarbellastraea and Porites from eight stratigraphically different sampling sites were measured by thermal ionization mass spectrometry. The ratios range from 0.708900 to 0.708958 corresponding to ages of 10 to 7 Ma (Tortonian to Early Messinian). Spectral analyses of multi-decadal time-series yield interannual δ18O variability with periods of ~2 and ~5 years, similar to that of modern records, indicating that pressure field systems comparable to those controlling the seasonality of present-day Mediterranean climate existed, at least intermittently, already during the Late Miocene. In addition to sea surface temperature (SST), δ18O composition of coral aragonite is controlled by other parameters such as local seawater composition which as a result of precipitation and evaporation, influences sea surface salinity (SSS). The Sr/Ca ratio is considered to be independent of salinity, and was used, therefore, as an additional proxy to estimate seasonality in SST. Major and trace element concentrations in coral aragonite determined by laser ablation inductively coupled plasma mass spectrometry yield significant variations along a transect perpendicular to coral growth increments, and record varying environmental conditions. The comparison between the average SST seasonality of 7°C and 9°C, derived from average annual δ18O (1.1‰) and Sr/Ca (0.579 mmol/mol) amplitudes, respectively, indicates that the δ18O-derived SST seasonality is biased by seawater composition, reducing the δ18O amplitude by 0.3‰. This value is equivalent to a seasonal SSS variation of 1‰, as observed under present-day Aegean Sea conditions. Concentration patterns of non-lattice bound major and trace elements, related to trapped particles within the coral skeleton, reflect seasonal input of suspended load into the reef environment. δ18O, Sr/Ca and non-lattice bound element proxy records, as well as geochemical compositions of the trapped particles, provide evidence for intense precipitation in the Eastern Mediterranean during winters. Winter rain caused freshwater discharge and transport of weathering products from the hinterland into the reef environment. There is a trend in coral δ18O data to more positive mean δ18O values (–2.7‰ to –1.7‰) coupled with decreased seasonal δ18O amplitudes (1.1‰ to 0.7‰) from 10 to 7 Ma. This relationship is most easily explained in terms of more positive summer δ18O. Since coral diversity and annual growth rates indicate more or less constant average SST for the Mediterranean from the Tortonian to the Early Messinian, more positive mean and summer δ18O indicate increasing aridity during the Late Miocene, and more pronounced during summers. The analytical results implicate that winter rainfall and summer drought, the main characteristics of the present-day Mediterranean climate, were already present in the Mediterranean region during the Late Miocene. Some models have argued that the Mediterranean climate did not exist in this region prior to the Pliocene. However, the data presented here show that conditions comparable to those of the present-day existed either intermittently or permanently since at least about 10 Ma.

From carbazole-containing and pi-expanded triangular trinuclear porphyrinoids

Zusammenfassung:rnDie vorliegende Arbeit beschreibt das Design und die Synthese neuartiger Porphyrinoide anhand der Modifikation und der π-Systemausdehnung an der Peripherie des Porphyrin-Gerüsts. Die Darstellung künstlicher Porphyrine ist von Interesse, da neue physiko-chemischen Eigenschaften erhalten und untersucht werden können. Die in dieser Arbeit vorgestellten Porphyrinoide wurden mit Hilfe von modernen Synthesemethoden wie den metallkatalysierten Kreuzkupplungen und somit durch Aryl-Aryl Verknüpfungen aufgebaut.rnDer erste Teil dieser Arbeit befasst sich mit der Modifikation des Porphyrin-Gerüsts. Porphyrine bestehen aus jeweils zwei Pyrrol- und Pyrrolenin-Einheiten, welche systematisch ausgetauscht wurden. Die Pyrrol-Einheiten wurden durch Carbazol ersetzt, das sich formal vom Pyrrol durch Anfügen von zwei Benzogruppen ableitet und deshalb besonders gut geeignet ist. Die Pyrrolenin-Einheiten wurden aus folgenden Gründen durch andere Heterozyklen wie Pyridin, Pyrrol oder Triazol ersetzt: rn* Nachbildung des stabilen Porphyrin trans-NH-Tautomers (Carbazol und Pyridin)rn* Nachbildung von (NH)4-Liganden wie Calix[4]pyrrol (Carbazol und Pyrrol)rn* Vereinigung von N-H und C-H Wasserstoffbrücken-Donor-Einheiten in einem Makrozyklus (Carbazol und Triazol)rnDie Synthese eines drei-Zentren Porphyrinoids mit ausgedehntem π-System wird im zweiten Teil der vorliegenden Arbeit beschrieben. Dieses Thema basiert auf der aktuellen Entwicklung von nicht-Edelmetall basierten Katalysatoren für die Reduktion von Sauerstoff. Hier werden derzeit N4 makrozyklische Metallkomplexe, die mehrere katalytisch aktive Stellen aufweisen, untersucht. In diesem Zusammenhang, hat die Gruppe von Prof. Müllen einen neuartigen drei-Zentren-Komplex entwickelt. Ausgehend von diesen Erkenntnissen, dient diese Arbeit zur Verbesserung der katalytischen Aktivität des drei-Zentren-Komplex durch die Variation von verschieden Substituenten. Hierbei wurden zwei wesentliche Konzepte verfolgt:rn* Vernetzung durch die Bildung von Netzwerken oder durch Pyrolyse in der Mesophasern* Verbesserung des Katalysator-Trägermaterial-KontaktsrnNeben den Synthesen wurden die Eigenschaften und möglichen Anwendungen dieser neuartigen Materialen untersucht, wie z.B. als Liganden für Übergangsmetalle, als Anionenrezeptoren oder als Elektrokatalysatoren für die Reduktion von Sauerstoff. rn

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.