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.

On the car sequencing problem: analysis and solution methods

This work deals with the car sequencing (CS) problem, a combinatorial optimization problem for sequencing mixed-model assembly lines. The aim is to find a production sequence for different variants of a common base product, such that work overload of the respective line operators is avoided or minimized. The variants are distinguished by certain options (e.g., sun roof yes/no) and, therefore, require different processing times at the stations of the line. CS introduces a so-called sequencing rule H:N for each option, which restricts the occurrence of this option to at most H in any N consecutive variants. It seeks for a sequence that leads to no or a minimum number of sequencing rule violations. In this work, CS’ suitability for workload-oriented sequencing is analyzed. Therefore, its solution quality is compared in experiments to the related mixed-model sequencing problem. A new sequencing rule generation approach as well as a new lower bound for the problem are presented. Different exact and heuristic solution methods for CS are developed and their efficiency is shown in experiments. Furthermore, CS is adjusted and applied to a resequencing problem with pull-off tables.

Modeling surface-atmosphere exchange of trace gases and energy within and above the Amazon rain forest

Die vorliegende Dissertation untersucht die biogeochemischen Vorgänge in der Vegetationsschicht (Bestand) und die Rückkopplungen zwischen physiologischen und physikalischen Umweltprozessen, die das Klima und die Chemie der unteren Atmosphäre beeinflussen. Ein besondere Schwerpunkt ist die Verwendung theoretischer Ansätze zur Quantifizierung des vertikalen Austauschs von Energie und Spurengasen (Vertikalfluss) unter besonderer Berücksichtigung der Wechselwirkungen der beteiligten Prozesse. Es wird ein differenziertes Mehrschicht-Modell der Vegetation hergeleitet, implementiert, für den amazonischen Regenwald parametrisiert und auf einen Standort in Rondonia (Südwest Amazonien) angewendet, welches die gekoppelten Gleichungen zur Energiebilanz der Oberfläche und CO2-Assimilation auf der Blattskala mit einer Lagrange-Beschreibung des Vertikaltransports auf der Bestandesskala kombiniert. Die hergeleiteten Parametrisierungen beinhalten die vertikale Dichteverteilung der Blattfläche, ein normalisiertes Profil der horizontalen Windgeschwindigkeit, die Lichtakklimatisierung der Photosynthesekapazität und den Austausch von CO2 und Wärme an der Bodenoberfläche. Desweiteren werden die Berechnungen zur Photosynthese, stomatären Leitfähigkeit und der Strahlungsabschwächung im Bestand mithilfe von Feldmessungen evaluiert. Das Teilmodell zum Vertikaltransport wird im Detail unter Verwendung von 222-Radon-Messungen evaluiert. Die ``Vorwärtslösung'' und der ``inverse Ansatz'' des Lagrangeschen Dispersionsmodells werden durch den Vergleich von beobachteten und vorhergesagten Konzentrationsprofilen bzw. Bodenflüssen bewertet. Ein neuer Ansatz wird hergeleitet, um die Unsicherheiten des inversen Ansatzes aus denjenigen des Eingabekonzentrationsprofils zu quantifizieren. Für nächtliche Bedingungen wird eine modifizierte Parametrisierung der Turbulenz vorgeschlagen, welche die freie Konvektion während der Nacht im unteren Bestand berücksichtigt und im Vergleich zu früheren Abschätzungen zu deutlich kürzeren Aufenthaltszeiten im Bestand führt. Die vorhergesagte Stratifizierung des Bestandes am Tage und in der Nacht steht im Einklang mit Beobachtungen in dichter Vegetation. Die Tagesgänge der vorhergesagten Flüsse und skalaren Profile von Temperatur, H2O, CO2, Isopren und O3 während der späten Regen- und Trockenzeit am Rondonia-Standort stimmen gut mit Beobachtungen überein. Die Ergebnisse weisen auf saisonale physiologische Änderungen hin, die sich durch höhere stomatäre Leitfähigkeiten bzw. niedrigere Photosyntheseraten während der Regen- und Trockenzeit manifestieren. Die beobachteten Depositionsgeschwindigkeiten für Ozon während der Regenzeit überschreiten diejenigen der Trockenzeit um 150-250%. Dies kann nicht durch realistische physiologische Änderungen erklärt werden, jedoch durch einen zusätzlichen cuticulären Aufnahmemechanismus, möglicherweise an feuchten Oberflächen. Der Vergleich von beobachteten und vorhergesagten Isoprenkonzentrationen im Bestand weist auf eine reduzierte Isoprenemissionskapazität schattenadaptierter Blätter und zusätzlich auf eine Isoprenaufnahme des Bodens hin, wodurch sich die globale Schätzung für den tropischen Regenwald um 30% reduzieren würde. In einer detaillierten Sensitivitätsstudie wird die VOC Emission von amazonischen Baumarten unter Verwendung eines neuronalen Ansatzes in Beziehung zu physiologischen und abiotischen Faktoren gesetzt. Die Güte einzelner Parameterkombinationen bezüglich der Vorhersage der VOC Emission wird mit den Vorhersagen eines Modells verglichen, das quasi als Standardemissionsalgorithmus für Isopren dient und Licht sowie Temperatur als Eingabeparameter verwendet. Der Standardalgorithmus und das neuronale Netz unter Verwendung von Licht und Temperatur als Eingabeparameter schneiden sehr gut bei einzelnen Datensätzen ab, scheitern jedoch bei der Vorhersage beobachteter VOC Emissionen, wenn Datensätze von verschiedenen Perioden (Regen/Trockenzeit), Blattentwicklungsstadien, oder gar unterschiedlichen Spezies zusammengeführt werden. Wenn dem Netzwerk Informationen über die Temperatur-Historie hinzugefügt werden, reduziert sich die nicht erklärte Varianz teilweise. Eine noch bessere Leistung wird jedoch mit physiologischen Parameterkombinationen erzielt. Dies verdeutlicht die starke Kopplung zwischen VOC Emission und Blattphysiologie.

Detection of small buried objects: asymptotic factorization and MUSIC

In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data. In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves. For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.

Aspects of poriferan (Suberites domuncula) apoptosis and innate immune system and evolutionary implications

Survivin, a unique member of the family of inhibitors of apoptosis (IAP) proteins, orchestrates intracellular pathways during cell division and apoptosis. Its central regulatory function in vertebrate molecular pathways as mitotic regulator and inhibitor of apoptotic cell death has major implications for tumor cell proliferation and viability, and has inspired several approaches that target survivin for cancer therapy. Analyses in early-branching Metazoa so far propose an exclusive role of survivin as a chromosomal passenger protein, whereas only later during evolution the second, complementary antiapoptotic function might have arisen, concurrent with increased organismal complexity. To lift the veil on the ancestral function(s) of this key regulatory molecule, a survivin homologue of the phylogenetically oldest extant metazoan taxon (phylum Porifera) was identified and functionally characterized. SURVL of the demosponge Suberites domuncula shares significant similarities with its metazoan homologues, ranging from conserved exon/intron structures to the presence of localization signal and protein-interaction domains, characteristic of IAP proteins. Whereas sponge tissue displayed a very low steady-state level, SURVL expression was significantly up-regulated in rapidly proliferating primmorph cells. In addition, challenge of sponge tissue and primmorphs with cadmium and the lipopeptide Pam3Cys-Ser-(Lys)4 stimulated SURVL expression, concurrent with the expression of newly discovered poriferan caspases (CASL and CASL2). Complementary functional analyses in transfected HEK-293 revealed that heterologous expression of poriferan survivin in human cells not only promotes cell proliferation but also augments resistance to cadmium-induced cell death. Taken together, these results demonstrate both a deep evolutionary conserved and fundamental dual role of survivin, and an equally conserved central position of this key regulatory molecule in interconnected pathways of cell cycle and apoptosis. Additionally, SDCASL, SDCASL2, and SDTILRc (TIR-LRR containing protein) may represent new components of the innate defense sentinel in sponges. SDCASL and SDCASL2 are two new caspase-homolog proteins with a singular structure. In addition to their CASc domains, SDCASL and SDCASL2 feature a small prodomain NH2-terminal (effector caspases) and a remarkably long COOH-terminal domain containing one or several functional double stranded RNA binding domains (dsrm). This new caspase prototype can characterize a caspase specialization coupling pathogen sensing and apoptosis, and could represent a very efficient defense mechanism. SDTILRc encompasses also a unique combination of domains: several leucine rich repeats (LRR) and a Toll/IL-1 receptor (TIR) domain. This unusual domain association may correspond to a new family of intracellular sensing protein, forming a subclass of pattern recognition receptors (PRR).

Copper and zinc stable isotope ratios as tracers of biogeochemical processes, sources and transport of Cu and Zn in soils

Copper and Zn are essential micronutrients for plants, animals, and humans; however, they may also be pollutants if they occur at high concentrations in soil. Therefore, knowledge of Cu and Zn cycling in soils is required both for guaranteeing proper nutrition and to control possible risks arising from pollution.rnThe overall objective of my study was to test if Cu and Zn stable isotope ratios can be used to investigate into the biogeochemistry, source and transport of these metals in soils. The use of stable isotope ratios might be especially suitable to trace long-term processes occurring during soil genesis and transport of pollutants through the soil. In detail, I aimed to answer the questions, whether (1) Cu stable isotopes are fractionated during complexation with humic acid, (2) 65Cu values can be a tracer for soil genetic processes in redoximorphic soils (3) 65Cu values can help to understand soil genetic processes under oxic weathering conditions, and (4) 65Cu and 66Zn values can act as tracers of sources and transport of Cu and Zn in polluted soils.rnTo answer these questions, I ran adsorption experiments at different pH values in the laboratory and modelled Cu adsorption to humic acid. Furthermore, eight soils were sampled representing different redox and weathering regimes of which two were influenced by stagnic water, two by groundwater, two by oxic weathering (Cambisols), and two by podzolation. In all horizons of these soils, I determined selected basic soil properties, partitioned Cu into seven operationally defined fractions and determined Cu concentrations and Cu isotope ratios (65Cu values). Finally, three additional soils were sampled along a deposition gradient at different distances to a Cu smelter in Slovakia and analyzed together with bedrock and waste material from the smelter for selected basic soil properties, Cu and Zn concentrations and 65Cu and 66Zn values.rnMy results demonstrated that (1) Copper was fractionated during adsorption on humic acid resulting in an isotope fractionation between the immobilized humic acid and the solution (65CuIHA-solution) of 0.26 ± 0.11‰ (2SD) and that the extent of fractionation was independent of pH and involved functional groups of the humic acid. (2) Soil genesis and plant cycling causes measurable Cu isotope fractionation in hydromorphic soils. The results suggested that an increasing number of redox cycles depleted 63Cu with increasing depth resulting in heavier 65Cu values. (3) Organic horizons usually had isotopically lighter Cu than mineral soils presumably because of the preferred uptake and recycling of 63Cu by plants. (4) In a strongly developed Podzol, eluviation zones had lighter and illuviation zones heavier 65Cu values because of the higher stability of organo-65Cu complexes compared to organo-63Cu complexes. In the Cambisols and a little developed Podzol, oxic weathering caused increasingly lighter 65Cu values with increasing depth, resulting in the opposite depth trend as in redoximorphic soils, because of the preferential vertical transport of 63Cu. (5) The 66Zn values were fractionated during the smelting process and isotopically light Zn was emitted allowing source identification of Zn pollution while 65Cu values were unaffected by the smelting and Cu emissions isotopically indistinguishable from soil. The 65Cu values in polluted soils became lighter down to a depth of 0.4 m indicating isotope fractionation during transport and a transport depth of 0.4 m in 60 years. 66Zn values had an opposite depth trend becoming heavier with depth because of fractionation by plant cycling, speciation changes, and mixing of native and smelter-derived Zn. rnCopper showed measurable isotope fractionation of approximately 1‰ in unpolluted soils, allowing to draw conclusions on plant cycling, transport, and redox processes occurring during soil genesis and 65Cu and 66Zn values in contaminated soils allow for conclusions on sources (in my study only possible for Zn), biogeochemical behavior, and depth of dislocation of Cu and Zn pollution in soil. I conclude that stable Cu and Zn isotope ratios are a suitable novel tool to trace long-term processes in soils which are difficult to assess otherwise.rn

Chemical exfoliation of graphene and its application in organic electronics and energy storage devices

Graphene, the thinnest two-dimensional material possible, is considered as a realistic candidate for the numerous applications in electronic, energy storage and conversion devices due to its unique properties, such as high optical transmittance, high conductivity, excellent chemical and thermal stability. However, the electronic and chemical properties of graphene are highly dependent on their preparation methods. Therefore, the development of novel chemical exfoliation process which aims at high yield synthesis of high quality graphene while maintaining good solution processability is of great concern. This thesis focuses on the solution production of high-quality graphene by wet-chemical exfoliation methods and addresses the applications of the chemically exfoliated graphene in organic electronics and energy storage devices.rnPlatinum is the most commonly used catalysts for fuel cells but they suffered from sluggish electron transfer kinetics. On the other hand, heteroatom doped graphene is known to enhance not only electrical conductivity but also long term operation stability. In this regard, a simple synthetic method is developed for the nitrogen doped graphene (NG) preparation. Moreover, iron (Fe) can be incorporated into the synthetic process. As-prepared NG with and without Fe shows excellent catalytic activity and stability compared to that of Pt based catalysts.rnHigh electrical conductivity is one of the most important requirements for the application of graphene in electronic devices. Therefore, for the fabrication of electrically conductive graphene films, a novel methane plasma assisted reduction of GO is developed. The high electrical conductivity of plasma reduced GO films revealed an excellent electrochemical performance in terms of high power and energy densities when used as an electrode in the micro-supercapacitors.rnAlthough, GO can be prepared in bulk scale, large amount of defect density and low electrical conductivity are major drawbacks. To overcome the intrinsic limitation of poor quality of GO and/or reduced GO, a novel protocol is extablished for mass production of high-quality graphene by means of electrochemical exfoliation of graphite. The prepared graphene shows high electrical conductivity, low defect density and good solution processability. Furthermore, when used as electrodes in organic field-effect transistors and/or in supercapacitors, the electrochemically exfoliated graphene shows excellent device performances. The low cost and environment friendly production of such high-quality graphene is of great importance for future generation electronics and energy storage devices. rn