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In this thesis viscoelastic material models are established to investigate the nature of continuous calving processes at Antarctic ice shelves. Physics-based descriptions of calving require appropriate fracture criteria to separate icebergs from the remaining ice shelf. Hence, criteria of the stress, the strain, and the self-similarity criterion are considered within finite-element computations. Crucial parameters in the models to determine the position of calving are the accurate knowledge of the geometry, especially the freeboard height, while the material parameters mainly influence the time span between two successive calving events. The extension to nonlinear material models is necessary to properly analyze the internal forces also for large deformations that occur for longer times of the viscous ice flow.

The main goal of this work was the study of the applicability of a polymer film heat exchanger concept for the applications in the chemical industry, such as the condensation of organic solvents. The polymer film heat exchanger investigated is a plate heat exchanger with very thin (0.025 – 0.1 mm) plates or films, which separate the fluids and enable the heat transfer. After a successful application of this concept to seawater desalination in a previous work, a further step is in chemical engineering, where the good chemical resistance of polymers in aggressive fluids is the challenge.
Two approaches were performed in this work. The first one was experimental and included the study of the chemical and mechanical resistance of preselected films, made of polymer materials, such as polyimide (PI), polyethylene terephthalate (PET) and polytetrafluoroethylene (PTFE). To simulate realistic operating conditions in a heat exchanger the films were exposed to a combined thermal (up to 90°C) and mechanical pressure loads (4-6 bar) with permanent contact with the relevant organic solvents, such as toluene, hexane, heptane and tetrahydrofuran (THF). Furthermore, a lab-scale apparatus and a full-scale demonstrator were manufactured in cooperation with two industrial partners. These were used for the investigation of the heat transfer performance for operating modes with and without phase change.
In addition to the experimental work, a coupled finite element –computational fluid dynamics (FEM-CFD)-model was developed, based on the fluid-structure-interaction (FSI). Two major tasks had to be solved here. The first one was the modelling of the condensation process, based on available mathematical models and energy balances. The second one was the consideration of the partially reversible deformation of the used film during operation. Since this deformation changes the geometry of the fluid channels also has an influence on the overall performance of the apparatus, a coupled FEM-CFD model was developed.
During the experimental study of the chemical resistance of the films, the PTFE film showed the best performance, and hence can be used for all four tested solvents. For the polyimide film, failures while exposed to THF were observed, and the PET film can only be used with water and hexane. With the used lab-scale heat exchanger and the full-scale demonstrator competitive overall heat transfer coefficients between 270 W/m²K and 700 W/m²K could be reached for the liquid-liquid (water-water, water-hexane) operation mode without phase change. For the condensation process, overall heat transfer coefficients of up to 1700/m²K could be obtained.
The numerical approach led to a well-functioning coupled model in a very small scale (1 cm²). An upscale, however, failed due to enormous hardware resources necessary required for the simulation of the entire full-scale demonstrator. The main reason for this is the very low thickness of the films, which leads to tiny mesh element sizes (<0.05 mm) necessary to model the deformation of the film. The modelling of the liquid-liquid heat transfer provided an acceptable accuracy (approx. 10%), but at very low rates the deviations were then higher (over 30%). The results of the condensation modelling were ambivalent. One the one hand a physically plausible model was developed, which could map the entire condensation process. On the other hand, the corresponding energy balance revealed major inaccuracy and hence could not be used for the determination of the overall heat transfer and showed the current limits of the FEM-CFD approach.

In this thesis we address two instances of duality in commutative algebra.
In the first part, we consider value semigroups of non irreducible singular algebraic curves
and their fractional ideals. These are submonoids of Z^n closed under minima, with a conductor and which fulfill special compatibility properties on their elements. Subsets of Z^n
fulfilling these three conditions are known in the literature as good semigroups and their ideals, and their class strictly contains the class of value semigroup ideals. We examine
good semigroups both independently and in relation with their algebraic counterpart. In the combinatoric setting, we define the concept of good system of generators, and we
show that minimal good systems of generators are unique. In relation with the algebra side, we give an intrinsic definition of canonical semigroup ideals, which yields a duality
on good semigroup ideals. We prove that this semigroup duality is compatible with the Cohen-Macaulay duality under taking values. Finally, using the duality on good semigroup ideals, we show a symmetry of the Poincaré series of good semigroups with special properties.
In the second part, we treat Macaulay’s inverse system, a one-to-one correspondence
which is a particular case of Matlis duality and an effective method to construct Artinian k-algebras with chosen socle type. Recently, Elias and Rossi gave the structure of the inverse system of positive dimensional Gorenstein k-algebras. We extend their result by establishing a one-to-one correspondence between positive dimensional level k-algebras and certain submodules of the divided power ring. We give several examples to illustrate
our result.

Die vorliegende Arbeit befasst sich mit der Untersuchung von Absorptionseigenschaften und elektronischer Kurzzeit-Dynamik von organischen Farbstoffmolekülen und supramolekularen Photokatalysatoren in der Gasphase. Dabei wurde erstmals sehr intensiv ein eine relativ unbekannte experimentelle Methode eingesetzt, nämlich die zeitaufgelöste, pump-probe (Anregung-Abfrage) Photofragmentations-Spektroskopie. Die Kombination eines kommerziellen Quadrupol Ionenfallen Massenspektrometers mit einem Femtosekunden Lasersystem erlaubt es die intrinsischen, elektronischen Eigenschaften molekularer, ionischer Systeme abzubilden. Neben Populationsdynamik angeregter Zustände wurden erstmals Schwingungs- und Rotationswellenpaket-Dynamik mit dieser Methode beobachtet und dokumentiert.
Im ersten Teil der Arbeit werden die Ergebnisse der Untersuchungen an einigen ausgewählten Fluoresecein-Derivaten und eines Carbocyanin-Farbstoffes präsentiert. Obwohl diese Modellsysteme zunächst nur dem Zweck dienen sollten die Möglichkeiten des experimentellen Aufbaus zu evaluieren, ergaben die Untersuchungen weiterhin tiefgreifende Einblicke in die elektronische Struktur isolierter organischer Farbstoffe, die bis heute in Literatur nicht dokumentiert worden sind.
Der zweite Teil befasst sich mit der Untersuchung an drei supramolekularen, ionischen Systemen zur photokatalytischen Wasserstofferzeugung. Dabei dienten wieder zwei der Systeme dem Zweck den experimentellen Aufbau zu evaluieren. Neben der elektronischen Populationsdynamik wurde mittels polarisationsabhängiger Messungen weitere Einblicke in den Elektronentransferprozess erhalten – ein Kernpunkt in der Wirkweise supramolekularer Katalysatoren. Die neugewonnen Erkenntnisse wurden schließlich verwendet um einen neuartigen Katalysator zu untersuchen. Dabei stellte sich heraus, dass die Labilität der Ligandensphäre am katalytischen Metallzentrum Untersuchungen am intakten System in Lösung stark beeinträchtigt und somit nur aussagekräftige Ergebnisse mittels einer Gasphasen Methode, einer wie der hier verwendeten, erhalten werden können.
Die experimentellen Ergebnisse werden unterstützt durch quantenchemische Berechnungen von energetischen Minimum-Strukturen, den Strukturen von Übergangszuständen, sowie der Berechnung von Schwingungs- und UV/Vis-Absorptionsspektren mittels (zeitabhängiger) Dichtefunktionaltheorie (DFT & TD-DFT).

In this dissertation convergence of binomial trees for option pricing is investigated. The focus is on American and European put and call options. For that purpose variations of the binomial tree model are reviewed.
In the first part of the thesis we investigated the convergence behavior of the already known trees from the literature (CRR, RB, Tian and CP) for the European options. The CRR and the RB tree suffer from irregular convergence, so our first aim is to find a way to get the smooth convergence. We first show what causes these oscillations. That will also help us to improve the rate of convergence. As a result we introduce the Tian and the CP tree and we proved that the order of convergence for these trees is \(O \left(\frac{1}{n} \right)\).
Afterwards we introduce the Split tree and explain its properties. We prove the convergence of it and we found an explicit first order error formula. In our setting, the splitting time \(t_{k} = k\Delta t\) is not fixed, i.e. it can be any time between 0 and the maturity time \(T\). This is the main difference compared to the model from the literature. Namely, we show that the good properties of the CRR tree when \(S_{0} = K\) can be preserved even without this condition (which is mainly the case). We achieved the convergence of \(O \left(n^{-\frac{3}{2}} \right)\) and we typically get better results if we split our tree later.

Wie Proteine sich innerhalb weniger Millisekunden korrekt falten können, ist eine der fundamentalen Fragen in der Biochemie. Ein beim Faltungsprozess durchlaufener Übergangszustand ist der molten globule Zustand (MG Zustand), der sich unter bestimmten Bedingungen stabilisieren und untersuchen lässt. In diesem Zustand ähnelt die Sekundärstruktur dem nativen Zustand, während die Tertiärstruktur eher dem vollständig entfalteten Zustand entspricht. In dieser Arbeit wurde der MG Zustand am Beispiel des Maltose bindenden Proteins (MBP) untersucht. Dazu wurde MBP bei pH 3,2 im MG-Zustand stabilisiert und dies mittels Fluoreszenz Spektroskopie bestätigt. Die Abstände zwischen definierten Aminosäuren im MG Zustand wurden durch Spinlabels, die an gezielt mutierten Cysteinpaaren angebracht wurden, mittels Elektronenspinresonanz (EPR) gemessen und mit den Abständen derselben Aminosäuren im nativen Zustand verglichen. Anhand von sieben verschiedenen Doppelmutanten wurde die periphere Struktur mittels gepulster EPR analysiert, zwei weitere Doppelmutanten dienten dazu, die Struktur der molekularen Bindungstasche von MBP mittels CW EPR zu untersuchen. Die Anwesenheit von Maltose führte im MG Zustand zu einer deutlichen Veränderung der Abstände bestimmter Spinlabels in der peripheren Struktur. Dies deutet darauf hin, dass MBP Maltose sogar im MG Zustand binden kann. Durch isotherme Titrationskalorimetrie (ITC) wurde diese Vermutung bestätigt: die Ergebnisse zeigen jedoch, dass der Bindungsprozess zwischen MBP und Maltose im MG Zustand mit 11 fach geringerer Bindungsenthalpie erfolgt wie im nativen Zustand. Die Abstände der Spinlabel Paare neben der Bindungstasche von MBP unterschieden sich im MG Zustand vom nativen Zustand weder mit noch ohne Maltose. Diese Ergebnisse weisen darauf hin, dass MBP im MG Zustand rund um die Bindungstasche bereits eine klar ausgebildete Tertiärstruktur besitzt. Um diese Befunde zu bestätigen, sollten nun Untersuchungen anhand weiterer Doppelmutanten und mittels empfindlicherer Messungen wie z.B. DQC durchgeführt werden.

Temporal Data Management and Incremental Data Recomputation with Wide-column Stores and MapReduce
(2017)

In recent years, ”Big Data” has become an important topic in academia
and industry. To handle the challenges and problems caused by Big Data,
new types of data storage systems called ”NoSQL stores” (means ”Not-only-
SQL”) have emerged.
”Wide-column stores” are one kind of NoSQL stores. Compared to relational database systems, wide-column stores introduce a new data model,
new IRUD (Insert, Retrieve, Update and Delete) semantics with support for
schema-flexibility, single-row transactions and data expiration constraints.
Moreover, each column stores multiple data versions with associated time-
stamps. Well-known examples are Google’s ”Big-table” and its open sourced
counterpart ”HBase”. Recently, such systems are increasingly used in business intelligence and data warehouse environments to provide decision support, controlling and revision capabilities.
Besides managing the current values, data warehouses also require management and processing of historical, time-related data. Data warehouses
frequently employ techniques for processing changes in various data sources
and incrementally applying such changes to the warehouse to keep it up-to-
date. Although both incremental data warehousing maintenance and temporal data management have been the subject of intensive research in the
relational database and finally commercial database products have picked up
the ability for temporal data processing and management, such capabilities
have not been explored systematically for today’s wide-column stores.
This thesis helps to address the shortcomings mentioned above. It care-
fully analyzes the properties of wide-column stores and the applicability
of mechanisms for temporal data management and incremental data ware-
house maintenance known from relational databases, extends well-known approaches and develops new capabilities for providing equivalent support in
wide-column stores.

In the present work the concept of decarboxylative couplings and the strategy to use carboxylates as directing groups for C-H functionalizations have been decisively improved in three ways. These concepts emphasize the multifaceted nature of aromatic carboxylic acids as expedient starting materials in homogeneous catalysis to construct highly desirable molecular scaffolds in a straightforward fashion.
In the first project, the restriction of decarboxylative biaryl synthesis to exclusively couple aryl halides with ortho-substituted benzoic acids has been overcome by a holistic optimization of a Cu/Pd bimetallic catalyst system. Long ago postulated, this is now the proof that decarboxylative cross-couplings are not intrinsically limited to different decarboxylation propensities of benzoic acids or hampered by excess halides, accessing for the first time the entire spectrum of aromatic carboxylic acids as starting materials for the decarboxylative biaryl synthesis. The second project uses the carboxyl moiety as directing group for the ortho-arylation with aryl bromides and -chlorides catalyzed by comparatively inexpensive ruthenium. The carboxylic acid group remains untouched after the ortho-functionalization giving the possibility to a wealth of further diversifications via decarboxylative ipso-substitutions. Within the same project, a Cu/Ru bimetallic catalyst system was found to be able to switch the decarboxylative biaryl coupling from the ipso- to the ortho-position, complementing the Cu/Pd system developed in the first project. In a third project, a redox neutral C-C bond formation revealed the full synthetic potential of the carboxyl group. The COOH moiety acts as a classical directing group for the C-H hydroarylation of internal alkynes to form highly desirable 2-vinyl benzoic acids. With propargylic alcohols the hydroarylation is followed by an in situ esterification, showing that after easing the C-H cleavage, the directing group can be transformed into another functional group, thus, acting as a transformable directing group. Most importantly, a new fascinating reaction mode is activated by embedding the decarboxylation within the C-H functionalization event. This mode of action is capable to solve regioselectivity issues that inherently occur when dealing with carboxylates as directing groups. A so-called deciduous directing group is cast off simultaneously within the C-H functionalization event, resulting in an inherently monoselective pathway.
These methods were developed with the permanent goal of ensuring high sustainability. They do require neither pre-functionalized starting materials nor additional oxidants and provide access to a number of chemically relevant molecules from abundant, inexpensive and toxicologically innocuous educts.

Nonwoven materials are used as filter media which are the key component of automotive filters such as air filters, oil filters, and fuel filters. Today, the advanced engine technologies require innovative filter media with higher performances. A virtual microstructure of the nonwoven filter medium, which has similar filter properties as the existing material, can be used to design new filter media from existing media. Nonwoven materials considered in this thesis prominently feature non-overlapping fibers, curved fibers, fibers with circular cross section, fibers of apparently infinite length, and fiber bundles. To this end, as part of this thesis, we extend the Altendorf-Jeulin individual fiber model to incorporate all the above mentioned features. The resulting novel stochastic 3D fiber model can generate geometries with good visual resemblance of real filter media. Furthermore, pressure drop, which is one of the important physical properties of the filter, simulated numerically on the computed tomography (CT) data of the real nonwoven material agrees well (with a relative error of 8%) with the pressure drop simulated in the generated microstructure realizations from our model.
Generally, filter properties for the CT data and generated microstructure realizations are computed using numerical simulations. Since numerical simulations require extensive system memory and computation time, it is important to find the representative domain size of the generated microstructure for a required filter property. As part of this thesis, simulation and a statistical approach are used to estimate the representative domain size of our microstructure model. Precisely, the representative domain size with respect to the packing density, the pore size distribution, and the pressure drop are considered. It turns out that the statistical approach can be used to estimate the representative domain size for the given property more precisely and using less generated microstructures than the purely simulation based approach.
Among the various properties of fibrous filter media, fiber thickness and orientation are important characteristics which should be considered in design and quality assurance of filter media. Automatic analysis of images from scanning electron microscopy (SEM) is a suitable tool in that context. Yet, the accuracy of such image analysis tools cannot be judged based on images of real filter media since their true fiber thickness and orientation can never be known accurately. A solution is to employ synthetically generated models for evaluation. By combining our 3D fiber system model with simulation of the SEM imaging process, quantitative evaluation of the fiber thickness and orientation measurements becomes feasible. We evaluate the state-of-the-art automatic thickness and orientation estimation method that way.

In this thesis, we consider a problem from modular representation theory of finite groups. Lluís Puig asked the question whether the order of the defect groups of a block \( B \) of the group algebra of a given finite group \( G \) can always be bounded in terms of the order of the vertices of an arbitrary simple module lying in \( B \).
In characteristic \( 2 \), there are examples showing that this is not possible in general, whereas in odd characteristic, no such examples are known. For instance, it is known that the answer to Puig's question is positive in case that \( G \) is a symmetric group, by work of Danz, Külshammer, and Puig.
Motivated by this, we study the cases where \( G \) is a finite classical group in non-defining characteristic or one of the finite groups \( G_2(q) \) or \( ³D_4(q) \) of Lie type, again in non-defining characteristic. Here, we generalize Puig's original question by replacing the vertices occurring in his question by arbitrary self-centralizing subgroups of the defect groups. We derive positive and negative answers to this generalized question.
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In addition to that, we determine the vertices of the unipotent simple \( GL_2(q) \)-module labeled by the partition \( (1,1) \) in characteristic \( 2 \). This is done using a method known as Brauer construction.