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Dissertation
Validation of a generalized model for the description of polycrystalline exchange-biased magnetic thin films
(2022)
Applications based on nano- and microscaled systems have become indispensable in many aspects in everyday life, industry, research and medicine. In this regard, thin film technology plays a crucial role with the physical properties of solids changing significantly when they are reduced to thin layers with thicknesses in the nanometer range. In this regime, a solid’s microstructure as well as boundary and surface effects start to dominate. A prominent example is the exchange bias effect, which results due to the ...
Dissertation
Finite Element Simulations for the Design of Therapeutic Approaches for Retinal Diseases
(2022)
The retinal disease age-related macular degeneration is the most common cause of vision loss in industrialized countries. In this thesis, motivated by the drug (antibody) treatment of this disease, we designed long-term three dimensional Finite Element simulations of the drug distribution in the healthy human eye. The underlying model consists of a time-dependent convection-diffusion equation coupled to a stationary Darcy equation describing the flow of the aqueous humor through the vitreous medium. We replaced the ...
Dissertation
Generalized Involutive Bases and Their Induced Free Resolutions
(2022-05)
In this thesis, we generalize several types of involutive and marked bases for ideals in quotient rings of commutative polynomial rings. We apply these new types of bases to the analysis of infinite free resolutions and of Hilbert schemes defined over certain types of quotient rings. We are mostly concerned with Pommaret and Janet bases; the marked bases we consider are marked over monomial submodules that are quasi-stable, i.e., that possess finite Pommaret bases.
Involutive bases of the types we consider induce ...
Dissertation
Algorithmic Reduction of Biochemical Reaction Networks
(2022-02-25)
The dynamics of species concentrations of chemical reaction networks are given by autonomous first-order ordinary differential equations. Singular perturbation methods allow the computation of approximate reduced systems that make explicit several time scales with corresponding invariant manifolds. This thesis presents:
1. An algorithmic approach for the computation of such reductions on solid analytical grounds. Required scalings are derived using tropical geometry. The existence of invariant manifolds is subject ...
Technischer Report
Dokumentation der Erhebungsinstrumente des Projekts WiGeMath
(2022-05)
Der Anlass für das Projekt WiGeMath („Wirkungen und Gelingensbedingungen von mathematischen Unterstützungsmaßnahmen in der Studieneingangsphase“ FKZ: 01PB14015A & 01PB14015B) war, dass Wirksamkeit und Gelingensbedingungen von Unterstützungsmaßnahmen in der Studieneingangsphase, die Schwierigkeiten im Übergang von der Schule zur Hochschule lindern sollten, vorher kaum systematisch und zielgerichtet untersucht wurden: Evaluationserhebungen beschränkten sich überwiegend auf lokale und ad hoc gestaltete Zufriedenheitsabfragen ...
Dissertation
The Importance of tRNA Modification and SSD1 Status for Protein Homeostasis and Cell Viability
(2022-03)
Chemical modifications of anticodon loop are required to support tRNA function in mRNA decoding and to prevent protein aggregation in the eukaryotic model system Saccharomyces cerevisiae. This work investigates the effects of mutation in the gene encoding the Deg1 pseudouridine synthase. It is known that the mutation of the human DEG1 orthologue PUS3 causes severe neurological and developmental defects, emphasizing the general importance of the modification. However, the exact cellular consequences of deg1/pus3mutation ...
Dissertation
Analysis of near-substrate magnetic particle transport for Lab-on-a-chip applications: stray field modulations, influence of particle properties and three-dimensional trajectories
(2022)
Die Entwicklung schneller und zuverlässiger Diagnostik ist ein wichtiges Ziel für die Früherkennung von Krankheiten. Standardisierte Labormethoden sind heutzutage meist langsam und mit hohen Kosten verbunden. Innerhalb der Lab-on-a-chip (LOC)-Technologie kann der Nachweis eines pathogenen Organismus auf die Größe eines kleinen Chips miniaturisiert werden, indem magnetische Partikel als Fängerobjekte integriert werden. Die Kombination einer statischen Magnetfeldlandschaft (MFL) mit zeitlich variierenden externen ...
Dissertation
Vergleichende phylogeographische und populationsgenetische Untersuchungen an der Pionierbaumgattung Macaranga (Euphorbiaceae) in Sundaland
(2022)
Die vorliegende Arbeit beschäftigt sich mit der Phylogeographie und Populationsgenetik der Pionierbaumgattung Macaranga in Sundaland, einer Region, die die Großen Sundainseln Sumatra, Borneo, Java und die malaiische Halbinsel umfasst. Eine Vielzahl der 300 in dieser Gattung enthaltenen Arten sind Wiederbesiedler gestörter Areale und sind daher in Sekundärwaldstrukturen besonders häufig. Im Rahmen dieser Dissertation wurden Studien in ganz Sundaland zu den sechs Arten M. tanarius (Tanarius-Artengruppe), M. gigantea, ...
Dissertation
Magnetic Textures and Magnetization Reversal Processes in Arrays of Ferromagnetic and Exchange-Biased Hollow Hemispheres
(2022)
The main objective of this thesis is to investigate hemispherical caps prepared by thin film deposition of magnetic material compositions on top of nano- and micrometer sized silica spheres. When compared to flat magnetic discs, these microcaps differ in their magnetic properties due to the curved and therefore three-dimensional shape. However, under certain conditions, both microstructures have previously been proven to express the famous magnetic vortex texture because of the confinement into a circular shape. ...
Dissertation
Electronic Theory of the Magnetic Order, Anisotropy and Reversal Processes in Rolled-Up Stripes and Thin Films
(2022)
A comprehensive multiscale approach consisting of a combination of state of the art, first principles quantum theory and the flexible statistical methodologies of complex systems is applied in order to achieve a detailed microscopic understanding of the magnetic properties of rolled-up transition-metal [TM] ultrathin films and stripes. A quantum electronic investigations of the effective interactions between the local magnetic moments is performed as a function of composition and rolling radius R including the limit ...