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Dissertation
High temperature-stable InGaAs QDs for the monolithic integration in external-cavity surface-emitting lasers
(2021)
Optically pumped vertical external-cavity surface-emitting lasers (VECSELs), also called semiconductor disk lasers (SDLs), benefit from the flexibility and versatility of the semiconductor material. With a simple cavity layout, fundamental transverse mode operation with a circular output beam and high beam quality is possible. They have excellent heat-sink properties and only require inexpensive multimode diode lasers for pumping. The complete VECSEL structure is only a few micrometers thick which leads to a strong ...
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
Symmetrien von Differentialgleichungen via Vessiot-Theorie
(2021-04)
Die übliche Definition des Symmetriebegriffs einer Differentialgleichung lautet wie folgt: Symmetrien sind Transformationen, die Lösungen wieder in Lösungen überführen. Modelliert man Differentialgleichungen als Untermannigfaltigkeiten eines Jetbündels, so lassen sich zwei Arten von Symmetrien unterscheiden: innere und äußere. Der erste Fall entspricht einer Transformation, die ausschließlich auf der Differentialgleichung definiert ist. Im zweiten Fall ist die betrachtete Transformation auf dem gesamten umgebenden ...