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Dissertation
Modeling of human vitreous as viscoelastic fluid considering the orientation of collagen fibers
(2021-11)
For the most common treatment of retinal diseases worldwide by drug distribution in the human vitreous we developed the mathematical model of the vitreous. Compare to previous works we focus on the vitreous as a viscoelastic fluid including its heterogeneous property due to the orientation of collagen fibers. By using the incompressible viscoelastic Burgers-type model based on experimental data as the specific constitutive equation in the setting of continuum mechanics we considered its non-Newtonian nature. This ...
Dissertation
Development of digital fluorescence light sheet microscopy for high-resolution optical imaging
(2021-12-15)
In modern biology investigating the morphological development of an organism is an inevitable task. Optical microscopy has been extensively used to monitor the live tissue changes in a model organism and it is typically used in conjunction with white light or fluorescence microscopy. The fluorescence microscopy occupies a significant place in biological research due to its ability to address various biological question at subcellular level of a biological sample. One of the more recent developments in fluorescence ...
Habilitation
Numerical Methods for Fluid Flow: High Order SBP Schemes, IMEX Advection-Diffusion Splitting and Positivity Preservation for Production-Destruction PDEs
(2021-01)
The current demands regarding the numerical simulation of fluid flow often require highly accurate computations to obtain a detailed resolution of the occurring physical phenomena. The basic concept for the construction of a fluid solver is to transfer the physical model into a numerical scheme which complies with the underlying physical principles such as conservation and balances of certain quantities. In addition, the numerical methods are required to be stable and efficient. Again, stability is often determined ...
Dissertation
Synthese von [3]Ferrocenophanen und Ferrocen-verbrückten Oligophosphanen zur (elektro-)chemischen Erzeugung Phosphor-basierter Radikale
(2021-12)
Phosphor-basierte Radikale wurden in der Vergangenheit neben der bewährten Verwendung zur Phosphanierung von (an-)organischen Verbindungen auch als Reduktionsmittel in Einzelelektronen-Transfer-Reaktionen, als Radikalstarter oder als Flammschutzmittel eingesetzt. Ein geeigneter Weg, solche Radikale zu erzeugen, führt über eine thermisch induzierte homolytische Spaltung einer zentralen, sterisch abgeschirmten, elektronenreichen Bindung wie in Bisaminodiphosphanen X₂P PX₂ (X = NR₂). Ein Nachteil sind hier die meist ...
Preprint
Identifying critical demand scenarios for the robust capacitated network design problem using principal component analysis
(2021-11-30)
In this paper, we consider the single-commodity robust network design problem. Given an undirected graph with capacity installation costs on its edges and a set S of scenarios with associated flow balance vectors that represent different scenarios of node supplies and demands, the goal is to find integer edge capacities that minimize the total installation cost and permit a feasible single commodity flow for each scenario. This problem arises, for example, in the design of power networks, which are dimensioned to ...
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
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 ...