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Dissertation
Fabrication and Investigation of Diamond Membranes for Photonic Nanostructures
(2023)
Due to its exceptional physical and chemical characteristics, diamond in a form of thin membranes is a particularly promising material for the fabrication of high-quality photonic devices. Especially for envisioned applications in quantum information technologies and communication, diamond gained, as a host material, an ever-increasing scientific interest based on remarkable properties of different color centers in its crystal lattice, e.g. nitrogen-vacancy centers, serving as single-photon emitters. As a high index ...
Dissertation
Analysis of a Coupled Fluid-Elastic Interaction Problem
(2023-01)
In this thesis, a non-linear system of partial differential equations is studied, describing the motions of an elastic structure which is immersed into an incompressible viscous fluid. The displacement of the elastic structure is modelled by a Lamé system and the fluid velocity as well as the fluid pressure are described by the Navier-Stokes equations. The structure and the fluid are coupled via two boundary conditions at the interface which correspond to continuity of velocities and forces. As the elasticity is ...
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
Application of Temporal Airy Pulses for investigating the origin of Laser Induced Periodic Surface Structures and for developing new tools in cell surgery and malignant tissue identification
(2023)
In this thesis, ultrashort Temporal Airy Pulses are used to study Laser Induced Periodic Surface Structures (LIPSS) in Part I and to enable the photoinjection of fluorescent markers into single living cells in Part II, Chapter 8. In both cases, the laser pulse excites a dielectric material (fused silica and water) and the special spatio-temporal dynamics of the interaction of a Temporal Airy Pulse with the dielectric is exploited to extend the shape of the excited region along the axis of laser propagation. For the ...
Habilitation
Computing Ground States for Fermi-Bose Mixtures through Efficient Numerical Methods
(2023-05)
In this work, we will first review the Quantum Mechanics theory to derive the main equations. Next, we will analyze these equations by Functional Analysis methods to find conditions for existence, uniqueness, multiplicity, and other properties as positivity. Next, we will review and develop some numerical methods for solving the nonlinear Schrödinger equation, its time version, generalizations with rotational terms, and systems of NLSE (NLSS). We notice that the main problem to run numerical methods is the memory ...
Dissertation
Control of Open Quantum Systems: Examples & Methods for Non-Markovian Dynamics
(2023)
Usually open quantum systems are considered to be under the influence of noise and therefore faulty. On the other hand, a controlled system is regarded as something stable and predictable. It is often neglected, that the two aspects are very closely related. A perfectly isolated quantum system will not be subject to environmental influences, but this makes it also impossible to interact with it in any manner. Controlling and measuring such a system is impossible and therefore of no technical relevance. Every system ...
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
Regulatory mechanisms of Protein kinase A - Isoform mediated fine-tuning
(2023)
cAMP-dependent protein kinase (PKA) is a crucial part in eukaryotic signal transduction and controls biological processes. With a multitude of substrates, a great variety of cellular functions are regulated by PKA. Regulation of metabolism, cell growth and -differentiation, conductivity of ion channels, movement of sperm cells, embryonic development, neuroplasticity as well as conversion of short- to long-term memory are just examples for the many tasks of the kinase. To achieve and coordinate these diverse functions, ...