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Dissertation
Development of UNCD-based multielectrode arrays for neuronal measurements
(2017-07-26)
The work in hand will show how some of diamond’s extraordinary features can be utilized in bio-applications especially for in vitro cultures of neuronal cells. Diamond has proven itself as an excellent material for bio-applications such as simple fluorescent microarrays over bioFET (field effect transistor) to bioMEMS (microelectro-mechanical systems). The reason does not only lie in its best known properties namely extreme hardness and high refractive index, but in its unique chemistry. As one of the modifications ...
Preprint
A free boundary approach to the Rosensweig instability of ferrofluids
(2017-04-18)
We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists in the ferro-hydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. The former constitute the strong form for the Euler-Lagrange equations of a convex-concave functional. We extend this functional in order to ...
Preprint
Balanced Viscosity solutions to a rate-independent system for damage
(2017-05-02)
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the ...
Dissertation
Optimierung von Nanostrukturen in Dielektrika für biomedizinische und technische Applikationen durch zeitlich geformte Femtosekunden-Laserpulse
(2017-09-28)
Das Ablationsverhalten von Dielektrika wird in Abhängigkeit von unterschiedlich zeitlich geformten Femtosekunden-Laserpulsen analysiert. Dabei entstehen unterschiedlich tiefe Strukturen im Nano- und Mikrometerbereich. In zwei Anwendungsbeispielen wird deren Anwendbarkeit für biomedizinische und technische Applikationen beschrieben.
Dissertation
Computing Quot Schemes
(2017-02-27)
The main goal of this thesis is to develop computational methods which allow effective computations on Hilbert and Quot schemes. At first we introduce marked bases over modules. They may be considered as a form of Gröbner basis which do not depend on a term order. Instead, one chooses for each generator some term as head module term such that the head module terms generate a prescribed monomial module. We show that the involutive normal form algorithm with respect to Pommaret division will terminate if the prescribed ...
Preprint
Convergence analysis of time-discretization schemes for rate-independent systems
(2017-12-21)
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is ...