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Dissertation
Energy landscapes and dynamics of magnetic nanostructures: disorder, structure, and magnetic field effects
(2020)
The static and dynamic magnetic properties of two-dimensional ensembles of dipole-coupled magnetic nanoparticles (NPs) are investigated from a theoretical perspective. Particular emphasis is put on the correlations between the geometrical arrangements of the NPs, their inherent structural disorder, and the cooperative magnetic dynamics of the nanostructures as a whole. To this aim a significant number of representative two-dimensional NP ensembles with different structural geometries and degrees of disorder are ...
Dissertation
Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions
(2022)
In this dissertation, we analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one.
The optimal control problem uses the external load as control variable and is constrained to normalized ...
Dissertation
Development of a Preconditioning Scheme for Real Gases using Asymptotic Expansions
(2022)
Bei der Beschreibung von Strömungen wird klassischerweise zwischen inkompressiblen und kompressiblen Bereichen unterschieden. Während inkompressible Strömungen durch ein divergenzfreies Geschwindigkeitsfeld charakterisiert werden, sind kompressible Strömungsfelder durch Expansionsfächer, Kontaktunstetigkeiten und Stoßwellen gekennzeichnet. Die beiden Bereiche werden damit durch stark unterschiedliche Systeme partieller Differentialgleichungen beschrieben. Diese Unterscheidung zeigt sich auch in der numerischen ...