E-Dissertationen: Suche
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Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables
(2018-05-11)
Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has ...
Heat Flows on Time-dependent Metric Measure Spaces
(2018-04-26)
We consider time-dependent metric measure spaces evolving as a super Ricci flow in the sense of Sturm. We haracterize these by means of the (time-dependent) heat flow. We establish equivalence of super Ricci flows, gradient ...
Lower semicontinuity, optimization and regularity of variational problems under general PDE constraints
(2018-04-12)
We investigate variational properties of integral functionals defined on spaces of measures satisfying a general PDE constraint. The study of these properties is motivated by the following three problems: existence of ...
Numerical methods in stochastic and two-scale shape optimization
(2018-04-26)
In this thesis, three different models of elastic shape optimization are described. All models use phase fields to describe the elastic shapes and regularize the interface length on some level or scale to control fine-scale ...
On the dynamics of correlations in Scaling limits of interacting particle systems
(2018-07-09)
In this work, we analyze the properties of two-particle correlations in the weak-coupling and plasma limit of interacting particle systems motivated by Bogolyubov's formal derivation of kinetic equations.
We prove ...
We prove ...
Discrete Riemannian Calculus and A Posteriori Error Control on Shape Spaces
(2018-01-04)
In this thesis, a novel discrete approximation of the curvature tensor on Riemannian manifolds is derived, efficient methods to interpolate and extrapolate images in the context of the time discrete metamorphosis model are ...
The Dirac operator under collapse with bounded curvature and diameter
(2018-09-26)
A sequence (Mi, gi)i of closed Riemannian manifolds with uniform bounded curvature and diameter collapses if it converges to a lower dimensional compact metric space (B,h). The limit space ......
Numerical Methods for Uncertainty Quantification in Gas Network Simulation
(2018-09-26)
When modeling the gas flow through a network, some elements such as pressure control valves can cause kinks in the solution. In this thesis we modify the method of simplex stochastic collocation such that it is applicable ...
On the stability of the blow-up for the wave maps and the cubic wave equation
(2018-07-16)
In Thesis is divided into two parts. In the first part, we study the stability of the blow-up for the wave maps equation whereas in the second part we address the stability of the blowup for the cubic wave equation in ...
On moduli spaces of Riemann surfaces: new generators in their unstable homology and the homotopy type of their harmonic compactification
(2018-07-10)
By M_g(m,n) we denote the moduli space of conformal structures on an oriented compact cobordism S_g(m,n) of genus g greater or equal 0 and with m+n greater or equal 0 enumerated, parametrized boundary components of which ...