E-Dissertationen: Suche
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Class forcing and second-order arithmetic
(2017-04-24)
We provide a framework in a generalization of Gödel-Bernays set theory for performing class forcing. The forcing theorem states that the forcing relation is a (definable) class in the ground model (definability lemma) and ...
Modeling and Simulation of cracks and fractures with peridynamics in brittle materials
(2017-04-24)
Today, ceramic materials are an essential component of batteries for electric cars. One key feature of this kind of battery is the safety of the ceramic core. Here, the precise approximation of the evolution of damage after ...
A phase-field model of dislocations on parallel slip planes
(2017-03-10)
We expand the Peierls-Nabarro phase-field model of dislocations on one active slip plane introduced by Koslowski, Cuitiño, and Ortiz to the case of multiple parallel slip planes embedded into a homogeneous anisotropic ...
Error analysis of regularized and unregularized least-squares regression on discretized function spaces
(2017-01-04)
In this thesis, we analyze a variant of the least-squares regression method which operates on subsets of finite-dimensional vector spaces.
In the first part, we focus on a regression problem which is constrained to ...
In the first part, we focus on a regression problem which is constrained to ...
Plasticity as the Γ-limit of a Dislocation Energy
(2017-07-19)
In this thesis, we derive macroscopic crystal plasticity models from mesoscopic dislocation models by means of Γ-convergence as the interatomic distance tends to zero. Crystal plasticity is the effect of a crystal undergoing ...
Numerical Methods for Optimal Transport and Elastic Shape Optimization
(2019-12-06)
In this thesis, we consider a novel unbalanced optimal transport model incorporating singular sources, we develop a numerical computation scheme for an optimal transport distance on graphs, we propose a simultaneous elastic ...
Functional Inequalities and Heat Kernel Asymptotics on Some Classes of Singular Riemannian Manifolds
(2019-11-13)
This thesis consists of two parts.
In the first part we are focusing on stratified pseudomanifolds equipped with an iterated edge metric. More specifically, in Chapter 1 we give the basic definitions and review some ...
In the first part we are focusing on stratified pseudomanifolds equipped with an iterated edge metric. More specifically, in Chapter 1 we give the basic definitions and review some ...
Renormalisation in discrete elasticity
(2019-10-10)
This thesis deals with the statistical mechanics of lattice models. It has two main contributions. On the one hand we implement a general framework for a rigorous renormalisation group approach to gradient models. This ...
Open Topological Field Theories and 2-Segal Objects
(2019-10-17)
In this thesis we analyze 2-dimensional open topological field theories in both 1-categorical and ∞-categorical contexts. Making use of the formalism, introduced by Dyckerhoff and Kapranov, of graphs structured over a ......
Small embeddings, forcing with side conditions, and large cardinal characterizations
(2019-09-26)
In this thesis, we provide new characterizations for several well-studied large cardinal notions. These characterizations will be of two types. Motivated by seminal work of Magidor, the first type characterizes large ...