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Cahn–Hilliard-type Equations: Robust Discretization and Efficient Implementation
(2009-05-11)
In this work, a robust and efficient numerical method to simulate Cahn–Hilliard-type equations is presented. The considered equations are of fourth order and contain two nonlinearities: one is the concentration-dependent ...
Intersections of arithmetic Hirzebruch-Zagier cycles
(2009-06-15)
We establish a close connection between the intersection multiplicities of three arithmetic Hirzebruch-Zagier cycles and the Fourier coefficients of the derivative of a certain Siegel-Eisenstein series. Our main result ...
The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics
(2009-04-17)
For the global behavior of solids in structural mechanics of nonlinear processes, local effects on the atomistic level play an important role. Often a direct numerical simulation of the macroscopic behavior by a complete ...
Zur Kohomologie und Spektraltheorie des Hodge-Laplaceoperators von Mannigfaltigkeiten mit gefaserter Spitzenmetrik
(2009-06-23)
Eine Mannigfaltigkeit X mit gefaserter Spitzenmetrik kann als Verallgemeinerung der geometrischen Struktur von lokal-symmetrischen Räumen vom Q-Rang Eins angesehen werden.
In der vorliegenden Arbeit ...
In der vorliegenden Arbeit ...
Cardinals as Ultrapowers: A Canonical Measure Analysis under the Axiom of Determinacy
(2009-11-11)
This thesis is in the field of Descriptive Set Theory and examines some consequences of the Axiom of Determinacy concerning partition properties that define large cardinals. The Axiom of Determinacy (AD) is a game-theoretic ...
An Application of Kolmogorov's Superposition Theorem to Function Reconstruction in Higher Dimensions
(2009-12-01)
In this thesis we present a Regularization Network approach to reconstruct a continuous function ƒ:[0,1]n→R from its function values ƒ(xj) on discrete data points xj, ...
On the notion of order in the stable module category
(2009-12-22)
The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG-modules, where k is a field of characteristic p and G is a ...
Pattern, Walls and Vortex: A micromagnetic excursion
(2009-11-05)
In this thesis, we analyse two different settings in the micromagnetic model, which is a mesoscopic variational model for the description of ferromagnets, more precisely the magnetisation m, which is a local average of ...
Orientation reversal of manifolds
(2009-03-06)
We study the phenomenon of chirality in the context of manifolds. An orientable manifold is called amphicheiral if it admits an orientation-reversing self-map and chiral if it does not. In addition to being continuous and ...
Generalized Snaith Splittings
(2009-02-05)
A Segal Γ-space A gives a homotopy functor A(X) and a connective homology theory h*(X;A) = π*(A(X)). The infinite symmetric product SP∞(X) and the configuration space C(R∞;X) ≅ ...