Inst. Mathematik

349 Items

Recent Submissions
On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law

Chaudhuri, Nilasis (2020-02-24)

In this paper our goal is to define a renormalized dissipative measure-valued (rDMV) solution of compressible Navier–Stokes system for fluids with non-monotone pressure–density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the weak (measure-valued)–strong uniqueness property of this rDMV solution with the help of relative ...

Structures in three-dimensional Euclidean space from hyperbolic tilings

Kolbe, Benedikt Maximilian (2020)

In this thesis we introduce a theory of isotopy classes of tilings with given symmetry group on hyperbolic surfaces, possibly punctured, nonorientable, and with boundary. We first generalise combinatorial tiling theory to incorporate tilings with tiles that are not closed disks. To establish a combinatorial theory for isotopy classes of tilings, based on Delaney-Dress tiling theory, we subseque...

Isothermic constrained Willmore tori

Tervooren, Jonas (2020)

This dissertation treats the classification of isothermic constrained Willmore tori. Jörg Richter proved in his dissertation that for every immersion f : M → R³ of an isothermic constrained Willmore torus, there exists a conformal change of the euclidean metric of R³ such that the surface has constant mean curvature (CMC) in a space form. We extended his proof such a way that it remains true if...

Iterative solution of discretized convection-diffusion problems

Echeverría Serur, Carlos (2020)

Certain approximation techniques for the numerical solution of partial differential equations result in linear algebraic systems where the coefficient matrix is nonsymmetric, nonnormal and ill-conditioned. This is the case for the finite difference discretization of the convection-diffusion equation posed on a Shishkin mesh treated in this work. We present a convergence analysis of the (algebra...

Some aspects of graph sparsification in theory and practice

Däubel, Karl (2020)

Many applications in transportation, telecommunication, logistics, biology or social networks, only to name a few examples, can be modelled by graphs. The size of graphs encountered in these applications is large, ranging from millions of vertices and edges in the European road network to billions of vertices and one hundred billion edges in the World-Wide Web graph. The order of magnitude of t...

Exact mixed-integer programming

Jarck, Kati (2020)

In this thesis, we develop and implement an efficient algorithm that can exactly solve instances of the mixed-integer programming problem that are given by rational data. For a feasible instance, a truly optimal solution will be computed; for an infeasible instance, a provably correct infeasibility certificate will be issued. Our exact mixed-integer programming solver is part of the constraint ...

Polyhedral surfaces of constant curvature and discrete uniformization

Kourimská, Hana (2020)

In this thesis we introduce a new discretization of the Gaussian curvature on piecewise flat surfaces. It is defined on the conical singularities of the surface and it is the quotient of the angle defect and the area of the Voronoi cell. We investigate the existence and uniqueness of metrics with constant discrete Gaussian curvature within discrete conformal classes of piecewise flat surfaces. ...

Multiple time-scale delay systems in mathematical biology and laser dynamics

Ruschel, Stefan (2020)

This thesis addresses the dynamical behavior of Delay Differential Equations (DDEs) with a multiple time-scale structure as a consequence of large delays, or additional small parameters. More specifically, it gives attention to the effects of delay-induced instabilities of equilibrium solutions as well as families of equilibrium solutions and discusses the corresponding nonlinear dynamical phen...

Tighter relaxations in mixed-integer nonlinear programming

Müller, Benjamin (2020)

Mixed-integer nonlinear programming (MINLP) is one of the most important classes of mathematical optimization problems that combines difficulties from mixed-integer linear programming and nonlinear programming, namely optimizing over a set that is described by integrality, linear, and nonlinear restrictions. This class of optimization problems is essential when constructing accurate models of r...

Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods

Grigoriu, Liliana (2019-11-29)

We survey results that address the problem of non-preemptive scheduling on parallel machines with fixed jobs or unavailability periods with the purpose of minimizing the maximum completion time. We consider both identical and uniform processors, and also address the special case of scheduling on nonsimultaneous parallel machines, which may start processing at different times. The discussed resu...

Points, lines, and circles:

Scheucher, Manfred (2020)

In this dissertation we investigate some problems from the field of combinatorics and computational geometry which involve basic geometric entities (points, lines, and circles). In the first part we look at Erdös-Szekeres type problems: The classical theorem by Erdös and Szekeres from 1935 asserts that, for every natural number 𝑘, every sufficiently large point set in general position contai...

Error analysis and model adaptivity for flows in gas networks

Stolwijk, Jeroen Johannes ; Mehrmann, Volker (2018-11-22)

In the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is...

Condition and homology in semialgebraic geometry

Tonelli Cueto, Josué (2019)

The computation of the homology groups of semialgebraic sets (given by Boolean formulas) remains one of the open challenges of computational semialgebraic geometry. Despite the search for an algorithm taking singly exponential time only on the number of variables, as of today, the existing algorithms are symbolic and doubly exponential. In this PhD thesis, we show how to obtain a numerical algo...

Derivation, asymptotic analysis and numerical solution of atomistically consistent phase-field models

Bergmann, Sibylle (2019)

In this thesis a systematic derivation and analysis of phase-field models with parameters based on molecular-dynamical simulations is developed. Applications of our models describe the anisotropic growth of solid-liquid interfaces during crystallization from a melt. We focus here on silicon, while other materials with different anisotropies and material parameters are also possible. We combine ...

Pesin's formula for translation invariant random dynamical systems

Senin, Vitalii (2019)

Pesin's formula asserts that metric entropy of a dynamical system is equal to the sum of its positive Lyapunov exponents, where metric entropy measures the chaoticity of the system, whereas Lyapunov exponents measure the asymptotic exponential rate of separation of nearby trajectories. It is well known, that this formula holds for dynamical systems on a compact Riemannian manifold with an invar...

Mathematical analysis of large-scale biological neural networks with delay

Mehri, Sima (2019)

It is well-known that the components of the solution to a system of N interacting stochastic differential equations with an averaged sum of interaction terms and with independent identically distributed (chaotic) initial values, as N tends to infinity, converge to the solutions of Vlasov-McKean equations, in which the averaged sum is replaced by the expectation. Since the solutions to the corre...

Methods for the temporal approximation of nonlinear, nonautonomous evolution equations

Eisenmann, Monika (2019)

Differential equations are an important building block for modeling processes in physics, biology, and social sciences. Usually, their exact solution is not known explicitly though. Therefore, numerical schemes to approximate the solution are of great importance. In this thesis, we consider the temporal approximation of nonlinear, nonautonomous evolution equations on a finite time horizon. We p...

Multicriteria linear optimisation with applications in sustainable manufacturing

Schenker, Sebastian (2019)

Multicriteria optimisation is concerned with optimising several objectives simultaneously. Assuming that all objectives are equally important but conflicting, we are interested in the set of nondominated points, i.e., the image set of solutions that cannot be improved in any objective without getting worse off in another one. This thesis comprises three parts. The first part considers the compu...

On the sign characteristics of Hermitian matrix polynomials

Mehrmann, Volker ; Noferini, Vanni ; Tisseur, Françoise ; Xu, Hongguo (2016-09-14)

The sign characteristics of Hermitian matrix polynomials are discussed, and in particular an appropriate definition of the sign characteristics associated with the eigenvalue infinity. The concept of sign characteristic arises in different forms in many scientific fields, and is essential for the stability analysis in Hamiltonian systems or the perturbation behavior of eigenvalues under structu...

Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data

Conrad, Tim O. F. ; Genzel, Martin ; Cvetkovic, Nada ; Wulkow, Niklas ; Leichtle, Alexander ; Vybiral, Jan ; Kutyniok, Gitta ; Schütte, Christof (2017)

Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) i...