Large Deviations Principle for Stochastic Scalar Conservation Laws

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. We therefore investigate a second order large deviations principle, thus providing a quantitative characterization of non-entropic solutions to the conservation law.Comment: 40 page

Bose-Einstein condensates with long-range dipolar interactions

Bose-Einstein condensation is a phase transition which atoms undergo when cooled near absolute zero temperature Since the theoretical prediction in 1924, and the spectacular experimental confirmation of Bose-Einstein condensation in 1995, a rich new field in physics has emerged studying ultracold degenerate quantum gases. Although these ultracold gases are very dilute, their properties are nevertheless strongly influenced by interatomic interactions. Usually, these interactions are dominated by short range, isotropic contact interactions. In contrast, the recently realised Bose-Einstein Condensate (BEC) of Chromium atoms contains long-range, anisotropic dipolar interactions leading to interesting new physics. In this graduation project, stationary states of such dipolar BECs in harmonic traps are investigated for various experimentally relevant parameters. Furthermore, the elementary excitations of the BEC are calculated, as well as its response to a rotating perturbation. Finally, some more advanced topics such as vortex interactions and condensate response to impurities are investigated. Bose-Einstein condensation is a phase transition which atoms undergo when cooled near absolute zero temperature Since the theoretical prediction in 1924, and the spectacular experimental confirmation of Bose-Einstein condensation in 1995, a rich new field in physics has emerged studying ultracold degenerate quantum gases. Although these ultracold gases are very dilute, their properties are nevertheless strongly influenced by interatomic interactions. Usually, these interactions are dominated by short range, isotropic contact interactions. In contrast, the recently realised Bose-Einstein Condensate (BEC) of Chromium atoms contains long-range, anisotropic dipolar interactions leading to interesting new physics. In this graduation project, stationary states of such dipolar BECs in harmonic traps are investigated for various experimentally relevant parameters. Furthermore, the elementary excitations of the BEC are calculated, as well as its response to a rotating perturbation. Finally, some more advanced topics such as vortex interactions and condensate response to impurities are investigated

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described