Transport of a two-phase flow with sharp interface in three dimensions
Tuesday, 24.10.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Bifurcation of the compressible Taylor vortex
Tuesday, 7.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Contact and Adhesion of Fractal Interfaces
Tuesday, 14.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Mini-Workshop on "Singular Variational Problems"
Sunday, 19.11.17, 10:00-11:00, Raum 226, Hermann-Herder-Str. 10
Luigi Berselli (U Pisa): Time averages and Reynolds equations for dissipative equations; \nGiuseppe Buttazzo (U Pisa): Shape optimization under uncertainty;\nPatrick Dondl (U Freiburg): A phase field model for Willmore’s energy with topological constraint;\nMichael Ruzicka (U Freiburg): On a Clement type operator; \nSoeren Bartels (U Freiburg): Semi-implicit time stepping for p-Laplace equations\n
Numerical homogenization by localized orthogonal decomposition and connections to the mathematical theory of homogenization
Tuesday, 28.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Additive manufacturing of scaffolds for bone regeneration
Tuesday, 5.12.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Dynamics of fronts in some singularly coupled Allen-Cahn equations
Tuesday, 16.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
When coupling the scalar Allen-Cahn model for phase separation with large scale linear fields, the dynamics of interfaces can be rather intriguing. We consider the one-dimensional situation and apply methods from spatial dynamics to identify and unfold singularities that complex motion even for a single interface. Specifically, we can imbed scalar singularities such as a butterfly catastrophe that yield accelerated and direction reversing fronts. In recent work we unfold a degenerate Takens-Bodganov point with additional oscillatory dynamics.
Residual-type a posteriori estimator for a quasi-static contact problem.
Tuesday, 23.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Pollicott-Ruelle-Resonanzen
Monday, 29.1.18, 14:00-15:00, Bibliothek Angewandte Mathematik, R216, RZ, Hermann-Herder-Strasse 10
Pollicott-Ruelle-Resonanzen werden auch klassische Resonanzen genannt. Sie lassen sich definieren als Eigenwerte des erzeugenden Vektorfelds des geodätischen Flusses auf dem (ko)-Sphärenbündel einer geeigneten Riemannschen Mannigfaltigkeit, wobei das Vektorfeld als Operator auf einem sogenannten anisotropen Sobolevraum aufgefasst wird. Das Gegenstück zu klassischen Resonanzen sind Quantenresonanzen, d.h. die Eigenwerte des Laplace-Beltrami-Operators. Wir betrachten, zunächst anhand eines einfachen Beispiels, Resultate und Forschungsfragen zu der Beziehung zwischen klassischen und Quanten-Resonanzen und den zugehörigen Resonanzzuständen.
Gradient Flow for a phase Field Model of the Willmore Energy
Tuesday, 30.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\nWe consider a phase field model for Willmore’s energy originally proposed by de Giorgi. In essence, the energy of this phase field model is given by taking the first variation of the well known Modica-Mortola energy and integrating the square of this variation. A Gamma-convergence result was proved in 2006 by Röger and Schätzle. In this presentation, we examine the viscous gradient flow of de Giorgi’s energy and prove existence of weak solutions using a Galerkin approximation. Finally, we give an outlook to the addition of further constraints for the energy, for example using a term to control certain topological properties of the phase field.