SFB 611:  Singular Phenomena and Scaling in Mathematical Models

• Subject Area: Mathematics
• Term: from 2002 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5485161

The increasing performance of computers has opened new perspectives in modeling: It has become possible to derive concrete predictions of realistic models, to compare them with experiments and to possibly adjust the model - all within short time. The goal of our mathematical collaborative research centre is to develop notions, theoretical and numerical methods which allow for a clean and at the same time efficient treatment of these models.
Our strategy lies in a close collaboration of theoretical analysis, numerical simulation and modeling. We plan to prove the potential of this combination through the successful treatment of selected, concrete phenomena. The leitmotivs of our approach are multiple scales hierarchies of models, singularities degeneracies, and asymptotic scaling laws self-similarity.
The multiple scales in the models are one of the main challenges for analysis and numerics. A separation of these scales suggests to work with hierarchies of models. We are particularly interested in hierarchies where the models on the different levels are of different type: discrete-continuous, stochastic-deterministic, discrete-kinetic-hydrodynamic. The spatial coupling of the different levels is a primary focus.

• DFG Programme: Collaborative Research Centres

Completed projects

• A01 - Analysis on collapsing manifolds and singular spaces (Project Heads Müller, Werner ;  Sturm, Karl-Theodor )
• A02 - Flows of probability measures and nonlinear stochastic evolutions (Project Head Sturm, Karl-Theodor )
• A03 - Investigation of geometric, analytic and dynamical invariants of degenerating families of negatively curved Riemannian manifolds (Project Head Hamenstädt, Ursula )
• A4 - Skalenbildung singuläres Verhalten von Diffusionsprzessen (Project Heads Frehse, Jens ;  Hamenstädt, Ursula )
• A5 - Stochastische Prozesse auf komplexen Strukturen, Homogenisierung und stochastische partielle Differentialgleichungen (Project Heads Albeverio, Sergio ;  Sturm, Karl-Theodor )
• A06 - Scaling limits of particle systems and stochastic interface dynamics (Project Heads Albeverio, Sergio ;  Alt, Hans Wilhelm ;  Eberle, Andreas )
• A7 - Geometrische Bedingungen auf freien Rändern (Project Head Schätzle, Reiner )
• A08 - Convergence of multi particle Monte Carlo methods for sampling and filtering (Project Heads Albeverio, Sergio ;  Eberle, Andreas )
• A09 - Stochastic Processes with Variable Scaling Parameters (Project Heads Kaßmann, Rolf Moritz ;  Sturm, Karl-Theodor )
• A10 - Differential equations with singular structures (Project Head Koch, Herbert )
• A11 - Metastability in stochastic dynamics (Project Head Bovier, Anton )
• A12 - Universality of fluctuations in mathematical models of physics (Project Head Ferrari, Patrik L. )
• B01 - Pattern formation in magnetic materials (Project Heads Kurzke, Matthias ;  Otto, Felix )
• B02 - Complex rheology (Project Head Otto, Felix )
• B03 - The goal of this project is tu understand the macroscopic roughening or coarsening of vrystal films growing by molecular beam epitaxy, based on a hierarchy of models (Project Heads Otto, Felix ;  Voigt, Axel )
• B04 - Analysis of multicomponent flows (Project Heads Conti, Sergio ;  Frehse, Jens )
• B05 - Dynamical contact phenomena in biological systems (Project Heads Alt, Wolfgang ;  von der Mosel, Heiko )
• B6 - Nichtlineare Wechselwirkungen bei piezoelektische angeregten Oberflächenwellen (Project Heads Botkin, Nikolai ;  Hoffmann, Karl-Heinz ;  Otto, Felix )
• B07 - Surface dynamics driven by embedded substances (Project Heads Alt, Wolfgang ;  Alt, Hans Wilhelm )
• B08 - Level set methods for geometric variational problems (Project Head Rumpf, Martin )
• B09 - Singulary perturbed variational problems from nonlinea elasticity (Project Head Conti, Sergio )
• C01 - Wavelet Methods for Systems of Operator Equations (Project Heads Griebel, Michael ;  Kunoth, Angela ;  Scherer, Karl )
• C02 - Adaptive and Robust Multilevel Methods for Space-Time Discretizations (Project Heads Gerstner, Thomas ;  Griebel, Michael )
• C03 - Modeling and simulation of dynamic wetting processes (Project Head Griebel, Michael )
• C04 - Microskopic effects at fluid interfaces (Project Heads Alt, Hans Wilhelm ;  Griebel, Michael )
• C5 - Punktdefekte in Silizium-Kristallen (Project Heads Griebel, Michael ;  Voigt, Axel )
• C06 - Coupled Microscale Simulation of Nonlinear Processes in Structural Mechanics (Project Heads Krause, Rolf ;  Schweitzer, Marc Alexander )
• C07 - Multiscale approximation of boundary value problems on stochastic domains (Project Heads Harbrecht, Helmut ;  Krause, Rolf )
• C08 - Reliable computation of singularities in geometric partial differential equations (Project Head Bartels, Sören )
• C09 - Multiscale problems and hierarchical matrices (Project Head Bebendorf, Mario )
• S - Zentrale Verwaltung (Project Head Otto, Felix )
• Z - Central tasks of the Collaborative Research Centre (Project Head Griebel, Michael )

• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Spokesperson: Professor Dr. Michael Griebel