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
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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
)
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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
)
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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
)
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A10 - Differential equations with singular structures
(Project Head
Koch, Herbert
)
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A11 - Metastability in stochastic dynamics
(Project Head
Bovier, Anton
)
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A12 - Universality of fluctuations in mathematical models of physics
(Project Head
Ferrari, Patrik L.
)
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B01 - Pattern formation in magnetic materials
(Project Heads
Kurzke, Matthias
;
Otto, Felix
)
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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
)
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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
)
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B09 - Singulary perturbed variational problems from nonlinea elasticity
(Project Head
Conti, Sergio
)
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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
)
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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
)
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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
)
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C09 - Multiscale problems and hierarchical matrices
(Project Head
Bebendorf, Mario
)
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S - Zentrale Verwaltung
(Project Head
Otto, Felix
)
-
Z - Central tasks of the Collaborative Research Centre
(Project Head
Griebel, Michael
)
