André Erhardt, Olaf Klein, Manuel Landstorfer, Rüdiger Müller, Leonie Schmeller, Alireza Selahi Moghaddam
from left to right: André Erhardt, Manuel Landstorfer, Leonie Schmeller, Olaf Klein, Barbara Wagner, Alireza Selahi Moghaddam, Ina Hohn, Rüdiger Müller
OverviewThe research group conducts research on multiscale and thermodynamic consistent modeling of complex materials. The main expertise are systematic asymptotic analysis, in particular for singularly perturbed free-boundary problems, and analysis of hysteresis properties. This is used to investigate fundamental processes that drive phase-transitions leading to micro- and nanostructuring of multi-phase materials and their interfaces.
Applications range from liquid polymers, hydrogels, polyelectrolyte gels, and further electrochemical systems, with the focus on problems in cell biology, regenerative medicine and lithium-ion batteries. For the corresponding systems of coupled partial differential equations the research group develops mathematical theory and numerical algorithms.
Main topicsMultiphase problems in soft and living materials:
The idea of this research topic is to develop mathematical models for material systems spanning problems in soft matter to living materials describing their intrinsic structural and dynamic properties across multiple scales. Current projects --> SPP2171, Math+ AA1-12, Math+ AA2-9
Hysteresis, electromagnetic-mechanical components, and uncertainty quantification
Parameters within hysteresis operators modeling real world objects, like e.g. electromagnetic-mechanical components, have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied.
- Partial Differential Equations
- Laser Dynamics
- Numerical Mathematics and Scientific Computing
- Nonlinear Optimization and Inverse Problems
- Interacting Random Systems
- Stochastic Algorithms and Nonparametric Statistics
- Thermodynamic Modeling and Analysis of Phase Transitions
- Nonsmooth Variational Problems and Operator Equations