Thermodynamic Modeling and Analysis of Phase Transitions
- Research Group -
Marion Dziwnik, Paul Gajewski, Clemens Guhlke, Olaf Klein, Manuel Landstorfer, Esteban Meca Álvarez, Rüdiger Müller
The research group drives thermodynamically consistent modeling, analysis and simulations of processes in materials of quite different kind. In this context desirable and undesired phase transitions occur and its prediction is mandatory in current key technologies.
Currently there are three core areas in the research group:
1. Mathematical models of electrochemical processes in the context of lithium-ion batteries
2. Mathematical models of nano-structured materials within photovoltaic applications and for complex liquids
3. Hysteresis of electro-magnetic-mechanical components and of biological systems
From a mathematical point of view the resulting models are represented by systems of nonlinear partial differential equations. Moreover, systems of stochastic ordinary differential equations are studied in the context of battery research. A further area is the realization of sharp limits of diffuse interface models by application of the methods of asymptotic analysis.
The foundations of the battery research were established within the Leibniz group Mathematical Models for Lithium-Ion Batteries that exists at WIAS during 2012-2014. Its funding results from a successful proposal within the competition procedure of the Leibniz Association.
- 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