Many important processes of industrial production and use of modern and functional materials are accompanied by phase transitions and hysteresis. In tight collaboration with users from industry, physics and chemistry existing as well as newly developed models are studied at WIAS regarding their practical relevance.
The phenomenon of coagulation occurs in a wide range of applications, e.g., in physics (aggregation of particles, growth of gas bubbles), meteorology (merging of drops in atmospheric clouds, aerosol transport), chemistry (hydrogels, reacting polymers, soot formation) and astrophysics (formation of stars and planets).
This work is focussed on the modeling of damage and on phase separation in modern solder materials for microelectronic devices.
Phase transitions and hysteresis are characteristics of energy storage problems. The aim is to formulate and analyse a thermodynamical model which discribes the storage problem.
Mathematical models and computational techniques are nowadays utilized in medical sciences for noninvasive diagnostic, diseases characterization, therapy planning, and treatment monitoring. The research at WIAS focuses on efficient and robust models for biological tissues and fluids, on the usage of advanced mathematical models in data assimilation and medical imaging applications, as well as on techniques in optimization, machine learning, and optimal control for decision support in biomedicine.
Many models in statistical physics contain random paths with interactions of various natures, like polymer models, where the path has a self-repellence and attractive interactions with the surrounding medium, or mass transport models in random medium, where the path carries a random mass that is increased and decreased, depending on the properties of the space visited, or self-intersection properties of the path. Also coupled nonlinear diffusion equations are used for modeling such phenomena.
Thin films play an important role in nature and many areas of technological applications. In particular on micro- and nanoscales technological processes such as dewetting or epitaxial growth are used to design surfaces with specific material properties. Apart from the need to derive mathematical decriptions, analyis and numerical simulation, that serve to accelerate the development of new technologies, it is also exciting to understand material behaviour on these small scales.
For more than a hundred years diverse processes and phenomena in the natural sciences have been modelled using random particle systems. At the WIAS macroscopic phenomena in such large systems are analyzed with particular focus on phase transitions such as percolation or gelation.
Nonlinear material models, multifunctional materials and hysteresis in connection with elasto-plastic processes
Many components in modern equipment rely on specific properties of so-called multifunctional materials. These materials are distinguished by the fact that therein properties like elastic deformability, thermal expansibility, magnetizability, or polarizability interact nontrivially like for instance in a piezo-crystal. At WIAS coupled models describing these properties are developed and analyzed.
Main Areas of Application
- Partial Differential Equations
- Numerical Mathematics and Scientific Computing
- Nonlinear Optimization and Inverse Problems
- Interacting Random Systems
- Thermodynamic Modeling and Analysis of Phase Transitions
- Nonsmooth Variational Problems and Operator Equations
- Numerical Methods for Innovative Semiconductor Devices
- Probabilistic Methods for Dynamic Communication Networks