The group contributes to the following application oriented research topics of WIAS:


Coagulation processes are typical in physics (merging of particles, growth of gas bubbles), meteorology (merging of droplets in clouds, transportation of aerosols), chemistry (hydrogels, formation of aerosols), chemistry (hydrogels, formation of soot), astrophysics (formation of planets). At WIAS, different types of models are investigated: probabilistically with complex Markov processes, analytically with kinetic equations and their properties, numerically with solvability and computational questions for these equations, and heuristically with theoretical descriptions. One of the main questions is under which conditions particularly large particles are formed in large systems, i.e. the occurrence of the gelation phase transition. [>> more]

Mathematical Models and Methods for Lithium-ion Batteries

In modern lithium-ion batteries, a variety of physicochemical processes occur simultaneously on various size and time scales. To systematically examine their influence and interactions within a battery, mathematical models are developed that represent the respective processes using partial differential equations. Using numerical methods, specific parameters of a battery can be calculated, such as the cell voltage as a function of state of charge. These models are continuously evolving to, for example, account for aging effects. [>> more]

Modeling of thin films and nano structures on substrates

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. [>> more]

Modeling, Simulation and Optimization for Biomedical Applications

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. [>> more]

Nonlinear material models, multifunctional materials and hysteresis in continuum mechanics.

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. [>> more]

Phase field models for complex materials and interfaces

This research topic focusses on modeling complex material systems with different phases including multiphase and interfacial flows, damage and fatigue modeling, topology optimization and complex materials. Physical phenomena modelled involve fluid flow, diffuse transport and (visco)elastic deformation in the context of phase separation and phase transitions. Applications range from biology to physics and engineering. [>> more]

Thermodynamic models for electrochemical systems

The behavior of electrochemical systems is widely investigated with continuum physics models. Applications range from single crystal electrochemistry to lithium batteries and fuel cells, from biological nano-pores to electrolysis and corrosion science, and further. [>> more]


Further application topics where the institute has expertise in:

Crystal growth under the influence of electromagnetic fields

n order to produce semiconductor components used in computers, mobile phones, laser devices or solar cells, semiconductor (single- and poly-) crystals of high quality are needed. The growth process of such crystals is complex and quite often expensive. It is important to find strategies to reduce the costs of the growth process and to improve the quality of the produced crystals. In this context electromagnetic fields often play an essential role. Applied mathematics, in particular the techniques of modeling, analysis, and simulation, is used to support the development of growth processes. [>> more]


This work is focussed on the design of nanostructures and semiconductor simulations in photovoltaics as well as the production of solar silicon. [>> more]

Production of solar silicon

Currently, solar cells are mainly produced by using multi-crystalline silicon. A part of the overall production costs of a usable solar module is due to crystal growth from the silicon melt. The aim of modern crystal growth processes is the reduction of these costs while also improving the quality of the grown crystals. [>> more]

Unwanted precipitates during heat treatment of GaAs single crystals

Before further processing for application in opto-electronic devices, single crystal GaAs wafer must be heat treated. However, arsenic-rich GaAs with a composition corresponding to the congruent melting point, exhibits unwanted arsenic precipitations during the heat treatment. [>> more]