Modeling of phase separation and damage in modern materials

This work is focussed on the modeling of damage and on phase separation in modern solder materials for microelectronic devices. [>> more]

Phase transition and hysteresis in the context of storage problems

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. [>> more]

Modeling, Simulation and Optimization for Biomedical Applications

Today, in medical science digital simulation instruments for processes in the human body are utilized in diagnistics and therapy planning. At WIAS, models for biological tissues, fluids, and their interaction as well as techniques in optimization and optimal control for decision support in biomedicin are devloped. [>> more]

Diffusion models in statistical physics

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, mass transport models, 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. [>> 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]

Particle-based modeling in the Sciences

For more than a hundred years diverse processes and phenomena in the natural sciences have been modelled using random particle systems. As a result ever more models that specify a large number of particles and rules for how they interact have been both proposed and mathematically analysed. [>> more]

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. [>> 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]

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]

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]