Partial Differential Equations

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

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. [>> more]

Modern semiconductor and optoelectronic devices such as semiconductor lasers or organic field-effect transistors are based on semiconductor structures, which e.g. can be given by doping profiles, heterostructures or nanostructures. For the qualitative and quantitative understanding of the properties of these devices, mathematical modeling and simulation of the most relevant and, respectively, of the limiting carrier transport processes is necessary. In the context of the Green Photonics Initiative new topics move into the focus of research, e.g. reduced energy consumption of devices, new applications in the field of renewable energies, communication and lighting. [>> more]

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

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]

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. [>> more]

The relatively large dimensions of semiconductor devices and the complexity of quantum-mechanical models require the consistent modeling of classical and quantum-mechanical descriptions via hybrid models, e.g. by coupling drift-diffusion models to quantum master equations of Lindblad type to describe embedded open quantum systems. Such hybrid models permit the modeling of complex devices such as quantum-dot lasers or single-photon emitters. [>> more]

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]

Archive

Further application topics where the institute has expertise in:

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