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


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 (reacting polymers, soot formation) and astrophysics (formation of stars and planets). [>> 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]

Mobile Communication Networks

Mobile telephones and similar devices are in wide and intensive use and place high demands on the networks to which they connect. The behaviour of individual users is, for practical purposes, unpredictable and the load on the network varies randomly in space and time. We study the probability of extreme overloading events which cause significant degradation in the user experience. Most problems can be solved by the installation of sufficient networking equipment, but this has a significant financial cost. Our work allows informed decisions to be made balancing cost and service quality. [>> more]

Numerical methods for the simulation of population balance systems

These applications are modeled by population balance systems. Accurate and efficient numerical methods will be developed, in collaboration with partners from academics and industry, which will be in the long term the basis of optimal control methods for the considered processes. [>> 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]


Further application topics where the institute has expertise in:

Stochastic Biological Evolution

Research in this field focuses on mathematical aspects of biological evolution through stochastic modelling. The main areas are the effects of complex fitness landscapes on molecular evolution, the study of sexual selection by stochastic modelling of mating preferences and emerging mating patterns, genealogies of the mathematical seed-bank model and mathematical modelling of controlled evolution under experimental conditions. [>> more]