Brief description: The main theme of my research is to understand the interplay between chaos in the microscopic motion of single particles and transport in many-particle systems on a macroscopic scale. In previous work I discovered a fractal parameter dependence of transport coefficients and analysed relations between chaos and transport in dissipative dynamical systems. More recently I got interested in anomalous transport phenomena emerging from microscopic dynamics that is much stronger correlated than ordinary Brownian motion. This theory is applied to understand experiments on biological cell migration and on the foraging of bumblebees. I also started to work on computer simulations of single-molecule diffusion in nanopores. My research in theoretical physics and applied mathematics thus stretches over the whole range from mathematical foundations towards experimental applications.

Example: Interplay between microscopic chaos and macroscopic transport in a simple model system: the dotted red line represents the trajectory of a point particle moving in a periodic array of scatterers. The diffusion coefficient of this system turns out to be a fractal under parameter variation. The other curves included in the figure represent magnifications of the diffusion coefficient in certain ranges of the parameter; more information?