Complex Systems

 The dynamics of complex systems can often be systematically analysed using stochastic approaches, such as diffusion approximations and random-matrix theory.  This approach may yield, as experience shows, surprisingly universal results: phenomena observed in complex systems in a wide range of different disciplines (Biology, Biological Physics, and Fluid Dynamics) can be understood in terms of simple and thus general mechanisms.

Most recently we have analysed stochastic models for the dynamics of particles suspended in turbulent flows and related questions in fluid dynamics, for the evolution and adaptation of biological populations, as well as statistical models describing the fluctuations of confined polymers.

Figure: patterns of particles suspended in a random flow. The figure illustrates a striking similarity with patterns seen at the bottom of a swimming pool on a sunny day.