Statistical Physics of Complex Systems

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

One focus of our research are suspensions of heavy particles in turbulent fluids. We formulate statistical models for such turbulent aerosols that can be rigorously analysed using methods from non-equilibrium statistical physics and dynamical-systems theory, and that allow to identify and describe the key mechanisms governing the large fluctuations observed in such systems. Most recently we extended and refined the models to describe the growth of tiny water droplets in turbulent clouds, and the dynamics of ice crystals settling through turbulent air in the atmosphere.

The Figure shows spatial patterns formed by particles in a random velocity field, obtained by statistical-model simulations (red corresponds to high particle-number density). The figure illustrates a striking similarity with light patterns seen at the bottom of a swimming pool on a sunny day [Wilkinson & Mehlig, Europhys. Lett. (2005)]. More on our Research.