Stochastic Modelling of Complex Systems

Much of the work in our centre is done at the interface of applied mathematics, statistical physics and the theory of stochastic processes, dealing with more complicated processes than Gaussian white noise. We study the dynamical and stochastic properties of complex systems driven by all kinds of complex noise sources. Staff members of the centre who work in this general area include (in alphabetic order) Adrian Baule, Christian Beck, Lennart Dabelow, Weini Huang, Rainer Klages, Anna Maltsev, and Thomas Prellberg. 

The specialties in our centre include the dynamics of Levy flights and Levy walks, anomalous diffusion processes, random packing problems, evolutionary dynamics, spectra of random matrices, superstatistical processes, generalised versions of statistical mechanics with more general entropy functions, stochastic thermodynamics, fluctuation theorems, systems driven by chaotic maps, and much more. Our work has applications in biophysics (generalised diffusion processes), medicine (cancer research), engineering (sustainable energy systems) and the environmental sciences (air pollution and water quality).

Subcellular calcium signalling: Model of heartbeat initiation (work by A. Maltsev et al.)

Tracer dynamics of particles in active suspensions (image from K. Kanazawa, T.G. Sano, A. Cairoli, A. Baule, Nature 579, 364 (2020))