Diffusion is one of the most fundamental transport processes taking place in biological and physico-chemical systems. The diffusing particles can be as small as water molecules or as big as pollen grains, whose erratic motions have been observed in the 19th century by the Scottish botanist Robert Brown. The theory of “normal” diffusion goes back to Fick and Einstein, and although most spatially unconfined diffusion processes are well described by Einstein’s theory, there is an ever increasing number of observations of “anomalous” diffusion, in particular in biological systems, which are not in agreement with this theory. Corresponding generalizations are often of purely mathematical nature and lack physical interpretation.

The idea of this project for this Consortium is to improve the understanding of the physical origins of anomalous diffusion by gathering together specialists whose expertise in diffusion phenomena is largely complementary to each other. The partners have considerable expertise in stochastic processes, statistical physics, large-scale computer simulations, and single particle tracking methods, and they have worked on anomalous diffusion considering very different length and time scales in fluids, soft matter, as well as in biological systems. Therefore, the added value expected to emerge from this network is profound. The first phase of the project will serve to broaden and consolidate the knowledge of all partners. In the second phase the partners will establish a basis for fundamental physical concepts leading to anomalous diffusion (such as bulk memory effects, geometry, boundary conditions, etc.) and their relation to established models. In this context, the impact of coarse-graining in time and space will be particularly emphasized.