A drop of ink in a glass of water spreads evenly, but in a cup with chunks of fruit jelly, the ink will take winding paths — sometimes getting stuck, sometimes slipping through. Similarly, molecules in living cells or porous materials don't move on a smooth field but through a disordered medium: denser in some places, thinner in others.
Standard models smooth out this disorder by averaging all obstacles into a single 'average viscosity.' But then an important detail is lost: a particle can get stuck for a long time in a dense region and then suddenly speed up. The new method of stochastic modeling with a map of local properties separates two effects: random delays due to heterogeneities and the medium's 'memory' of the particle's past movements. It's like predicting traffic jams not just by the average city speed but also by the locations of traffic lights and potholes.
The authors tested the method in numerical experiments: from short particle trajectories, they could predict how the motion would look over a long time and recover the spread of medium properties. This approach could be useful for studying drug diffusion in tissues or ions in batteries, where the medium is inherently heterogeneous.
Diffusion in living cells is often anomalous: molecules can move slower or faster than predicted by Einstein's classical formula, due to the crowded environment, a 'crowd' of proteins and organelles.