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.
as written by the authors arXiv:2604.16825
We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential, SD-GLE utilizes a variational Bayesian framework with a random field prior to explicitly disentangle static spatial disorder from viscoelastic friction. Numerical results demonstrate the limits of standard GLEs, whereas SD-GLE accurately extrapolates long-time dynamics to capture the anomalous diffusion crossover from short trajectories and recover the ensemble statistical properties inherent to the disordered nature of these systems.
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.