A particle wanders through a medium scattered with obstacles. Sometimes it pushes them aside like a snowplow, and it was thought that this pushing is what eventually stops the motion. But in three-dimensional space, that mechanism doesn't work.
It turns out that stopping arises from rare events: every so often, a particle randomly finds itself in a trap, and all exits close, as if doors slam shut. The probability of such an event at each step is almost independent of how many steps have already been taken. Therefore, the number of particles that haven't gotten stuck decays exponentially, like tea cooling down.
This discovery allows predicting how far a particle will travel in a given time, knowing only two numbers: its typical speed and the probability of getting stuck at one step. Such a simple rule works across different lattices and dimensions.
This view of motion in porous media helps understand how drugs spread through tissues, pollutants through soil, or heat through insulation. Rare but decisive events turn out to be more important than constant friction.
as written by the authors arXiv:2603.04048
Tracer-media interactions can give rise to transport phenomena beyond classical models; e.g., obstacle pushing can eliminate percolation. We demonstrate that the existing "snowplow" mechanism proposed to explain this effect fails in 3D. We show that confinement is governed by emergent trapping-rare "door-closing" events that occur with an approximately constant probability per step at low obstacle densities, thus yielding exponential survival. This allows prediction of the time-dependent mean-squared displacement from short-time estimates of the diffusion constant and trapping probability, providing a minimal description of pushing-induced arrest across lattices and dimensions.
Even if obstacles occupy only a small fraction of the volume, particles still get stuck: traps arise randomly, but inevitably.
In Stanisław Lem's novel "The Invincible," microrobots form a cloud that moves as a single entity, but individual 'particles' can get stuck in crevices — similar to the traps described here.