Diffusion/Subdiffusion in the Pushy Random Walk

TL;DR

This paper introduces the pushy random walk model to study how active particles interact with dense, deformable media, revealing subdiffusive and localized behaviors in different dimensions.

Contribution

The paper presents a minimal model for active particle interactions with dense media, demonstrating subdiffusive cavity growth and a diffusion-localization transition.

Findings

In 1D, the cavity length grows subdiffusively over time.

In 2D, increasing obstacle density causes a transition from diffusion to localization.

Transport in crowded media is qualitatively reshaped by tracer-induced rearrangements.

Abstract

We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions of active particles with dense, deformable media. Using scaling arguments and numerical simulations, we show that in one dimension the walker carves out an obstacle-free cavity whose length grows subdiffusively over time. In two dimensions, increasing obstacle density drives a transition from free diffusion to localized behavior, where the walker is trapped within a cavity whose radius again grows subdiffusively with time. These results show how tracer-induced rearrangements qualitatively reshape transport in crowded media and provide a minimal framework for describing diffusion in deformable environments.