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Pushy Random Walk: A Minimal Model for Transport in Deformable Media
Ofek Lauber Bonomo1,2, Itamar Shitrit2, Shlomi Reuveni2
1New York University, Center for Urban Science and Progress, Tandon School of Engineering, Brooklyn, New York, USA.
Physical Review Letters
|July 31, 2026
Summary
A novel "pushy random walk" model shows active particles can carve paths through dense media. This tracer-induced rearrangement fundamentally alters transport in crowded environments.
Area of Science:
- Physics
- Statistical Mechanics
- Soft Matter Physics
Background:
- Active particles interact with surrounding media.
- Transport in crowded, deformable environments is complex.
- Understanding tracer-particle dynamics is crucial for soft matter systems.
Purpose of the Study:
- Introduce a minimal model for active particle interactions in dense media.
- Investigate the transport dynamics of a 'pushy random walk'.
- Analyze how obstacle density affects walker behavior and cavity formation.
Main Methods:
- Theoretical analysis using scaling arguments.
- Numerical simulations of the random walk process.
- Examination of one- and two-dimensional systems.
Main Results:
- In 1D, the walker creates an obstacle-free cavity with subdiffusive length growth.
- In 2D, increasing obstacle density causes a transition from diffusion to localized behavior.
- Walker-induced cavity radius exhibits subdiffusive growth in 2D.
Conclusions:
- Tracer-induced rearrangements significantly reshape transport in crowded media.
- The pushy random walk model provides insights into active particle behavior.
- Subdiffusive cavity growth characterizes transport in these dense systems.
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