Active matter · nonlinear dynamics

Active Matter: Vicsek Model + Run-and-Tumble

Active Matter: Vicsek Model + Run-and-Tumble
fig. Active Matter: Vicsek Model + Run-and-Tumble

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The notebook runs on its own once it loads, so give it about 10 seconds while Python starts up in your browser, and the simulations begin animating. Move the sliders and everything recomputes live. The code is shown alongside the output so you can read exactly how it works; the full editable source is linked below.

Two faces of active matter in one place. The Vicsek model is the crowd: a few hundred self-propelled particles that each steer toward the average heading of their neighbours, with a little noise mixed in. Turn the noise up and the flock scatters; turn it down and the whole swarm commits to a single direction. That switch is a real phase transition, and the order parameter follows it as I sweep the noise. Run-and-tumble is the single cell: a swimmer that runs straight, reorients at random, and runs again. Its mean-squared displacement starts ballistic and turns diffusive right around the tumble time, and the effective diffusion constant I read off matches the analytic value.

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