Motility-Induced Phase Separation (MIPS)

Self-propelled particles cluster without attractive forces

Clusters:
φ_dense:
Run-and-tumble particles: each moves at speed v₀ in a fixed direction, tumbling randomly with rate λ. Slow particles accumulate in crowded regions; fast particles escape — creating positive feedback that drives phase separation into dense (liquid) and dilute (gas) phases with NO attractive interactions. This is MIPS.