Motility-Induced Phase Separation (MIPS)

Self-propelled particles spontaneously separate into dense & dilute phases — no attractive forces needed.

2.0
0.03
0.25
9
MIPS arises because fast particles slow down in dense regions (via collisions), creating a feedback: slow → accumulate → denser → slower. The critical condition is Péclet number Pe = v₀/(Dᵣ·σ) exceeding a threshold. Here λ ≈ Dᵣ (rotational diffusion). Dense cluster = liquid phase; sparse background = gas phase — all from purely repulsive, self-propelled particles.