Active Brownian Particles

Motility-Induced Phase Separation (MIPS)

ẋᵢ = v₀ n̂ᵢ − μ∇U + ξᵢ
θ̇ᵢ = √(2Dᵣ)·ηᵢ

Effective temp:
T_eff = T(1 + v₀²τᵣ/2D)

MIPS spinodal:
∂μ_eff/∂ρ < 0

Self-propulsion v₀ 3.0

Rotational diff. Dᵣ 0.5

Packing density φ 0.35

Repulsion strength ε 5

clusters: — largest: —

MIPS (Cates & Tailleur 2015): purely repulsive self-propelled particles spontaneously phase-separate at high activity. Particles slow down in dense regions (more collisions), which concentrates them further — a positive feedback. No attractive forces needed. The spinodal condition ∂μ_eff/∂ρ<0 predicts phase separation onset.