Active Gel — Polar Order & Toner–Tu Dynamics
Self-propelled particles with velocity alignment: flocking transition & giant number fluctuations
Flock Parameters
Particles N =
300
Noise η =
0.30
Alignment radius r =
50
Speed v₀ =
2.0
Pause
Reinitialize
Order
Polar order φ
—
Phase
—
Mean speed
—
Toner-Tu (1995): continuum theory
∂_t ρ + v_0 ∇·P̂ = 0
∂_t P + λ(P·∇)P = (a−b|P|²)P + K∇²P + ...
Critical noise η_c: ordered↔disordered
Ordered phase: φ = |Σv̂_i|/N > 0
Giant density fluctuations: ΔN ~ N^{3/4}