Active Matter — Polar Alignment & Flocking (Vicsek Model)

Vicsek model: self-propelled particles align with neighbors — order-disorder phase transition

Parameters

Noise η: 0.3 Speed v₀: 2.0 Interaction range r: 15 N particles: 150

φ = —

Vicsek et al. 1995: Each particle moves at speed v₀, updates direction to average of neighbors within r plus noise η. At low η → ordered flock (φ≈1). High η → disorder. Phase transition is 1st order in 2D (Chaté 2008). Goldstone modes: giant density fluctuations.