Pedestrian dynamics — lane formation and bottleneck flow
Flow rate: — ped/s | Mean speed: —
Helbing (1995): mᵢ(dvᵢ/dt) = mᵢ(v₀eᵢ−vᵢ)/τ + Σⱼf_ij + walls. Self-driving force: pedestrian accelerates toward desired direction at speed v₀ with time constant τ. Social repulsion: f_ij = A·exp((rᵢⱼ−dᵢⱼ)/B)·n̂ᵢⱼ. At high density: arch formation at bottleneck, intermittent flow, lane formation in bidirectional flow. Colors encode speed (red=slow, blue=fast).