← All Labs

Anomalous Diffusion — Sub and Superdiffusion

Normal diffusion: ⟨x²⟩ ∝ t. Anomalous: ⟨x²⟩ ∝ t^α — from trapped particles to Lévy flights

Particle Trajectories
MSD = ⟨x²(t)⟩ (log-log)
Slope α = —
Normal (Brownian): steps ~ Gaussian, ⟨x²⟩ = 2Dt (α=1). Subdiffusion: particle gets trapped (power-law waiting times), ⟨x²⟩ ~ t^α, α<1. Protein diffusion in cytoplasm. Superdiffusion (Lévy): occasional huge jumps (power-law step sizes), ⟨x²⟩ ~ t^α, α>1. Albatross foraging, human travel. Log-log slope of MSD gives α — compare to reference lines.