Anomalous Diffusion & Subdiffusion

Beyond Brownian motion: ⟨x²⟩ ~ t^α
MSD = 2D_α t^α  |  α<1: subdiffusion, α>1: superdiffusion
Anomaly α 1.00
Num particles 8
Mode
Anomalous diffusion breaks the classical ⟨x²⟩∝t law. Subdiffusion (α<1): particles get trapped — common in crowded biological cells, gels, and fractal media. Superdiffusion (α>1): long jumps dominate — turbulent flows, foraging animals. Mechanisms: Continuous-Time Random Walks (waiting time power law), fractional Brownian motion (correlated steps), Lévy flights (heavy-tail jump lengths).