Anomalous Diffusion
MSD ∝ t^α: normal (α=1), subdiffusion (α<1, CTRW), superdiffusion (α>1, Lévy flights). Compare walkers in real time.
Normal MSD: —
Sub MSD: —
Lévy MSD: —
Step: 0
Mean squared displacement MSD(t) = ⟨r²(t)⟩ ∝ t^α classifies diffusion: α=1 (Brownian, Gaussian steps), α<1 (subdiffusion, CTRW — long waiting times, e.g. proteins in crowded cells), α>1 (superdiffusion, Lévy flights — power-law jump sizes P(l) ∝ l^{-μ}, e.g. foraging animals, light in disordered media). Fractional Brownian motion gives α≠1 with correlated steps. The MSD log-log plot slope directly measures α.