Anomalous Diffusion — CTRW & Montroll-Weiss Theory
Continuous Time Random Walk with power-law waiting times · ⟨x²⟩ ~ t^α
Parameters
Anomalous exponent α:
0.7
Number of walkers:
30
Steps per frame:
3
Reset Simulation
Pause
α<1 sub-diffusion
α=1 normal
α>1 super-diffusion
Montroll-Weiss theory:
CTRW with waiting time PDF ψ(t) ~ t^{-1-α} gives MSD ⟨x²(t)⟩ ~ t^α.
α < 1: sub-diffusion (trapping, glassy systems)
α = 1: normal Brownian motion
α > 1: super-diffusion (Lévy flights)
Mittag-Leffler function E_α(-λt^α) governs relaxation instead of simple exponential.