Tempered anomalous diffusion in heterogeneous systems

Passive tracers in heterogeneous media experience preasymptotic transport with scale-dependent anomalous diffusion, before eventually converging to the asymptotic diffusion limit. We propose a novel tempered model to capture the slow convergence of sub-diffusion to a diffusion limit for passive tracers in heterogeneous media. Previous research used power-law waiting times to capture the time-nonlocal transport process. Here those waiting times are exponentially tempered, to capture the natural cutoff of retention times. The model is validated against particle concentrations from detailed numerical simulations and field measurements, at various scales and geological environments.