Premium
Tempered anomalous diffusion in heterogeneous systems
Author(s) -
Meerschaert Mark M.,
Zhang Yong,
Baeumer Boris
Publication year - 2008
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2008gl034899
Subject(s) - diffusion , anomalous diffusion , limit (mathematics) , convergence (economics) , cutoff , statistical physics , diffusion process , scale (ratio) , physics , mechanics , computer science , mathematics , innovation diffusion , mathematical analysis , thermodynamics , knowledge management , quantum mechanics , economics , economic growth
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.