Diffusion in disordered media

Shlomo Havlin, Daniel Ben-Avraham

Research output: Contribution to journalArticlepeer-review

1699 Scopus citations

Abstract

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.

Original languageEnglish
Pages (from-to)695-798
Number of pages104
JournalAdvances in Physics
Volume36
Issue number6
DOIs
StatePublished - 1 Jan 1987

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