Diffusion in disordered media

1987/01/01 by Shlomo Havlin, Daniel Ben-Avraham, Daniel ben‐Avraham · 1,808 citations
Materials Science · Mathematics · Physics and Astronomy · #Anomalous diffusion #Cluster (spacecraft) #Computer science #Condensed matter physics #Conductivity #Critical exponent #Diffusion #Directed percolation #Electrical resistivity and conductivity #Fractal #Geometry #Innovation diffusion #Lattice (music) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Phase transition #Physics #Quantum mechanics #Random walk #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.1080/00018738700101072

published in Advances In Physics 36(6), 695-798 (Taylor & Francis)

openalex publication_date 1987/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

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