Abstract
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.
Keywords
Statistical physicsAnomalous diffusionScalingPercolation theoryPercolation (cognitive psychology)DiffusionRandom walkFractalPercolation critical exponentsPercolation thresholdLattice (music)Directed percolationCluster (spacecraft)PhysicsCondensed matter physicsMathematicsPhase transitionComputer scienceInnovation diffusionCritical exponentQuantum mechanicsMathematical analysisElectrical resistivity and conductivityConductivityGeometry
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 36
- Issue
- 6
- Pages
- 695-798
- Citations
- 1773
- Access
- Closed
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Cite This
Shlomo Havlin,
Daniel ben‐Avraham
(1987).
Diffusion in disordered media.
Advances In Physics
, 36
(6)
, 695-798.
https://doi.org/10.1080/00018738700101072
Identifiers
- DOI
- 10.1080/00018738700101072