Percolation

"Percolate" redirects here. For the computer language, see PeRColate.

In physics, chemistry and materials science, percolation (from Lat. percōlāre, to filter or trickle through) concerns the movement and filtering of fluids through porous materials (for more details see percolation theory). During the last five decades, percolation theory, an extensive mathematical model of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology as well as in geography.

Percolation typically exhibits universality. Statistical physics concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are useful to characterize percolation properties. Combinatorics is commonly employed to study percolation thresholds. Applications / specific examples include:

• coffee percolation, where the solvent is water, the permeable substance is the coffee grounds, and the soluble constituents are the chemical compounds that give coffee its color, taste, and aroma
• movement of weathered material down on a slope under the earth's surface
• the act of 'upwards' claiming; whereby a claimed subject who is claimed by another entity, is funneled to their claimer
• cracking of trees with the presence of two conditions, sunlight and under the influence of pressure
• Robustness of networks to random and targeted attacks
• Transport in porous media
• Epidemic spreading
• Surface roughening
• Network robustness

See also

• Conductance
• Self-organization
• Self-organized criticality
• Percolation theory
• Percolation threshold
• Groundwater recharge
• Septic tanks
• Critical exponents
• Phase transition
• Complex network
• Epidemic spreading
• Immunization
• Branched polymers
• Fragmentation
• Supercooled water
• Polymerization
• Gelation
• Porous and amorphous material
• Galactic structure

References

• Harry Kesten, What is percolation? Notices of the AMS, May 2006.
• Muhammad Sahimi. Applications of Percolation Theory. Taylor & Francis, 1994. ISBN 0-7484-0075-3 (cloth), ISBN 0-7484-0076-1 (paper)
• Geoffrey Grimmett. Percolation (2. ed). Springer Verlag, 1999.
• D.Stauffer and A.Aharony. Introduction to Percolation Theory
• A. Bunde, S. Havlin (Editors) Fractals and Disordered Systems, Springer, 1996
• S. Kirkpatrick Percolation and conduction Rev. Mod. Phys. 45, 574, 1973
• D. Ben-Avraham, S. Havlin Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press, 2000

External links

• Introduction to Percolation Theory: short course by Shlomo Havlin