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 geology. In Geology, percolation is filtration of water through soil and permeable rocks. The water flows to groundwater storage (aquifers)

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

By analytical studies, only few exact results can be obtained for percolation. Hence, many results have been obtained from computer simulations. The current fastest algorithm for percolation was published in 2000 by Mark Newman and Robert Ziff.[1]

See also

References

  • 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)
  • Percolation (2. ed). Springer Verlag, 1999.
  • D.Stauffer and A.Aharony. Introduction to Percolation Theory
  • A. Bunde, Fractals and Disordered Systems, Springer, 1996
  • S. Kirkpatrick Percolation and conduction Rev. Mod. Phys. 45, 574, 1973
  • D. Ben-Avraham, Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press, 2000

External links

  • Introduction to Percolation Theory: short course by Shlomo Havlin


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