For the mathematical and statistical physics term, see percolation theory.
Percolation (from Latinpercolare, "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.
Fig. 1: In coffee percolation, soluble compounds leave the coffee grounds and join the water to form coffee. Insoluble compounds (and granulates) remain within the coffee filter.
Fig. 2: Percolation in a square lattice (Click to animate)
During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation refers to filtration of water through soil and permeable rocks. The water flows to recharge the groundwater in the water table and aquifers. In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of water, a percolation test is needed beforehand to determine whether the intended structure is likely to succeed or fail. In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 – p; the corresponding problem is called site percolation, see Fig. 2.
Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used. The current fastest algorithm for percolation was published in 2000 by Mark Newman and Robert Ziff.[1]
Examples
Coffee percolation (see Fig. 1), 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.
Cracking of trees with the presence of two conditions, sunlight and pressure.
Collapse and robustness of biological virus shells to random subunit removal (experimentally-verified fragmentation of viruses).[2][3][4]
Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
Potential sites for septic systems are tested by the "perc test". Example/theory: A hole (usually 6–10 inches in diameter) is dug in the ground surface (usually 12–24" deep). Water is filled in to the hole, and the time is measured for a drop of one inch in the water surface. If the water surface quickly drops, as usually seen in poorly-graded sands, then it is a potentially good place for a septic "leach field". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.
^Newman, Mark; Ziff, Robert (2000). "Efficient Monte Carlo Algorithm and High-Precision Results for Percolation". Physical Review Letters. 85 (19): 4104–4107. arXiv:cond-mat/0005264. Bibcode:2000PhRvL..85.4104N. CiteSeerX10.1.1.310.4632. doi:10.1103/PhysRevLett.85.4104. PMID 11056635. S2CID 747665.
^Brunk, Nicholas E.; Twarock, Reidun (2021-07-23). "Percolation Theory Reveals Biophysical Properties of Virus-like Particles". ACS Nano. American Chemical Society (ACS). 15 (8): 12988–12995. doi:10.1021/acsnano.1c01882. ISSN 1936-0851. PMC8397427. PMID 34296852.
^Brunk, Nicholas E.; Lee, Lye Siang; Glazier, James A.; Butske, William; Zlotnick, Adam (2018). "Molecular jenga: The percolation phase transition (collapse) in virus capsids". Physical Biology. 15 (5): 056005. Bibcode:2018PhBio..15e6005B. doi:10.1088/1478-3975/aac194. PMC6004236. PMID 29714713.
^Lee, Lye Siang; Brunk, Nicholas; Haywood, Daniel G.; Keifer, David; Pierson, Elizabeth; Kondylis, Panagiotis; Wang, Joseph Che-Yen; Jacobson, Stephen C.; Jarrold, Martin F.; Zlotnick, Adam (2017). "A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid". Protein Science. 26 (11): 2170–2180. doi:10.1002/pro.3265. PMC5654856. PMID 28795465.
^Grassberger, Peter (1983). "On the Critical Behavior of the General Epidemic Process and Dynamical Percolation". Mathematical Biosciences. 63 (2): 157–172. doi:10.1016/0025-5564(82)90036-0.
^Newman, M. E. J. (2002). "Spread of epidemic disease on networks". Physical Review E. 66 (1 Pt 2): 016128. arXiv:cond-mat/0205009. Bibcode:2002PhRvE..66a6128N. doi:10.1103/PhysRevE.66.016128. PMID 12241447. S2CID 15291065.
percolation, mathematical, statistical, physics, term, percolation, theory, from, latin, percolare, filter, trickle, through, physics, chemistry, materials, science, refers, movement, filtering, fluids, through, porous, materials, described, darcy, broader, ap. For the mathematical and statistical physics term see percolation theory Percolation from Latin percolare to filter or trickle through in physics chemistry and materials science refers to the movement and filtering of fluids through porous materials It is described by Darcy s law Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation Fig 1 In coffee percolation soluble compounds leave the coffee grounds and join the water to form coffee Insoluble compounds and granulates remain within the coffee filter Fig 2 Percolation in a square lattice Click to animate Contents 1 Background 2 Examples 3 See also 4 References 5 Further readingBackground EditDuring the last decades percolation theory the mathematical study of percolation has brought new understanding and techniques to a broad range of topics in physics materials science complex networks epidemiology and other fields For example in geology percolation refers to filtration of water through soil and permeable rocks The water flows to recharge the groundwater in the water table and aquifers In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of water a percolation test is needed beforehand to determine whether the intended structure is likely to succeed or fail In two dimensional square lattice percolation is defined as follows A site is occupied with probability p or empty in which case its edges are removed with probability 1 p the corresponding problem is called site percolation see Fig 2 Percolation typically exhibits universality Statistical physics concepts such as scaling theory renormalization phase transition critical phenomena and fractals are used to characterize percolation properties Combinatorics is commonly employed to study percolation thresholds Due to the complexity involved in obtaining exact results from analytical models of percolation computer simulations are typically used The current fastest algorithm for percolation was published in 2000 by Mark Newman and Robert Ziff 1 Examples EditCoffee percolation see Fig 1 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 Cracking of trees with the presence of two conditions sunlight and pressure Collapse and robustness of biological virus shells to random subunit removal experimentally verified fragmentation of viruses 2 3 4 Transport in porous media Spread of diseases 5 6 Surface roughening citation needed Dental percolation increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus Potential sites for septic systems are tested by the perc test Example theory A hole usually 6 10 inches in diameter is dug in the ground surface usually 12 24 deep Water is filled in to the hole and the time is measured for a drop of one inch in the water surface If the water surface quickly drops as usually seen in poorly graded sands then it is a potentially good place for a septic leach field If the hydraulic conductivity of the site is low usually in clayey and loamy soils then the site is undesirable See also EditBranched polymer Conductance Critical exponents Fragmentation Gelation Giant component Groundwater recharge Immunization Network theory Percolation critical exponents Percolation theory Percolation threshold Polymerization Self organization Self organized criticality Septic tank Supercooled water Water pipe percolatorReferences Edit Newman Mark Ziff Robert 2000 Efficient Monte Carlo Algorithm and High Precision Results for Percolation Physical Review Letters 85 19 4104 4107 arXiv cond mat 0005264 Bibcode 2000PhRvL 85 4104N CiteSeerX 10 1 1 310 4632 doi 10 1103 PhysRevLett 85 4104 PMID 11056635 S2CID 747665 Brunk Nicholas E Twarock Reidun 2021 07 23 Percolation Theory Reveals Biophysical Properties of Virus like Particles ACS Nano American Chemical Society ACS 15 8 12988 12995 doi 10 1021 acsnano 1c01882 ISSN 1936 0851 PMC 8397427 PMID 34296852 Brunk Nicholas E Lee Lye Siang Glazier James A Butske William Zlotnick Adam 2018 Molecular jenga The percolation phase transition collapse in virus capsids Physical Biology 15 5 056005 Bibcode 2018PhBio 15e6005B doi 10 1088 1478 3975 aac194 PMC 6004236 PMID 29714713 Lee Lye Siang Brunk Nicholas Haywood Daniel G Keifer David Pierson Elizabeth Kondylis Panagiotis Wang Joseph Che Yen Jacobson Stephen C Jarrold Martin F Zlotnick Adam 2017 A molecular breadboard Removal and replacement of subunits in a hepatitis B virus capsid Protein Science 26 11 2170 2180 doi 10 1002 pro 3265 PMC 5654856 PMID 28795465 Grassberger Peter 1983 On the Critical Behavior of the General Epidemic Process and Dynamical Percolation Mathematical Biosciences 63 2 157 172 doi 10 1016 0025 5564 82 90036 0 Newman M E J 2002 Spread of epidemic disease on networks Physical Review E 66 1 Pt 2 016128 arXiv cond mat 0205009 Bibcode 2002PhRvE 66a6128N doi 10 1103 PhysRevE 66 016128 PMID 12241447 S2CID 15291065 Further reading EditKesten Harry What is percolation in Notices of the AMS May 2006 Sahimi Muhammad Applications of Percolation Theory Taylor amp Francis 1994 ISBN 0 7484 0075 3 cloth ISBN 0 7484 0076 1 paper Grimmett Geoffrey Percolation 2 ed Springer Verlag 1999 Stauffer Dietrich and Aharony Ammon Introduction to Percolation Theory Taylor amp Francis 1994 revised second edition ISBN 9780748402533 Kirkpatrick Scott Percolation and Conduction in Reviews of Modern Physics 45 574 1973 Rodrigues Edouard Remarkable properties of pawns on a hexboard Archived 2021 12 09 at the Wayback Machine Bollobas Bela Riordan Oliver Percolation Cambridge University Press 2006 ISBN 0521872324 Grimmett Geoffrey Percolation Springer 1999 Retrieved from https en wikipedia org w index php title Percolation amp oldid 1124811133, wikipedia, wiki, book, books, library,
