38:
54:
235:". 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 "
153:
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
97:. 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.
192:
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
206:
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
548:
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).
110:
754:
724:
716:
158:
216:
Collapse and robustness of biological virus shells to random subunit removal (experimentally-verified fragmentation of viruses).
228:
Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
800:
295:
239:". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.
320:
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113:, has brought new understanding and techniques to a broad range of topics in physics, materials science,
335:
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359:; Ziff, Robert (2000). "Efficient Monte Carlo Algorithm and High-Precision Results for Percolation".
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125:, percolation refers to filtration of water through soil and permeable rocks. The water flows to
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Brunk, Nicholas E.; Lee, Lye Siang; Glazier, James A.; Butske, William; Zlotnick, Adam (2018).
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600:(1983). "On the Critical Behavior of the General Epidemic Process and Dynamical Percolation".
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In coffee percolation, soluble compounds leave the coffee grounds and join the water to form
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493:"Molecular jenga: The percolation phase transition (collapse) in virus capsids"
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Cracking of trees with the presence of two conditions, sunlight and pressure.
450:
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477:
434:"Percolation Theory Reveals Biophysical Properties of Virus-like Particles"
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Movement of weathered material down on a slope under the earth's surface.
53:
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62:
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42:
627:
Newman, M. E. J. (2002). "Spread of epidemic disease on networks".
52:
36:
89: 'to filter, trickle through') refers to the movement and
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are planned to dispose of substantial amounts of water, a
772:
45:. Insoluble compounds (and granulates) remain within the
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of fluids through porous materials. It is described by
30:
For the mathematical and statistical physics term, see
749:, Taylor & Francis, 1994, revised second edition,
231:
Potential sites for septic systems are tested by the "
444:(8). American Chemical Society (ACS): 12988–12995.
432:Brunk, Nicholas E.; Twarock, Reidun (2021-07-23).
181:are used to characterize percolation properties.
154:problem is called site percolation, see Fig. 2.
27:Filtration of fluids through porous materials
8:
773:Remarkable properties of pawns on a hexboard
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795:, Cambridge University Press, 2006,
121:, and other fields. For example, in
747:Introduction to Percolation Theory
709:Applications of Percolation Theory
25:
165:concepts such as scaling theory,
57:Percolation in a square lattice.
157:Percolation typically exhibits
711:, Taylor & Francis, 1994.
296:Percolation critical exponents
185:is commonly employed to study
1:
762:"Percolation and Conduction"
614:10.1016/0025-5564(82)90036-0
109:, the mathematical study of
403:10.1103/PhysRevLett.85.4104
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659:10.1103/PhysRevE.66.016128
321:Self-organized criticality
219:Transport in porous media.
29:
766:Reviews of Modern Physics
105:During the last decades,
602:Mathematical Biosciences
517:10.1088/1478-3975/aac194
451:10.1021/acsnano.1c01882
362:Physical Review Letters
745:; and Aharony, Ammon;
739:Springer Verlag, 1999.
696:"What is percolation?"
187:percolation thresholds
83:
58:
50:
336:Water pipe percolator
306:Percolation threshold
56:
40:
806:Grimmett, Geoffrey;
771:Rodrigues, Edouard;
760:Kirkpatrick, Scott;
736:Percolation (2. ed).
281:Groundwater recharge
651:2002PhRvE..66a6128N
509:2018PhBio..15e6005B
385:2000PhRvL..85.4104N
225:Surface roughening.
222:Spread of diseases.
163:Statistical physics
147:septic drain fields
143:infiltration basins
778:2021-12-09 at the
743:Stauffer, Dietrich
731:Grimmett, Geoffrey
707:Sahimi, Muhammad;
701:Notices of the AMS
635:(1 Pt 2): 016128.
598:Grassberger, Peter
301:Percolation theory
261:Critical exponents
175:critical phenomena
141:. In places where
107:percolation theory
59:
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32:percolation theory
629:Physical Review E
560:(11): 2170–2180.
369:(19): 4104–4107.
331:Supercooled water
316:Self-organization
197:and Robert Ziff.
71:materials science
16:(Redirected from
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357:Newman, Mark
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286:Immunization
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159:universality
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119:epidemiology
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808:Percolation
793:Percolation
704:, May 2006.
326:Septic tank
256:Conductance
237:leach field
195:Mark Newman
135:water table
131:groundwater
111:percolation
95:Darcy's law
75:percolation
18:Percolating
818:Categories
801:0521872324
343:References
101:Background
77:(from
719:(cloth),
460:1936-0851
389:CiteSeerX
233:perc test
91:filtering
85:percolare
67:chemistry
776:Archived
727:(paper).
675:15291065
667:12241447
584:28795465
535:29714713
478:34296852
438:ACS Nano
411:11056635
271:Gelation
244:See also
201:Examples
179:fractals
139:aquifers
127:recharge
647:Bibcode
575:5654856
526:6004236
505:Bibcode
469:8397427
381:Bibcode
133:in the
123:geology
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671:S2CID
637:arXiv
415:S2CID
371:arXiv
81:
79:Latin
797:ISBN
751:ISBN
721:ISBN
713:ISBN
663:PMID
580:PMID
531:PMID
474:PMID
456:ISSN
407:PMID
177:and
137:and
129:the
655:doi
610:doi
570:PMC
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