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{{for|the mathematical and statistical physics term|percolation theory}}

[[File:Percolation.gif|thumb|在正方形格子中过滤(点击动画)|链接=Special:FilePath/Percolation.gif]]

[[File:Manual coffee preperation.jpg|thumb|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]].]]

在[[物理]]、[[化学]]和[[材料科学]]中， 渗流 '''Percolation'''指的是流体通过多孔材料的运动和过滤。

这是'''<font color = '#ff8000'>达西定律</font>'''所描述的。

这是'''<font color = '#ff8000'>达西定律</font>'''所描述的。

==Background背景==

==背景==

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.

在过去的几十年里，'''渗流理论Percolation theory（'''渗流的数学研究），给物理学、材料科学、'''复杂网络Percolation theory'''、'''流行病学'''和其他领域带来了新的理解和技术。例如，在'''地质学'''中，渗滤指的是水通过土壤和渗透性岩石的过滤。这些水流入地下水和蓄水层补给地下水。在计划排放大量水的渗滤池或化粪池的地方，需要事先进行渗流试验，以确定预期的结构是否可能实现。

[[组合数学]]是研究[[渗流阈值]]的常用方法。

[[组合数学]]是研究[[渗流阈值]]的常用方法。

 

* 咖啡渗滤，其中溶剂是水，渗透性物质是咖啡渣，可溶成分是使咖啡具有颜色、味道和香气的化合物。

 

* 风化运动：地表下斜坡上风化物质的运动。

* 树木的开裂有两种情况的存在，阳光和压力的影响。

 

* 生物病毒壳对随机亚基去除的崩溃和鲁棒性(实验验证了病毒的碎片和拆卸)。<ref>{{Cite journal |doi = 10.1088/1478-3975/aac194|pmid = 29714713|pmc = 6004236|title = Molecular jenga: The percolation phase transition (collapse) in virus capsids|journal = Physical Biology|volume = 15|issue = 5|pages = 056005|year = 2018|last1 = Brunk|first1 = Nicholas E.|last2 = Lee|first2 = Lye Siang|last3 = Glazier|first3 = James A.|last4 = Butske|first4 = William|last5 = Zlotnick|first5 = Adam|bibcode = 2018PhBio..15e6005B}}</ref><ref>{{Cite journal |doi = 10.1002/pro.3265|pmid = 28795465|pmc = 5654856|title = A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid|journal = Protein Science|volume = 26|issue = 11|pages = 2170–2180|year = 2017|last1 = Lee|first1 = Lye Siang|last2 = Brunk|first2 = Nicholas|last3 = Haywood|first3 = Daniel G.|last4 = Keifer|first4 = David|last5 = Pierson|first5 = Elizabeth|last6 = Kondylis|first6 = Panagiotis|last7 = Wang|first7 = Joseph Che-Yen|last8 = Jacobson|first8 = Stephen C.|last9 = Jarrold|first9 = Martin F.|last10 = Zlotnick|first10 = Adam}}</ref>

* 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.

* 网络对随机和目标攻击的鲁棒性。<ref>{{cite journal |author=R. Cohen and S. Havlin|year=2010 |title=Complex Networks: Structure, Robustness and Function |journal=Cambridge University Press}}</ref>

*咖啡渗流，

* 多孔介质中的输送。

* Movement of weathered material down on a slope under the earth's surface.

* 疫情蔓延。<ref name="ParshaniCarmi2010">{{cite journal |last1=Parshani |first1=Roni |last2=Carmi |first2=Shai |last3=Havlin |first3=Shlomo |title=Epidemic Threshold for the Susceptible-Infectious-Susceptible Model on Random Networks |journal=Physical Review Letters |volume=104 |issue=25 |pages=258701 |year=2010 |issn=0031-9007 |doi=10.1103/PhysRevLett.104.258701 |pmid=20867419 |arxiv = 0909.3811 |bibcode = 2010PhRvL.104y8701P}}</ref><ref>{{cite journal |last1=Grassberger |first1=Peter |author-link1=Peter Grassberger |title=On the Critical Behavior of the General Epidemic Process and Dynamical Percolation |journal=Mathematical Biosciences |volume=63 |issue=2 <!-- |month=April -->|pages=157–172 |year=1983 |doi=10.1016/0025-5564(82)90036-0 }}</ref>

 

* 牙齿渗漏，增加牙冠下的龋坏率，因为环境有利于链球菌突变体和乳酸菌的生长。

 

* 化粪池系统的潜在地点将通过“perk测试”进行测试。

* Collapse and robustness of biological virus shells to random subunit removal (experimentally verified fragmentation and disassembly of viruses).<ref>{{Cite journal |doi = 10.1088/1478-3975/aac194|pmid = 29714713|pmc = 6004236|title = Molecular jenga: The percolation phase transition (collapse) in virus capsids|journal = Physical Biology|volume = 15|issue = 5|pages = 056005|year = 2018|last1 = Brunk|first1 = Nicholas E.|last2 = Lee|first2 = Lye Siang|last3 = Glazier|first3 = James A.|last4 = Butske|first4 = William|last5 = Zlotnick|first5 = Adam|bibcode = 2018PhBio..15e6005B}}</ref><ref>{{Cite journal |doi = 10.1002/pro.3265|pmid = 28795465|pmc = 5654856|title = A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid|journal = Protein Science|volume = 26|issue = 11|pages = 2170–2180|year = 2017|last1 = Lee|first1 = Lye Siang|last2 = Brunk|first2 = Nicholas|last3 = Haywood|first3 = Daniel G.|last4 = Keifer|first4 = David|last5 = Pierson|first5 = Elizabeth|last6 = Kondylis|first6 = Panagiotis|last7 = Wang|first7 = Joseph Che-Yen|last8 = Jacobson|first8 = Stephen C.|last9 = Jarrold|first9 = Martin F.|last10 = Zlotnick|first10 = Adam}}</ref>

* 例子：在地面上挖一个洞(通常直径6-10英寸)(通常12-24英寸深)。把水灌进洞里，以水滴在水面上一英寸为单位测量时间。如果水面迅速下降，就像通常在分级不佳的沙子中看到的那样，那么它是一个潜在的化粪池“沥滤场”的好地方。如果场地的导流能力很低(通常是粘土和壤土)，那么这个场地是不可取的。

 

* 交通渗流。<ref>{{cite journal |author=D. Li, B. Fu, Y. Wang, G. Lu, Y. Berezin, H.E. Stanley, S. Havlin|year=2015|title=Percolation transition in dynamical traffic network with evolving critical bottlenecks|journal=PNAS|volume=112|issue=3|pages=669–72|doi=10.1073/pnas.1419185112|pmid=25552558|pmc=4311803|bibcode=2015PNAS..112..669L}}</ref>

* Robustness of networks to random and targeted attacks.<ref>{{cite journal |author=R. Cohen and S. Havlin|year=2010 |title=Complex Networks: Structure, Robustness and Function |journal=Cambridge University Press}}</ref>

 

* Transport in porous media.

 

* [[Epidemic spreading]].<ref name="ParshaniCarmi2010">{{cite journal |last1=Parshani |first1=Roni |last2=Carmi |first2=Shai |last3=Havlin |first3=Shlomo |title=Epidemic Threshold for the Susceptible-Infectious-Susceptible Model on Random Networks |journal=Physical Review Letters |volume=104 |issue=25 |pages=258701 |year=2010 |issn=0031-9007 |doi=10.1103/PhysRevLett.104.258701 |pmid=20867419 |arxiv = 0909.3811 |bibcode = 2010PhRvL.104y8701P}}</ref><ref>{{cite journal |last1=Grassberger |first1=Peter |author-link1=Peter Grassberger |title=On the Critical Behavior of the General Epidemic Process and Dynamical Percolation |journal=Mathematical Biosciences |volume=63 |issue=2 <!-- |month=April -->|pages=157–172 |year=1983 |doi=10.1016/0025-5564(82)90036-0 }}</ref>

 

* Surface roughening.{{citation needed|date=October 2014}}

 

* 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 "[[Percolation test|perk 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 "[[Septic drain field|leach field]]". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.

 

* Traffic percolation.<ref>{{cite journal |author=D. Li, B. Fu, Y. Wang, G. Lu, Y. Berezin, H.E. Stanley, S. Havlin|year=2015|title=Percolation transition in dynamical traffic network with evolving critical bottlenecks|journal=PNAS|volume=112|issue=3|pages=669–72|doi=10.1073/pnas.1419185112|pmid=25552558|pmc=4311803|bibcode=2015PNAS..112..669L}}</ref>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

==References==

==References==

{{Reflist}}

{{Reflist}}

 

==扩展阅读==

 

==Further reading扩展阅读==

* [[Harry Kesten|Kesten, Harry]]; [http://www.ams.org/notices/200605/what-is-kesten.pdf "What is percolation?"], in ''[[Notices of the AMS]]'', May 2006.

* [[Harry Kesten|Kesten, Harry]]; [http://www.ams.org/notices/200605/what-is-kesten.pdf "What is percolation?"], in ''[[Notices of the AMS]]'', May 2006.

* Sahimi, Muhammad; ''Applications of Percolation Theory'', Taylor & Francis, 1994. {{ISBN|0-7484-0075-3}} (cloth), {{ISBN|0-7484-0076-1}} (paper).

* Sahimi, Muhammad; ''Applications of Percolation Theory'', Taylor & Francis, 1994.

* [[Geoffrey Grimmett|Grimmett, Geoffrey]]; ''[http://www.statslab.cam.ac.uk/~grg/papers/perc/perc.html Percolation (2. ed).]'' Springer Verlag, 1999.

* [[Geoffrey Grimmett|Grimmett, Geoffrey]]; ''[http://www.statslab.cam.ac.uk/~grg/papers/perc/perc.html Percolation (2. ed).]'' Springer Verlag, 1999.

* Stauffer, Dietrich ; and Aharony, Ammon; ''Introduction to Percolation Theory'', Taylor & Francis, 1994, revised second edition, {{ISBN|9780748402533}}.

* Stauffer, Dietrich ; and Aharony, Ammon; ''Introduction to Percolation Theory'', Taylor & Francis, 1994, revised second edition

* Bunde, Armin; [[Shlomo Havlin|Havlin, Shlomo]] (editors); ''[http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php Fractals and Disordered Systems]'', Springer, 1996.

* Bunde, Armin; [[Shlomo Havlin|Havlin, Shlomo]] (editors); ''[http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php Fractals and Disordered Systems]'', Springer, 1996.

* Rodrigues, Edouard; [http://www.jeudhex.com Remarkable properties of pawns on a hexboard]

* Rodrigues, Edouard; [http://www.jeudhex.com Remarkable properties of pawns on a hexboard]

* Cohen, Reuven; and Havlin, Shlomo; [http://havlin.biu.ac.il/img/book2009.pdf ''Complex Networks: Structure, Robustness and Function''], Cambridge University Press, 2010, {{ISBN|978-0521841566}}.

* Cohen, Reuven; and Havlin, Shlomo; [http://havlin.biu.ac.il/img/book2009.pdf ''Complex Networks: Structure, Robustness and Function''], Cambridge University Press, 2010

 

 

 

 

 

 

 

 

 

 

[[Category:Systems theory]]

[[Category:Systems theory]]

[[Category:Combinatorics]]

[[Category:Combinatorics]]

[[分类: 组合数学]]

[[分类: 组合数学]]

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[[Category:待整理页面]]