“渗流”的版本间的差异

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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。
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[[文件:Manual coffee preperation.jpg|替代=|缩略图|在咖啡过滤的时候，可溶性化合物离开咖啡渣并加入水形成[[咖啡]]。不溶性化合物(和颗粒)留在咖啡过滤器中。]]
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[[文件:Percolation.gif|替代=|缩略图|网格中的渗流。]]
  
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{{for|the mathematical and statistical physics term|percolation theory}}
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[[File:Percolation.gif|thumb|在正方形格子中过滤(点击动画)|链接=Special:FilePath/Percolation.gif]]
  
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[[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]].]]
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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。
  
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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.]]
 
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在咖啡过滤中，可溶性化合物离开咖啡渣并加入水形成[[咖啡]]。不溶性化合物(和颗粒)留在咖啡过滤器中。]
 
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[[File:Percolation.gif|thumb|Percolation in a square lattice (Click to animate)]]
 
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Percolation in a square lattice (Click to animate)
 
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[[File:Percolation.gif|thumb|在正方形格子中过滤(点击动画)]]
 
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In [[physics]], [[chemistry]] and [[materials science]], '''percolation''' (from [[Latin]] ''percōlāre'', "to filter" or "trickle through") refers to the movement and [[filtration|filtering]] of fluids through porous materials.
 
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In physics, chemistry and materials science, percolation (from Latin percōlāre, "to filter" or "trickle through") refers to the movement and filtering of fluids through porous materials.
 
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在[[物理]]、[[化学]]和[[材料科学]]中， '''percolation ''' (从[[拉丁语]] ''percōlāre''，“ to filter过滤”或“ trickle through缓缓流过”)指的是流体通过多孔材料的运动和过滤。
 
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It is described by [[Darcy's law]].
 
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It is described by Darcy's law.
 
  
 
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。
  
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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.
 
  
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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.
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人们已经开发出了更广泛的可以描述以格子或图形为模型系统的连通性的应用，将其类比于过滤问题中渗流能力的调节。
  
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人们已经开发出了更广泛的应用，这些应用覆盖了许多以格子或图形为模型系统的连通性，类似于过滤问题中调节渗流能力的格子组件的连通性。
 
  
  
  
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==Background背景==
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==背景==
  
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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 network]]s, [[epidemiology]], and other fields. For example, in [[geology]], percolation refers to filtration of water through soil and permeable rocks. The water flows to [[groundwater recharge|recharge]] the [[groundwater]] in the [[water table]] and [[aquifer]]s. In places where [[infiltration basin]]s or [[septic drain field]]s 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.
 
  
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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.
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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。
  
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在过去的几十年里，'''<font color = '#ff8000'>渗流理论Percolation theory</font>'''，渗流的数学研究，给物理学、材料科学、'''<font color = '#ff8000'>复杂网络Percolation theory</font>'''、'''<font color = '#ff8000'>流行病学</font>'''和其他领域带来了新的理解和技术。例如，在'''<font color = '#ff8000'>地质学</font>'''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。
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渗流作用具有典型的普遍性。[[统计物理概念]]中，如[[标度理论]]，[[重整化]]，[[相变]]，[[临界现象]]和[[分形]]这些词语用于描述渗流特性。渗流是水在重力作用下，通过孔隙和土壤中的其他空间向下运动的描述。
  
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Percolation typically exhibits [[universality (dynamical systems)|universality]]. [[Statistical physics]] concepts such as scaling theory, [[renormalization]], [[phase transition]], [[critical phenomena]] and [[fractal]]s are used to characterize percolation properties. Percolation is the downward movement of water through pores and other spaces in the soil due to gravity.
 
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Percolation typically exhibits universality. Statistical physics concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties. Percolation is the downward movement of water through pores and other spaces in the soil due to gravity.
 
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渗流作用具有典型的普遍性。[[统计物理概念]]中，如[[标度理论]]，[[重整化]]，[[相变]]，[[临界现象]]和[[分形]]这些词语用于描述渗流特性。渗透是在重力作用下，水通过孔隙和土壤中的其他空间向下运动。
 
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[[Combinatorics]] is commonly employed to study [[percolation threshold]]s.
 
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Combinatorics is commonly employed to study percolation thresholds.
 
  
 
[[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。
  
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由于从渗流分析模型获得精确结果非常复杂，人们通常使用计算机来进行模拟。目前最快的渗流算法是由[[马克 · 纽曼|马克 · 纽曼Mark Newman]]和[[罗伯特 · 齐夫|罗伯特 · 齐夫Robert Ziff]]在2000年发表的。<ref name="newman">{{cite journal |last=Newman |first=Mark |author-link=Mark Newman |last2=Ziff |first2=Robert |title=Efficient Monte Carlo Algorithm and High-Precision Results for Percolation |journal=[[Physical Review Letters]] |volume=85 |issue=19 |pages=4104–4107 |year=2000 |doi=10.1103/PhysRevLett.85.4104 |pmid=11056635 |arxiv=cond-mat/0005264 |bibcode=2000PhRvL..85.4104N |citeseerx=10.1.1.310.4632 }}</ref>
  
  
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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.<ref name="newman">{{cite journal |last=Newman |first=Mark |author-link=Mark Newman |last2=Ziff |first2=Robert |title=Efficient Monte Carlo Algorithm and High-Precision Results for Percolation |journal=[[Physical Review Letters]] |volume=85 |issue=19 |pages=4104–4107 |year=2000 |doi=10.1103/PhysRevLett.85.4104 |pmid=11056635 |arxiv=cond-mat/0005264 |bibcode=2000PhRvL..85.4104N |citeseerx=10.1.1.310.4632 }}</ref>
 
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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.
 
  
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由于从渗流分析模型获得精确结果所涉及的复杂性，人们通常使用计算机来进行模拟。目前最快的逾渗算法是由[[马克 · 纽曼]]和[[罗伯特 · 齐夫]]在2000年发表的。<ref name="newman">{{cite journal |last=Newman |first=Mark |author-link=Mark Newman |last2=Ziff |first2=Robert |title=Efficient Monte Carlo Algorithm and High-Precision Results for Percolation |journal=[[Physical Review Letters]] |volume=85 |issue=19 |pages=4104–4107 |year=2000 |doi=10.1103/PhysRevLett.85.4104 |pmid=11056635 |arxiv=cond-mat/0005264 |bibcode=2000PhRvL..85.4104N |citeseerx=10.1.1.310.4632 }}</ref>
 
  
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==实例==
  
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* 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。
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* 风化运动：地表下斜坡上风化物质的运动。
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==Examples实例==
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* 树木的开裂有两种情况的存在，阳光和压力的影响。
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* 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>
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* 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.
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* 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>
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*咖啡渗流，
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* 多孔介质中的输送。
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* Movement of weathered material down on a slope under the earth's surface.
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* 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>
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* 表面粗化。
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* Cracking of trees with the presence of two conditions, sunlight and under the influence of pressure.
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* 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。
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* 化粪池系统的潜在地点将通过“perk测试”进行测试。
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* 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>
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* 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。
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* 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>
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* 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>
 
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* Transport in porous media.
 
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* [[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>
 
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* Surface roughening.{{citation needed|date=October 2014}}
 
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* Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
 
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* 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.
 
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* 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>
 
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==See also参见==
 
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{{colbegin|colwidth=18em}}
 
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* [[Branched polymer]]
 
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* [[Conductance (graph)|Conductance]]
 
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* [[Critical exponents]]
 
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* [[Fragmentation (chemistry)|Fragmentation]]
 
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* [[Gelation]]
 
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* [[Groundwater recharge]]
 
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* [[Immunization]]
 
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* [[Network theory]]
 
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* [[Percolation critical exponents]]
 
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* [[Percolation theory]]
 
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* [[Percolation threshold]]
 
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* [[Polymerization]]
 
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* [[Self-organization]]
 
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* [[Self-organized criticality]]
 
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* [[Septic tank]]
 
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* [[Supercooled water]]
 
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* [[Water pipe percolator]]
 
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{{colend}}
 
  
 
==References==
 
==References==
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{{Reflist}}
 
{{Reflist}}
  
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==扩展阅读==
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==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.
  
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* Sahimi, Muhammad; ''Applications of Percolation Theory'', Taylor & Francis, 1994. {{ISBN|0-7484-0075-3}} (cloth), {{ISBN|0-7484-0076-1}} (paper).
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* 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.
  
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* Stauffer, Dietrich ; and Aharony, Ammon; ''Introduction to Percolation Theory'', Taylor & Francis, 1994, revised second edition, {{ISBN|9780748402533}}.
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* 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.
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* 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]
  
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* 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}}.
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* Cohen, Reuven; and Havlin, Shlomo; [http://havlin.biu.ac.il/img/book2009.pdf ''Complex Networks: Structure, Robustness and Function''], Cambridge University Press, 2010
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* [[Béla Bollobás|Bollobás, Béla]]; [[Oliver Riordan|Riordan, Oliver]]; ''Percolation'', Cambridge University Press, 2006, {{ISBN|0521872324}}.
 
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* Grimmett, Geoffrey; ''Percolation'', Springer, 1999
 
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==External links外部链接==
 
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*[http://havlin.biu.ac.il/course3.php Introduction to Percolation Theory: short course by Shlomo Havlin]
 
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{{Authority control}}
 
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* [http://havlin.biu.ac.il/course3.php Introduction to Percolation Theory: short course by Shlomo Havlin]
  
 
[[Category:Systems theory]]
 
[[Category:Systems theory]]
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Category:Systems theory
 
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[[范畴: 系统论]]
 
  
 
[[Category:Combinatorics]]
 
[[Category:Combinatorics]]
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Category:Combinatorics
 
  
 
[[分类: 组合数学]]
 
[[分类: 组合数学]]
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<noinclude>
 
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<small>This page was moved from [[wikipedia:en:Percolation]]. Its edit history can be viewed at [[渗流/edithistory]]</small></noinclude>
 
  
 
[[Category:待整理页面]]
 
[[Category:待整理页面]]

2022年4月22日 (五) 22:26的版本

在咖啡过滤的时候，可溶性化合物离开咖啡渣并加入水形成咖啡。不溶性化合物(和颗粒)留在咖啡过滤器中。
网格中的渗流。
在正方形格子中过滤(点击动画)

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。


这是达西定律所描述的。


人们已经开发出了更广泛的可以描述以格子或图形为模型系统的连通性的应用，将其类比于过滤问题中渗流能力的调节。



背景

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。

渗流作用具有典型的普遍性。统计物理概念中，如标度理论，重整化，相变，临界现象和分形这些词语用于描述渗流特性。渗流是水在重力作用下，通过孔隙和土壤中的其他空间向下运动的描述。


组合数学是研究渗流阈值的常用方法。

由于从渗流分析模型获得精确结果非常复杂，人们通常使用计算机来进行模拟。目前最快的渗流算法是由马克 · 纽曼Mark Newman和罗伯特 · 齐夫Robert Ziff在2000年发表的。[1]



实例

  • 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)。[2][3]
  • 网络对随机和目标攻击的鲁棒性。[4]
  • 多孔介质中的输送。
  • 疫情蔓延。[5][6]
  • 表面粗化。
  • 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。
  • 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。[7]

References

  1. ↑ 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.
  2. ↑ 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.
  3. ↑ 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.
  4. ↑ R. Cohen and S. Havlin (2010). "Complex Networks: Structure, Robustness and Function". Cambridge University Press.
  5. ↑ Parshani, Roni; Carmi, Shai; Havlin, Shlomo (2010). "Epidemic Threshold for the Susceptible-Infectious-Susceptible Model on Random Networks". Physical Review Letters. 104 (25): 258701. arXiv:0909.3811. Bibcode:2010PhRvL.104y8701P. doi:10.1103/PhysRevLett.104.258701. ISSN 0031-9007. PMID 20867419.
  6. ↑ 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.
  7. ↑ D. Li, B. Fu, Y. Wang, G. Lu, Y. Berezin, H.E. Stanley, S. Havlin (2015). "Percolation transition in dynamical traffic network with evolving critical bottlenecks". PNAS. 112 (3): 669–72. Bibcode:2015PNAS..112..669L. doi:10.1073/pnas.1419185112. PMC 4311803. PMID 25552558.{{cite journal}}: CS1 maint: multiple names: authors list (link)

扩展阅读

  • Sahimi, Muhammad; Applications of Percolation Theory, Taylor & Francis, 1994.
  • Stauffer, Dietrich ; and Aharony, Ammon; Introduction to Percolation Theory, Taylor & Francis, 1994, revised second edition
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