Random sequential adsorption: Difference between revisions
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[[File:Random Sequential Adsorption Disks1.png|thumb|200px|Jamming in the random sequential adsorption (RSA) of circular disks.]] |
[[File:Random Sequential Adsorption Disks1.png|thumb|200px|Jamming in the random sequential adsorption (RSA) of circular disks.]] |
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The blocking process has been studied in detail in terms of the ''[[random sequential adsorption]]'' (RSA) model.<ref name=evans>J. W. Evans, Rev. Mod. Phys. 65 (1993) 1281-1329.</ref> The simplest RSA model related to deposition of spherical particles considers irreversible adsorption of circular disks. One disk after another is placed randomly at a surface. Once a disk is placed, it sticks at the same spot, and cannot be removed. When an attempt to deposit a disk would result in an overlap with an already deposited disk, this attempt is rejected. Within this model, the surface is initially filled rapidly, but the more one approaches saturation the slower the surface is being filled. Within the RSA model, saturation is referred to as jamming. For circular disks, jamming occurs at a coverage of 0.547. When the depositing particles are polydisperse, much higher surface coverage can be reached, since the small particles will be able to deposit into the holes in between the larger deposited particles. On the other hand, rod like particles may lead to much smaller coverage, since a few misaligned rods may block a large portion of the surface. |
The blocking process has been studied in detail in terms of the ''[[random sequential adsorption]]'' (RSA) model.<ref name=evans>J. W. Evans, Rev. Mod. Phys. 65 (1993) 1281-1329.</ref> The simplest RSA model related to deposition of spherical particles considers irreversible adsorption of circular disks. One disk after another is placed randomly at a surface. Once a disk is placed, it sticks at the same spot, and cannot be removed. When an attempt to deposit a disk would result in an overlap with an already deposited disk, this attempt is rejected. Within this model, the surface is initially filled rapidly, but the more one approaches saturation the slower the surface is being filled. Within the RSA model, saturation is referred to as jamming. For circular disks, jamming occurs at a coverage of 0.547. When the depositing particles are polydisperse, much higher surface coverage can be reached, since the small particles will be able to deposit into the holes in between the larger deposited particles. On the other hand, rod like particles may lead to much smaller coverage, since a few misaligned rods may block a large portion of the surface. |
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== Percolation thresholds for 2d systems == |
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{| class="wikitable" |
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|- |
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! system |
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! Saturated coverage |
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|- |
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| disks |
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| 0.5617,<ref name="Cherkasova09">{{cite journal |
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| last = Cherkasova |
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| first = V. A. |
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| authorlink = |
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|author2=Yu. Yu. Tarasevich |author3=N. I. Lebovka |author4=and N.V. Vygornitskii |
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| title = Percolation of the aligned dimers on a square lattice |
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| journal = Eur. Phys. J. B |
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| volume = 74 |
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| issue = 2 |
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| year = 2010 |
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| doi = 10.1140/epjb/e2010-00089-2 |
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| url = |
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| pages = 205–209 |bibcode = 2010EPJB...74..205C |arxiv = 0912.0778 }} |
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</ref> 0.562 <ref name="VanderwalleGalamKramer00">{{cite journal |
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| last = Vanderwalle |
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| first = N. |
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| authorlink = |
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|author2= S. Galam |
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|author3= M. Kramer |
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| title = A new universality for random sequential deposition of needles |
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| journal = Eur. Phys. J. B |
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| volume = 14 |
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| issue = 3 |
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| year = 2000 |
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| pages = 407–410 |
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| doi = 10.1007/s100510051047}} |
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</ref> |
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|- |
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|} |
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== Percolation thresholds for random sequentially adsorbed particles == |
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{| class="wikitable" |
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|- |
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! system |
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! z |
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! Site Threshold |
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|- |
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| dimers on a square lattice |
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| 4 |
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| 0.5617,<ref name="Cherkasova09">{{cite journal |
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| last = Cherkasova |
|||
| first = V. A. |
|||
| authorlink = |
|||
|author2=Yu. Yu. Tarasevich |author3=N. I. Lebovka |author4=and N.V. Vygornitskii |
|||
| title = Percolation of the aligned dimers on a square lattice |
|||
| journal = Eur. Phys. J. B |
|||
| volume = 74 |
|||
| issue = 2 |
|||
| year = 2010 |
|||
| doi = 10.1140/epjb/e2010-00089-2 |
|||
| url = |
|||
| pages = 205–209 |bibcode = 2010EPJB...74..205C |arxiv = 0912.0778 }} |
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</ref> 0.562 <ref name="VanderwalleGalamKramer00">{{cite journal |
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| last = Vanderwalle |
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| first = N. |
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| authorlink = |
|||
|author2= S. Galam |
|||
|author3= M. Kramer |
|||
| title = A new universality for random sequential deposition of needles |
|||
| journal = Eur. Phys. J. B |
|||
| volume = 14 |
|||
| issue = 3 |
|||
| year = 2000 |
|||
| pages = 407–410 |
|||
| doi = 10.1007/s100510051047}} |
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</ref> |
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|- |
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| dimers on a triangular lattice |
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| 6 |
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| 0.4872(8)<ref name="CornetteRamirezPastorNieto03">{{cite journal |
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| last = Cornette |
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| first = V. |
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| authorlink = |
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| author2= A. J. Ramirez-Pastor |author3=F. Nieto |
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| title = Dependenceofthepercolationthresholdonthe sizeofthepercolatingspecies |
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| journal = Physica A |
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| volume = 327 |
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| issue = |
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| year = 2003 |
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| doi =10.1016/S0378-4371(03)00453-9 |
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| pages = 71–75 }} |
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</ref> |
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|- |
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| dimers and 5% impurities, triangular lattice |
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| 6 |
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| 0.4832(7) <ref name="BudinskiPetkovicEtAl16">{{cite journal |
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| last = Budinski-Petkovic |
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| first = Lj |
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| authorlink = |
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|author2= I. Loncarevic | author3= Z. M. Jacsik |author4=and S. B. Vrhovac |
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| title = Jamming and percolation in random sequential adsorption of extended objects on a triangular lattice with quenched impurities |
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| journal = J. Stat. Mech.: Th. Exp. |
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| volume = 2016 |
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| issue = |
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| year = 2016 |
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| doi = 10.1088/1742-5468/2016/05/053101 |
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| pages = 053101}} |
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</ref> |
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|- |
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| linear 3-mers on a square lattice |
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| 4 |
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| 0.528<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| 3-site 120° angle, 5% impurities, triangular lattice |
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| 6 |
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| 0.4574(9)<ref name="BudinskiPetkovicEtAl16"/> |
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|- |
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| 3-site triangles, 5% impurities, triangular lattice |
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| 6 |
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| 0.5222(9)<ref name="BudinskiPetkovicEtAl16"/> |
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|- |
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| linear trimers and 5% impurities, triangular lattice |
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| 6 |
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|0.4603(8) <ref name="BudinskiPetkovicEtAl16"/> |
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|- |
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| linear 4-mers on a square lattice |
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| 4 |
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| 0.504<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| linear 5-mers on a square lattice |
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| 4 |
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| 0.490<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| linear 6-mers on a square lattice |
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| 4 |
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| 0.479<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| linear 8-mers on a square lattice |
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| 4 |
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| 0.474<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| linear 10-mers on a square lattice |
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| 4 |
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| 0.469<ref name="VanderwalleGalamKramer00"/> |
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|- |
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| parallel dimers on a square lattice |
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| 4 |
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| 0.5683<ref name="Cherkasova09"/> |
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|- |
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|} |
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The threshold gives the fraction of sites occupied by the objects when site percolation first takes place (not at full jamming). For longer dimers see Ref.<ref name="KondratPekalski">{{cite journal |
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| last =Kondrat |
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| first = Grzegorz |
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| authorlink = |
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|author2=Andrzej Pękalski |
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| title = Percolation and jamming in random sequential adsorption of linear segments on a square lattice |
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| journal = Phys. Rev. E |
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| volume = 63 |
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| issue = 5 |
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| year = 2001 |
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| pages = 051108 |
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| doi = 10.1103/PhysRevE.63.051108}} |
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</ref> |
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==See also== |
==See also== |
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*[[Adsorption]] |
*[[Adsorption]] |
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*[[Particle deposition]] |
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==References== |
==References== |
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Revision as of 23:52, 12 July 2017
Random sequential adsorption (RSA) refers to a process where particles are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb themselves and do not move for the rest of the process. RSA can be carried out in computer simulation, in a mathematical analysis, or (approximately) in an experiments. It was first studied in one-dimensional models: the attachment of pendant groups in a polymer chain by Flory, and the car-parking problem by Renyi. In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc.
An important result is the maximum surface coverage. Here we list that coverage for many systems.
The blocking process has been studied in detail in terms of the random sequential adsorption (RSA) model.[1] The simplest RSA model related to deposition of spherical particles considers irreversible adsorption of circular disks. One disk after another is placed randomly at a surface. Once a disk is placed, it sticks at the same spot, and cannot be removed. When an attempt to deposit a disk would result in an overlap with an already deposited disk, this attempt is rejected. Within this model, the surface is initially filled rapidly, but the more one approaches saturation the slower the surface is being filled. Within the RSA model, saturation is referred to as jamming. For circular disks, jamming occurs at a coverage of 0.547. When the depositing particles are polydisperse, much higher surface coverage can be reached, since the small particles will be able to deposit into the holes in between the larger deposited particles. On the other hand, rod like particles may lead to much smaller coverage, since a few misaligned rods may block a large portion of the surface.
Percolation thresholds for 2d systems
| system | Saturated coverage |
|---|---|
| disks | 0.5617,[2] 0.562 [3] |
Percolation thresholds for random sequentially adsorbed particles
| system | z | Site Threshold |
|---|---|---|
| dimers on a square lattice | 4 | 0.5617,[2] 0.562 [3] |
| dimers on a triangular lattice | 6 | 0.4872(8)[4] |
| dimers and 5% impurities, triangular lattice | 6 | 0.4832(7) [5] |
| linear 3-mers on a square lattice | 4 | 0.528[3] |
| 3-site 120° angle, 5% impurities, triangular lattice | 6 | 0.4574(9)[5] |
| 3-site triangles, 5% impurities, triangular lattice | 6 | 0.5222(9)[5] |
| linear trimers and 5% impurities, triangular lattice | 6 | 0.4603(8) [5] |
| linear 4-mers on a square lattice | 4 | 0.504[3] |
| linear 5-mers on a square lattice | 4 | 0.490[3] |
| linear 6-mers on a square lattice | 4 | 0.479[3] |
| linear 8-mers on a square lattice | 4 | 0.474[3] |
| linear 10-mers on a square lattice | 4 | 0.469[3] |
| parallel dimers on a square lattice | 4 | 0.5683[2] |
The threshold gives the fraction of sites occupied by the objects when site percolation first takes place (not at full jamming). For longer dimers see Ref.[6]
See also
References
- ^ J. W. Evans, Rev. Mod. Phys. 65 (1993) 1281-1329.
- ^ a b c Cherkasova, V. A.; Yu. Yu. Tarasevich; N. I. Lebovka; and N.V. Vygornitskii (2010). "Percolation of the aligned dimers on a square lattice". Eur. Phys. J. B. 74 (2): 205–209. arXiv:0912.0778. Bibcode:2010EPJB...74..205C. doi:10.1140/epjb/e2010-00089-2.
- ^ a b c d e f g h Vanderwalle, N.; S. Galam; M. Kramer (2000). "A new universality for random sequential deposition of needles". Eur. Phys. J. B. 14 (3): 407–410. doi:10.1007/s100510051047.
- ^ Cornette, V.; A. J. Ramirez-Pastor; F. Nieto (2003). "Dependenceofthepercolationthresholdonthe sizeofthepercolatingspecies". Physica A. 327: 71–75. doi:10.1016/S0378-4371(03)00453-9.
- ^ a b c d Budinski-Petkovic, Lj; I. Loncarevic; Z. M. Jacsik; and S. B. Vrhovac (2016). "Jamming and percolation in random sequential adsorption of extended objects on a triangular lattice with quenched impurities". J. Stat. Mech.: Th. Exp. 2016: 053101. doi:10.1088/1742-5468/2016/05/053101.
- ^ Kondrat, Grzegorz; Andrzej Pękalski (2001). "Percolation and jamming in random sequential adsorption of linear segments on a square lattice". Phys. Rev. E. 63 (5): 051108. doi:10.1103/PhysRevE.63.051108.