Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/71420
DC Field | Value | Language |
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dc.contributor | 應數系 | en_US |
dc.creator | 陳隆奇 | zh_TW |
dc.creator | Chen, Lung-Chi | en_US |
dc.date | 2011.03 | en_US |
dc.date.accessioned | 2014-11-13T09:23:25Z | - |
dc.date.available | 2014-11-13T09:23:25Z | - |
dc.date.issued | 2014-11-13T09:23:25Z | - |
dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/71420 | - |
dc.description.abstract | We consider a version of directed bond percolation on a square lattice whose vertical edges are directed upward with probabilities pvpv and horizontal edges are directed rightward with probabilities phph and 1 in alternate rows. Let τ(M,N)τ(M,N) be the probability that there is a connected directed path of occupied edges from (0,0)(0,0) to (M,N)(M,N). For each View the MathML sourceph∈[0,1],pv=(0,1) and aspect ratio α=M/Nα=M/N fixed, it was established (Chen and Wu, 2006) [9] that there is an View the MathML sourceαc=[1−pv2−ph(1−pv)2]/2pv2 such that, as N→∞N→∞, τ(M,N)τ(M,N) is 11, 00, and 1/21/2 for α>αcα>αc, α<αcα<αc, and α=αcα=αc, respectively. In particular, for ph=0ph=0 or 11, the model reduces to the Domany–Kinzel model (Domany and Kinzel, 1981 [7]). In this article, we investigate the rate of convergence of τ(M,N)τ(M,N) and the asymptotic behavior of View the MathML sourceτ(Mn−,N) and View the MathML sourceτ(Mn+,N), where View the MathML sourceMn−/N↑αc and View the MathML sourceMn+/N↓αc as N↑∞N↑∞. Moreover, we obtain a susceptibility on the rectangular net {(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}{(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}. The proof is based on the Berry–Esseen theorem. | en_US |
dc.format.extent | 295316 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | en_US | - |
dc.relation | Physica A, 390(3), 419-426 | en_US |
dc.subject | Domany–Kinzel model;Directed percolation;Compact directed percolation;Asymptotic behavior;Critical behavior;Susceptibility;Exact solutions;Berry–Esseen theorem | en_US |
dc.title | Asymptotic Behavior for a Version of Directed Percolation on the Square Lattice | en_US |
dc.type | article | en |
dc.identifier.doi | 10.1016/j.physa.2010.09.039 | - |
dc.doi.uri | http://dx.doi.org/10.1016/j.physa.2010.09.039 | - |
item.fulltext | With Fulltext | - |
item.languageiso639-1 | en_US | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.grantfulltext | restricted | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | 期刊論文 |
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File | Description | Size | Format | |
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419-426.pdf | 288.39 kB | Adobe PDF2 | View/Open |
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