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題名 Dimer Coverings on the Sierpinski Gasket 作者 張書銓
Chang, Shu-Chiuan;Lung-Chi Chen
陳隆奇貢獻者 應數系 關鍵詞 Dimers;Sierpinski gasket;Entropy;Recursion relations;Exact solution 日期 2008.05 上傳時間 13-Nov-2014 17:22:02 (UTC+8) 摘要 We present the number of dimer coverings N d (n) on the Sierpinski gasket SG d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as TeX , is calculated to be ln (2)/3 exactly for SG 2. The numbers of dimers on the generalized Sierpinski gasket SG d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG 3 is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of TeX with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. 關聯 Journal of Statistical Physics, 131(4), 631-650 資料類型 article dc.contributor 應數系 en_US dc.creator (作者) 張書銓 zh_TW dc.creator (作者) Chang, Shu-Chiuan;Lung-Chi Chen en_US dc.creator (作者) 陳隆奇 zh_TW dc.date (日期) 2008.05 en_US dc.date.accessioned 13-Nov-2014 17:22:02 (UTC+8) - dc.date.available 13-Nov-2014 17:22:02 (UTC+8) - dc.date.issued (上傳時間) 13-Nov-2014 17:22:02 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/71414 - dc.description.abstract (摘要) We present the number of dimer coverings N d (n) on the Sierpinski gasket SG d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as TeX , is calculated to be ln (2)/3 exactly for SG 2. The numbers of dimers on the generalized Sierpinski gasket SG d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG 3 is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of TeX with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. en_US dc.format.extent 727891 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.relation (關聯) Journal of Statistical Physics, 131(4), 631-650 en_US dc.subject (關鍵詞) Dimers;Sierpinski gasket;Entropy;Recursion relations;Exact solution en_US dc.title (題名) Dimer Coverings on the Sierpinski Gasket en_US dc.type (資料類型) article en
