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題名 | Universal Scaling Functions for Percolation Models=展透模型之普適尺度函數 |
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作者 | 胡進錕; Hu, Chin-kun; |
期刊 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
出版日期 | 19990500 |
卷期 | 23:3 1999.05[民88.05] |
頁次 | 頁331-347 |
分類號 | 331.5 |
語文 | eng |
關鍵詞 | 展透模型; 普適尺度函數; Percolation; Critical phenomena; Finite-size scaling; Universality; |
中文摘要 | 許多數學、物理及生命科學的問題可用展透模型描述。本論文回顧筆者及合作者 近年來在展透模型普適量及普適尺度函數所作成的研究。我們研究的量包括存在或然率E□、 展透或然率P、出現n個展透集團的機率W□等。本論文評述的主題包括: (1)系統的邊界條件和寬高比與尺度函數的關係。 (2)晶格展透模型E□和P的普適尺度函數。 (3)晶格展透模型W□的普適尺度函數。 (4)連續展透模型E□和W□的普適尺度函數。 (5)q狀態相關展透模型之普適尺度函數。 (6)邊界條件與平均展透數。 本論文最後提及一些相關的發展及值得進一步研究的問題。 |
英文摘要 | Many problems in mathematics, physical sciences, and life sciences can be described by percolation models. In this paper, we review our recent work in universal quantities and universal finite-size scaling functions (UFSSF's) of percolatin models. The quantities we consider include the existence probability (also called the spanning probability), E□, the percolation probability, P, and the probability of the appearance of n percolating clusters, W□. The topics under discussion include: (1) boundary conditions, aspect ratios, and finite-size scaling functions; (2) UFSSF's of E□ and P in lattice percolation models; (3) UFSSF's of W□ in lattice percolation models; (4) UFSSF's of E□ and W□ in continuum percolation models; (5) UFSSF's of the q-state bond-correlated percolation model and q-state Potts model without nonuniversal metric factors; and (6) boundary conditions and the average number of percolating clusters. Some other related developments and problems for further research are also discussed. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。