Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (4): 521-527.
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(Beijing Normal University Press, Beijing 100875)
Online:
Published:
Abstract:
This paper will study the percolation model on one kind of lattice fractals(lattice nested fractals), prove that there is no critical phenomenon for this percolation model and give one law of exponent decay. Moreover, it will prove that there is no critical phenomenon for bond percolation model on finite branched graph.
Key words: Lattice nested fractals, Percolation, Critical phenomenon, Law of exponent decay, Finite branched graph
CLC Number:
Lu Jiansheng. Percolation Model on Lattice Nested Fractals[J].Acta mathematica scientia,Series A, 2000, 20(4): 521-527.
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http://121.43.60.238/sxwlxbA/EN/Y2000/V20/I4/521
1.Ｃｈｅｎ Ｍｕｆａ．Ｆｒｏｍ Ｍａｒｋｏｖｃｈａｉｎｓｔｏｎｏｎｅｑｕｉｌｉｂｒｉｕｍｐａｒｔｉｃｌｅｓｙｓｔｅｍｓ．Ｓｉｎｇａｐｏｒｅ：ＷｏｒｌｄＳｃｉｅｎｔｉｆｉｃ，１９９２ ２ ＤｕｒｒｅｔｔＲＴ．Ｌｅｃｔｕｒｅｎｏｔｅｓｏｎｐａｒｔｉｃｌｅｓｙｓｔｅｍｓａｎｄｐｅｒｃｏｌａｔｉｏｎ．ＷａｄｓｗｏｒｔｈａｎｄＢｒｏｏｋｓ／Ｃｏｌｅ，ＰａｃｉｆｉｃＧｒｏｖｅ，Ｃａｌｉｆｏｒｎｉａ．１９８８ ３ ＤｕｒｒｅｔｔＲ Ｔ．Ｔｅｎｌｅｃｔｕｒｅｓｏｎｐａｒｔｉｃｌｅｓｙｓｔｅｍｓ．ＬｅｃｔｕｒｅＮｏｔｅｓｉｎ Ｍａｔｈｅｍａｔｉｃｓ，１９９５，１６０８：９７－２０１ ４ ＥｓｓａｍＪＷ，ＦｉｓｈｅｒＭ Ｅ．Ｓｏｍｅｃｌｕｓｔｅｒｓｉｚｅａｎｄｐｅｒｃｏｌａｔｉｏｎｐｒｏｂｌｅｍｓ．ＪｏｕｒｎａｌｏｆＭａｔｈｅｍａｔｉｃａｌＰｈｙｓｉｃｓ，１９６１（２）：６０９－６１９ ５ ＦｉｓｈｅｒＭ Ｅ．Ｃｒｉｔｉｃａｌｐｒｏｂａｂｉｌｉｔｉｅｓｆｏｒｃｌｕｓｔｅｒｓｉｚｅａｎｄｐｅｒｃｏｌａｔｉｏｎｐｒｏｂｌｅｍｓ．ＪｏｕｒｎａｌｏｆＭａｔｈｅｍａｔｉｃａｌＰｈｙｓｉｃｓ，１９６１，（２）：６２０－６２７ ６ Ｈｕｔｃｈｉｎｓｏｎ．Ｆｒａｃｔａｌｓａｎｄｓｅｌｆｓｉｍｉｌａｒｉｔｙ．ＩｎｄｉａｎａＵｎｉｖｅｒｓｉｔｙ ＭａｔｈＪ，１９８１，３０：７１３－７４７ ７ ＫｕｓｕｏｋａＳ．Ｄｉｆｆｕｓｉｏｎｐｒｏｃｅｓｓｅｓｏｎｎｅｓｔｅｄｆｒａｃｔａｌｓ．ＬｅｃｔｕｒｅＮｏｔｅｓｉｎ Ｍａｔｈｅｍａｔｉｃｓ，１９９２，３９－９８ ８ Ｌｉｎｄｓｔｒｍ Ｔ．Ｂｒｏｗｎｉａｎｍｏｔｉｏｎｏｎｎｅｓｔｅｄｆｒａｃｔａｌｓ．Ｍｅｍ ＡｍｅｒＭａｔｈＳｏｃ，１９９０，４２０ ９ 吕建生．ＳｉｅｒｐｉｎｓｋｉＣａｒｐｅｔ格点图上的渗流模型及其临界现象．数学学报，１９９９，４２（３）：５４５－５５０ １０ 吕建生．ＳｉｅｒｐｉｎｓｋｉＧａｓｋｅｔ格点图上的渗流模型．数学进展，１９９９，２８（６）：５１９－５２６
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