Fractal and Multifractal Approaches to Percolation: Some Exact and Not-So-Exact Results
DOI: 10.1007/978-1-4613-8734-3_16
关键词: Percolation 、 Multifractal system 、 Percolation theory 、 Mathematical proof 、 Calculus 、 Fractal 、 Combinatorics 、 Mathematics 、 Percolation threshold 、 Percolation critical exponents 、 Fractal dimension on networks
摘要: I feel flattered to be included in such an impressive group of talks by mathematically gifted people. The last rigorous proof that was completely “my own” 1968 (Stanley 1968a) and this is now 1986. Hence accepting Professor Kesten’s kind invitation assume my role unveil a set percolation results that—unlike those “the book” (Kesten 1981)— has not yet reached the stage proofs. Accordingly, shall focus mainly on relatively recent developments theory, some which almost certainly may amenable exact analysis.
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H. Eugene Stanley, Connectivity: A Primer in Phase Transitions and Critical Phenomena for Students of Particle Physics Springer, Boston, MA. pp. 1- 42 ,(1983) , 10.1007/978-1-4613-3509-2_1
H. E. Stanley, P. J. Reynolds, S. Redner, F. Family, Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels Real-Space Renormalization. Series: Topics in Current Physics. ,vol. 30, pp. 169- 206 ,(1982) , 10.1007/978-3-642-81825-7_7
H. Eugene STANLEY, FRACTAL CONCEPTS IN AGGREGATION AND GELATION: AN INTRODUCTION Kinetics of Aggregation and Gelation. pp. 1- 4 ,(1984) , 10.1016/B978-0-444-86912-8.50006-7
Real-space renormalization Springer Berlin Heidelberg. ,(1982) , 10.1007/978-3-642-81825-7
H. E. Stanley, A. Coniglio, W. Klein, H. Nakanishi, S. Redner, P. J. Reynolds, G. Shlifer, Critical Phenomena: Past, Present and "Future" Springer, Berlin, Heidelberg. pp. 22- 38 ,(1980) , 10.1007/978-3-642-67592-8_2
Richard Zallen, Guy Deutscher, Joan Adler, Percolation Structures and Processes ,(1983)
Nicole Ostrowsky, Harry Eugene Stanley, On growth and form : fractal and non-fractal patterns in physics ogff. ,vol. 100, ,(1986)
F. Zernike, The propagation of order in co-operative phenomena: Part I. The AB case Physica D: Nonlinear Phenomena. ,vol. 7, pp. 565- 585 ,(1940) , 10.1016/S0031-8914(40)90008-8
H. Eugene Stanley, Form: An Introduction to Self-Similarity and Fractal Behavior Springer, Dordrecht. pp. 21- 53 ,(1986) , 10.1007/978-94-009-5165-5_2
Guy Deutscher, Experimental relevance of percolation Lecture Notes in Physics. pp. 26- 40 ,(1981) , 10.1007/BFB0012541