PMID: 11909136Mar 23, 2002Paper

Nonuniversality of invasion percolation in two-dimensional systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Mark A KnackstedtAdrian P Sheppard

Abstract

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension D(f) of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, D(f) approximately equal to 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.

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Citations

Nov 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergey V BuldyrevH Eugene Stanley
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Roland Glantz, Markus Hilpert
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S B SantraJahir Abbas Ahmed
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A D AraújoJ S Andrade
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Megan E Frary, Christopher A Schuh
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A D AraújoH J Herrmann
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Quinn NorrisJohn B Rundle
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Victor E BruniniW Craig Carter

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