The origin of power-law emergent scaling in large binary networks

D. P. Almond, C. J. Budd, M. A. Freitag, G. W. Hunt, N. J. McCullen, N. D. Smith

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We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.
Original languageEnglish
Pages (from-to)1004-1027
JournalPhysica A: Statistical Mechanics and its Applications
Issue number4
Early online date2 Nov 2012
Publication statusPublished - 15 Feb 2013


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