The origin of power-law emergent scaling in large binary networks
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 392 (2013)
Issue (Month): 4 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Emergent scaling; Complex systems; Binary networks; Composite materials; Effective medium approximation; Dielectric response; Generalised eigenvalue spectrum;
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