The Origin of Power-Law Emergent Scaling in Large Binary Networks

Details The Origin of Power-Law Emergent Scaling in Large Binary Networks The Origin of Power-Law Emergent Scaling in Large Binary Networks

2012-04-25

arxiv.org/abs/1204.5601v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

In this paper 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.

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