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 and N.D. Smith

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 4, 1004-1027

Abstract: 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.

Keywords: Emergent scaling; Complex systems; Binary networks; Composite materials; Effective medium approximation; Dielectric response; Generalised eigenvalue spectrum (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:4:p:1004-1027

DOI: 10.1016/j.physa.2012.10.035

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