The origin of power-law emergent scaling in large binary networks |
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Authors: | DP Almond CJ BuddMA Freitag GW HuntNJ McCullen ND Smith |
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Institution: | Center for Nonlinear Mechanics, University of Bath, BA2 7AY, UK |
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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. |
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Keywords: | Emergent scaling Complex systems Binary networks Composite materials Effective medium approximation Dielectric response Generalised eigenvalue spectrum |
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