The origin of power-law emergent scaling in large binary networks
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.
Year of publication: |
2013
|
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Authors: | Almond, D.P. ; Budd, C.J. ; Freitag, M.A. ; Hunt, G.W. ; McCullen, N.J. ; Smith, N.D. |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 392.2013, 4, p. 1004-1027
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Publisher: |
Elsevier |
Subject: | Emergent scaling | Complex systems | Binary networks | Composite materials | Effective medium approximation | Dielectric response | Generalised eigenvalue spectrum |
Saved in:
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