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.
|Journal||Physica A: Statistical Mechanics and its Applications|
|Early online date||2 Nov 2012|
|Publication status||Published - 15 Feb 2013|
Almond, D. P., Budd, C. J., Freitag, M. A., Hunt, G. W., McCullen, N. J., & Smith, N. D. (2013). The origin of power-law emergent scaling in large binary networks. Physica A: Statistical Mechanics and its Applications, 392(4), 1004-1027. https://doi.org/10.1016/j.physa.2012.10.035