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.
Physica A Statistical Mechanics and its Applications
- Pub Date:
- February 2013
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Materials Science;
- Mathematical Physics;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems