The origin of powerlaw emergent scaling in large binary networks
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 powerlaw 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.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 February 2013
 DOI:
 10.1016/j.physa.2012.10.035
 arXiv:
 arXiv:1204.5601
 Bibcode:
 2013PhyA..392.1004A
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Materials Science;
 Mathematical Physics;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 doi:10.1016/j.physa.2012.10.035