Cluster, backbone and elastic backbone structures of the multiple invasion percolation

We study the cluster, the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. We investigate the behavior of the mass, the number of red sites (i. e., sites through which all the current passes) and loops of those structures. Their corresponding scaling exponents are also estimated. By construction, the mass of the optimized model scales exactly with the gyration radius of the cluster - we verify that this also happens to the backbone. Our simulation shows that the red sites almost disappear, indicating that the cluster has achieved a high degree of connectivity.