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

TL;DR

This paper investigates the structural properties of clusters, backbones, and elastic backbones in multiple invasion percolation models, revealing scaling behaviors and connectivity features through simulation.

Contribution

It introduces a detailed analysis of cluster and backbone structures in optimized invasion percolation, including scaling exponents and connectivity insights.

Findings

Mass scales with gyration radius in optimized models

Red sites nearly disappear, indicating high connectivity

Backbone mass scales exactly with cluster gyration radius

Abstract

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.