Invariant percolation properties in some continuum systems

In this work we study the influence of the eccentricity on the topological and dynamic properties of 2D systems with monodispersed isotropically distributed overlapping ellipses. This type of system has been proposed in the literature as an adequate model for composites of conductive nanoparticles dispersed in insulating matrices. We extend the available information on the influence of the eccentricity on the percolation threshold and the electrical conductivity in such composites. By applying Monte Carlo simulations, we have modeled the dynamics of 2D disordered systems and found, for ellipses, an eccentricity invariant dynamic behavior that is also present in the widthless-stick limit case and in rectangles. This behavior appears upon the use of a particular definition of the normalized proximity to the percolation threshold. Our study suggests that this invariance might also arise in systems with other particle geometries having the widthless stick as a limit case. We further suggest how the presence of this invariance may facilitate the numerical and experimental understanding of conductor-insulator nanocomposites.