2025/10/09 by D. J. Priour, Priour, D. J.
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2510.08296
openalex publication_date 2025/10/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density ρc1 or networks of interstitial void volumes ceasing to exist above a signficantly higher threshold ρc2. In this work, we interpret these percolation transitions as, respectively, the low and high density boundaries of percolating exposed surfaces which either ensheath clusters of impermeable particles or line tunnel-like voids. Moreover, we find in the thermodynamic limit exposed surfaces are either sheaths or tunnels with a second order phase transition from the former to the latter at a density threshold ρc* intermediate between ρc1 and ρc2. We calculate critical inclusion densities with a new method which identifies exposed free surfaces in a geometrically exact manner with a computational cost scaling only linearly in the system volume. We obtain ρc1, ρc2, and ρc* for a variety of grain geometries, including each of the Platonic solids, truncated icosahedra, and structurally disordered inclusions formed from cubes subject to a random sequence of slicing planes. In the case of the latter, we find a limiting value of 5% for the critical porosity at the void percolation threshold as the number of sustained slices per cube becomes large.