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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2510.08296 |
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- 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 $ρ_{c1}$ or networks of interstitial void volumes ceasing to exist above a signficantly higher threshold $ρ_{c2}$. 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 $ρ_{c*}$ intermediate between $ρ_{c1}$ and $ρ_{c2}$. 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 $ρ_{c1}$, $ρ_{c2}$, and $ρ_{c*}$ 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.