Abstract
The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction φc or the critical reduced number density ηc), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that φc (or ηc) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.
| Original language | English (US) |
|---|---|
| Article number | 032107 |
| Journal | Physical Review E |
| Volume | 99 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 6 2019 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics
Cite this
Continuum percolation of congruent overlapping polyhedral particles : Finite-size-scaling analysis and renormalization-group method. / Xu, Wenxiang; Zhu, Zhigang; Jiang, Yaqing; Jiao, Yang.
In: Physical Review E, Vol. 99, No. 3, 032107, 06.03.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Continuum percolation of congruent overlapping polyhedral particles
T2 - Finite-size-scaling analysis and renormalization-group method
AU - Xu, Wenxiang
AU - Zhu, Zhigang
AU - Jiang, Yaqing
AU - Jiao, Yang
PY - 2019/3/6
Y1 - 2019/3/6
N2 - The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction φc or the critical reduced number density ηc), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that φc (or ηc) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.
AB - The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction φc or the critical reduced number density ηc), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that φc (or ηc) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.
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U2 - 10.1103/PhysRevE.99.032107
DO - 10.1103/PhysRevE.99.032107
M3 - Article
VL - 99
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 3
M1 - 032107
ER -