Continuum percolation of congruent overlapping polyhedral particles: Finite-size-scaling analysis and renormalization-group method

Wenxiang Xu, Zhigang Zhu, Yaqing Jiang, Yang Jiao

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number032107
JournalPhysical Review E
Volume99
Issue number3
DOIs
StatePublished - Mar 6 2019

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Continuum Percolation
renormalization group methods
Percolation Threshold
Congruent
Finite-size Scaling
Dodecahedron
Icosahedron
Renormalization Group
Overlapping
Octahedron
Triangular pyramid
continuums
scaling
Regular hexahedron
Effective Properties
Transport Properties
Correlation Length
Volume Fraction
tetrahedrons
Mechanical Properties

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 journalArticle

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