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Related Experiment Videos

Continuum percolation for randomly oriented soft-core prisms.

Martin O Saar1, Michael Manga

  • 1Department of Earth and Planetary Science, University of California Berkeley, Berkeley, California 94720, USA. saar@seismo.berkeley.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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This study explores continuum percolation in 3D randomly oriented soft-core prisms, finding critical excluded volumes agree with other shapes for high anisotropies. Cubes, with minimal anisotropy, yield maximum values close to spheres.

Area of Science:

  • Statistical Physics
  • Materials Science
  • Computational Modeling

Background:

  • Continuum percolation describes the formation of connected clusters in systems of overlapping objects.
  • Understanding percolation thresholds is crucial for predicting material properties and phase transitions.
  • Previous studies focused on simpler shapes like spheres and ellipsoids, leaving complex polyhedra less explored.

Purpose of the Study:

  • To investigate continuum percolation phenomena in three-dimensional randomly oriented soft-core polyhedra (prisms).
  • To compare percolation behavior of prisms with other shapes (ellipsoids, rods, etc.) across a wide range of aspect ratios.
  • To analyze the influence of shape anisotropy and orientation on percolation thresholds and critical volume fractions.

Main Methods:

Related Experiment Videos

  • Utilized computational simulations to model continuum percolation of randomly oriented soft-core prisms.
  • Varied prism aspect ratios over six orders of magnitude, encompassing biaxial and triaxial forms.
  • Calculated critical total average excluded volume (n(c)) and critical object volume fraction (phi(c)).

Main Results:

  • For high shape anisotropies, prisms exhibit critical total average excluded volumes (n(c)) comparable to ellipsoids and rods.
  • Cubes, representing minimal shape anisotropy, yield the highest prism percolation values (n(c) ≈ 2.79, phi(c) ≈ 0.22), approaching sphere values.
  • Critical volume fraction (phi(c)) decreases with increasing aspect ratio for prisms and shows convergence with ellipsoids at extreme anisotropies.

Conclusions:

  • The average excluded volume () is a key concept explaining percolation differences between various shapes.
  • Shape anisotropy significantly impacts percolation thresholds, with near-equant shapes like cubes and spheres showing higher critical volume fractions.
  • The relationship B(c)=n(c)=2C(c) is confirmed for prisms, linking percolation to network connectivity.