Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles.

@article{Torquato2012EffectOD,
  title={Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles.},
  author={Salvatore Torquato and Yang Jiao},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={87 2},
  pages={
          022111
        }
}
  • S. TorquatoY. Jiao
  • Published 29 September 2012
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study the effect of dimensionality on the percolation threshold η(c) of identical overlapping nonspherical convex hyperparticles in d-dimensional Euclidean space R(d). This is done by formulating a scaling relation for η(c) that is based on a rigorous lower bound [Torquato, J. Chem. Phys. 136, 054106 (2012)] and a conjecture that hyperspheres provide the highest threshold, for any d, among all convex hyperparticle shapes (that are not a trivial affine transformation of a hypersphere). This… 

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