Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses.

  title={Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses.},
  author={Salvatore Torquato and Yang Jiao},
  journal={The Journal of chemical physics},
  volume={137 7},
  • S. TorquatoY. Jiao
  • Published 18 August 2012
  • Computer Science
  • The Journal of chemical physics
In the first paper of this series [S. Torquato, J. Chem. Phys. 136, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in d-dimensional Euclidean space R(d) were obtained, including lower bounds on the percolation threshold. In the present investigation, we provide additional analytical results for certain cluster statistics, such as the concentration of k-mers and related quantities, and obtain an upper bound on the percolation threshold η(c… 

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