Strong dependence of percolation thresholds on polydispersity

@article{Mecke2002StrongDO,
  title={Strong dependence of percolation thresholds on polydispersity},
  author={K. R. Mecke and A. Seyfried},
  journal={EPL (Europhysics Letters)},
  year={2002},
  volume={58},
  pages={28 - 34}
}
Monte Carlo simulations for a large family of discretized Boolean models exhibit complex dependencies of the percolation threshold not only on shape and correlations but also on the polydispersity of the constituents (pores). A pronounced peak of the critical volume fraction as a function of the density fraction is found for large-size ratios of the pores. Such an increase of more than 10% even for small changes in composition of less than 1% is important in material science, where the accurate… 

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References

SHOWING 1-3 OF 3 REFERENCES

Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics

The aim of this paper is to point out the importance of geometric functionals in statistical physics. Integral geometry furnishes a suitable family of morphological descriptors, known as Minkowski

Do interactions raise or lower a percolation threshold?

Une etude par methode Monte Carlo dans le cas de particules spheriques, montre qu'une plus forte force d'interaction peut soit augmenter, soit diminuer la fraction volumique necessaire a la

Computer Simulation and Percolation Theory Applied to Concrete