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References

  1. Scher, H. and Zallen, R. (1970) Critical density in percolation processes, J. Chem. Phys. 53, 3759.

    Article  CAS  Google Scholar 

  2. Zallen, R. and Scher, H. (1971) Percolation on a continuum and the localization-delocalization transition in amorphous semiconductors, Phys. Rev. B. 4, 4471.

    Article  Google Scholar 

  3. Zallen, R. (1998) The Physics of Amorphous Solids, John Wiley and Sons, New York. pp. 183–191.

    Google Scholar 

  4. In the seventies, the Xerox lab in Palo Alto was the site of some now-famous computer-science examples: Hiltzik, M.A. (1999) Dealers of Lighting, Harper, New York.

    Google Scholar 

  5. Harvey Scher, now at the Weizmann Institute, has commented on technology as a rich source of scientific questions in his recent Festschrift article: Scher, H. (2000) Reminiscences, J. Phys. Chem. B 104, 3768.

    Article  Google Scholar 

  6. Reference [3], p. 170.

    Google Scholar 

  7. Suding, P.N. and Ziff, R.M. (1999) Site percolation thresholds for Archimedean lattices, Phys. Rev. E 60, 275.

    Article  CAS  Google Scholar 

  8. Fitzpatrick, J.P., Malt, R.B., and Spaepen, F. (1974) Percolation theory and the conductivity of random close packed mixtures of hard spheres, Physics Letters 47A, 207.

    Google Scholar 

  9. Ottavi, H., Clerc, J.P., Giraud, G., Roussenq, J., Guyon, E., and Mitescu, C.D. (1978) Electrical conductivity of conducting and insulating spheres: an application of some percolation concepts, J. Phys. C: Solid State Phys. 11, 1311.

    Article  CAS  Google Scholar 

  10. Lee, S.I., Song, Y., Noh, T.W., Chen, X.D., and Gaines, J.R. (1986) Experimental observation of nonuniversal behavior of the conductivity exponent for three-dimensional continuum percolation systems, Phys. Rev. B 34, 6719.

    CAS  Google Scholar 

  11. Domb, C. and Sykes, M.F. (1960) Cluster size in random mixtures and percolation processes, Phys. Rev. 122, 170.

    Google Scholar 

  12. Shklovskii, B.I. and Efros, A.L. (1984) Electrical Properties of Doped Semiconductors, Springer-Verlag, Berlin, p. 106.

    Google Scholar 

  13. Nan, C.W. (1993) Physics of inhomogeneous inorganic materials, Prog. Mater. Sci. 37, 1.

    Article  CAS  Google Scholar 

  14. Viswanathan, R. and Heaney, M.B. (1995) Direct imaging of the percolation network in a three-dimensional disordered conductor-insulator composite, Phys. Rev. Letters 75, 4433.

    Article  CAS  Google Scholar 

  15. Heaney, M.B. (1995) Measurement and interpretation of nonuniversal critical exponents in disordered conductor/insulator composites, Phys. Rev. B 52, 12477.

    Article  CAS  Google Scholar 

  16. Heaney, M.B. (1997) Electrical transport measurements of a carbon-black/polymer composite, Physica A 241, 296.

    Article  CAS  Google Scholar 

  17. Wu, J., and McLachlan, D.S. (1997) Percolation exponents and thresholds obtained from the nearly ideal continuum percolation system graphite/boron-nitride, Phys. Rev. B 56, 1236.

    CAS  Google Scholar 

  18. Wu, J., and McLachlan, D.S. (1997) Percolation exponents and thresholds in two nearly ideal anisotropic continuum systems, Physica A 241, 360.

    Article  CAS  Google Scholar 

  19. Halperin, B.I., Feng, S., and Sen, P.N. (1985) Differences between lattice and continuum percolation transport exponents, Phys. Rev. Letters 54, 2391.

    Article  Google Scholar 

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© 2002 Kluwer Academic Publishers

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Zallen, R. (2002). The Sixteen-Percent Solution: Critical Volume Fraction for Percolation. In: Thorpe, M.F., Phillips, J.C. (eds) Phase Transitions and Self-Organization in Electronic and Molecular Networks. Fundamental Materials Research. Springer, Boston, MA. https://doi.org/10.1007/0-306-47113-2_3

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  • DOI: https://doi.org/10.1007/0-306-47113-2_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46568-0

  • Online ISBN: 978-0-306-47113-1

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