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Electrical Properties of Percolation Clusters: Exact Results on a Deterministic Fractal

  • J. P. Clerc
  • G. Giraud
  • J. M. Laugier
  • J. M. Luck
Part of the Springer Proceedings in Physics book series (SPPHY, volume 5)

Abstract

We study general electrical properties of percolation clusters through a Deterministic Fractal Lattice, generalizing a model proposed by Kirkpatrick. The model admits an exact renormalization group transformation, and hence most physical quantities are exactly computable. We focus our attention on the frequency-dependence of the impedance and the loss angle, on the transient response to an arbitrary input signal, and to the amplification of resistor noise (Flicker or 1/f noise).

Keywords

Noise Spectrum Percolation Cluster Critical Regime Loss Angle Resistor Noise 
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References

  1. [1]
    J.P. CLERC, G. GIRAUD, J.M. LAUGIER, and J.M. LUCK, J. Phys. A (1985, to appear).Google Scholar
  2. [2]
    S. KIRKPATRICK, Les Houches Summer School “Ill Condensed Matter” eds R. Balian, R. Maynard and G. Toulouse (North-Holland, Amsterdam, 1979).Google Scholar
  3. [3]
    B.B MANDELBROT, “Fractals: Form, Chance and Dimension” (Freeman, San Francisco, 1977).MATHGoogle Scholar
  4. [4]
    J.M. LUCK, J. Phys. A (1985, to appear) N.B. A more complete bibliography can be found in ref. [1]Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • J. P. Clerc
    • 1
  • G. Giraud
    • 1
  • J. M. Laugier
    • 1
  • J. M. Luck
    • 2
  1. 1.D.P.S.D. Université de ProvenceMarseille CedexFrance
  2. 2.SPHT, CEN SaclayGif-sur-Yvette CedexFrance

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