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Introduction to Multifractality

  • Chapter
Disorder and Fracture

Part of the book series: NATO ASI Series ((NSSB,volume 204))

Abstract

We introduce the basic concepts of multifractality by considering the example of the current distribution inside a random resistor network right at the percolation threshold. An infinite set of critical exponents governs the scaling of the moments of the distribution of currents with the system size. The “Legendre transform” of this series is shown to be connected to the histogram of the current distribution, through the formalism of multifractality.

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Author information

Author notes

  1. Alex Hansen

    Present address: Dept. of Physics, University of Oslo, P.O.box 1048, Blindern, 0316, Oslo 3, Norway

Authors and Affiliations

  1. Laboratoire de Physique et Mécanique de la Matière Hétérogène, Ecole Supérieure de Physique et Chimie Industrielles de Paris URA CNRS 857, 10 rue Vauquelin, F-75231, Paris Cédex 05, France

    Stéphane Roux & Alex Hansen

  2. CERAM, ENPC, La Courtine, BP 105, F-93194, Noisy-le-Grand Cédex, France

    Stéphane Roux

Authors
  1. Stéphane Roux
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  2. Alex Hansen
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Editor information

Editors and Affiliations

  1. Ecole Supérieure de Physique et Chimie Industrielles de Paris, Paris, France

    J. C. Charmet  & S. Roux  & 

  2. Université de Paris-Sud, Orsay, France

    E. Guyon

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© 1990 Plenum Press, New York

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Roux, S., Hansen, A. (1990). Introduction to Multifractality. In: Charmet, J.C., Roux, S., Guyon, E. (eds) Disorder and Fracture. NATO ASI Series, vol 204. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6864-3_2

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  • DOI: https://doi.org/10.1007/978-1-4615-6864-3_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-43576-8

  • Online ISBN: 978-1-4615-6864-3

  • eBook Packages: Springer Book Archive

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