Scale Invariance and Beyond

Les Houches Workshop, March 10–14, 1997

  • B. Dubrulle
  • F. Graner
  • D. Sornette

Part of the Centre de Physique des Houches book series (LHWINTER, volume 7)

Table of contents

  1. Front Matter
    Pages I-21
  2. Scale Invariance

    1. Front Matter
      Pages 23-23
    2. Concept

      1. F. Graner
        Pages 25-35
    3. Tools

      1. A. Arneodo, B. Audit, E. Bacry, S. Manneville, J. F. Muzy, S. G. Roux
        Pages 37-51
      2. Rama Cont, Marc Potters, Jean-Philippe Bouchaud
        Pages 75-85
    4. Examples Condensed Matter Systems

      1. James P. Sethna, Olga Perkovic, Karin A. Dahmen
        Pages 87-97
      2. Y. Bréchet, M. Lebyodkin
        Pages 107-118
      3. H. E. Stanley, S. T. Harrington, P. H. Poole, F. Sciortino
        Pages 119-132
    5. From Cosmology to Earthquakes

    6. Form Biology to Finance

      1. Matteo Marsili
        Pages 173-183
      2. Daniel Zajdenweber
        Pages 185-194
      3. B. Chopard, R. Chatagny
        Pages 195-205
  3. Beyond Scale Invariance

    1. Front Matter
      Pages 207-207
    2. From Scale Invariance to Scale Covariance

    3. Scale Symmetry Breaking

      1. Didier Sornette
        Pages 235-247
      2. Laurent Nottale
        Pages 249-261
      3. L. Biferale
        Pages 263-274
      4. B. Dubrulle
        Pages 275-286
  4. Back Matter
    Pages 287-287

About these proceedings


This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance.


condensed matter condensed matter physics critical point dimensional analysis exponents fluctuations fractal intermittency phase transition physics power law renormalization group scale covariance singularity turbulence

Editors and affiliations

  • B. Dubrulle
    • 1
  • F. Graner
    • 2
  • D. Sornette
    • 3
    • 4
  1. 1.CNRSCEA/DSM/DAPNIA/Service d’AstrophysiqueGif-sur-YvetteFrance
  2. 2.CNRS, UMR 5588, Laboratoire de Spectrométrie PhysiqueUniversité Grenoble I — Joseph FourierSaint-Martin-d’Hères cedexFrance
  3. 3.Laboratoire de Physique de la Matière CondenséeCNRS and Université de Nice-Sophia AntipolisNiceFrance
  4. 4.Department of Earth and Space Sciences and Institute of Geophysics and Planetary PhysicsUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-64000-4
  • Online ISBN 978-3-662-09799-1
  • Buy this book on publisher's site
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