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Scale Invariance and Beyond

Les Houches Workshop, March 10–14, 1997

  • Conference proceedings
  • © 1997

Overview

Editors:
  1. B. Dubrulle

    1. CNRS, CEA/DSM/DAPNIA/Service d’Astrophysique, Gif-sur-Yvette, France

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  2. F. Graner

    1. CNRS, UMR 5588, Laboratoire de Spectrométrie Physique, Université Grenoble I — Joseph Fourier, Saint-Martin-d’Hères cedex, France

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  3. D. Sornette

    1. Laboratoire de Physique de la Matière Condensée, CNRS and Université de Nice-Sophia Antipolis, Nice, France
      Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, USA

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  • This is a book on scale invariance, a field that has become very fashionable since the work of Mandelbrot on factals and the success of the renormalization group of Kadanoff-Wilson.

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

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Table of contents (21 papers)

  1. Front Matter

    Pages I-21
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  2. Scale Invariance

    1. Front Matter

      Pages 23-23
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    2. Concept

      1. Scale Invariance Without Mechanism ?
        • F. Graner
        Pages 25-35

    3. Tools

      1. Scale Invariance and Beyond: What Can We Learn from Wavelet Analysis ?
        • A. Arneodo, B. Audit, E. Bacry, S. Manneville, J. F. Muzy, S. G. Roux
        Pages 37-51
      2. Fractional Derivatives in Static and Dynamic Scaling
        • R. Hilfer
        Pages 53-62
      3. Multi-Dimensional Self-Similarity, and Self-Gravitating N-Body Systems
        • R. N. Henriksen
        Pages 63-73
      4. Scaling in Stock Market Data: Stable Laws and Beyond
        • Rama Cont, Marc Potters, Jean-Philippe Bouchaud
        Pages 75-85

    4. Examples Condensed Matter Systems

      1. Hysteresis, Avalanches, and Barkhausen Noise
        • James P. Sethna, Olga Perkovic, Karin A. Dahmen
        Pages 87-97
      2. Burgers Turbulence and the Energy Landscape of Randomly Pinned Objects
        • J.-Ph. Bouchaud
        Pages 99-105
      3. Power Laws and Scale Invariance in Physical Metallurgy
        • Y. Bréchet, M. Lebyodkin
        Pages 107-118
      4. Scale Invariance in Fluids with Anticorrelated Entropy-Specific Volume Fluctuations
        • H. E. Stanley, S. T. Harrington, P. H. Poole, F. Sciortino
        Pages 119-132

    5. From Cosmology to Earthquakes

      1. Scale Invariance(s) in the Cosmic Matter Distribution?
        • M. Lachièze-Rey
        Pages 133-146
      2. Scale Invariance of the Avalanche Effect in Phase Transition Modulated Mantle Mixing
        • S. L. Butler, W. R. Peltier
        Pages 147-157
      3. Scale Invariance of Earthquakes
        • L. Knopoff
        Pages 159-172

    6. Form Biology to Finance

      1. Models for Evolution and Extinction
        • Matteo Marsili
        Pages 173-183
      2. Scale Invariance in Economics and in Finance
        • Daniel Zajdenweber
        Pages 185-194
      3. Models of Artificial Foreign Exchange Markets
        • B. Chopard, R. Chatagny
        Pages 195-205

  3. Beyond Scale Invariance

    1. Front Matter

      Pages 207-207
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    2. From Scale Invariance to Scale Covariance

      1. From Scale-Invariance to Scale-Covariance in Out-of-Equilibrium Systems
        • A. Pocheau
        Pages 209-223
      2. Turbulence: Statistical Approach
        • B. Castaing
        Pages 225-234
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Keywords

About this book

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.

Editors and Affiliations

  • CNRS, CEA/DSM/DAPNIA/Service d’Astrophysique, Gif-sur-Yvette, France

    B. Dubrulle

  • CNRS, UMR 5588, Laboratoire de Spectrométrie Physique, Université Grenoble I — Joseph Fourier, Saint-Martin-d’Hères cedex, France

    F. Graner

  • Laboratoire de Physique de la Matière Condensée, CNRS and Université de Nice-Sophia Antipolis, Nice, France

    D. Sornette

  • Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, USA

    D. Sornette

Bibliographic Information

  • Book Title: Scale Invariance and Beyond

  • Book Subtitle: Les Houches Workshop, March 10–14, 1997

  • Editors: B. Dubrulle, F. Graner, D. Sornette

  • Series Title: Centre de Physique des Houches

  • DOI: https://doi.org/10.1007/978-3-662-09799-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-64000-4Published: 21 January 1998

  • eBook ISBN: 978-3-662-09799-1Published: 09 November 2013

  • Edition Number: 1

  • Number of Pages: XIX, 287

  • Number of Illustrations: 24 b/w illustrations

  • Additional Information: Jointly published with EDP Sciences, Les Ulis, France

  • Topics: Complex Systems, Condensed Matter Physics, Geophysics/Geodesy, Statistical Physics and Dynamical Systems

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