Scale Invariance and Beyond (1997)
Dubrulle, B., Gif-sur-Yvette, France
Graner, F., St. Martin d'Heres, France
Sornette, D., CNRS, Nice, France (Eds.)
Les Houches Workshop, March 10-14, 1997
1997. XIX, 286 pp. 3-540-64000-2
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.
Editorial Review
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Keywords
Critical Point, Dimensional Analysis, Exponents, Intermittency, Fluctuations, Fractal, Power Law, Renormalization Group, Scale Covariance, Singularity, Turbulence.
Contents
Scale Invariance Without Mechanism?- Scale Invariance and Beyond: What Can We Learn from Wavelet Analysis?- Fractional Derivatives in Static and Dynamic Scaling.- Multi-dimensional Self-similarity, and Self-gravitating N-Body Systems.- Scaling in Stock Market Data: Stable Laws and Beyond.- Hysteresis, Avalanches, and Barkhausen Noise.- Burgers Turbulence and the Energy Landscape of Randomly Pinned Objects.- Scale Invariance in Fluids with Anticorrelated Entropy-Specific Volume Fluctuations.- Scale Invariance(s) in the Cosmic Matter Distribution.- etc.
Series
Les Houches. Edited by EDP Sciences and Springer, Berlin, 1997