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This book presents a complete tour of formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology. The text offers a thorough conceptual background and a simple account of a wide range of applications.

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During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance.
The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.

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Foreword by Pierre-Gilles de Gennes.- Introduction.- Change of State in Matter.- Fractal Geometry.- Universality as a Consequence of Scale Invariance.- Diffusion.- The Percolation Transition.- Scaling Concepts in Polymer Physics.- Superconducting Cuprates.- Growth Mechanisms and Interface Roughness.- Dynamical Systems, Chaos and Turbulence.- Self-Organized Critical Phenomena.- Scale Invariance in Biology.- Power and Limits of Scaling Approaches

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From the reviews:
"The book begins with an introduction to scale invariance in the context of critical behaviors. ... In addition to the high quality of its numerous diagrams and plots and the admirable readability of its equations and fonts, Scale Invariance is well written and surprisingly engaging. ... The authors also do an excellent job of including the history of the topics they present; they make wise decisions about when to include significant historical details ... . The diligent reader will benefit from Scale Invariance ... ." (John R. Saylor, Physics Today, November, 2012)

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