Scale Invariance

1. Front Matter

   Pages i-xv

   PDF

2. Changes of States of Matter

   • Annick Lesne, Michel Laguës

   Pages 1-41

3. Fractal Geometry

   • Annick Lesne, Michel Laguës

   Pages 43-53

4. Universality as a Consequence of Scale Invariance

   • Annick Lesne, Michel Laguës

   Pages 55-107

5. Diffusion

   • Annick Lesne, Michel Laguës

   Pages 109-165

6. The Percolation Transition

   • Annick Lesne, Michel Laguës

   Pages 167-195

7. Spatial Conformation of Polymers

   • Annick Lesne, Michel Laguës

   Pages 197-230

8. High Temperature Superconductors

   • Annick Lesne, Michel Laguës

   Pages 231-257

9. Growth and Roughness of Interfaces

   • Annick Lesne, Michel Laguës

   Pages 259-291

10. Dynamical Systems, Chaos and Turbulence

    • Annick Lesne, Michel Laguës

    Pages 293-344

11. Self-Organised Criticality

    • Annick Lesne, Michel Laguës

    Pages 345-360

12. Scale Invariance in Biology

    • Annick Lesne, Michel Laguës

    Pages 361-384

13. Power and Limits of Scaling Approaches

    • Annick Lesne, Michel Laguës

    Pages 385-390

14. Back Matter

    Pages 391-397

    PDF

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.

• Critical phenomena
• Critical phenomena in materials growth
• Critical phenomena in natural sciences
• Fractal geometry
• Growth mechanisms of materials
• Phase transitions
• Scale invariance in biology
• Scaling concepts in material physics
• Scaling concepts in pyhsics/biology
• Self-organized critical phenomena
• Universality and scale invariance
• complexity

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)

• Labo. Physique Théorique de la, Matière Condensée (LPTMC), Université Paris VI, Paris CX 05, France

  Annick Lesne

• ESPCI, Paris, France

  Michel Lagües

Policies and ethics