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From Scale-Invariance to Scale-Covariance in Out-of-Equilibrium Systems

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Scale Invariance and Beyond

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

Abstract

In principle, the concept of scale-invariance enables relevant information to be gained on physical systems by different means. For example, minimization of the set of independent variables from dimensional analysis, selection of self-similar laws from evolution equations, selection of power laws for functions of a single scaling variable and characterization of geometry by a fractal dimension. In practice however, most of these approaches hardly apply. Various reasons for this include the fact that selection of power laws is invalid for multivariable functions, selection of other self-similar laws requires analytic modelling of systems, physical cut-offs (e.g. finite size effects) break scale-invariance (e.g. scale-similarity) and forbid fractal.

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References

  1. Pocheau A., Phys.Rev.E 49 (1994) 1109–1122

    Article  MathSciNet  ADS  Google Scholar 

  2. Pocheau A. and Queiros-Condé D.,Phys.Rev.Lett. 76 (1996) 3352–3355

    Article  ADS  Google Scholar 

  3. Pocheau A. and Queiros-Condé D., Europhys..Lett. 35 (1996) 439–444

    Article  ADS  Google Scholar 

  4. Pocheau A., Europhys.Lett. 35 (1996) 183–188

    Article  ADS  Google Scholar 

  5. Nottale L., Fractal space-time and microphysics, World Scientific (1993)

    Google Scholar 

  6. Sivashinsky G.I., Combust.Sci.Technol. 62 (1988) 77–96

    Article  Google Scholar 

  7. Yakhot V., Combust.Sci.Technol. 60 (1988) 191–214

    Article  MathSciNet  Google Scholar 

  8. Clavin P. and Williams F.A., J.Fluid Mech. 90 (1979) 589–604

    Article  ADS  MATH  Google Scholar 

  9. Villermaux E. and Gagne Y., Phys.Rev.Lett. 73 (1994) 252–255

    Article  ADS  Google Scholar 

  10. Dubrulle B. and Graner F., J.Physique II France 6 (1996) 797–816

    Article  ADS  Google Scholar 

  11. Dubrulle B. and Graner F., J.Physique II France 6 (1996) 817–824

    Article  ADS  Google Scholar 

  12. Dubrulle B. and Graner F., Submitted to Phys.Rev.E. (1996)

    Google Scholar 

  13. Weyl H., Naturwissenschaften 19 (1931) 49

    Article  ADS  Google Scholar 

  14. Frisch U., Turbulence, Cambridge University Press (1995)

    Google Scholar 

  15. She Z-S. and Levesque E., Phys.Rev.Lett. 72 (1994) 336

    Article  ADS  Google Scholar 

  16. Dubrulle B., Phys. Rev. Lett. 73 (1994) 959

    Article  ADS  Google Scholar 

  17. She Z-S. and Waymire E.C., Phys.Rev.Lett. 74 (1995) 262

    Article  ADS  Google Scholar 

  18. Cont R., Potters M. and Bouchaud J.P., Lecture 5, these proceedings Mantegna R. N. and Stanley HE., Phys.Rev Lett. 73 (1994) 2946

    Article  Google Scholar 

  19. Koponen I., Phys.Rev.E 52 (1995) 1197

    Article  ADS  Google Scholar 

  20. Dubrulle B., private communication

    Google Scholar 

  21. Anselmet F., Gagne Y., Hopfinger E.J. and Antonia R.A., J.Fluid Mech. 140 (1984) 63–89

    Article  ADS  Google Scholar 

  22. Benzi R., Ciliberto S., Baudet C. and Ruiz Chavarria G., Physica D80 (1995) 385–398

    MathSciNet  MATH  Google Scholar 

  23. Chen S. and Cao N., Phys.Rev.E 52 (1995) 5757

    Article  MathSciNet  ADS  Google Scholar 

  24. Nelkin M., Phys.Rev.E 52 (1995) 4610

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRPHE, Université Aix-Marseille I & II, CNRS, Centre de Saint-Jérôme, Case 252, 13397, Marseille, France

    A. Pocheau

Authors
  1. A. Pocheau
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Editor information

Editors and Affiliations

  1. CNRS, CEA/DSM/DAPNIA/Service d’Astrophysique, L’Orme des Merisiers 709, 91191, Gif-sur-Yvette, France

    B. Dubrulle

  2. CNRS, UMR 5588, Laboratoire de Spectrométrie Physique, Université Grenoble I — Joseph Fourier, B.P. 87, 38402, Saint-Martin-d’Hères cedex, France

    F. Graner

  3. Laboratoire de Physique de la Matière Condensée, CNRS and Université de Nice-Sophia Antipolis, Parc Valrose, 06108, Nice, France

    D. Sornette

  4. Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, 90095-1567, Los Angeles, California, USA

    D. Sornette

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© 1997 Springer-Verlag Berlin Heidelberg

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Pocheau, A. (1997). From Scale-Invariance to Scale-Covariance in Out-of-Equilibrium Systems. In: Dubrulle, B., Graner, F., Sornette, D. (eds) Scale Invariance and Beyond. Centre de Physique des Houches, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09799-1_16

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  • DOI: https://doi.org/10.1007/978-3-662-09799-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64000-4

  • Online ISBN: 978-3-662-09799-1

  • eBook Packages: Springer Book Archive

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