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Critical Wrinkling of Depinned Interfaces, Strings and Membranes

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Part of the book series: NATO ASI Series ((ASIC,volume 415))

Abstract

Interface dynamics governed by punktuated dynamics become self organized critical. In the critical state we observe temporal multiscaling of the interface profile and the activity pattern exhibits non trivial power law correlations in both space and time. This intermittent activity is characterized by avalanches which connect regions of recent local activity. These avalanches display scale invariance. An extension of the presented concepts to evolving strings leads to a new universality class.

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References

  1. K. Sneppen, Phys.Rev.Lett. 69, 3539 (1992).

    Article  ADS  Google Scholar 

  2. D. Wilkinson and J.F. Willemsen, J.Phys.A 16, 3365 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Havlin, A.-L. Barabási, S.V.C. Buldyrev, K. Peng, M. Schwartz, H.E. Stanley and T. Vicsek, in Proc. of Granada Conference on “Fractals”, eds. P. Meakin and L. Sander (Plenum Press, New York, 1992 ).

    Google Scholar 

  4. M.A. Rubio, C. Edwards, A. Dougherty and J.P. Gollup, Phys. Rev. Lett. 63, 1685 (1989); 65, 1389 (1990).

    Google Scholar 

  5. V.K. Horváth, F. Family and T.Vicsek, Phys. Rev. Lett. 65, 1388 (1990), J. Phys A 24, L-25 (1991).

    Google Scholar 

  6. M. Kardar, G. Parisi and Y.-C. Zhang, Phys.Rev.Lett. 56, 889 (1986).

    Article  ADS  MATH  Google Scholar 

  7. Lei-Han Tang and H. Leschhorn, comment to appear in Phys. Rev. Lett.

    Google Scholar 

  8. K.Sneppen and M.H.Jensen, reply to appear in Phys. Rev. Lett.

    Google Scholar 

  9. K.Sneppen, M.H.Jensen, Phys.Rev.Lett., in press (1993).

    Google Scholar 

  10. K.Sneppen, M.H. Jensen, NBI preprint 93/15, submitted to PRL.

    Google Scholar 

  11. P. Bak and K. Sneppen, BNL preprint, Submitted to Nature. Propose a model of co-evolution dynamics by a sequence of metastable complex systems each with a minimal random barrier for possible changes. The system evolves by locating the overall lowest barrier and updating this and its two nearest neighbours to new random barriers. This dynamics can be justified by exponential separation of timescales associated to an interpretation of the barriers as energies and the driving performed at very low temperature. Power laws will be observed for distances smaller than a correlation length which increases with decreasing temperature.

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© 1993 Springer Science+Business Media Dordrecht

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Sneppen, K., Jensen, M.H. (1993). Critical Wrinkling of Depinned Interfaces, Strings and Membranes. In: Riste, T., Sherrington, D. (eds) Phase Transitions and Relaxation in Systems with Competing Energy Scales. NATO ASI Series, vol 415. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1908-5_21

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  • DOI: https://doi.org/10.1007/978-94-011-1908-5_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4843-9

  • Online ISBN: 978-94-011-1908-5

  • eBook Packages: Springer Book Archive

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