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Self Organized Criticality in Simple Growth Models

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Growth Patterns in Physical Sciences and Biology

Part of the book series: NATO ASI Series ((NSSB,volume 304))

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Abstract

A stimulating development in the analysis of complex systems has been the hypothesis of self organized criticality 1,2. The main assumption is that such systems evolve towards a state where small perturbations can give rise to changes (catastrophes) of all sizes. This state describes the most unstable situation compatible with some kind of equilibrium. The distribution of catastrophes, because of its inherent scale invariance, is characterized by power laws. In previous work, we have checked that this hypothesis is well satisfied in systems which evolve into a steady state far from equilibrium3. The model we analyzed is Diffusion Limited Aggregation4, for which a comprehensive amount of work is already available4.

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References

  1. P. Bak, C. Tang and K. Wisenfeld, Phys. Rev. Lett. 59, 381 (1987), and Phys. Rev. A 38, 364 (1988).

    Article  PubMed  Google Scholar 

  2. P. Bak, K. Chen and M. Creutz, Nature 342, 780 (1989).

    Article  Google Scholar 

  3. O. Pla, F. Guinea and E. Louis, Phys. Rev. A 42, 6270 (1990).

    Article  PubMed  Google Scholar 

  4. T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47 1400 (1981); Phys. Rev. B27 5686 (1983).

    Article  CAS  Google Scholar 

  5. L. Niemeyer, L. Pietronero and H. J. Wiesmann, Phys. Rev. Lett. 52 1033 (1984).

    Article  Google Scholar 

  6. T. Hwa and M. Kardar, Phys. Rev. Lett. 62, 1813 (1989), G. Grinstein, D.-H. Lee and S. Sachdev, ibid 64, 1927 (1990).

    Article  PubMed  Google Scholar 

  7. P. L. Garrido, J. L. Lebowitz, C. Maes and H. Spohn, Phys. Rev. A 42, 1954 (1990).

    Article  PubMed  Google Scholar 

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Author information

Author notes

  1. O. Plat

    Present address: Department of Physics, University of Michigan, Ann Arbor, MI, 48109-1120, USA

Authors and Affiliations

  1. Instituto de Ciencia de Materiales (CSIC) Facultad de Ciencias, Universidad Autónoma, 28049, Madrid, Spain

    O. Plat & F. Guinea

  2. Departamento de Física Aplicada, Universidad de Alicante, Apartado 99, 03080, Alicante, Spain

    E. Louis

Authors
  1. O. Plat
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  2. F. Guinea
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  3. E. Louis
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Editor information

Editors and Affiliations

  1. CSIC-Universidad de Granada, Granada, Spain

    Juan Manuel Garcia-Ruiz

  2. Universidad de Alicante, Alicante, Spain

    Enrique Louis

  3. University of Oslo, Oslo, Norway

    Paul Meakin

  4. University of Michigan, Ann Arbor, Michigan, USA

    Leonard M. Sander

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© 1993 Springer Science+Business Media New York

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Plat, O., Guinea, F., Louis, E. (1993). Self Organized Criticality in Simple Growth Models. In: Garcia-Ruiz, J.M., Louis, E., Meakin, P., Sander, L.M. (eds) Growth Patterns in Physical Sciences and Biology. NATO ASI Series, vol 304. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2852-4_23

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  • DOI: https://doi.org/10.1007/978-1-4615-2852-4_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6235-7

  • Online ISBN: 978-1-4615-2852-4

  • eBook Packages: Springer Book Archive

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