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Phys Rev Lett. 2013 Apr 5;110(14):145501. Epub 2013 Apr 2.

Non-Gaussian nature of fracture and the survival of fat-tail exponents.

Author information

1
Department of Physics, University of Oslo, PB 1048 Blindern, NO-0316 Oslo, Norway.
2
Institut de Physique du Globe de Strasbourg, UMR 7516 CNRS, Université de Strasbourg, 5 Rue René Descartes, F-67084 Strasbourg Cedex, France and Centre for Advanced Study, The Norwegian Academy of Science and Letters, Drammensveien 78, NO-0271 Oslo, Norway.
3
Centre for Advanced Study, The Norwegian Academy of Science and Letters, Drammensveien 78, NO-0271 Oslo, Norway and Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS UMR 5672, 46 Allée d'Italie, 69364 Lyon Cedex 07, France.
4
Department of Physics, University of Oslo, PB 1048 Blindern, NO-0316 Oslo, Norway and Centre for Advanced Study, The Norwegian Academy of Science and Letters, Drammensveien 78, NO-0271 Oslo, Norway.

Abstract

We study the fluctuations of the global velocity V(l)(t), computed at various length scales l, during the intermittent mode-I propagation of a crack front. The statistics converge to a non-Gaussian distribution, with an asymmetric shape and a fat tail. This breakdown of the central limit theorem (CLT) is due to the diverging variance of the underlying local crack front velocity distribution, displaying a power law tail. Indeed, by the application of a generalized CLT, the full shape of our experimental velocity distribution at large scale is shown to follow the stable Levy distribution, which preserves the power law tail exponent under upscaling. This study aims to demonstrate in general for crackling noise systems how one can infer the complete scale dependence of the activity--and extreme event distributions--by measuring only at a global scale.

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