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Prediction of catastrophes: An experimental model

Randall D. Peters1, Martine Le Berre2, and Yves Pomeau3

  • 1Department of Physics, Mercer University, Macon, Georgia, USA
  • 2Institut des Sciences Moléculaires d'Orsay ISMO-CNRS, Université Paris-Sud, Bâtiment 210, 91405 Orsay, France
  • 3Department of Mathematics, University of Arizona, Tucson, Arizona, USA

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Phys. Rev. E 86, 026207 – Published 16 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.026207

Abstract

Catastrophes of all kinds can be roughly defined as short-duration, large-amplitude events following and followed by long periods of “ripening.” Major earthquakes surely belong to the class of “catastrophic” events. Because of the space-time scales involved, an experimental approach is often difficult, not to say impossible, however desirable it could be. Described in this article is a “laboratory” setup that yields data of a type that is amenable to theoretical methods of prediction. Observations are made of a critical slowing down in the noisy signal of a solder wire creeping under constant stress. This effect is shown to be a fair signal of the forthcoming catastrophe in two separate dynamical models. The first is an “abstract” model in which a time-dependent quantity drifts slowly but makes quick jumps from time to time. The second is a realistic physical model for the collective motion of dislocations (the Ananthakrishna set of equations for unstable creep). Hope thus exists that similar changes in the response to noise could forewarn catastrophes in other situations, where such precursor effects should manifest early enough.

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References (22)

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  12. This product came from Tel-Atomic, Inc., a company that specializes in “Tools for Teaching Advanced Physics.” It is no longer available as a commercial product. One reason this instrument is no longer manufactured was the loss, due to a factory fire, of readily available chips that constituted the key component (NE5521n integrated circuit) used in the support electronics for its displacement sensor [13]. The same first example of fully differential capacitive sensors is also employed (except employed as a pair, for mechanical common mode rejection of noise) with different electronics, in another of the company's instruments, the computerized Cavendish balance [14].
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  22. R. D. Peters, M. Le Berre, and Y. Pomeau, arXiv:1204.1551.

Outline

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Phys. Rev. E 86, 026207– Published 16 August, 2012
  • Received 6 April 2012

©2012 American Physical Society

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