Prediction of catastrophes: An experimental model

Randall Peters (1) , Martine Le Berre (2) , Yves Pomeau (3)

1 Department of Physics
2 ISMO - Institut des Sciences Moléculaires d'Orsay
3 Department of Mathematics [University of Arizona]

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.

Domaines: Systèmes dynamiques [math.DS]

Randall Peters, Martine Le Berre, Yves Pomeau. Prediction of catastrophes: An experimental model. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2012, 86, pp.026207. ⟨hal-00728769⟩