| Abstract: | Natural phenomena are often, if not always, time dependent. Therefore It makes sense to try to find patterns of behaviour allowing (perhaps) to guess in a given situation the type of time dependence one observes.
Indeed we know well what is a steady state, a periodic behaviour, a chaotic dynamics. This does not exhaust all possibilities. With Martine Le Berre, we tried to understand how to explain the occurence of catastrophes in dynamical systems. By this, we understand a sudden variation of finite amplitude of the quantities describing a given system. Examples of such catastrophes are widespread in Nature: Earthquakes, Supernovae, etc. From the observation one realises that a large parameter is present, the ratio of the long time scale (for the slow evolution) to the short time (the duration of the quick burst). For Earthquakes, this ratio is about 10^9, ratio of hundred years to a fraction of a minute. For Supernova explosions this ratio may reach 10^{14}. I'll try to explain how to put this in a coherent framework. This allowed us to predict concretely slip events observed in the creeping of a soft metal. This prediction is based on changes observed in the noise spectrum, following an idea by V.A.
Dubrovskiy and V.N. Sergeev. In our approach we put in evidemnce that the prediction can be made at a time significantly earlier than the event itself. |
