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Théorie de la percolation et dynamique des côtes rocheuses

le 18 juin 2014

Andrea Baldassarri (ISC-CNR, Rome) got his PhD at the University of Paris Sud (Orsay) with a thesis on the ”Statistics of persistent extreme events “.



Percolation theory and rocky coast dynamics. Percolation theory grows at the fertile boundary where geometry meets disorder and probability. It is an active research topic in mathematics and physics, where it appears as a cornerstone of the study of phase transitions and fractal geometries. Several natural phenomena has been related to percolation and described using simple percolation models.

After a brief introduction, with particular attention to critical phenomena, I will discuss the problem of rocky coast erosion. In particular I will describe a new approach to the analysis of the episodic dynamics of cliff collapses. Recent measurements from the field suggest that several quantities characterizing the geometry of the collapses are distributed in frequency as power laws, for large sizes.

Moreover some power law relations are observed, for instance, between the eroded surface at the cliff top and the maximal penetration depth of the sea. This observation
points to a geometrical property of cliff failures, indicating that their shape is statistically similar for different failure magnitudes. Power laws are familiar in the physics of critical systems and percolation. The corresponding exponents satisfy precise relations and they are proven to be universal features, common to many different systems. Following the approach typical of statistical physics, we propose a "scaling hypothesis'' resulting in a relation between the exponents under study.

In collaboration with B.Sapoval, I developed a numerical model of marine erosion that yields numerical values for the exponents. Despite the minimal definition of the model, its behavior is strikingly close to the real statistics, and the exponents resulting from extensive numerical simulations fairly agree with the ones measured on the field.

These results suggest that the mathematical theory of percolation, which lies behind our simple model, can possibly be used as a guide to decipher the physics of rocky coast erosion and could provide precise predictions to the statistics of cliff collapses.
Type :
Séminaires - conférences
Lieu(x) :
Campus de Cachan
Pavillon des Jardins

ENS Cachan : les professeurs invités en 2014

His interests in non-equilibrium statistical physics and complex systems drove him to study several problems related to granular matter, slow dynamics and aging in spin glass models, etching and corrosion processes in aluminum films, erosion of rocky coasts, fractal geomorphology of planets.

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