Thermodynamics and roughening of solid-solid interfaces
Most large earthquakes are followed by a slow post-seismic deformation. The deformation is usually thought to be localized directly on the rupture plane and the slow relaxation of the fault is interpreted as creation of new solid-solid contacts. Here we study the morphological stability of interfaces between reactive and deformable rocks of the Earth's crust. Under certain conditions the interface can become unstable, corrugate, and develop roughness at various scales when submitted to non-hydrostatic stress.
Fracture and fracture networks
Fracture mechanics deals with the interaction between a propagating fracture tip and its host medium and the typically non-trivial processes leading to material yielding. Generally, any material is damaged in the vicinity of a crack tip; it is irreversibly changed by plastic deformations and by the appearance of micro cracks and voids. We have developed methods based on conformal mapping techniques to analyze the interaction between an in-plane moving crack tip and nearby damage cavities. With these methods we have addressed how the damage zone in front of a fracture may cause "universal" properties of fracture such as the roughening of fracture surface. Moreover we have studied fracturing induced by volume changing processes such as cooling, serpentinization and desiccation.
Laplacian growth and fractals
Laplacian fractals are paradigmatic examples for the spontaneous growth of fractal patterns in natural systems. In particular, two such examples have attracted an enormous amount of interest: viscous fingering and diffusion-limited aggregation (DLA). Viscous fingering is realized when a less viscous fluid displaces a more viscous fluid contained in the narrow gap between two glass plates (a Hele-Shaw cell). DLA is realized as a computer experiment in which a fractal cluster is grown by releaseing a fixed-size random walker from infinity, allowing it to walk until it hits any particle already belonging to the cluster. We have developed methods based on iterated conformal maps to offer an accurate determination of the fractal and multifractal properties of the harmonic measure.
Microstructure and Grain Growth in Ice
The ice-cores from the Greenland ice sheet provide detailed information on climate and weather conditions to about 120kyr before present. In addition, the ice-cores provide an excellent and unique laboratory for research on the temporal evolution of ice crystals or more generally grain growth in polycrystalline materials. In the upper 80m of the ice sheet, the yearly snow precipitation gradually compacts to a close packing of ice crystals. The structure of the ice crystal packing can be obtained by preparing thin sections of ice core samples. We have developed a model of grain growth consistent with data and observations and where the grain evolution is controlled by the competition between a grain coarsening mechanism (normal grain growth) and grain refinement (the division of crystals in two or more fragments). The model predicts very well the temporal evolution of the grain size distribution.