### Microscopic derivation of moving interfaces

The derivation of macroscopic properties of physical systems is an expanding research area. In particular, the rigorous microscopic description of moving interfaces, the understanding of macroscopic nonlocal effects, and the mathematical apprehension of the underlying atomic mechanisms, are important matters of research. These arduous problems have encountered several obstacles in the last decades among the statistical physics community. The ANR project MICMOV gathers five young researchers, from three distinct areas, for an interdisciplinary purpose.

More precisely, the class of kinetically constrained lattice gases, which has been introduced in the 1980's in glassy dynamics contains microscopic dynamics which accurately illustrate moving interfaces. The macroscopic evolution of such particle systems is often expected to be the solution to a Stefan problem, with notably a free boundary between the active and frozen regions. We would like to derive Stefan problems as hydrodynamic limits of kinetically constrained lattice gases which contain active-absorbing phase transitions, and derive new hydrodynamic equations, which combine nonlocal macroscopic effects (such as fractional diffusion) and porous medium type propagation.

### Members

**
Guillaume Barraquand: ** *Chargé de recherches CNRS,* Laboratoire de Physique de l'ENS Paris

**
Oriane Blondel: ** *Chargée de recherches CNRS,* Institut Camille Jordan, Université Lyon 1

**
Clément Cancès: ** *Chargé de recherches Inria,* Inria, Université de Lille

**
Maxime Herda: ** *Chargé de recherches Inria,* Inria, Université de Lille

**
Marielle Simon: ** *Chargée de recherches Inria,* Inria, Université de Lille

### Students

**Sonia Velasco:**

*Stage de recherche (M2),*ENS de Lyon

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