# Team presentation

MEPHYSTO is a joint team of Inria, Université Libre de Bruxelles, Université Lille 1, and CNRS.

The general research activity of the team concerns the development, the analysis, and the numerical approximation of random models for physics.

# Research themes

The team is concerned with the study of the effect of randomness in PDEs and in physics. Randomness naturally occurs in the models of physics, due to disorder generated by thermalization (cf. statistical physics), due to the very structure of matter (cf. polymer-chain networks), or due to a lack of information/observations on the system (cf. uncertainties).

Our objective is twofold. First we aim at developping analytical and numerical tools to understand the interplay of randomness and PDEs in simple but meaningful models. Second we shall study a couple of more specific models motivated by our collaborations with physicists.

The first main part of the project concerns problems in random media such as homogenization or statistical physics models (such as the simple exclusion process). For homogenization the aim is to develop a quantitative theory to relate the law of the solution to the law of the random medium. For statistical physics models the aim is to rigorously justify some scaling laws and thermodynamic/hydrodynamic limits. Some of the specific problems under investigation require the development of fairly general numerical methods, such as numerical homogenization methods.

The second main part of the project is motivated by our collaborations with

- physicists of the laser physics department of Lille (PhLAM) within the activities of the labex CEMPI
- polymer physicists at ESPCI and CEA

In particular we are interested in the study of Schrödinger equations with random potentials or initial data that model optical fibers and the study of random networks of polymer-chains.

# International and industrial relations

Industrial relation: ANDRA

Academic contacts in mathematics:

- Université Paris Dauphine,
- UPMC,
- Ecole Centrale Paris,
- ENS Lyon,
- Université de Toulouse,
- Université catholique de Louvain,
- Max Planck Institute for Mathematics in the Sciences,
- Stanford University,
- Università di Torino

Academic contacts in physics:

- PhLAM,
- CEA,
- ESPCI,
- Observatoire de Nice,
- University of Reykjavik,
- Missouri University of Science and Technology