MEPHYSTO Research team
Quantitative methods for stochastic models in physics
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.
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,
- 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:
- Observatoire de Nice,
- University of Reykjavik,
- Missouri University of Science and Technology
Research teams of the same theme :
- ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
- CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments
- CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
- DEFI - Shape reconstruction and identification
- ECUADOR - Program transformations for scientific computing
- GAMMA3 - Automatic mesh generation and advanced methods
- IPSO - Invariant Preserving SOlvers
- MATHERIALS - MATHematics for MatERIALS
- MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
- MOKAPLAN - Advances in Numerical Calculus of Variations
- NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
- NANO-D - Algorithms for Modeling and Simulation of Nanosystems
- POEMS - Wave propagation: mathematical analysis and simulation
- RAPSODI - Reliable numerical approximations of dissipative systems