Energy and materials for the Futures

Course Coordinators : B. Desprès and E. Cancès

Energies and Materials for Futures (EMF) is one of the five Majors that the Mathematical Modelling speciality offers. It is the second year of the Masters degree in "Mathematics and its Applications".

Energy production, as well as the use of all sorts of conventional and alternative energy sources, will soon require a reinforcement of basic and applied research. Conventional energy can refer to hydropower, nuclear fission, oil, etc. Alternative energy can mean nuclear fusion, wind, photovoltaic, etc. In all these fields it is necessary to take into account complex phenomena such as modelling in the form of systems of partial differential equations (PDE) and their numerical resolutions are critical for progress in scientific research.

Likewise, the development of new chemical compounds and new materials (micro and nanostructured composite materials, graphene and carbon nanotubes, biomaterials, metamaterials, intelligent materials, etc.) has produced spectacular progress in all areas of engineering. This research is also increasingly based on the numerical simulation of models involving PDEs, as well as on stochastic models.

The EMF Major (Energies and Materials for the Futures) aims to offer a coherent course structure which tackles some of the main aspects of these themes.

The fundamental courses deal with variational approximations and the numerical simulation of elliptical PDEs (MU5MAM36), the theoretical and numerical study of hyperbolic systems of conservation laws used mainly in fluid mechanics (MU5MAM16), the coupling of models on various scales (MU5MAM34) and the numerical simulation of stochastic models (MU5MAM35).

The specialized courses of the “energy” stream focus on incompressible fluid mechanics (5MM24), complex flow systems (for example: from compressible or two-phase flow models used for the heart of nuclear power plants to the models of hydropower dams, (MU5MAM27), and kinetic models (or particle model of matter), whose theoretical dimensions are dealt with in this course (MU5MAM28).

The specialized courses of the “materials” stream focus on spectral theory and variational methods used in particular in the quantum forms of matter (MU5MAM87), solid and fluid biomaterial models (5MM26), and numerical and mathematical methods used in molecular scale simulations (MU5MAM38).

Finally, the course (MU5MAM21) introduces specific numerical methods of high precision in diverse systems.

The proposed courses enable students to acquire at the same time proficiency in the theoretical analysis of PDEs and in the numerical analysis of the most recent approximation methods used to simulate them, as well as expertise in one or various areas of application with a focus on modelling. This Major is offered in partnership with the Ecole Nationale des Ponts et des Chaussées (ENPC).

Course title Lecturer(s) Type Course Code
Variational approximations of PDEs Yvon Maday Fundamental MU5MAM36
Reject [CG] Theoretical and Numerical Aspects Frédéric Legoll Fundamental MU5MAM34
Probabilistic Numerical Methods Tony Lelièvre Fundamental MU5MAM35
Theoretical and Numerical Analysis of Hyperbolic Systems of Conservation Laws Grégoire Allaire Fondamental MU5MAM16
Introduction to stochastic PDEs Anne de Bouard Fundamental MU5MAM63
Spectral theory and variational methods Eric Cancès & Mathieu Lewin Specialised MU5MAM87
Discontinuous Galerkin methods and applications Alexandre Ern Specialised MU5MAM21
Cinetic models and hydrodynamic limits François Golse Specialised MU5MAM28
Theoretical and numerical aspects of incompressible fluids Pascal Frey, Yannick Privat Specialised MU5MAM57
Hyperbolic models for complex flow in the field of energy Jacques Sainte-Marie Specialised MU5MAM27
Mathematical methods and numerical analysis for molecular simulation. Gabriel Stoltz Specialised MU5MAM38