In an increasing numbers of scientific and industrial applications, modeling and digital simulation play a key role to understand and analyse complexe physics phenomenon involved. A common feature to this energy, space, biolocial, mechanical, fluids, etc. systems is around the notion of dynamic systems, which time evolution and stability/instability fields govern the qualitative properties of solutions. These systems are particularly multi-scales, namely they involve a wide variety of time and space scales. They pose many difficulties when trying to develop a precise digital resolution in order to provide tools for predicting their reliable dynamics.
In this course we will study exemples in various application fields, like combustion, fluid mechanics, population dynamics, non-linear chemical dynamics or biomedical engineering, which is assemble under the rubric "reactive environment" (an environment involving "species" that "react" with each other with a certain complexity level involving a wide range of time and space scales).
The course is based on a first central theme of an understranding of what is a hierarchy of model s at different scales. We offer to identify issues in mathematical terms in order to understand and analyse the dynamic of these finished dimension systems,
The course will provide expertise in the following topics:mathematical analysis, digital sheme for differential equation systems, analysis of stability systems - bifurcation, digital implementation and program library allowing digital simulation or analys of bifurcations. will allow an analys of the dynamic but also an understanding of digital schemata originally from a precise and simulation, and an opening to issues in terms of applications. All of the techniques proposed will be illustrated using simple exemples that are symptomatics of the issues of complex systems encountered in applications. A mini project enable to implement notions and methods taught, and tackle to systems applied.
The course will be taught by a teaching team formed by Mr. Massot (teacher at Ecole Polytechnique - CMAP), Laurent Séries (Computational Research Engineer Ecole Polytechnique - CMAP), Taraneh Sayadi (Research fellow CNRS - IJLRA - UMPC - Sorbonne Université) and Ruben Di Battista (PhD student DGA/X - CMAP).
Course language: French
- Profesor: Breden Maxime
- Profesor: Gallois Sylvain
- Profesor: Houssier Quentin
- Profesor: Loison Arthur
- Profesor: Massot Marc
- Profesor: Series Laurent