In-depth courses in conjunction with the Transport and Diffusion module will be proposed. The course structure will be flexible, personal work on documents playing a key role, eventually preceded by some introcutory courses. They will lead to a detailed thesis and a defense.
Here are two types of proposed subjects:
- Collective move models
Collective dynamics appear at every scale of the living world: from bacteria to birds, orgnanisms arrange themselves to move efficiently in groups. Duplicate this type of decentralized organization is also an active research field in robotics. Based on recent works, students will build a model for a specific scope. This model study will be conducted thanks to digital simulations and the derivation of macroscopic models.
- Pattern formation phenomenon
In 1952, Alan Turing proposed an unstability model to explain the pattern formation in biology. Based on the spectral analysis of parabolic PDEs, its analysis produced several works in development biology, and more recently in ecology and evolutive biology. Students will study these dynamics from existing models developing adapted digital codes and proposing analysis methods (spectral methods or energy methods depending the problems).
- Profesor: Golse François
- Profesor: Raoul Gael