SEMINAIRE MERCREDI 7 MARS 2007
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Jean-Luc Thiffeault
Imperial College, Angleterre

Titre: Les aspects topologiques du mélange

Abstract: In a fluid, stirring is usually necessary to overcome the slow
diffusion of most substances. This is important in a wide range of
applications, from industry to geophysics. Here I focus on a
prototypical application, the stirring of a two-dimensional viscous
fluid with rods. Mathematically, stirring rods can be viewed as
'punctures' in a two-dimensional surface. They present topological
obstructions to material lines in the fluid. The theory developed by
Nielsen and Thurston to classify the possible periodic motions in such
a system can be used to decide which stirring methods are best. Global
aspects of the concentration field of a substance in the stirring
device can then be determined via 'train tracks', which are skeletons
of an important structure called the unstable foliation. Since there
are only a limited number of possible train tracks, all stirring
protocols can be classified, as well as their properties. This can be
extended to completely general situations where rods are replaced by
periodic orbits. I will present experimental and numerical examples of
all these concepts. Finally, I will introduce a stirring device
designed and optimized using these topological principles.