A traditional presentation of the laboratory would involve putting forward mathematical tools that are studied and used. That would be neglecting the important fact that a substantial part of the work is placed at the interface with other sciences and that those tools are developped or simply used having in mind a better understanding of models coming directly from applications. That would also be neglecting the fact that the same mathematical tool can be used in fields as far apart as signal analysis and quantum chemistry. A presentation in structured teams would probably hide this double reality. In the present configuratrion, researchers are open to work in whatever subject is presented to them and are strongly encouraged to put their skills in common as opportunities arise.

The UMR (Mixed Research Unit) hosts many internationally recognized scientific personalities. While maintaining my scientific legitimacy, I coordinate it relying on the advice of the council of the laboratory. With the Deputy Director Edwige Godlewski, I strive to infuse dynamism which pushes researchers to work here every day ... and be open to new applications. Professors, researchers and PhD students meet and exchange easily. Many pairings are born over coffee ! To ensure consistency in the laboratory, "internal days" are held three times a yea during which each of us tells the other what he’s presently working on.

#### NUMEROUS COLLABORATIONS WITh THE INUDSTRY.

We work with large companies such as PFA, Saint-Gobain, EADS, Michelin, EDF, many car (equipment) makers .... and CEA. We just began a major modeling work for the magnetic fusion project "ITER" at Cadarache. We would like to extend our collaboration to SMEs : they can also become more competitive through mathematics.

#### NOT ONLY APPLIED MATHEMATICS.

Mathematics is a world in which we find ourselves well. Once a problem is solved, other questions arise. If they are not directly motivated by applications, they could later shed light to some phenomenon interesting physicists or chemists. Fluid mechanics is a major theme of our research : if the equations have been known for over a century, we still do not know if the problem is well posed ! The analysis of the Navier-Stokes equations requires our scientists to think differently, and progress is gradually building-up knowledge on the subject. We have also developed approaches to more reliable computer calculations, the ’a posteriori estimates’. They allow numerical analysts and engineers to quantify the distance between the mathematical resolution and reality.

#### MAIN FIELDS OF APPLICATIONS.

We are strengthening our work in the biomedical field through partnerships, for example with doctors from the Necker or Pitié-Salpêtrière hospitals. We especially worked on the aftermath of an operation performed to newborns, coarctation of the aorta. As a teenager, heart failure is associated with images of aortas poorly redrawn, angular or bent too. Is the deformation induced by the heart failure or vice versa ? To help physicians answer this question, we simulate a blood flow pulsating in a "mathematical elastic hose" and analyze the fluid flow. We then understand the differences in pressure, movement of the aorta, its resistance ... Mathematical modeling is used to focus on the dominant phenomena and thus provide a better understanding of the root causes of a disease.

#### LUNGS ARE NOT AS EASILY SIMULATED AS HEART…

They do not have a single engine as the heart pump : all cells act like little bellows. Breathing involves 23 successive bifurcations : our models begin to reproduce until the tenth. The ones we do not manage yet to be imaged ... we imagine !

Yvon Maday - 09/05/12