## Section: Application Domains

### Swimming at low-Reynolds number

The study of the swimming strategies of micro-organisms is attracting increasing attention in the recent literature. This is both because of the intrinsic biological interest, and for the possible implications these studies may have on the design of bio-inspired artificial replicas reproducing the functionalities of biological systems. In the case of micro-swimmers, the surrounding fluid is dominated by the viscosity effects of the water and becomes reversible. This feature, known as the scallop theorem in that context needs to be circumvented when one wants to swim with strokes that produce a net motion of the swimmer. In this regime, it turns out that the dynamic of a micro-swimmer could be expressed as an ordinary differential equation. First of all, by stating that the swimmer controls its own shape, we focus on finding the best strategy to swim (by minimizing a time or an energy). Moreover, we work on the control and optimal control of magnetic micro-swimmers. The latter micro-device is charged in order to be deformed by an external magnetic field. In this case, the control functions are the external magnetic field. And we wonder whether it is possible to control the position of the swimmer by acting on this external magnetic field. We are also interested in the associated optimal control problem (acting on the magnetic field in such a way that the swimmer reaches a desired position as soon as possible).