**Marco Morandotti**

**Afilliation:**Department of Mathematical Sciences, Carnegie Mellon University

**Title:**Self-propulsion in viscous fluids through shape variations

**Abstract:**I will present a model for micro-swimmers in viscous fluids, both plain and particulate. Given the Reynolds number is very low, Stokes' and Brinkman equations can be used to govern the velocity and the pressure of the surrounding, infinite fluid. Imposing a no-slip boundary condition, allows to relate the deformation of the swimmer to the fluid velocity field, while self-propulsion is the constraint through which we can reduce, via an integral representation of the viscous forces and momenta, the equations of motion for the swimmer to a system of six ODEs. Under mild regularity assumptions, an existence and uniqueness theorem for the motion is proved. Eventually, I will focus on the case of a flagellum swimming in a viscous fluid. In this case, the equations of motion are derived from an approximate theory, and optimality results are discussed. This is joint work with Gianni Dal Maso and Antonio DeSimone.

**Slides:**MorandottiMarco.pdf

**Video File:**race.avi