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Self-propulsion in viscous fluids through shape variations

Lunedi' 19 Settembre 2011 - Marco Morandotti

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Lunedi` 19 Settembre 2011 alle ore 12:15 in aula 2AB40 Marco Morandotti (SISSA, Trieste) terra' un seminario dal titolo "Self-propulsion in viscous fluids through shape variations".

-Abstract
I will present a model for micro-swimmers in viscous fluids. In the vanishing Reynolds number regime, Stokes' (or Brinkman's, in case of a particulate fluid) equation 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 a monodimensional swimmer in a viscous fluid. In this case, the equations of motion are derived from an approximate theory, and optimality and control theoretic results are discussed. This is joint work with Gianni Dal Maso and Antonio DeSimone.

Rif. int. M. Bardi, C. Marchi, F. Rampazzo

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