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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Marco Morandotti
Center for Nonlinear Analysis, Carnegie Mellon University
Title: Self-propulsion in viscous fluids through shape deformation.

Abstract: I will present a model for micro-swimmers in viscous fluids, both plain and particulate. Given that the Reynolds number is very low, Stokes' and Brinkman's equations can be used to govern the velocity and the pressure of the surrounding, infinite fluid. Imposing a no-slip boundary condition allows relating 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 one-dimensional swimmer in a viscous fluid. In this case, the equations of motion are derived from an approximate theory, and optimality results are discussed. This is partially joint work with Gianni Dal Maso and Antonio DeSimone (SISSA, Trieste, Italy).

Recording: http://mm.math.cmu.edu/recordings/cna/CNA-MarcoMorandotti-Apr-17-2012.avi
Recording: http://mm.math.cmu.edu/recordings/cna/CNA-MarcoMorandotti-Apr-17-2012.mp4
Date: Tuesday, April 17, 2012
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer