Mathematics Colloquia and Seminars

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At the small scale of a cell swimming in water, inertial effects are unimportant. Therefore, the motion of the fluid is governed by Stokes equations, which are linear. Nevertheless, there are many situations in which nonlinear effects are important. In this talk I will describe two such situations. The first is swimming in a viscoelastic material, which is motivated by the fact that many microorganisms move in non-Newtonian media such as mucus. I will present a simple model that shows how fading memory affects swimming speed. We will also present experimental results for a helix swimming in a viscoelastic fluid. The second situation I will consider is the synchronization of rotors via hydrodynamic interactions. This problem is motivated by the observed coordination of nearby beating cilia.