# Mathematics Colloquia and Seminars

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### Swimming on small scales: Physical and mathematical constraints

**PDE and Applied Math Seminar**

Speaker: | Eric Lauga, University of California, San Diego |

Location: | 1147 MSB |

Start time: | Tue, Feb 23 2010, 4:10PM |

Fluid mechanics plays a crucial role in many cellular processes. One example is the external fluid mechanics of motile cells such as bacteria, spermatozoa, and essentially half of the microorganisms on earth. These organisms typically possess flagella, slender whiplike appendages which are actuated in a periodic fashion in a fluid environment, thereby giving rise to propulsion. The type of periodic actuation which cannot be exploited for locomotion was established in 1977 by Purcell, and is referred to as the Scallop theorem: It states that, due to the linearity of Stokes's equations of motion, time-reversible movement (i.e. movement identical under time-reversal) cannot not lead to any average locomotion. In this talk, we ask the following question: What physical and mathematical ingredients are necessary to escape the constraints of the Scallop theorem?