How Microorganisms swim using gauge theory

Professor Richard Montgomery, Department of Mathematics, University of California, Santa Cruz

In 1989 the physicists Shapere and Wilczek showed that gauge theory provides a framework for understanding swimming in very viscous fluids. They used this framework to describe how spheres and circles can swim using infinitesimal shape deformations. Although the framework is quite elegant, these swimming strokes had been understood using traditional fluid dynamics by biofluiddynamicists. I will describe how Kurt Ehlers, a graduate student at UCSC, was able to use the Shapere-Wilczek framework to move beyond circles and spheres to describe the swimming of planar ellipses and other more general classes of 2 dimensional objects. The methods promise to work for 3 dimensional objects with rotational symmetry as well. To obtain his results Ehlers significantly clarified and simplified the framework of Shapere and Wilczek. We will describe the resulting algorithm for calculating swimming strokes at low Reynold's number. We will suggest possible applications, including one for a miniature very low Reynolds number pump.