# DE Seminar / Applied Math Colloquium: Dr. Silas Alben

## University of Michigan

Friday, March 29, 2019

2:00 PM - 3:00 PM

2:00 PM - 3:00 PM

Mathematics/Psychology : 104

**Title:**Dynamics and locomotion of flexible foils in fluid and frictional environments

**Speaker: **Silas Alben, University of Michigan

**Abstract:**Flexible foils have long been used as a generic model for the bodies and appendages of organisms (e.g. fish and snakes) in locomotion. To understand the range of possible dynamics including efficient locomotion, we have used analysis and computations together with experiments to study flexible foils in fluid and frictional environments. In both situations, resonances can occur at certain flapping frequencies, scaled by elastic and fluid parameters. Resonances correspond to peaks in propulsive force, but also input power supplied to the foil, and are often states of low efficiency. Other generic phenomena are the transition from periodic to non-periodic and chaotic dynamics as the heaving amplitude increases or the bending rigidity decreases, and the spontaneous emergence of traveling wave motions. We have determined more generally which planar snake motions are optimal for efficiency. The optimal motions help to explain the widespread observations of traveling wave motions in biological snakes.