Mathematics Colloquia and Seminars

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The dynamics of bodies immersed in fluids is a sub ject of great practical and biolog- ical interest. Fluid/body interaction systems are ubiquitous, ranging from large-scale applications like swimming and flying, to more recent work in the fields of microfluidic devices, materials engineering, and micro-scale biofluiddynamics. We will discuss two such problems, motivated by recent experiments in the NYU Applied Math Lab. First, in order to understand the role of flexibility in flapping flight, we analyze a heaving wing system with passive pitching. Experimental results are reproduced qualitatively: we find flapping frequencies corresponding to very efficient locomotion, a regime of under-performance when compared to a rigid wing, and a bi-stable regime where the flapping wing can move either “forward” or “backward.” We find that a particular phase relationship corresponds to this direction reversal, and we consider the importance of various dimensionless parameters. Second, we will discuss a fluid-ratchet mechanism that is exhibited by a shape- changing body in an oscillating fluid. We find that such a body can maintain its altitude, or even ascend, against a gravitational force. Simple analytical models are shown to match the dynamics explored in numerical simulations. Other related phe- nomena are also considered.