GALCIT Colloquium

During this talk, I will present three optimization calculations involving the interaction between a fluid and a deformable biological organism. The first problem is to calculate the branch diameters in a tree such that it can resist wind-induced fracture with the least amount of matter. As I will show, this calculation yields a simple law that was first observed by Leonardo da Vinci more than 500 years ago: the cross-sectional area of branches is conserved on average across branching nodes. The second problem arises from the following observation: cilia, which are whip-like organelles ubiquitously used by eukaryotic cells, possesses a highly conserved internal structure; however their beating kinematics can be very diverse. To address this diversity, the optimal pumping kinematics of an elastic filament attached to a wall will be computed in the limit of small Reynolds number. Finally, the third problem concerns the optimization of undulatory swimming, a mode of locomotion used by the majority of aquatic animals. Given a certain volume of neutrally buoyant material, what form should this volume assume and what undulatory motion should it perform such that the energetic costs are minimized, the swimming velocity is maximized or any trade-off between the two?