On the form of fish and trees

During this talk, I will consider two distinct problems of fluid-structure interactions applied to biological systems.
First, I will address an optimization problem of undulatory swimming at high Reynolds number: Given a certain volume of neutrally buoyant material, what form should this volume take and what motion should it perform such that the energetic cost is minimized, the swimming velocity is maximized, or any trade-off between the two?
Second, I will discuss Leonardo???s rule for trees, which states that the cross-sectional area of branches is conserved across branching nodes. I will show that this rule arises naturally in self-similar branching structures designed to resist wind-induced loads.