Nick Moore
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MATHEMATICS COLLOQUIUM
Speaker: Nick Moore Abstract. In many natural settings, moving boundaries interact with fluid flows in a nontrivial way. I will discuss how to model such interactions in the context of two examples, one taking inspiration from geophysics and the other from biology. In the first, I will discuss how fluid flows sculpt solid material through the processes of erosion and dissolution. Due to the interaction with the surrounding flow, a solid body converges to an equilibrium form as it shrinks. The final shape, though, is process dependent, with erosion forming sharp features and dissolution smooth ones. In each case, determining the equilibrium shape can be posed as a singular Riemann-Hilbert problem, and a class of exact solutions captures both equilibrium geometries. The Riemann-Hilbert framework thus unifies these two distinct physical processes. The second part of my talk will address how flying and swimming animals exploit wing/fin flexibility to enhance their performance. To model how the flow interacts with the elastic wing/fin, I combine asymptotic analysis of the Euler equations with a fast Chebyshev PDE solver for the beam equation. Numerical optimization shows that concentrating flexibility near a wing-F¢s leading edge maximizes thrust production, and this arrangement resembles the torsional-joint mechanism found in insect wings. |