Applied Math Seminar
Spring Quarter 2007
Friday October 26, 3:15p.m.Jon Wilkenin
Shape Optimization of Swimming Sheets.
Motivated by the propulsion mechanisms adopted by gastropods, we consider shape optimization of a flexible sheet which propels itself over a thin layer of viscous fluid by propagating deformation waves along its body. We use a lubrication approximation to model the dynamics and derive the relevant Euler-Lagrange equations to optimize swimming speed and efficiency. We present a fast, highly accurate method for solving the optimization equations and explore the solution in various singular limits. We also monitor the validity of the model using a new rigorous error estimate for Reynolds' approximation.
Seminar website: http://math.stanford.edu/~applmath/