Quick Links



2014-04-15 - Kathleen Hoffman
2014-10-14 - Howard Elman


2011-02-01 - Shawn Walker


Tuesday, February 1, 2011
101 Stanley Thomas Hall
Tulane University (Uptown)

Refreshments will be served


Shawn W. Walker, Department of Mathematics, Louisiana State University


Shape Optimization of Chiral Propellers in 3-D Stokes Flow


Locomotion at the micro-scale is important in biology and in industrial applications such as targeted drug delivery and micro-fluidics. We present results on the optimal shape of a rigid body locomoting in 3-D Stokes flow.  The actuation consists of applying a fixed moment and constraining the body to only move along the moment axis; this models the effect of an external magnetic torque on an object made of magnetically susceptible material. The shape of the object is parametrized by a 3-D centerline with a given cross-sectional shape. No a priori assumption is made on the centerline. We show there exists a minimizer to the infinite dimensional optimization problem in a suitable infinite class of admissible shapes. We develop a variational (constrained) descent method which is well-posed for the continuous and discrete versions of the problem. Sensitivities of the cost and constraints are computed variationally via shape differential calculus. Computations are accomplished by a boundary integral method to solve the Stokes equations, and a finite element method to obtain  descent directions for the optimization algorithm. We show examples of locomotor shapes with and without different fixed payload/cargo shapes.

Center for Computational Science, Stanley Thomas Hall 402, New Orleans, LA 70118