Ricardo Cortez, Pendergraft William Larkin Duren Professor, Mathematics Department, Tulane University.
Many interesting biological phenomena involve thin flexible filaments interacting with a fluid. Some examples are the motion of microorganisms through the actuation of flagella, the coordinated motion of cilia, and the swimming of spermatozoa. I will present computational models of microscopic filaments in a fluid based on the method of regularized Stokeslets, which is a technique for removing the singularity of fundamental solutions of certain partial differential equations. Examples will include simulations of sperm motility that shed light on the effect of asymmetry in the flagellar beat patterns and on interactions with a nearby surface, which are important in fertilization. Effects of elastic polymers immersed in the fluid are incorporated through a network of cross-linked nodes where each link is modeled by a simple viscoelastic element. If time allows, I will also present ongoing work with passive fibers in shear flows.