Do Barnacles Understand Advection and Diffusion?
Dan Anderson, George Mason University
Barnacles have been studied by scientists and biologists since the time of Charles Darwin (1850s). In their adult stage, these marine-dwelling invertebrates permanently attach themselves to a substrate that may be a rocky tidal shoreline, a ship or sailboat hull or possibly other marine life such as a whale. As a consequence, barnacles are also well known for their bio-fouling tendencies that can plague the shipping industry and other maritime activities. Attached as they are to their substrate while residing inside their exoskeleton, barnacles rely on the physics of fluid mechanics and diffusion as well as a good choice of home to provide a nearby food supply. In their larval stage barnacles are swimmers and also rely on advection and diffusion to find a good home. In addition to the external fluid environment, barnacles have a complex internal structure that involves, among other things, micro-scale channels through which fluid and/or chemicals can be transported.
The object of the present project is to explore models for advection and/or diffusion in the context of population dynamics models for adult and larval stage barnacles and also to investigate possible transport mechanisms inside the barnacle. The specific tasks involved in this project will include background reading/research on barnacles, mathematical modeling techniques, numerical solutions of ordinary and partial differential equations as well as asymptotic methods.