Dr. Danielle D. Carr Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010
Mathematical biology is the study of the life sciences that uses mathematical models to help predict and interpret what we observe. My research can be broken into two distinct areas. One is based on the mathematical model that governs the transport system inside the nerve cell. This gives rise to a reaction-hyperbolic system of PDE's for which global existence of solutions is proven. The second area involves a computational method used to describe swimming of the lamprey fish. This method solves the Navier-Stokes equations for viscous, incompressible fluids. This study will be useful in determining the fundamental properties of neural networks that govern involuntary rhythmic behavior of vertebrates.