The Ph.D. Program in Computational Biology & Bioinformatics (CBB) is an integrative, multi-disciplinary training program that encompasses biology using computational and quantitative methods. In and out of the classroom, students learn to apply the tools of statistics, mathematics, computer science and informatics to biological problems. Vibrant and innovative research in these fields provides exciting interactions between biological and computational scientists. Because CBB is based in the Duke Center for Genomic and Computational Biology (GCB), it offers a unique opportunity for students to become tomorrow's leaders in genome sciences.
The focus of our research group is to use mathematical modeling techniques to better understand aspects of renal physiology. In particular, we are interested in the efficiency and synergy of various mechanisms of renal hemodynamics. We work with physiologists to formulate detailed models of the renal hemodynamics. Model simulations and predictions are then used to better understand hemodynamic mechanisms in physiological and pathophysiological conditions.
Multiscale numerical methods. I develop multiscale numerical methods---multi-implicit Picard integral deferred correction methods---for the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widely-differing characteristic time scales (e.g., combustion, transport of air pollutants, etc.). These methods avoid the solution of nonlinear coupled equations, and allow processes to decoupled (like in operating-splitting methods) while generating arbitrarily high-order solutions.
Numerical methods for immersed boundary problems. I develop numerical methods to simulate fluid motion driven by forces singularly supported along a boundary immersed in an incompressible fluid.