Fluid dynamics has historically been a driving force in applied mathematics and scientific computing. In biological settings, a level of complexity is added to traditional fluid dynamics since typically biological flows are unsteady, involve active and elastic interfaces, fluid-structure interactions and transport of chemical signals. This Research and Training project, led by faculty in the Departments of Mathematics and Biomedical Engineering at Tulane University, recognizes the need for students trained at the interface of mathematics and the biomedical sciences. Three graduate students, six undergraduate students and two postdoctoral fellows will be supported each year. A broad spectrum of research projects will be emphasized that span mathematical analysis, development and analysis of numerical methods for partial differential equations, modeling of complex biological systems, three-dimensional simulations on high-performance computers, and a two-way coordination of modeling with experiments. Training activities will include a curriculum with core courses from both the Department of Mathematics and the Department of Biomedical Engineering, regular group meetings, a monthly Biofluids All-Hands meeting, a wet-lab and internship program for graduate students and postdocs, professional development seminars, an annual Carnival Focus Days (CFD) workshop and high-performance computing training activities. Moreover, undergraduate students will be fully-integrated into research teams through academic year involvement and intensive summer research.
Mathematics has had a huge impact on the engineering, biological and physical sciences through its development of theoretical analyses and numerical methods. Biological fluid dynamics, in addition to its direct applications in physiology and oceanography, provides a rich educational and training platform for students in the mathematical sciences. Undergraduates, graduate students and postdoctoral students will work in teams, with representation from both Mathematics and Biomedical Engineering, and with an emphasis on the interplay between theory, computation and experiment. Research projects will be motivated by applications, including microorganism motility, pulmonary mechanics, biosensors and cellular biomechanics. All graduate and postdoctoral students will participate in an internship, either at Tulane University or at a partner institution, where they can work side-by-side with experimentalists, develop a comprehensive understanding of various aspects of the research project, and participate in the life of a working fluids lab. The co-PIs, all co-founders of Tulane's Center for Computational Science, have demonstrated commitment to this model of training. They are, themselves, diverse, and have been actively involved in increasing the number of US women and minorities in scientific research. This training program will attract diverse American nationals into the mathematical sciences.
