Department of Mathematical Sciences
University of Delaware
501 Ewing Hall
Newark, DE 19716
Phone: (302) 831- 1869
Fax: (302) 831- 4511
Ph.D., Applied Mathematics, Northwestern University – 1991
M.S., Mechanical Engineering, Santa Clara University – 1987
B.S., Mechanical Engineering, Santa Clara University – 1983
Dr. Braun’s current research focuses on several areas. The primary area is tear film dynamics in the human eye. A hierarchy of models in under development for the tear film dynamics that describes the evolution of the tear film over multiple blink cycles. There are challenges in both developing the mathematical models in the first place as well as in their solution via computational methods. The mathematical models use the lubrication approximation to derive nonlinear partial differential equations for the film thickness and other variables of interest; translation of ophthalmology and optometry literature into appropriate equations is a significant part of the project. Solving the resulting models is very difficult for many standard methods and new computational methods are under development for these challenging dynamical problems.
A second area of interest is dynamics on networks; an epidemiological model for alcohol problems was developed with several collaborators. The model uses a threshold for each person (node) on social networks (Poisson random graphs and small world networks) and a nonlinear equation for the state of each person to calculate the evolution of the population (a given network configuration). The model can simulate different treatment strategies. This type of theory is readily adapted to other networks besides social networks.
Prior to joining the University of Delaware, Dr. Braun was a postdoctoral scientist in what is now the Mathematical and Computational Sciences Division of the Information Technology Laboratory at the National Institute of Standards and Technology in Gaithersburg, MD, from 1991 to 1995.