for Nonlinear Analysis
RTG Postdoctoral Associate
Office: Wean Hall 7122
Math 21-369: Numerical Methods
Time: Monday, Wednesday, Friday 12:30-1:20
Room: Porter Hall A18A
This course provides an introduction to the use of computers to solve
scientific problems. A variety of numerical algorithms and applications
will be discussed. In-class demonstrations and examples will be
presented using MATLAB.
My research interests include the
dynamics of fluid flow, specifically thin liquid films. My PhD thesis
focused on the spreading of an initially uniform layer of liquid driven
by surfactant (a surface tension reducing agent). I investigated
this problem using numerical techniques and asymptotic methods. We also
compared the mathematical model, a fourth order nonlinear PDE system of
equations: one equation for the height of the film and another for the
surfactant concentration, to experimental results.
I am currently examing the flow of a
thin film when a droplet of another substance is deposited. This
problem encorporates various issues including the non-newtonian
behavior of the underlying film and that the droplet carries soluble
surfactant. This work is
in collaboration with the Interfacial
Physics Group at Carnegie Mellon. We are investigating the
spreading of an aerosol medicine in the lungs as a treatment for cystic
- E. R. Peterson, M. Shearer, Radial Spreading of Surfactant on a
Thin Liquid Film, Applied Mathematics Research Express, 2010.
- E. Peterson, M. Shearer, T. Witelski, R. Levy, Stability of
Traveling Waves in Thin Liquid Films Driven by Gravity and Surfactant,
Proceedings, Proceedings of Symposia in Applied Mathematics, Vol 67, No
2, 855-868, 2009.
- A. Denies, E. Peterson, D. Boeckner, J. Boyle, A. Keighley, J.
Kogut, J. Lubben, R. Rebarber, R. Ryan, B. Tenhumberg, S. Townley, A.J.
Tyre, Robust Population Management Under Uncertainty for Structured
Populations Models, Ecological Applications, Vol 12, No. 8, pp.
- Ph.D. in Applied Mathematics from North Carolina State
University, Raleigh, NC, August 2010
- M.S. in Applied Mathematics from North Carolina State Univeristy,
Raleigh, NC, May 2009
- B.S. in Mathematics from Wittenberg University, Springfield, OH,