North Carolina State University
Applied Mathematics Graduate Student
Office: SAS 3223
Foundations of Advanced Mathematics
Time: Tuesday, Thursday 11:45am-1:00pm
Room: SAS 1218
Introduction to mathematical proof with focus on properties of the real
number system. Elementary symbolic logic, mathematical induction,
algebra of sets, relations, functions, countability. Algebraic and
completeness properties of the reals.
- M.S. in Applied Mathematics from North Carolina State University,
Raleigh, NC, May 2009
- B.S. in Mathematics from Wittenberg University, Springfield, OH,
I am currently working with Dr. Michael
Shearer studying the flow
. We are studying thin films influenced by
surfactant (a surface tension
reducing agent) both on a horizontal
substrate and an inclined plane. Some applications for this research
are surfactant replacement therapy, coating flows, and food science.
The motion of the film is modeled in the lubrication approximation by a
fourth order system of nonlinear PDE. On the inclined plane the film is
driven by both surfactant and gravity. A traveling wave solution
exists for this system which consists of a piecewise constant height
profile and a piecewise linear surfactant profile. We are
examining the stability of this solution both numerically and
analytically. Along with Daniels' Nonlinear
, we are also considering a film on a horizontal substrate
driven only by surfactant. We are experimentally studying the
location of the surfactant molecules in relation to the movement of the
height of the film. Numerically we model the evolution of the
height of the film with respect to the surfactant concentration. When
physical influences such as gravity, capillarity and surface diffusion
are ignored the system of equations emits a self-similar solution. We
are examining these solutions both numerically and asymptotically.
- E. Peterson, M. Shearer, T.
Witelski, R. Levy, Stability of
Traveling Waves in Thin Liquid Films Driven by Gravity and Surfactant,
Proceedings, 12th International Conference on Hyperbolic Problems:
Theory, Numerics, Applications, Hyp 2008, To appear.
- 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. 2175-2183, 2007
- Joint Mathematics Meetings, San Francisco, CA, Spreading Surfactant on a Thin Liquid Layer,
- APS-DFD, Minneapolis, MN, Surfactant
Spreading on a Thin Liquid Layer: Modeling and Theory, November
- SIAM Annual Meeting, Denver, CO, Insoluble Surfactant Spreading on a
Horizontal Thin Liquid Film, July 2009
- Triangle Soft Matter Workshop, North Carolina State University, Thin Fluid Films with Surfactant,
poster and soundbite, May 2009
- SAS Hall Dedication, North Carolina State University, Thin Fluid Films with Surfactant,
poster, May 2009
- Higher Order Geometric Evolution Equations: Theory and
Applications from Microfluidics to Image Understanding, IMA-University
of Minnesota, Thin Fluid Films with
Surfactant, poster, March 2009.
- North Carolina State University Graduate Recruitment Day, Shock Waves: Flow of Thin Liquid Films,
- Thin Films Day, North Carolina State University, Flow of Thin Films with Surfactant:
Behavior of Perturbations, January 2009
- Promoting Diversity at the Graduate Level in Mathematics: a
National Forum, MSRI, October 2008