Ellen
Peterson

North Carolina State University

Applied Mathematics Graduate Student

Office: SAS 3223

erpeters@ncsu.edu

Office: SAS 3223

erpeters@ncsu.edu

MA 225-003:
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.

CV

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.

CV

Education:

- M.S. in Applied Mathematics from North Carolina State University, Raleigh, NC, May 2009
- B.S. in Mathematics from Wittenberg University, Springfield, OH, May 2006

Current Research:

Funding:

I am currently working with Dr. Michael
Shearer studying the flow
of thin
liquid films. 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
Lab, 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,
January 2010

- APS-DFD, Minneapolis, MN, Surfactant
Spreading on a Thin Liquid Layer: Modeling and Theory, November
2009

- 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, February 2009
- 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

Funding:

- NSF Research Training Group (RTG): Mathematics of Materials January 2008-present