Ellen Peterson

  Picture of Ellen  
North Carolina State University
Applied Mathematics Graduate Student
Office: SAS 3223

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.


Current Research:

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.