Michael B. Gratton, Graduate Student

Michael B. Gratton

I work on thin fluid film and related nonlinear parabolic partial differential equations.

Office Location:  021 Physics Bldg
Office Phone:  (919)-660-2833
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~mgratton/

Education:

PhDDuke University2008
MADuke University2004
BSHarvey Mudd College2002
Specialties:

Applied Math
Research Interests: Dewetting and coarsening of thin fluid films

Current projects: Coarsening thin films, Distribution models for coarsening systems, Dewetting instabilities in thin films

Liquid films will "bead" into droplets when spread thin over a surface. The beading (dewetting) depends on the liquid and the surface, and will often leave the drops connected by a nanometers-thick adsorbed layer of fluid.
I study the interactions of these connected drops, specifically the slow dynamics that cause these drops to aggregate into fewer, larger drops. I use numerical simulation of a dynamical system derived from the lubrication equation, Liftshitz-Slyozov-Wagner style distribution equation models, and direct simulation of the PDE to study the phenomena.

Areas of Interest:

Thin Fluid Films
Surfactants
Coarsening
Dynamical Systems
Mathematical Modeling

Keywords:

fluid films • coarsening • dynamical systems • mathematical modeling

Duties:

Graduate Student Representative 2004 -- 2005, 2006 -- 2007
Recent Publications

  1. M.B. Gratton and T.P. Witelski, Coarsening of dewetting thin films subject to gravity, Phys. Rev. E., vol. 77 (January, 2008), pp. 016301
  2. M.B. Gratton et. al., Backward Diffusion methods for digital halftoning, in Proceedings of the Twenty-Second Annual Workshop on Mathematical Problems in Industry (June, 2006), pp. 1 -- 15
Selected Curriculum Innovations

  1. Curriculum Innovations, 2007    
Selected Other

  1. Math Problems in Industry (MPI) Workshop, June, 2004, University of Deleware    
  2. Graduate Student Mathematical Modeling Camp, June, 2004, Rensselaer Polytechnic Institute    
  3. Math Problems in Industry (MPI) Workshop, June, 2005, Worcester Polytechnic Institute    
  4. Graduate Student Mathematical Modeling Camp, June, 2005, Rensselaer Polytechnic Institute    
  5. Math Problems in Industry (MPI) Workshop, June, 2006, Olin College    
  6. Math Problems in Industry (MPI) Workshop, June, 2007, University of Delaware    
  7. Mathematics in Medicine Study Group 2007, September 10, 2007, University of Southampton    
Selected Meetings

  1. Gravity's effect on thin film coarsening, September 19, 2007, Imperial College (Euromech 2007)    
  2. Backwards diffusion methods in digital halftoning, October, 2007, SIAM Conference on Mathematics in Industry (Philadelphia)    
  3. Coarsening of unstable thin films subject to gravity, November, 2007, American Physical Society/Division of Fluid Dynamics