Math @ Duke

Michael B. Gratton, Graduate Student
I work on thin fluid film and related nonlinear parabolic partial differential equations. Please note: Michael has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
 Education:
PhD  Duke University  2008 
MA  Duke University  2004 
BS  Harvey Mudd College  2002 
 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 nanometersthick 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, LiftshitzSlyozovWagner 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
 Curriculum Vitae
 Recent Publications
 M.B. Gratton and T.P. Witelski, Coarsening of dewetting thin films subject to gravity,
Phys. Rev. E., vol. 77
(January, 2008),
pp. 016301
 M.B. Gratton et. al., Backward Diffusion methods for digital halftoning,
in Proceedings of the TwentySecond Annual Workshop on Mathematical Problems in Industry
(June, 2006),
pp. 1  15
 Selected Curriculum Innovations
 Curriculum Innovations, 2007
 Selected Other
 Mathematics in Medicine Study Group 2007, September 10, 2007, University of Southampton
 Math Problems in Industry (MPI) Workshop, June, 2007, University of Delaware
 Math Problems in Industry (MPI) Workshop, June, 2006, Olin College
 Math Problems in Industry (MPI) Workshop, June, 2005, Worcester Polytechnic Institute
 Graduate Student Mathematical Modeling Camp, June, 2005, Rensselaer Polytechnic Institute
 Math Problems in Industry (MPI) Workshop, June, 2004, University of Deleware
 Graduate Student Mathematical Modeling Camp, June, 2004, Rensselaer Polytechnic Institute
 Selected Meetings
 Coarsening of unstable thin films subject to gravity, November, 2007, American Physical Society/Division of Fluid Dynamics
 Backwards diffusion methods in digital halftoning, October, 2007, SIAM Conference on Mathematics in Industry (Philadelphia)
 Gravity's effect on thin film coarsening, September 19, 2007, Imperial College (Euromech 2007)


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

