Math @ Duke
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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:
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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
- 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 Twenty-Second 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)
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dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
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