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

Office Location: | 021 Physics |

Office Phone: | (919)-660-2833 |

Email Address: | |

Web Page: | http://www.math.duke.edu/~mgratton/ |

Starting Year: |
2002 |

Advisor(s): |
Thomas Peter Witelski |

Thesis Title: |
Coarsening of thin fluid films |

Defense Date: |
2008/04/09 |

**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 filmsLiquid 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**- 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

- M.B. Gratton and T.P. Witelski,

**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)