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Thomas P. Witelski, Professor of Mathematics and Professor of Mechanical Engineering and Materials Science
My primary area of expertise is the solution of nonlinear ordinary and partial differential equations for models of physical systems. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in engineering and applied science. Focuses of my work include problems in viscous fluid flow, dynamical systems, and industrial applications. Approaches for mathematical modelling to formulate reduced systems of mathematical equations corresponding to the physical problems is another significant component of my work.
Office Location:  295 Physics Bldg, Box 90320, Durham, NC 277080320 
Office Phone:  (919) 6602841 
Email Address:  
Web Pages:  http://fds.duke.edu/db/aas/math/faculty/witelski http://www.researcherid.com/rid/G53892016 
Teaching (Spring 2018):
 MATH 577.01, MATHEMATICAL MODELING
Synopsis
 Gray 228, TuTh 10:05 AM11:20 AM
 Office Hours:
 Mondays 10:00amnoon and Tuesdays noon2:30pm
 Education:
Ph.D. California Institute of Technology 1995 B.S.E. Cooper Union 1991
 Specialties:

Applied Math
Applied Math
 Research Interests: Fluid Dynamics, Perturbation Methods, Asymptotic Analysis, Nonlinear Ordinary and Partial differential equations
My primary area of expertise is the solution of nonlinear ordinary and partial differential equations via perturbation methods. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in physical systems. Focuses of my work include problems in viscous fluid flow, industrial applications, flow in porous media, mathematical biology, and granular materials. Through my research I am working to extend the understanding of nonlinear diffusion processes in physical systems. Studying problems in a range of different fields has given me a unique opportunity to interact with a diverse set of collaborators and to transfer analytic techniques across the traditional boundaries that separate fields.
 Areas of Interest:
Fluid dynamics
Partial differential equations
Asymptotics/Perturbation methods
Industrial and Applied mathematics
 Keywords:
Differential equations, Nonlinear • Differential equations, Parabolic • Fluid dynamics • Surface Tension
 Current Ph.D. Students
(Former Students)
 Weifan Liu
 Postdocs Mentored
 Rachel Levy (July, 2005  June, 2007)
 Anne Catlla (2005  2008)
 Anand Jayaraman (September 1, 2004  August 15, 2005)
 Sandra Wieland (January 1, 2004  December, 2004)
 Linda Smolka (April 8, 2002  July 1, 2004)
 Karl Glasner (2001/122002/05)
 Mark Bowen (2000/032001/12)
 Undergraduate Researches Supervised
 Veronica Ciocanel (May, 2010  May, 2012)
Honorable mention for 2012 Faculty Scholar, Graduation with Distinction in Mathematics: Modeling and numerical simulation of the nonlinear dynamics of the forced planar string pendulum  Jeremy Semko (May, 2009  May, 2010)
Thesis: Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface  Lingren Zhang (July, 2006  September, 2006)
Thesis: The Motion of Sets of Vortices
Undergraduate summer research  Qinzheng Tian (July, 2005  September, 2005)
Thesis: Simulation of Newtonian fluid fluid between rotating cylinders
Undergraduate summer research
 Veronica Ciocanel (May, 2010  May, 2012)
 Recent Publications
(More Publications)
(search)
 Gao, Y; Ji, H; Liu, JG; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol. 350 (July, 2017), pp. 1325 [doi]
 Ji, H; Witelski, TP, Finitetime thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol. 342 (March, 2017), pp. 115 [doi]
 George, C; Virgin, LN; Witelski, T, Experimental study of regular and chaotic transients in a nonsmooth system, International Journal of NonLinear Mechanics, vol. 81 (2016), pp. 5564 [doi]
 Sanaei, P; Richardson, GW; Witelski, T; Cummings, LJ, Flow and fouling in a pleated membrane filter, Journal of Fluid Mechanics, vol. 795 (2016), pp. 3659 [doi]
 Smolka, LB; McLaughlin, CK; Witelski, TP, Oil capture from a water surface by a falling sphere, Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 497 (2016), pp. 126132, ISSN 09277757 [doi]
Journal editorial boards
 Journal of Engineering Mathematics
 Discrete and Continuous Dynamical Systems B
 European Journal of Applied Mathematics
 Journal of Mathematical Analysis and Applications
 International Journal of Mathematics and Math Sciences
 Research on fluid dynamics of thin viscous films

Mathematical Problems in Industry Workshop 2007: University of Delaware, June 1115,2007
 Scientific Computing and Applied Mathematics
 Applied Math Web Resources guide
 myX: a simple C/C++ programming interface for X11 graphics
 As seen on RateMyProfessors.com
 Tom's favorite integral
 Great quotes in mathematical modeling
 Colin: It's obvious!
Peter: It's "obvious" in what sense?
[...]
Colin: [paraphrased] Nevermind, its wrong :)
 Colin: It's obvious!