
Thomas P. Witelski, Professor of Mathematics and CNCS: Center for nonlinear and complex systems 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.
 Contact Info:
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)
 Postdocs Mentored
 Undergraduate Research 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
 Recent Publications
(More Publications)
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 Ji, H; Witelski, TP, Instability and dynamics of volatile thin films, vol. 3 no. 2
(February, Submitted, 2018) [doi]
 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]
Journal editorial boards
Other Activities
