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Research Interests for Thomas P. Witelski

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, dynamical systems, and industrial applications. 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.

Keywords:
Differential equations, Nonlinear, Differential equations, Parabolic, Fluid dynamics, Surface Tension
Areas of Interest:

Fluid dynamics
Partial differential equations
Asymptotics/Perturbation methods
Industrial and Applied mathematics

Recent Publications   (search)
  1. Gao, Y; Ji, H; Liu, J-G; 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. 13-25 [doi]
  2. Ji, H; Witelski, TP, Finite-time thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol. 342 (March, 2017), pp. 1-15 [doi]
  3. George, C; Virgin, LN; Witelski, T, Experimental study of regular and chaotic transients in a non-smooth system, International Journal of Non-Linear Mechanics, vol. 81 (2016), pp. 55-64 [doi]
  4. Sanaei, P; Richardson, GW; Witelski, T; Cummings, LJ, Flow and fouling in a pleated membrane filter, Journal of Fluid Mechanics, vol. 795 (2016), pp. 36-59 [doi]
  5. 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. 126-132, ISSN 0927-7757 [doi]

 

dept@math.duke.edu
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fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320