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, 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

Recent Publications
  1. T.P. Witelski, The subtle art of blowing bubbles (News and Views: Fluid Dynamics), Nature Physics, vol. 5 (May, 2009), pp. 315-316 (doi:10.1038/nphys1265.) [=NDgyMTgzMzQS1&mt=1&rt=0]
  2. H.-J. Hwang and T.P. Witelski, Short-time Pattern formation in thin film equations, Discrete and Continuous Dynamical Systems A, vol. 23 no. 3 (March, 2009), pp. 867-885, ISSN 1078-0947 (doi: 10.3934/dcds.2009.23.867.) [displayArticles.jsp]
  3. M. B. Gratton and T.P. Witelski, Transient and self-similar dynamics in thin film coarsening, Physica D, vol. 238 no. 23-24 (2009), pp. 2380-2394
  4. L. B. Smolka and T. P. Witelski, On the planar extensional motion of an inertially driven liquid sheet, Physics of Fluids, vol. 21 no. 4 (2009), pp. 042101 [042101]
  5. T.P. Witelski and M. Bowen, Singular perturbation theory, Scholarpedia, vol. 4 no. 4 (2009), pp. 3951 [Singular_perturbation_theory]