Thomas P. Witelski

Thomas P. Witelski
  • Professor in the Department of Mathematics
  • Professor in the Department of Mechanical Engineering and Materials Science (Secondary)
External address: 295 Physics Bldg, Box 90320, Durham, NC 27708-0320
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2841

Research Areas and Keywords

Analysis

perturbation methods

Computational Mathematics

numerical partial differential equations

PDE & Dynamical Systems

fluid dynamics, nonlinear partial differential equations, dynamical systems, perturbation methods

Physical Modeling

fluid dynamics

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.

Education & Training
  • Ph.D., California Institute of Technology 1995

  • B.S.E., The Cooper Union 1991

Catllá, A. J., et al. “On spiking models for synaptic activity and impulsive differential equations.” Siam Review, vol. 50, no. 3, Sept. 2008, pp. 553–69. Scopus, doi:10.1137/060667980. Full Text

DiCarlo, D. A., et al. “Nonmonotonic traveling wave solutions of infiltration into porous media.” Water Resources Research, vol. 44, no. 2, Feb. 2008. Scopus, doi:10.1029/2007WR005975. Full Text

Gratton, M. B., and T. P. Witelski. “Coarsening of unstable thin films subject to gravity.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 77, no. 1 Pt 2, Jan. 2008, p. 016301. Epmc, doi:10.1103/physreve.77.016301. Full Text

Aguareles, M., et al. “Interaction of spiral waves in the Complex Ginzburg-Landau equation.” Physical Review Letters, vol. 101, no. 224101, 2008.

Gratton, M. B., and T. P. Witelski. “Coarsening of dewetting thin films subject to gravity.” Physical Review E, vol. 77, no. 016301, 2008, pp. 1–11.

Schaeffer, D. G., et al. “Boundary-value problems for hyperbolic equations related to steady granular flow.” Mathematics and Mechanics of Solids, vol. 12, no. 6, Dec. 2007, pp. 665–99. Scopus, doi:10.1177/1081286506067325. Full Text

Levy, R., et al. “Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves.” European Journal of Applied Mathematics, vol. 18, no. 6, Dec. 2007, pp. 679–708. Scopus, doi:10.1017/S0956792507007218. Full Text

Witelski, T. P., et al. “Growing surfactant waves in thin liquid films driven by gravity.” Applied Mathematics Research Express, vol. 2006, Dec. 2006. Scopus, doi:10.1155/AMRX/2006/15487. Full Text

Bowen, M., and T. P. Witelski. “The linear limit of the dipole problem for the thin film equation.” Siam Journal on Applied Mathematics, vol. 66, no. 5, Oct. 2006, pp. 1727–48. Scopus, doi:10.1137/050637832. Full Text

Witelski, T. P., and S. W. Rienstra. “Introduction to practical asymptotics III.” Journal of Engineering Mathematics, vol. 53, no. 3–4, Dec. 2005, p. 199. Scopus, doi:10.1007/s10665-005-9027-9. Full Text

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