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
Links

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., Cooper Union 1991

Glasner, K. B., and T. P. Witelski. “Coarsening dynamics of dewetting films..” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 67, no. 1 Pt 2, Jan. 2003. Epmc, doi:10.1103/physreve.67.016302. Full Text

Witelski, TP. "Intermediate asymptotics for Richards' equation in a finite layer." Journal of Engineering Mathematics 45.3-4 (2003): 379-399. Full Text

Schaeffer, David G., et al. “One-dimensional solutions of an elastoplasticity model of granular material.” Math. Models and Methods in Appl. Sciences, vol. 13, 2003, pp. 1629–71.

Bernoff, A. J., and T. P. Witelski. “Linear stability of source-type similarity solutions of the thin film equation.” Applied Mathematics Letters, vol. 15, no. 5, Jan. 2002, pp. 599–606. Scopus, doi:10.1016/S0893-9659(02)80012-X. Full Text

Witelski, T. P., et al. “A discrete model for an ill-posed nonlinear parabolic PDE.” Physica D: Nonlinear Phenomena, vol. 160, no. 3–4, Dec. 2001, pp. 189–221. Scopus, doi:10.1016/S0167-2789(01)00350-5. Full Text

Vaynblat, D., et al. “Symmetry and self-similarity in rupture and pinchoff: A geometric bifurcation.” European Journal of Applied Mathematics, vol. 12, no. 3, Dec. 2001, pp. 209–32. Scopus, doi:10.1017/S0956792501004375. Full Text

Bertozzi, A. L., et al. “Dewetting films: Bifurcations and concentrations.” Nonlinearity, vol. 14, no. 6, Nov. 2001, pp. 1569–92. Scopus, doi:10.1088/0951-7715/14/6/309. Full Text

Vaynblat, D., et al. “Rupture of thin viscous films by van der waals forces: Evolution and self-similarity.” Physics of Fluids, vol. 13, no. 5, Jan. 2001, pp. 1130–41. Scopus, doi:10.1063/1.1359749. Full Text

Witelski, T. P., et al. “Critical wave speeds for a family of scalar reaction-diffusion equations.” Applied Mathematics Letters, vol. 14, no. 1, Jan. 2001, pp. 65–73. Scopus, doi:10.1016/S0893-9659(00)00114-2. Full Text

Witelski, T. P., and A. J. Bernoff. “Dynamics of three-dimensional thin film rupture.” Physica D: Nonlinear Phenomena, vol. 147, no. 1–2, Dec. 2000, pp. 155–76. Scopus, doi:10.1016/S0167-2789(00)00165-2. Full Text

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