Thomas P. Witelski
- Professor in the Department of Mathematics
- Professor in the Department of Mechanical Engineering and Materials Science (Secondary)
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.
Shearer, M., et al. “Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness.” Mathematical Models and Methods in Applied Sciences, vol. 13, no. 11, Nov. 2003, pp. 1629–71. Scopus, doi:10.1142/S0218202503003069. Full Text
Witelski, T. P., and M. Bowen. “ADI schemes for higher-order nonlinear diffusion equations.” Applied Numerical Mathematics, vol. 45, no. 2–3, May 2003, pp. 331–51. Scopus, doi:10.1016/S0168-9274(02)00194-0. Full Text
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, p. 016302. 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