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.
Aguareles, M., et al. “Motion of spiral waves in the complex Ginzburg-Landau equation.” Physica D: Nonlinear Phenomena, vol. 239, no. 7, Apr. 2010, pp. 348–65. Scopus, doi:10.1016/j.physd.2009.12.003. Full Text
Bernoff, A. J., and T. P. Witelski. “Stability and dynamics of self-similarity in evolution equations.” Journal of Engineering Mathematics, vol. 66, no. 1, Jan. 2010, pp. 11–31. Scopus, doi:10.1007/s10665-009-9309-8. Full Text
Witelski, T. P. “The subtle art of blowing bubbles (News and Views: Fluid Dynamics).” Nature Physics, vol. 5, May 2009, pp. 315–16.
Hwang, H. J., and T. P. Witelski. “Short-time pattern formation in thin film equations.” Discrete and Continuous Dynamical Systems, vol. 23, no. 3, Mar. 2009, pp. 867–85. Scopus, doi:10.3934/dcds.2009.23.867. Full Text
Gratton, M. B., and T. P. Witelski. “Transient and self-similar dynamics in thin film coarsening.” Physica D: Nonlinear Phenomena, vol. 238, no. 23–24, Jan. 2009, pp. 2380–94. Scopus, doi:10.1016/j.physd.2009.09.015. Full Text
Smolka, L. B., and T. P. Witelski. “On the planar extensional motion of an inertially driven liquid sheet.” Physics of Fluids, vol. 21, no. 4, Jan. 2009. Scopus, doi:10.1063/1.3094026. Full Text
Witelski, T. P. “Fluid dynamics: The subtle art of blowing bubbles.” Nature Physics, vol. 5, no. 5, Jan. 2009, pp. 315–16. Scopus, doi:10.1038/nphys1265. Full Text
Santillan, S. T., et al. “Large oscillations of beams and columns including self-weight.” International Journal of Non Linear Mechanics, vol. 43, no. 8, Oct. 2008, pp. 761–71. Scopus, doi:10.1016/j.ijnonlinmec.2008.04.007. Full Text
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