# 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.

Aydemir, E., et al. “The effect of polar lipids on tear film dynamics.” *Bulletin of Mathematical Biology*, vol. 73, no. 6, June 2011, pp. 1171–201. *Epmc*, doi:10.1007/s11538-010-9555-y.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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