# 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.

Witelski, T. P. “Preface to the special issue on “Thin films and fluid interfaces”.” *Journal of Engineering Mathematics*, vol. 94, no. 1, Oct. 2015. *Scopus*, doi:10.1007/s10665-014-9760-z.
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Dijksman, Joshua A., et al. “Obtaining self-similar scalings in focusing flows..” *Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics*, vol. 92, no. 4, Oct. 2015. *Epmc*, doi:10.1103/physreve.92.043016.
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Witelski, T., et al. “A driven system of impacting pendulums: Experiments and simulations.” *Journal of Sound and Vibration*, vol. 333, no. 6, Mar. 2014, pp. 1734–53. *Scopus*, doi:10.1016/j.jsv.2013.11.004.
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Hall Taylor, N. S., et al. “A new model for disturbance waves.” *International Journal of Multiphase Flow*, vol. 66, Jan. 2014, pp. 38–45. *Scopus*, doi:10.1016/j.ijmultiphaseflow.2014.06.004.
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Smolka, L. B., and T. P. Witelski. “Biaxial extensional motion of an inertially driven radially expanding liquid sheet.” *Physics of Fluids*, vol. 25, no. 6, Jan. 2013. *Scopus*, doi:10.1063/1.4811389.
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Chapman, S. Jonathan, et al. “Exponential Asymptotics for Thin Film Rupture..” *Siam Journal of Applied Mathematics*, vol. 73, 2013, pp. 232–53.

Huang, Y., et al. “Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions.” *Applied Mathematics Letters*, vol. 25, no. 12, Dec. 2012, pp. 2317–21. *Scopus*, doi:10.1016/j.aml.2012.06.023.
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Witelski, T., et al. “Preface: Special issue on fluid dynamics, analysis and numerics.” *Discrete and Continuous Dynamical Systems Series B*, vol. 17, no. 4, June 2012. *Scopus*, doi:10.3934/dcdsb.2012.17.4i.
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Wiebe, R., et al. “A parametrically forced nonlinear system with reversible equilibria.” *International Journal of Bifurcation and Chaos*, vol. 22, no. 6, Jan. 2012. *Scopus*, doi:10.1142/S0218127412300200.
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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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Six graduate students participated in the May 15, 2016 graduation ceremonies to celebrate earning their PhDs in Mathematics. Their thesis topics were impressive and varied, and reflected the breadth of study in the department. Their advisors and... read more »