# 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., and M. Bowen. *Methods of Mathematical Modelling: Continuous Systems and Differential Equations*. 2015, pp. 1–305. *Scopus*, doi:10.1007/978-3-319-23042-9.
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Dijksman, Joshua A., et al. “Erratum: Obtaining self-similar scalings in focusing flows [Phys. Rev. E 92, 043016 (2015)].” *Physical Review. E*, vol. 101, no. 5–2, May 2020, p. 059902. *Epmc*, doi:10.1103/physreve.101.059902.
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Witelski, T. P. “Nonlinear dynamics of dewetting thin films.” *Aims Mathematics*, vol. 5, no. 5, Jan. 2020, pp. 4229–59. *Scopus*, doi:10.3934/math.2020270.
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Dijksman, J. A., et al. “Thermal Marangoni-driven dynamics of spinning liquid films.” *Physical Review Fluids*, vol. 4, no. 8, Aug. 2019. *Scopus*, doi:10.1103/PhysRevFluids.4.084103.
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Bowen, M., and T. P. Witelski. “Pressure-dipole solutions of the thin-film equation.” *European Journal of Applied Mathematics*, vol. 30, no. 2, Apr. 2019, pp. 358–99. *Scopus*, doi:10.1017/S095679251800013X.
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Gao, Y., et al. “A vicinal surface model for epitaxial growth with logarithmic free energy.” *Discrete and Continuous Dynamical Systems Series B*, vol. 23, no. 10, Dec. 2018, pp. 4433–53. *Scopus*, doi:10.3934/dcdsb.2018170.
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Chiou, Jian-Geng, et al. “Principles that govern competition or co-existence in Rho-GTPase driven polarization.” *Plos Comput Biol*, vol. 14, no. 4, Apr. 2018, p. e1006095. *Pubmed*, doi:10.1371/journal.pcbi.1006095.
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Ji, H., and T. P. Witelski. “Instability and dynamics of volatile thin films.” *Physical Review Fluids*, vol. 3, no. 2, Feb. 2018. *Scopus*, doi:10.1103/PhysRevFluids.3.024001.
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Gao, Y., et al. “Global existence of solutions to a tear film model with locally elevated evaporation rates.” *Physica D: Nonlinear Phenomena*, vol. 350, July 2017, pp. 13–25. *Scopus*, doi:10.1016/j.physd.2017.03.005.
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Ji, H., and T. P. Witelski. “Finite-time thin film rupture driven by modified evaporative loss.” *Physica D: Nonlinear Phenomena*, vol. 342, Mar. 2017, pp. 1–15. *Scopus*, doi:10.1016/j.physd.2016.10.002.
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Sanaei, P., et al. “Flow and fouling in a pleated membrane filter.” *Journal of Fluid Mechanics*, vol. 795, May 2016, pp. 36–59. *Scopus*, doi:10.1017/jfm.2016.194.
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## Pages

Peterson, Ellen, et al. “Stability of traveling waves in thin liquid films driven by gravity and surfactant.” *Hyperbolic Problems: Theory, Numerics and Applications, Part 2*, edited by E. Tadmor et al., vol. 67, AMER MATHEMATICAL SOC, 2009, pp. 855-+.

Witelski, T. P. “Computing finite-time singularities in interfacial flows.” *Modern Methods in Scientific Computing and Applications*, edited by A. Bourlioux et al., vol. 75, SPRINGER, 2002, pp. 451–87.

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The Math department congratulates its faculty members Tori Akin, Rann Bar-on, Sarah Schott, Hugh Bray and Tom Witelski. They have been recognized by Academic Affairs for their contribution to teaching excellence at Duke. These faculty are in the... read more »

Graduate Student and new PhD, Hangjie (Jessie) Ji, was recognized by the Society for Industrial and Applied Mathematics (SIAM) for her "outstanding efforts and accomplishments" on behalf of the Duke University SIAM chapter. She is pictured here with... read more »

SIAM is the Society of Industrial and Applied Mathematics. We formed this chapter to promote collaboration, interdisciplinary activities, and fellowship between graduate students in the Mathematics and other related departments. Our newly formed... read more »

The Mathematical Problems in Industry (MPI) is a week long workshop where companies bring real world problems to students and researchers in mathematics to find solutions. MPI takes place at a different university every summer. This is the first... read more »

A thin liquid film is a layer of fluid that has a breadth much greater than its depth. A representative example is the tear film that coats your eye to protect it: the thickness of this coating is only a few micrometers but its breadth is a few... read more »