# Thomas Peter 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

##### Computational Mathematics

##### PDE & Dynamical Systems

##### Physical Modeling

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 Bowen, M.* Methods of Mathematical Modelling: Continuous Systems and Differential Equations.* September 18, 2015.
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Ji, H, and Witelski, TP. "Instability and dynamics of volatile thin films." *Physical Review Fluids* 3.2 (February 1, 2018).
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Gao, Y, Ji, H, Liu, J-G, and Witelski, TP. "Global existence of solutions to a tear film model with locally elevated evaporation rates." *Physica D: Nonlinear Phenomena* 350 (July 2017): 13-25.
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Ji, H, and Witelski, TP. "Finite-time thin film rupture driven by modified evaporative loss." *Physica D: Nonlinear Phenomena* 342 (March 2017): 1-15.
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Smolka, LB, McLaughlin, CK, and Witelski, TP. "Oil capture from a water surface by a falling sphere." *Colloids and Surfaces A: Physicochemical and Engineering Aspects* 497 (May 2016): 126-132.
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Sanaei, P, Richardson, GW, Witelski, T, and Cummings, LJ. "Flow and fouling in a pleated membrane filter." *Journal of Fluid Mechanics* 795 (May 2016): 36-59.
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George, C, Virgin, LN, and Witelski, T. "Experimental study of regular and chaotic transients in a non-smooth system." *International Journal of Non-Linear Mechanics* 81 (May 2016): 55-64.
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Dijksman, JA, Mukhopadhyay, S, Gaebler, C, Witelski, TP, and Behringer, RP. "Obtaining self-similar scalings in focusing flows." *Physical review. E, Statistical, nonlinear, and soft matter physics* 92.4 (October 22, 2015): 043016-.
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Witelski, TP. "Preface to the special issue on “Thin films and fluid interfaces”." *Journal of Engineering Mathematics* 94.1 (October 2015): 1-3.
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Hall Taylor, N, Hewitt, I, Ockendon, J, and Witelski, T. "A new model for disturbance waves." *International Journal of Multiphase Flow* 66 (November 2014): 38-45.
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Witelski, T, Virgin, LN, and George, C. "A driven system of impacting pendulums: Experiments and simulations." *Journal of Sound and Vibration* 333.6 (March 17, 2014): 1734-1753.
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## Pages

Peterson, E, Shearer, M, Witelski, TP, and Levy, R. "Stability of traveling waves in thin liquid films driven by gravity and surfactant." 2009.

Witelski, TP. "Computing finite-time singularities in interfacial flows." 2002.

## Pages

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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 »

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 »