Thomas P. Witelski | Scholars@Duke

Thomas P. Witelski
Professor in the Department of Mathematics

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.

Current Appointments & Affiliations

Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2011
Professor in the Department of Mechanical Engineering and Materials Science, Pratt School of Engineering, Duke University 2016

Contact Information

295 Physics Bldg, Box 90320, Durham, NC 27708-0320
Box 90320, Durham, NC 27708-0320
witelski@math.duke.edu (919) 660-2841
Google Scholar
MathSciNet: 357178
Methods of Mathematical Modeling textbook
Methods of Mathematical Modeling: list of typos
Primary webpage at math.duke.edu
Publons

Background
Education, Training, & Certifications
- Ph.D., California Institute of Technology 1995
- B.S.E., Cooper Union 1991
Duke Appointment History
- Professor in the Department of Mechanical Engineering and Materials Science, Mechanical Engineering and Materials Science, Pratt School of Engineering 2012 - 2015
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2005 - 2011
- Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1998 - 2005
Leadership & Clinical Positions at Duke
- Liaison to Masters Programs, August 2019
Recognition
Awards & Honors
- Top 5% teaching. Duke Arts and Science. April 13, 2018
- Top 5% teaching. Duke Arts and Science. February 22, 2017
- Faculty Early Career Development (CAREER) Program. National Science Foundation. 2003
- Sloan Research Fellowship-Mathematics. Alfred P. Sloan Foundation. 2000
Expertise
Subject Headings
Research
External Relationships
- Discrete and Continuous Dynamical Systems Series B (journal)
- European Journal of Applied Mathematics
- Journal of Engineering Mathematics
Publications & Artistic Works
Selected Publications
- Books
  - Witelski, T., and M. Bowen. Methods of Mathematical Modelling: Continuous Systems and Differential Equations, 2015. https://doi.org/10.1007/978-3-319-23042-9.
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- Academic Articles
  - Dijksman, J. A., S. Mukhopadhyay, R. P. Behringer, and T. P. Witelski. “Thermal Marangoni-driven dynamics of spinning liquid films.” Physical Review Fluids 4, no. 8 (August 19, 2019). https://doi.org/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 30, no. 2 (April 1, 2019): 358–99. https://doi.org/10.1017/S095679251800013X.
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  - Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems Series B 23, no. 10 (December 1, 2018): 4433–53. https://doi.org/10.3934/dcdsb.2018170.
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  - Chiou, Jian-Geng, Samuel A. Ramirez, Timothy C. Elston, Thomas P. Witelski, David G. Schaeffer, and Daniel J. Lew. “Principles that govern competition or co-existence in Rho-GTPase driven polarization.” Plos Comput Biol 14, no. 4 (April 2018): e1006095. https://doi.org/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 3, no. 2 (February 1, 2018). https://doi.org/10.1103/PhysRevFluids.3.024001.
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  - Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “Global existence of solutions to a tear film model with locally elevated evaporation rates.” Physica D: Nonlinear Phenomena 350 (July 1, 2017): 13–25. https://doi.org/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 342 (March 1, 2017): 1–15. https://doi.org/10.1016/j.physd.2016.10.002.
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  - Sanaei, P., G. W. Richardson, T. Witelski, and L. J. Cummings. “Flow and fouling in a pleated membrane filter.” Journal of Fluid Mechanics 795 (May 25, 2016): 36–59. https://doi.org/10.1017/jfm.2016.194.
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  - Smolka, L. B., C. K. McLaughlin, and T. P. Witelski. “Oil capture from a water surface by a falling sphere.” Colloids and Surfaces A: Physicochemical and Engineering Aspects 497 (May 20, 2016): 126–32. https://doi.org/10.1016/j.colsurfa.2016.02.026.
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  - George, C., L. N. Virgin, and T. Witelski. “Experimental study of regular and chaotic transients in a non-smooth system.” International Journal of Non Linear Mechanics 81 (May 1, 2016): 55–64. https://doi.org/10.1016/j.ijnonlinmec.2015.12.006.
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  - Witelski, T. P. “Preface to the special issue on “Thin films and fluid interfaces”.” Journal of Engineering Mathematics 94, no. 1 (October 29, 2015). https://doi.org/10.1007/s10665-014-9760-z.
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  - Dijksman, Joshua A., Shomeek Mukhopadhyay, Cameron Gaebler, Thomas P. Witelski, and Robert P. Behringer. “Obtaining self-similar scalings in focusing flows..” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 92, no. 4 (October 22, 2015). https://doi.org/10.1103/physreve.92.043016.
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  - Witelski, T., L. N. Virgin, and C. George. “A driven system of impacting pendulums: Experiments and simulations.” Journal of Sound and Vibration 333, no. 6 (March 17, 2014): 1734–53. https://doi.org/10.1016/j.jsv.2013.11.004.
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  - Hall Taylor, N. S., I. J. Hewitt, J. R. Ockendon, and T. P. Witelski. “A new model for disturbance waves.” International Journal of Multiphase Flow 66 (January 1, 2014): 38–45. https://doi.org/10.1016/j.ijmultiphaseflow.2014.06.004.
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  - Chapman, S Jonathan, Philippe H. Trinh, and Thomas P. Witelski. “Exponential Asymptotics for Thin Film Rupture.” Siam Journal of Applied Mathematics 73 (2013): 232–53.
  - Smolka, L. B., and T. P. Witelski. “Biaxial extensional motion of an inertially driven radially expanding liquid sheet.” Physics of Fluids 25, no. 6 (January 1, 2013). https://doi.org/10.1063/1.4811389.
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  - Huang, Y., T. P. Witelski, and A. L. Bertozzi. “Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions.” Applied Mathematics Letters 25, no. 12 (December 1, 2012): 2317–21. https://doi.org/10.1016/j.aml.2012.06.023.
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  - Witelski, T., D. Ambrose, A. Bertozzi, A. Layton, Z. Li, and M. Minion. “Preface: Special issue on fluid dynamics, analysis and numerics.” Discrete and Continuous Dynamical Systems Series B 17, no. 4 (June 1, 2012). https://doi.org/10.3934/dcdsb.2012.17.4i.
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  - Wiebe, R., L. N. Virgin, and T. P. Witelski. “A parametrically forced nonlinear system with reversible equilibria.” International Journal of Bifurcation and Chaos 22, no. 6 (January 1, 2012). https://doi.org/10.1142/S0218127412300200.
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  - Aydemir, E., C. J. W. Breward, and T. P. Witelski. “The effect of polar lipids on tear film dynamics..” Bulletin of Mathematical Biology 73, no. 6 (June 2011): 1171–1201. https://doi.org/10.1007/s11538-010-9555-y.
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  - Aguareles, M., S. J. Chapman, and T. Witelski. “Motion of spiral waves in the complex Ginzburg-Landau equation.” Physica D: Nonlinear Phenomena 239, no. 7 (April 1, 2010): 348–65. https://doi.org/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 66, no. 1 (January 1, 2010): 11–31. https://doi.org/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 5 (May 2009): 315–16.
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  - Hwang, H. J., and T. P. Witelski. “Short-time pattern formation in thin film equations.” Discrete and Continuous Dynamical Systems 23, no. 3 (March 1, 2009): 867–85. https://doi.org/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 238, no. 23–24 (January 1, 2009): 2380–94. https://doi.org/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 21, no. 4 (January 1, 2009). https://doi.org/10.1063/1.3094026.
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  - Witelski, T. P. “Fluid dynamics: The subtle art of blowing bubbles.” Nature Physics 5, no. 5 (January 1, 2009): 315–16. https://doi.org/10.1038/nphys1265.
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  - Santillan, S. T., R. H. Plaut, T. P. Witelski, and L. N. Virgin. “Large oscillations of beams and columns including self-weight.” International Journal of Non Linear Mechanics 43, no. 8 (October 1, 2008): 761–71. https://doi.org/10.1016/j.ijnonlinmec.2008.04.007.
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  - Catllá, A. J., D. G. Schaeffer, T. P. Witelski, E. E. Monson, and A. L. Lin. “On spiking models for synaptic activity and impulsive differential equations.” Siam Review 50, no. 3 (September 1, 2008): 553–69. https://doi.org/10.1137/060667980.
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  - DiCarlo, D. A., R. Juanes, T. LaForce, and T. P. Witelski. “Nonmonotonic traveling wave solutions of infiltration into porous media.” Water Resources Research 44, no. 2 (February 1, 2008). https://doi.org/10.1029/2007WR005975.
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  - Gratton, M. B., and T. P. Witelski. “Coarsening of unstable thin films subject to gravity.” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 77, no. 1 Pt 2 (January 4, 2008): 016301. https://doi.org/10.1103/physreve.77.016301.
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  - Aguareles, M., S. J. Chapman, and T. P. Witelski. “Interaction of spiral waves in the Complex Ginzburg-Landau equation.” Physical Review Letters 101, no. 224101 (2008).
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  - Gratton, M. B., and T. P. Witelski. “Coarsening of dewetting thin films subject to gravity.” Physical Review E 77, no. 016301 (2008): 1–11.
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  - Levy, R., M. Shearer, and T. P. Witelski. “Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves.” European Journal of Applied Mathematics 18, no. 6 (December 1, 2007): 679–708. https://doi.org/10.1017/S0956792507007218.
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  - Schaeffer, D. G., M. Shearer, and T. P. Witelski. “Boundary-value problems for hyperbolic equations related to steady granular flow.” Mathematics and Mechanics of Solids 12, no. 6 (December 1, 2007): 665–99. https://doi.org/10.1177/1081286506067325.
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  - Witelski, T. P., M. Shearer, and R. Levy. “Growing surfactant waves in thin liquid films driven by gravity.” Applied Mathematics Research Express 2006 (December 1, 2006). https://doi.org/10.1155/AMRX/2006/15487.
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  - Bowen, M., and T. P. Witelski. “The linear limit of the dipole problem for the thin film equation.” Siam Journal on Applied Mathematics 66, no. 5 (October 25, 2006): 1727–48. https://doi.org/10.1137/050637832.
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  - Münch, A., B. Wagner, and T. P. Witelski. “Lubrication models with small to large slip lengths.” Journal of Engineering Mathematics 53, no. 3–4 (December 1, 2005): 359–83. https://doi.org/10.1007/s10665-005-9020-3.
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  - Witelski, T. P., and S. W. Rienstra. “Introduction to practical asymptotics III.” Journal of Engineering Mathematics 53, no. 3–4 (December 1, 2005). https://doi.org/10.1007/s10665-005-9027-9.
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  - Glasner, K. B., and T. P. Witelski. “Collision versus collapse of droplets in coarsening of dewetting thin films.” Physica D: Nonlinear Phenomena 209, no. 1-4 SPEC. ISS. (September 15, 2005): 80–104. https://doi.org/10.1016/j.physd.2005.06.010.
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  - Haskett, R. P., T. P. Witelski, and J. Sur. “Localized Marangoni forcing in driven thin films.” Physica D: Nonlinear Phenomena 209, no. 1-4 SPEC. ISS. (September 15, 2005): 117–34. https://doi.org/10.1016/j.physd.2005.06.019.
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  - Fetzer, R., K. Jacobs, A. Münch, B. Wagner, and T. P. Witelski. “New slip regimes and the shape of dewetting thin liquid films..” Physical Review Letters 95, no. 12 (September 14, 2005). https://doi.org/10.1103/physrevlett.95.127801.
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  - Witelski, T. P. “Motion of wetting fronts moving into partially pre-wet soil.” Advances in Water Resources 28, no. 10 SPEC. ISS. (January 1, 2005): 1133–41. https://doi.org/10.1016/j.advwatres.2004.06.006.
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  - Sur, Jeanman, Thomas P. Witelski, and Robert P. Behringer. “Steady-profile fingering flows in Marangoni driven thin films..” Physical Review Letters 93, no. 24 (December 7, 2004). https://doi.org/10.1103/physrevlett.93.247803.
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  - Borucki, L. J., T. Witelski, C. Please, P. R. Kramer, and D. Schwendeman. “A theory of pad conditioning for chemical-mechanical polishing.” Journal of Engineering Mathematics 50, no. 1 (December 1, 2004): 1–24. https://doi.org/10.1023/B:ENGI.0000042116.09084.00.
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  - Smolka, L. B., A. Belmonte, D. M. Henderson, and T. P. Witelski. “Exact solution for the extensional flow of a viscoelastic filament.” European Journal of Applied Mathematics 15, no. 6 (December 1, 2004): 679–712. https://doi.org/10.1017/S0956792504005789.
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  - Witelski, T. P., A. J. Bernoff, and A. L. Bertozzi. “Blowup and dissipation in a critical-case unstable thin film equation.” European Journal of Applied Mathematics 15, no. 2 (April 1, 2004): 223–56. https://doi.org/10.1017/S0956792504005418.
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  - Shearer, M., D. G. Schaeffer, and T. P. Witelski. “Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness.” Mathematical Models and Methods in Applied Sciences 13, no. 11 (November 1, 2003): 1629–71. https://doi.org/10.1142/S0218202503003069.
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  - Witelski, T. P. “Nonlinear Differential Equations, Mechanics and Bifurcation.” Discrete and Continuous Dynamical Systems Series B 3, no. 4 (November 1, 2003).
  - Witelski, T. P., and M. Bowen. “ADI schemes for higher-order nonlinear diffusion equations.” Applied Numerical Mathematics 45, no. 2–3 (May 1, 2003): 331–51. https://doi.org/10.1016/S0168-9274(02)00194-0.
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  - Glasner, K. B., and T. P. Witelski. “Coarsening dynamics of dewetting films..” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 67, no. 1 Pt 2 (January 10, 2003). https://doi.org/10.1103/physreve.67.016302.
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  - Schaeffer, David G., M. Shearer, and T. Witelski. “One-dimensional solutions of an elastoplasticity model of granular material.” Math. Models and Methods in Appl. Sciences 13 (2003): 1629–71.
  - Witelski, TP. "Intermediate asymptotics for Richards' equation in a finite layer." Journal of Engineering Mathematics 45, no. 3-4 (2003): 379-399. Full Text
  - Bernoff, A. J., and T. P. Witelski. “Linear stability of source-type similarity solutions of the thin film equation.” Applied Mathematics Letters 15, no. 5 (January 1, 2002): 599–606. https://doi.org/10.1016/S0893-9659(02)80012-X.
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  - Witelski, T. P., D. G. Schaeffer, and M. Shearer. “A discrete model for an ill-posed nonlinear parabolic PDE.” Physica D: Nonlinear Phenomena 160, no. 3–4 (December 15, 2001): 189–221. https://doi.org/10.1016/S0167-2789(01)00350-5.
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  - Vaynblat, D., J. R. Lister, and T. P. Witelski. “Symmetry and self-similarity in rupture and pinchoff: A geometric bifurcation.” European Journal of Applied Mathematics 12, no. 3 (December 1, 2001): 209–32. https://doi.org/10.1017/S0956792501004375.
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  - Bertozzi, A. L., G. Grün, and T. P. Witelski. “Dewetting films: Bifurcations and concentrations.” Nonlinearity 14, no. 6 (November 1, 2001): 1569–92. https://doi.org/10.1088/0951-7715/14/6/309.
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  - Vaynblat, D., J. R. Lister, and T. P. Witelski. “Rupture of thin viscous films by van der waals forces: Evolution and self-similarity.” Physics of Fluids 13, no. 5 (January 1, 2001): 1130–41. https://doi.org/10.1063/1.1359749.
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  - Witelski, T. P., K. Ono, and T. J. Kaper. “Critical wave speeds for a family of scalar reaction-diffusion equations.” Applied Mathematics Letters 14, no. 1 (January 1, 2001): 65–73. https://doi.org/10.1016/S0893-9659(00)00114-2.
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  - Witelski, T. P., and A. J. Bernoff. “Dynamics of three-dimensional thin film rupture.” Physica D: Nonlinear Phenomena 147, no. 1–2 (December 1, 2000): 155–76. https://doi.org/10.1016/S0167-2789(00)00165-2.
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  - Witelski, T. P., K. Ono, and T. J. Kaper. “On axisymmetric traveling waves and radial solutions of semi-linear elliptic equations.” Natural Resource Modeling 13, no. 3 (January 1, 2000): 339–88. https://doi.org/10.1111/j.1939-7445.2000.tb00039.x.
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  - Witelski, T. P., and A. J. Bernoff. “Stability of self-similar solutions for van der Waals driven thin film rupture.” Physics of Fluids 11, no. 9 (January 1, 1999): 2443–45. https://doi.org/10.1063/1.870138.
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  - Witelski, T. P., and F. Hendriks. “Large bearing number stability analysis for tango class gas bearing sliders.” Tribology Transactions 42, no. 3 (January 1, 1999): 668–74. https://doi.org/10.1080/10402009908982268.
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  - Witelski, T. P., and F. Hendriks. “Stability of gas bearing sliders for large bearing number: Convective instability of the tapered slider©.” Tribology Transactions 42, no. 1 (January 1, 1999): 216–22. https://doi.org/10.1080/10402009908982211.
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  - Bernoff, A. J., A. L. Bertozzi, and T. P. Witelski. “Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff.” Journal of Statistical Physics 93, no. 3–4 (November 1, 1998): 725–76.
  - Brenner, M. P., and T. P. Witelski. “On spherically symmetric gravitational collapse.” Journal of Statistical Physics 93, no. 3–4 (November 1, 1998): 863–99.
  - Witelski, T. P., A. Y. Grosberg, and T. Tanaka. “On the properties of polymer globules in the high density limit.” Journal of Chemical Physics 108, no. 21 (June 1, 1998): 9144–49. https://doi.org/10.1063/1.476361.
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  - Witelski, T. P. “Equilibrium interface solutions of a degenerate singular Cahn-Hilliard equation.” Applied Mathematics Letters 11, no. 5 (January 1, 1998): 127–33. https://doi.org/10.1016/S0893-9659(98)00092-5.
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  - Witelski, T. P. “Horizontal infiltration into wet soil.” Water Resources Research 34, no. 7 (January 1, 1998): 1859–63. https://doi.org/10.1029/98WR00775.
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  - Witelski, T. P. “Dynamics of air bearing sliders.” Physics of Fluids 10, no. 3 (January 1, 1998): 698–708. https://doi.org/10.1063/1.869595.
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  - Witelski, T. P., and A. J. Bernoff. “Self-similar asymptotics for linear and nonlinear diffusion equations.” Studies in Applied Mathematics 100, no. 2 (January 1, 1998): 153–93. https://doi.org/10.1111/1467-9590.00074.
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  - Witelski, T. P. “Similarity solutions of the lubrication equation.” Applied Mathematics Letters 10, no. 5 (September 12, 1997): 107–13. https://doi.org/10.1016/S0893-9659(97)00092-X.
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  - Witelski, T. P. “Segregation and mixing in degenerate diffusion in population dynamics.” Journal of Mathematical Biology 35, no. 6 (January 1, 1997): 695–712. https://doi.org/10.1007/s002850050072.
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  - Witelski, TP. "Perturbation Analysis for Wetting Fronts in Richards' Equation." Transport in Porous Media 27, no. 2 (January 1, 1997): 121-134. Full Text
  - Witelski, T. P. “Traveling wave solutions for case II diffusion in polymers.” Journal of Polymer Science, Part B: Polymer Physics 34, no. 1 (January 15, 1996): 141–50. https://doi.org/10.1002/(SICI)1099-0488(19960115)34:1<141::AID-POLB12>3.0.CO;2-E.
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  - Cohen, D. S., and T. P. Witelski. “Inaccessible states in time-dependent reaction diffusion.” Studies in Applied Mathematics 97, no. 4 (January 1, 1996): 301–19. https://doi.org/10.1002/sapm1996974301.
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  - Witelski, T. P. “The structure of internal layers for unstable nonlinear diffusion equations.” Studies in Applied Mathematics 97, no. 3 (January 1, 1996): 277–300. https://doi.org/10.1002/sapm1996973277.
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  - Witelski, T. P. “Stopping and merging problems for the porous media equation.” Ima Journal of Applied Mathematics (Institute of Mathematics and Its Applications) 54, no. 3 (December 1, 1995): 227–43. https://doi.org/10.1093/imamat/54.3.227.
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  - Witelski, T. P., and D. S. Cohen. “Perturbed reversible systems.” Physics Letters A 207, no. 1–2 (October 23, 1995): 83–86. https://doi.org/10.1016/0375-9601(95)00662-M.
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  - Witelski, T. P., and D. S. Cohen. “Forbidden Regions for Shock Formation in Diffusive Systems.” Studies in Applied Mathematics 95, no. 3 (October 1, 1995): 297–317. https://doi.org/10.1002/sapm1995953297.
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  - Cohen, D. S., A. B. White, and T. P. Witelski. “Shock formation in a multidimensional viscoelastic diffusive system.” Siam Journal on Applied Mathematics 55, no. 2 (January 1, 1995): 348–68. https://doi.org/10.1137/S0036139993269333.
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  - Witelski, T. P. “Shocks in nonlinear diffusion.” Applied Mathematics Letters 8, no. 5 (January 1, 1995): 27–32. https://doi.org/10.1016/0893-9659(95)00062-U.
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  - Witelski, T. P. “Merging traveling waves for the porous-Fisher's equation.” Applied Mathematics Letters 8, no. 4 (January 1, 1995): 57–62. https://doi.org/10.1016/0893-9659(95)00047-T.
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  - Witelski, T. P. “An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation.” Journal of Mathematical Biology 33, no. 1 (November 1, 1994): 1–16. https://doi.org/10.1007/BF00160171.
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  - Witelski, T., P. Ng, J. Y. Joseph Lundy, and J. Bove. “An application of pattern recognition and infrared spectroscopy to water analysis.” International Journal of Environmental Analytical Chemistry 44, no. 2 (May 1, 1991): 127–36. https://doi.org/10.1080/03067319108027542.
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  - JI, H. A. N. G. J. I. E., and T. H. O. M. A. S. P. WITELSKI. “Steady states and dynamics of a thin-film-type equation with non-conserved mass.” European Journal of Applied Mathematics, n.d., 1–34. https://doi.org/10.1017/s0956792519000330.
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  - Witelski, Thomas, and Mark Bowen. “Singular perturbation theory.” Scholarpedia 4, no. 4 (n.d.): 3951–3951. https://doi.org/10.4249/scholarpedia.3951.
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- Conference Papers
  - Peterson, Ellen, Michael Shearer, Thomas P. Witelski, and Rachel Levy. “Stability of traveling waves in thin liquid films driven by gravity and surfactant.” In Hyperbolic Problems: Theory, Numerics and Applications, Part 2, edited by E. Tadmor, J. Liu, and A. Tzavaras, 67:855-+. AMER MATHEMATICAL SOC, 2009.
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  - Witelski, T. P. “Computing finite-time singularities in interfacial flows.” In Modern Methods in Scientific Computing and Applications, edited by A. Bourlioux, M. J. Gander, and G. Sabidussi, 75:451–87. SPRINGER, 2002.
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