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.
Office Hours
Please email me to request a meeting time
Current Appointments & Affiliations
- Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2011
- Director of Graduate Studies in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2022
- Professor in the Department of Mechanical Engineering and Materials Science, Pratt School of Engineering, Duke University 2016
- Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science, Thomas Lord Department of Mechanical Engineering and Materials Science, Pratt School of Engineering 2021
Contact Information
- 120 Science Drive, Durham, NC 27708-0320
- 295 Physics Building, Box 90320, Durham, NC 27708-0320
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witelski@math.duke.edu
(919) 660-2841
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#Personal Website
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Google Scholar
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MathSciNet: 357178
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Methods of Mathematical Modeling textbook
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Methods of Mathematical Modeling: list of typos
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ORCID: 0000-0003-0789-9859
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Thin films research
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Web of Science ResearcherID: G-5389-2016
- Background
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Education, Training, & Certifications
- Ph.D., California Institute of Technology 1995
- B.S.E., The Cooper Union 1991
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Previous Appointments & Affiliations
- Professor in the Department of Mechanical Engineering and Materials Science, Thomas Lord Department of 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
- Recognition
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Awards & Honors
- Expertise
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Subject Headings
- Research
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External Relationships
- Discrete and Continuous Dynamical Systems Series B (journal)
- European Journal of Applied Mathematics
- Journal of Engineering Mathematics
- Springer Nature
- Publications & Artistic Works
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Selected Publications
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Books
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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.Full Text
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Academic Articles
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Bowen, M., J. R. King, and T. P. Witelski. “CAUCHY-DIRICHLET PROBLEMS FOR THE POROUS MEDIUM EQUATION.” Discrete and Continuous Dynamical Systems Series A 43, no. 3–4 (March 1, 2023): 1143–74. https://doi.org/10.3934/dcds.2022182.Full Text
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Kim, Ruby, and Thomas P. Witelski. “Uncovering the dynamics of a circadian-dopamine model influenced by the light-dark cycle.” Mathematical Biosciences 344 (February 2022): 108764. https://doi.org/10.1016/j.mbs.2021.108764.Full Text
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Nakad, M., T. Witelski, J. C. Domec, S. Sevanto, and G. Katul. “Taylor dispersion in osmotically driven laminar flows in phloem.” Journal of Fluid Mechanics 913 (January 1, 2021). https://doi.org/10.1017/jfm.2021.56.Full Text Open Access Copy
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Zhu, Haodong, Peiran Zhang, Zhanwei Zhong, Jianping Xia, Joseph Rich, John Mai, Xingyu Su, et al. “Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices.” Science Advances 7, no. 2 (January 2021): eabc7885. https://doi.org/10.1126/sciadv.abc7885.Full Text
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Aguareles, M., S. J. Chapman, and T. Witelski. “Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains.” Physica D: Nonlinear Phenomena 414 (December 15, 2020). https://doi.org/10.1016/j.physd.2020.132699.Full Text Open Access Copy
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Ji, Hangjie, and Thomas Witelski. “Steady states and dynamics of a thin-film-type equation with non-conserved mass.” European Journal of Applied Mathematics 31, no. 6 (December 1, 2020): 968–1001. https://doi.org/10.1017/s0956792519000330.Full Text Open Access Copy
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Liu, Weifan, and Thomas P. Witelski. “Steady states of thin film droplets on chemically heterogeneous substrates.” Ima Journal of Applied Mathematics 85, no. 6 (November 25, 2020): 980–1020. https://doi.org/10.1093/imamat/hxaa036.Full Text Open Access Copy
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Dijksman, Joshua A., Shomeek Mukhopadhyay, Cameron Gaebler, Thomas P. Witelski, and Robert P. Behringer. “Erratum: Obtaining self-similar scalings in focusing flows [Phys. Rev. E 92, 043016 (2015)].” Physical Review. E 101, no. 5–2 (May 2020): 059902. https://doi.org/10.1103/physreve.101.059902.Full Text
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Witelski, T. P. “Nonlinear dynamics of dewetting thin films.” Aims Mathematics 5, no. 5 (January 1, 2020): 4229–59. https://doi.org/10.3934/math.2020270.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text Open Access Copy Link to Item
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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 2015): 043016. https://doi.org/10.1103/physreve.92.043016.Full Text
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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.Full Text
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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.Full Text
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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 25, no. 6 (June 1, 2013). https://doi.org/10.1063/1.4811389.Full Text
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Chapman, S Jonathan, Philippe H. Trinh, and Thomas P. Witelski. “Exponential Asymptotics for Thin Film Rupture.” Siam J. Appl. Math. 73 (2013): 232–53. https://doi.org/10.1137/120872012.Full Text
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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.Full Text
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Li, Zhilin, Anita T. Layton, Andrea Bertozzi, David M. Ambrose, Thomas Witelski, Michael L. Minion, and Michael L. Butters, R. “Preface.” Discrete and Continuous Dynamical Systems Series B 17, no. 4 (February 2012). https://doi.org/10.3934/dcdsb.2012.17.4i.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Link to Item
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Witelski, Thomas P., and Mark Bowen. “Singular perturbation theory.” Scholarpedia 4 (April 7, 2009): 3951–3951. https://doi.org/10.4249/scholarpedia.3951.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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).Link to Item
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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.Link to Item
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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 2008): 016301. https://doi.org/10.1103/physreve.77.016301.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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): 199. https://doi.org/10.1007/s10665-005-9027-9.Full Text
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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.Full Text
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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.Full Text
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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 2005): 127801. https://doi.org/10.1103/physrevlett.95.127801.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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 2004): 247803. https://doi.org/10.1103/physrevlett.93.247803.Full Text
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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.Full Text
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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.Full Text
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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).
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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.Full Text
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Witelski, T. P. “Intermediate asymptotics for Richards' equation in a finite layer.” Journal of Engineering Mathematics 45, no. 3–4 (April 1, 2003): 379–99. https://doi.org/10.1023/A:1022609020200.Full Text
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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 2003): 016302. https://doi.org/10.1103/physreve.67.016302.Full Text
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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.
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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 (January 1, 1998): 725–76. https://doi.org/10.1023/b:joss.0000033251.81126.af.Full Text
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Brenner, M. P., and T. P. Witelski. “On spherically symmetric gravitational collapse.” Journal of Statistical Physics 93, no. 3–4 (January 1, 1998): 863–99. https://doi.org/10.1023/b:joss.0000033167.19114.b8.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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Witelski, T. P. “Perturbation Analysis for Wetting Fronts in Richards' Equation.” Transport in Porous Media 27, no. 2 (January 1, 1997): 121–34. https://doi.org/10.1023/A:1006513009125.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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Witelski, T., P. Ng, J. Ying, J. Jundy, and J. Bove. “An application of pattern recognition and infrared spectroscopy to water analysis.” International Journal of Environmental Analytical Chemistry 44, no. 2 (1991): 127–36.
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Conference Papers
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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.Link to Item
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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.Link to Item
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Witelski, Thomas, Pejman Sanaei, Chris Breward, Meredith Ellis, Saem Han, Benjamin Holzer, Hangjie Ji, et al. “Evaporation and deposition in porous media Working Paper,” n.d. https://doi.org/10.33774/miir-2022-wq8fl.Full Text
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- Teaching & Mentoring
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Recent Courses
- MATH 551: Applied Partial Differential Equations and Complex Variables 2023
- MATH 895: Internship 2023
- MATH 553: Asymptotic and Perturbation Methods 2022
- MATH 575: Mathematical Fluid Dynamics 2022
- MATH 577: Mathematical Modeling 2022
- MATH 790-90: Minicourse in Advanced Topics 2022
- MATH 799: Special Readings 2022
- MATH 551: Applied Partial Differential Equations and Complex Variables 2021
- MATH 577: Mathematical Modeling 2021
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- Dynamics of thin films of volatile fluids. Fluid mechanics seminar series. University of Nottingham, School of Mathematics. December 8, 2022 2022
- Moving boundary problems for evaporating fluids. Undergraduate Analysis and PDE seminar series. University of North Carolina, Chapel Hill. November 4, 2022 2022
- Evaporation vs. condensation in dewetting viscous thin films. OCIAM @ 30 conference. Mathematical Institute. June 24, 2019 2019
- Dynamics of non-conservative fluid thin films. Modelling of Thin Liquid Films – Asymptotics vs. Gradient Dynamics Banff Workshop 19w5148. Banff International Research Station. May 2, 2019 2019
- Finite-time rupture in thin films driven by non-conservative effects. Making a Splash: Droplets, Jets and Other Singularities Workshop. ICERM. March 21, 2017 2017
- Multiscale dynamics of dewetting fluid films. Applied PDE Seminar. Dept of Applied Math, University of Washington. November 17, 2016 2016
- Directions for Graduate and Undergraduate Modeling Courses. 2016 SIAM Annual Meeting. SIAM. July 13, 2016 2016
- Experimental study of regular and chaotic transients in a non-smooth system. Dynamics Days US 2016. January 8, 2016 2016
- Nonlinear dynamics of dewetting thin films. May 29, 2014 2014
- Multiscale dynamics of dewetting fluids. July 1, 2013 2013
- Crowd-dynamics-driven instabilities of bridges. June 11, 2013 2013
- Basic questions on the design and efficiency of toothbrushes. May 17, 2013 2013
- Modeling studies of the dynamics of read/write heads in computer hard disk drives. July 26, 2012 2012
- The influence of surfactants on transient behaviors in forced film thinning. Workshop on Surfactant Driven Thin Film Flows. Fields Institute. February 23, 2012 2012
- Nonlinear dynamics of driven coupled impacting pendula. January 20, 2012 2012
- Transient and self-similar dynamics in thin film coarsening. July 18, 2010 2010
- Transient and self-similar dynamics in thin film coarsening. July 18, 2010 2010
- Transient Stability Analysis for an Inertially-driven Extensional Motion of a Planar Liquid Sheet. May 26, 2010 2010
- Transient Stability Analysis for an Inertially-driven Extensional Motion of a Planar Liquid Sheet. May 26, 2010 2010
- Transient and self-similar dynamics in thin film coarsening. May 24, 2010 2010
- Mean field model of droplet coarsening. April 17, 2010 2010
- Mean field models and transient effects for coarsening dynamics in fluid films. April 13, 2010 2010
- Coarsening: transient and self-similar dynamics in 1-D. March 12, 2010 2010
- Perturbation analysis for impulsive differential equations. Duke Math Grad/Faculty seminar. February 12, 2010 2010
- Film coarsening: transient and self-similar dynamics in 1-D. August 11, 2009 2009
- Coarsening of Dewetting Films I: the Influence of Gravity. July 9, 2009 2009
- Perturbation Analysis for Impulsive Differential Equations. July 9, 2009 2009
- On computing solutions of thin film equations. April 4, 2009 2009
- Coarsening: transient and self-similar dynamics in 1-D. April 1, 2009 2009
- Coarsening: transient and self-similar dynamics in 1-D. March 23, 2009 2009
- Coarsening dynamics of thin fluid films. November 1, 2008 2008
- Coarsening dynamics of dewetting fluid films. September 6, 2008 2008
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Service to the Profession
- Committee chair : Gene Golub SIAM Summer School Committee. Society of Industrial and Applied Mathematics (SIAM). January 2018 - December 2018 2018
- Faculty Mentor . Graduate Student Mathematical Modeling Camp 2017 (GSMMC). Rensselaer Polytechnic Institute, Dept of Math. June 14, 2017 - June 17, 2017 2017
- Main organizer. 2016 Mathematical Problems in Industry (MPI) Workshop. Duke University. June 13, 2016 - June 17, 2016 2016
- Member of organizing committee. Dynamics Days 2016 US. Duke University. January 7, 2016 - January 10, 2016 2016
- Associate Editor. Journal of Engineering Mathematics. 2016 2016
- Member of the editorial board. Mathematics-in-Industry Case Studies. 2016 2016
- Associate Director. Statistics and Applied Mathematical Sciences Institute (SAMSI). SAMSI. July 1, 2014 - June 30, 2017 2014 - 2017
- Member of board of Series Editors. Springer Texts in Applied Mathematics. Springer Publishing. 2014 2014
- Member of organizing committee. Flows and Patterns: The Physics of Fluids, Granular Materials, and Soft Matter. Duke University. October 12, 2013 - October 13, 2013 2013
- Faculty Mentor. Graduate Student Mathematical Modeling Camp 2013 (GSMMC). Rensselaer Polytechnic Institute, Dept of Math. . June 11, 2013 - June 14, 2013 2013
- Member of organizing committee. BIRS workshop 12w5035: Thin liquid films and fluid interfaces: models, experiments and applications. December 9, 2012 - December 14, 2012 2012
- Faculty Mentor : Graduate Student Mathematical Modeling Camp 2011 (GSMMC). June 11, 2011 - June 12, 2011 2011
- Member of organizing committee : Dynamics Days 2011. January 5, 2011 - January 8, 2011 2011
- Committee member : Gene Golub SIAM Summer School Committee. Society of Industrial and Applied Mathematics (SIAM). January 1, 2011 - December 2017 2011 - 2017
- Main guest editor : FAN (Fluid Dynamics, Analysis, Numerics) proceedings/ JT Beale Special issue DCDSB. January 2011 - January 2012 2011 - 2012
- co-Editor-in-Chief : Journal of Engineering Mathematics. January 1, 2011 - December 31, 2015 2011 - 2015
- Chair, organizing committee : FAN2010: Fluid dynamics, Analysis and Numerics (A conference in honor of Thomas Beale). June 28, 2010 - June 30, 2010 2010
- Faculty mentor/problem presenter. 2nd UK Graduate Modelling Camp. University of Oxford, Mathematical Institute, OCCAM Oxford Centre for Collaborative Applied Mathematics. April 6, 2010 - April 9, 2010 2010
- Member of organizing committee : CTMS Workshop: Theory and Applications of Multiscale Modeling. September 11, 2009 - September 12, 2009 2009
- Minisymposium sessions co-organizer : SIAM 2009 Annual meeting, MS65/MS76 Contemporary Applications of Perturbation and Asymptotic Methods I/II. July 9, 2009 - July 10, 2009 2009
- Division Editor : Journal of Mathematical Analysis and Applications. July 2009 - December 2014 2009 - 2014
- Faculty Mentor. Graduate Student Mathematical Modeling Camp (GSMMC). Rensselaer Polytechnic Institute, Department of Mathematics. June 9, 2009 - June 12, 2009 2009
- Associate Editor. Discrete and Continuous Dynamical Systems, series B. 2006 2006
- Associate Editor. European Journal of Applied Mathematics. 2004 2004
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Service to Duke
- Director of Graduate Studies. Duke University Department of Mathematics. July 1, 2022 2022
- Duke Libraries. Library 2030 Initiative Faculty Steering Group. April 2021 - June 2021 2021
- Duke Mathematics Department. Teaching Committee, committee Chair. May 2020 2020
- Liaison to Masters Programs. Duke Mathematics Department. August 2019 2019
- Duke Mathematics Department. Self-Study document for external review. February 2018 2018
- Oral exam committees for students (MA, PhD). January 2018 - December 2018 2018
- Duke Graduate School. Executive Committee of the Graduate Faculty (ECGF). August 2017 - May 2019 2017 - 2019
- Duke University. Library Council. 2013 - 2019 2013 - 2019
- Executive Committee of the Graduate Faculty (ECGF). September 1, 2010 - April 1, 2012 2010 - 2012
- Duke Mathematics Department. Director of Graduate Studies. July 1, 2009 - June 30, 2011 2009 - 2011
- Duke Mathematics Department. Director of Graduate Studies. January 2005 - August 2005 2005
- Academic Council. April 2002 - April 2004 2002 - 2004
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