Thomas Peter Witelski | Scholars@Duke

Thomas Peter 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
Primary webpage at math.duke.edu
ResearcherID: G-5389-2016

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
Recognition
Awards & Honors
- Faculty Early Career Development (CAREER) Program. National Science Foundation. 2003
- Sloan Research Fellowship-Mathematics. Alfred P. Sloan Foundation. 2000
Expertise
Subject Headings
Publications & Artistic Works
Selected Publications
- Books
  - Witelski, T, and Bowen, M. Methods of Mathematical Modelling: Continuous Systems and Differential Equations. September 18, 2015. Full Text
- Conference Papers
  - Peterson, E, Shearer, M, Witelski, TP, and Levy, R. "Stability of traveling waves in thin liquid films driven by gravity and surfactant." 2009. Link to Item
  - Witelski, TP. "Computing finite-time singularities in interfacial flows." 2002. Link to Item
- Journal Articles
  - Chiou, J-G, Ramirez, SA, Elston, TC, Witelski, TP, Schaeffer, DG, and Lew, DJ. "Principles that govern competition or co-existence in Rho-GTPase driven polarization." Plos Computational Biology 14, no. 4 (April 12, 2018): e1006095-null. Full Text Open Access Copy
  - Ji, H, and Witelski, TP. "Instability and dynamics of volatile thin films." Physical Review Fluids 3, no. 2 (February 1, 2018). Full Text
  - 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. Full Text
  - Ji, H, and Witelski, TP. "Finite-time thin film rupture driven by modified evaporative loss." Physica D: Nonlinear Phenomena 342 (March 2017): 1-15. Full Text
  - Gao, Y, Ji, H, Liu, J-G, and P. Witelski, T. "A vicinal surface model for epitaxial growth with logarithmic free energy." Discrete & Continuous Dynamical Systems B 22, no. 11 (2017): 1-21. Full Text
  - 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. Full Text
  - 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. Full Text
  - 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. Full Text
  - 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, no. 4 (October 22, 2015): 043016-. Full Text
  - Witelski, TP. "Preface to the special issue on “Thin films and fluid interfaces”." Journal of Engineering Mathematics 94, no. 1 (October 2015): 1-3. Full Text
  - 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. Full Text
  - Witelski, T, Virgin, LN, and George, C. "A driven system of impacting pendulums: Experiments and simulations." Journal of Sound and Vibration 333, no. 6 (March 17, 2014): 1734-1753. Full Text
  - Smolka, LB, and Witelski, TP. "Biaxial extensional motion of an inertially driven radially expanding liquid sheet." PHYSICS OF FLUIDS 25, no. 6 (June 2013). Full Text Link to Item
  - Chapman, SJ, Trinh, PH, and Witelski, TP. "Exponential Asymptotics for Thin Film Rupture." SIAM Journal of Applied Mathematics 73 (2013): 232-253. Full Text
  - Huang, Y, Witelski, TP, and Bertozzi, AL. "Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions." Applied Mathematics Letters 25, no. 12 (2012): 2317-2321. Full Text
  - Wiebe, R, Virgin, LN, and Witelski, TP. "A parametrically forced nonlinear system with reversible equilibria." International Journal of Bifurcation and Chaos 22, no. 6 (2012). Full Text
  - Witelski, T, Ambrose, D, Bertozzi, A, Layton, A, Li, Z, and Minion, M. "Preface: Special issue on fluid dynamics, analysis and numerics." Discrete and Continuous Dynamical Systems - Series B 17, no. 4 (2012): i-ii. Full Text
  - Aydemir, E, Breward, CJW, and Witelski, TP. "The effect of polar lipids on tear film dynamics." Bulletin of Mathematical Biology 73, no. 6 (June 2011): 1171-1201. Full Text
  - Aguareles, M, Chapman, SJ, and Witelski, T. "Motion of spiral waves in the complex Ginzburg-Landau equation." Physica D: Nonlinear Phenomena 239, no. 7 (2010): 348-365. Full Text
  - Bernoff, AJ, and Witelski, TP. "Stability and dynamics of self-similarity in evolution equations." Journal of Engineering Mathematics 66, no. 1 (2010): 11-31. Full Text
  - Witelski, TP. "The subtle art of blowing bubbles (News and Views: Fluid Dynamics)." Nature Physics 5 (May 2009): 315-316. (Academic Article) Link to Item
  - Witelski, TP. "The subtle art of blowing bubbles." Nature Physics 5, no. 5 (May 2009): 315-316. Full Text
  - Gratton, MB, and Witelski, TP. "Transient and self-similar dynamics in thin film coarsening." Physica D: Nonlinear Phenomena 238, no. 23-24 (2009): 2380-2394. Full Text
  - Hwang, HJ, and Witelski, TP. "Short-time pattern formation in thin film equations." Discrete and Continuous Dynamical Systems 23, no. 3 (2009): 867-885. Full Text
  - Smolka, LB, and Witelski, TP. "On the planar extensional motion of an inertially driven liquid sheet." Physics of Fluids 21, no. 4 (2009). Full Text
  - Witelski, TP, and Bowen, M. "Singular perturbation theory." Scholarpedia 4 (2009): 3951-3951. Full Text
  - Aguareles, M, Chapman, SJ, and Witelski, TP. "Interaction of spiral waves in the Complex Ginzburg-Landau equation." Physical Review Letters 101, no. 224101 (2008). (Academic Article) Link to Item
  - Catllá, AJ, Schaeffer, DG, Witelski, TP, Monson, EE, and Lin, AL. "On Spiking Models for Synaptic Activity and Impulsive Differential Equations." Siam Review 50, no. 3 (January 2008): 553-569. Full Text
  - DiCarlo, DA, Juanes, R, LaForce, T, and Witelski, TP. "Nonmonotonic traveling wave solutions of infiltration into porous media." Water Resources Research 44, no. 2 (2008). Full Text
  - Gratton, MB, and Witelski, TP. "Coarsening of dewetting thin films subject to gravity." Physical Review E 77, no. 016301 (2008): 1-11. (Academic Article) Link to Item
  - Gratton, MB, and Witelski, TP. "Coarsening of unstable thin films subject to gravity." Phys Rev E Stat Nonlin Soft Matter Phys 77, no. 1 Pt 2 (January 2008): 016301-. Full Text Link to Item
  - Santillan, ST, Plaut, RH, Witelski, TP, and Virgin, LN. "Large oscillations of beams and columns including self-weight." International Journal of Non-Linear Mechanics 43, no. 8 (2008): 761-771. Full Text
  - Levy, R, Shearer, M, and Witelski, TP. "Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves." European Journal of Applied Mathematics 18, no. 6 (2007): 679-708. Full Text
  - Schaeffer, DG, Shearer, M, and Witelski, TP. "Boundary-value problems for hyperbolic equations related to steady granular flow." Mathematics and Mechanics of Solids 12, no. 6 (2007): 665-699. Full Text
  - Bowen, M, and Witelski, TP. "The linear limit of the dipole problem for the thin film equation." SIAM Journal on Applied Mathematics 66, no. 5 (2006): 1727-1748. Full Text
  - Witelski, TP, Shearer, M, and Levy, R. "Growing surfactant waves in thin liquid films driven by gravity." Applied Mathematics Research eXpress 2006 (2006). Full Text
  - Fetzer, R, Jacobs, K, Münch, A, Wagner, B, and Witelski, TP. "New slip regimes and the shape of dewetting thin liquid films." Phys Rev Lett 95, no. 12 (September 16, 2005): 127801-. Full Text Link to Item
  - Glasner, KB, and Witelski, TP. "Collision versus collapse of droplets in coarsening of dewetting thin films." Physica D: Nonlinear Phenomena 209, no. 1-4 SPEC. ISS. (2005): 80-104. Full Text
  - Haskett, RP, Witelski, TP, and Sur, J. "Localized Marangoni forcing in driven thin films." Physica D: Nonlinear Phenomena 209, no. 1-4 SPEC. ISS. (2005): 117-134. Full Text
  - Münch, A, Wagner, B, and Witelski, TP. "Lubrication models with small to large slip lengths." Journal of Engineering Mathematics 53, no. 3-4 (2005): 359-383. Full Text
  - Witelski, TP, and Rienstra, SW. "Introduction to practical asymptotics III." Journal of Engineering Mathematics 53, no. 3-4 (2005): 199--. Full Text
  - Witelski, TP. "Motion of wetting fronts moving into partially pre-wet soil." Advances in Water Resources 28, no. 10 SPEC. ISS. (2005): 1133-1141. Full Text
  - Sur, J, Witelski, TP, and Behringer, RP. "Steady-profile fingering flows in Marangoni driven thin films." Phys Rev Lett 93, no. 24 (December 10, 2004): 247803-. Full Text Link to Item
  - Borucki, LJ, Witelski, T, Please, C, Kramer, PR, and Schwendeman, D. "A theory of pad conditioning for chemical-mechanical polishing." Journal of Engineering Mathematics 50, no. 1 (2004): 1-24. Full Text
  - Smolka, LB, Belmonte, A, Henderson, DM, and Witelski, TP. "Exact solution for the extensional flow of a viscoelastic filament." European Journal of Applied Mathematics 15, no. 6 (2004): 679-712. Full Text
  - Witelski, TP, Bernoff, AJ, and Bertozzi, AL. "Blowup and dissipation in a critical-case unstable thin film equation." European Journal of Applied Mathematics 15, no. 2 (2004): 223-256. Full Text
  - Witelski, TP, and Bowen, M. "ADI schemes for higher-order nonlinear diffusion equations." Applied Numerical Mathematics 45, no. 2-3 (May 2003): 331-351. Full Text
  - Glasner, KB, and Witelski, TP. "Coarsening dynamics of dewetting films." Phys Rev E Stat Nonlin Soft Matter Phys 67, no. 1 Pt 2 (January 2003): 016302-. Full Text Link to Item
  - Schaeffer, DG, Shearer, M, and Witelski, T. "One-dimensional solutions of an elastoplasticity model of granular material." Math. Models and Methods in Appl. Sciences 13 (2003): 1629-1671. (Academic Article)
  - Shearer, M, Schaeffer, DG, and Witelski, TP. "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 (2003): 1629-1671. Full Text
  - Witelski, TP. "Intermediate asymptotics for Richards' equation in a finite layer." Journal of Engineering Mathematics 45, no. 3-4 (2003): 379-399. Full Text
  - Witelski, TP. "Nonlinear Differential Equations, Mechanics and Bifurcation." Discrete and Continuous Dynamical Systems - Series B 3, no. 4 (2003): i-.
  - Bernoff, AJ, and Witelski, TP. "Linear stability of source-type similarity solutions of the thin film equation." Applied Mathematics Letters 15, no. 5 (2002): 599-606.
  - Bertozzi, AL, Grün, G, and Witelski, TP. "Dewetting films: Bifurcations and concentrations." Nonlinearity 14, no. 6 (2001): 1569-1592. Full Text
  - Vaynblat, D, Lister, JR, and Witelski, TP. "Rupture of thin viscous films by van der waals forces: Evolution and self-similarity." Physics of Fluids 13, no. 5 (2001): 1130-1141. Full Text
  - Vaynblat, D, Lister, JR, and Witelski, TP. "Symmetry and self-similarity in rupture and pinchoff: A geometric bifurcation." European Journal of Applied Mathematics 12, no. 3 (2001): 209-232. Full Text
  - Witelski, TP, Ono, K, and Kaper, TJ. "Critical wave speeds for a family of scalar reaction-diffusion equations." Applied Mathematics Letters 14, no. 1 (2001): 65-73. Full Text
  - Witelski, TP, Schaeffer, DG, and Shearer, M. "A discrete model for an ill-posed nonlinear parabolic PDE." Physica D: Nonlinear Phenomena 160, no. 3-4 (2001): 189-221. Full Text
  - Witelski, TP, and Bernoff, AJ. "Dynamics of three-dimensional thin film rupture." Physica D: Nonlinear Phenomena 147, no. 1-2 (2000): 155-176. Full Text
  - Witelski, TP, and Bernoff, AJ. "Stability of self-similar solutions for van der Waals driven thin film rupture." PHYSICS OF FLUIDS 11, no. 9 (September 1999): 2443-2445. Full Text Link to Item
  - Witelski, TP, and Hendriks, F. "Stability of gas bearing sliders for large bearing number: Convective instability of the tapered slider." Tribology Transactions 42, no. 1 (1999): 216-222.
  - Witelski, TP. "Large bearing number stability analysis for tango class gas bearing sliders©." Tribology Transactions 42, no. 3 (1999): 668-674.
  - Witelski, TP. "Horizontal infiltration into wet soil." Water Resources Research 34, no. 7 (July 1998): 1859-1863. Full Text
  - Bernoff, AJ, Bertozzi, AL, and Witelski, TP. "Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff." Journal of Statistical Physics 93, no. 3-4 (1998): 725-776.
  - Brenner, MP, and Witelski, TP. "On spherically symmetric gravitational collapse." Journal of Statistical Physics 93, no. 3-4 (1998): 863-899.
  - Witelski, TP, Grosberg, AY, and Tanaka, T. "On the properties of polymer globules in the high density limit." Journal of Chemical Physics 108, no. 21 (1998): 9144-9149.
  - Witelski, TP, and Bernoff, AJ. "Self-similar asymptotics for linear and nonlinear diffusion equations." Studies in Applied Mathematics 100, no. 2 (1998): 153-193.
  - Witelski, TP. "Equilibrium interface solutions of a degenerate singular Cahn-Hilliard equation." Applied Mathematics Letters 11, no. 5 (1998): 127-133.
  - Witelski, TP. "Dynamics of air bearing sliders." Physics of Fluids 10, no. 3 (1998): 698-708.
  - Witelski, TP. "Similarity solutions of the lubrication equation." Applied Mathematics Letters 10, no. 5 (1997): 107-113.
  - 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, TP. "Segregation and mixing in degenerate diffusion in population dynamics." Journal of Mathematical Biology 35, no. 6 (1997): 695-712.
  - Cohen, DS, and Witelski, TP. "Inaccessible states in time-dependent reaction diffusion." Studies in Applied Mathematics 97, no. 4 (1996): 301-319.
  - Witelski, TP. "Traveling wave solutions for case II diffusion in polymers." Journal of Polymer Science, Part B: Polymer Physics 34, no. 1 (1996): 141-150.
  - Witelski, TP. "The structure of internal layers for unstable nonlinear diffusion equations." Studies in Applied Mathematics 97, no. 3 (1996): 277-300.
  - WITELSKI, TP, and COHEN, DS. "FORBIDDEN REGIONS FOR SHOCK FORMATION IN DIFFUSIVE SYSTEMS." STUDIES IN APPLIED MATHEMATICS 95, no. 3 (October 1995): 297-317. Link to Item
  - Cohen, DS, Jr, ABW, and Witelski, TP. "Shock formation in a multidimensional viscoelastic diffusive system." SIAM Journal on Applied Mathematics 55, no. 2 (1995): 348-368.
  - Witelski, TP, and Cohen, DS. "Perturbed reversible systems." Physics Letters A 207, no. 1-2 (1995): 83-86.
  - Witelski, TP. "Shocks in nonlinear diffusion." Applied Mathematics Letters 8, no. 5 (1995): 27-32. Full Text
  - Witelski, TP. "Merging traveling waves for the porous-Fisher's equation." Applied Mathematics Letters 8, no. 4 (1995): 57-62.
  - Witelski, TP. "Stopping and merging problems for the porous media equation." IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) 54, no. 3 (1995): 227-243. Full Text
  - Witelski, TP. "An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation." Journal of Mathematical Biology 33, no. 1 (1994): 1-16. Full Text
  - Witelski, T, Ng, P, Ying, J, Jundy, J, and Bove, J. "An application of pattern recognition and infrared spectroscopy to water analysis." International Journal of Environmental Analytical Chemistry 44, no. 2 (1991): 127-136. (Academic Article)
  - BOWEN, M, and WITELSKI, TP. "Pressure-dipole solutions of the thin-film equation(Published online)." European Journal of Applied Mathematics : 1-42. Full Text
Teaching & Mentoring
Recent Courses
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Service to the Profession
Service to Duke
- Duke University. Library Council. 2013 - 2019 2013 - 2019
- Executive Committee of the Graduate Faculty (ECGF). September 1, 2010 - April 1, 2012 2010 - 2012
- Director of Graduate Studies. July 1, 2009 - June 30, 2011 2009 - 2011

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Education, Training, & Certifications

Duke Appointment History

Awards & Honors

Subject Headings

Selected Publications

Books

Conference Papers

Journal Articles

Recent Courses

Presentations & Appearances

Service to the Profession

Service to Duke