Thomas P. Witelski

Bio

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.

Education

• B.S.E. The Cooper Union, 1991
• Ph.D. California Institute of Technology, 1995

Positions

• Professor in the Department of Mathematics
• Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science
• Professor in the Department of Mechanical Engineering and Materials Science

Awards, Honors, and Distinctions

• Top 5% teaching. Duke Arts and Science. 2018
• Top 5% teaching. Duke Arts and Science. 2017
• Faculty Early Career Development (CAREER) Program. National Science Foundation. 2003
• Sloan Research Fellowship-Mathematics. Alfred P. Sloan Foundation. 2000

Courses Taught

• MATH 895: Internship
• MATH 799: Special Readings
• MATH 790-90: Minicourse in Advanced Topics
• MATH 577: Mathematical Modeling
• MATH 575: Mathematical Fluid Dynamics
• MATH 553: Asymptotic and Perturbation Methods
• MATH 551: Applied Partial Differential Equations and Complex Variables

Publications

• Orizaga S, Witelski T. IMEX methods for thin-film equations and Cahn–Hilliard equations with variable mobility. Computational Materials Science. 2024 Jul 1;243.
• Ji H, Witelski TP. COARSENING OF THIN FILMS WITH WEAK CONDENSATION. SIAM Journal on Applied Mathematics. 2024 Jan 1;84(2):362–86.
• Chapman SJ, Dallaston MC, Kalliadasis S, Trinh PH, Witelski TP. The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics. Physica D: Nonlinear Phenomena. 2023 Nov 1;453.
• Bowen M, King JR, Witelski TP. CAUCHY-DIRICHLET PROBLEMS FOR THE POROUS MEDIUM EQUATION. Discrete and Continuous Dynamical Systems- Series A. 2023 Mar 1;43(3–4):1143–74.
• Sanaei P, Breward C, Ellis M, Han S, Holzer B, Ji H, et al. Evaporation and deposition in porous media. In 2022.
• Kim R, Witelski TP. Uncovering the dynamics of a circadian-dopamine model influenced by the light-dark cycle. Mathematical biosciences. 2022 Feb;344:108764.
• Zhu H, Zhang P, Zhong Z, Xia J, Rich J, Mai J, et al. Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices. Science advances. 2021 Jan;7(2):eabc7885.
• Nakad M, Witelski T, Domec JC, Sevanto S, Katul G. Taylor dispersion in osmotically driven laminar flows in phloem. Journal of Fluid Mechanics. 2021 Jan 1;913.
• Aguareles M, Chapman SJ, Witelski T. Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains. Physica D: Nonlinear Phenomena. 2020 Dec 15;414.
• Ji H, Witelski T. Steady states and dynamics of a thin-film-type equation with non-conserved mass. European Journal of Applied Mathematics. 2020 Dec 1;31(6):968–1001.
• Liu W, Witelski TP. Steady states of thin film droplets on chemically heterogeneous substrates. IMA Journal of Applied Mathematics. 2020 Nov 25;85(6):980–1020.
• Dijksman JA, Mukhopadhyay S, Gaebler C, Witelski TP, Behringer RP. Erratum: Obtaining self-similar scalings in focusing flows [Phys. Rev. E 92, 043016 (2015)]. Physical review E. 2020 May;101(5–2):059902.
• Witelski TP. Nonlinear dynamics of dewetting thin films. AIMS Mathematics. 2020 Jan 1;5(5):4229–59.
• Dijksman JA, Mukhopadhyay S, Behringer RP, Witelski TP. Thermal Marangoni-driven dynamics of spinning liquid films. Physical Review Fluids. 2019 Aug 19;4(8).
• Bowen M, Witelski TP. Pressure-dipole solutions of the thin-film equation. European Journal of Applied Mathematics. 2019 Apr 1;30(2):358–99.
• Gao Y, Ji H, Liu JG, Witelski TP. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B. 2018 Dec 1;23(10):4433–53.
• Chiou J-G, Ramirez SA, Elston TC, Witelski TP, Schaeffer DG, Lew DJ. Principles that govern competition or co-existence in Rho-GTPase driven polarization. PLoS Comput Biol. 2018 Apr;14(4):e1006095.
• Ji H, Witelski TP. Instability and dynamics of volatile thin films. Physical Review Fluids. 2018 Feb 1;3(2).
• Gao Y, Ji H, Liu JG, Witelski TP. Global existence of solutions to a tear film model with locally elevated evaporation rates. Physica D: Nonlinear Phenomena. 2017 Jul 1;350:13–25.
• Ji H, Witelski TP. Finite-time thin film rupture driven by modified evaporative loss. Physica D: Nonlinear Phenomena. 2017 Mar 1;342:1–15.
• Sanaei P, Richardson GW, Witelski T, Cummings LJ. Flow and fouling in a pleated membrane filter. Journal of Fluid Mechanics. 2016 May 25;795:36–59.
• Smolka LB, McLaughlin CK, Witelski TP. Oil capture from a water surface by a falling sphere. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016 May 20;497:126–32.
• George C, Virgin LN, Witelski T. Experimental study of regular and chaotic transients in a non-smooth system. International Journal of Non-Linear Mechanics. 2016 May 1;81:55–64.
• Witelski TP. Preface to the special issue on “Thin films and fluid interfaces”. Journal of Engineering Mathematics. 2015 Oct 29;94(1).
• Dijksman JA, Mukhopadhyay S, Gaebler C, Witelski TP, Behringer RP. Obtaining self-similar scalings in focusing flows. Physical review E, Statistical, nonlinear, and soft matter physics. 2015 Oct;92(4):043016.
• Witelski T, Bowen M. Methods of Mathematical Modelling: Continuous Systems and Differential Equations. 2015.
• Witelski T, Virgin LN, George C. A driven system of impacting pendulums: Experiments and simulations. Journal of Sound and Vibration. 2014 Mar 17;333(6):1734–53.
• Hall Taylor NS, Hewitt IJ, Ockendon JR, Witelski TP. A new model for disturbance waves. International Journal of Multiphase Flow. 2014 Jan 1;66:38–45.
• Smolka LB, Witelski TP. Biaxial extensional motion of an inertially driven radially expanding liquid sheet. Physics of Fluids. 2013 Jun 1;25(6).
• Chapman SJ, Trinh PH, Witelski TP. Exponential Asymptotics for Thin Film Rupture. SIAM J Appl Math. 2013;73:232–53.
• Huang Y, Witelski TP, Bertozzi AL. Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions. Applied Mathematics Letters. 2012 Dec 1;25(12):2317–21.
• Li Z, Layton AT, Bertozzi A, Ambrose DM, Witelski T, Minion ML, et al. Preface. Discrete and Continuous Dynamical Systems - Series B. 2012 Feb;17(4).
• Wiebe R, Virgin LN, Witelski TP. A parametrically forced nonlinear system with reversible equilibria. International Journal of Bifurcation and Chaos. 2012 Jan 1;22(6).
• Aydemir E, Breward CJW, Witelski TP. The effect of polar lipids on tear film dynamics. Bulletin of mathematical biology. 2011 Jun;73(6):1171–201.
• Aguareles M, Chapman SJ, Witelski T. Motion of spiral waves in the complex Ginzburg-Landau equation. Physica D: Nonlinear Phenomena. 2010 Apr 1;239(7):348–65.
• Bernoff AJ, Witelski TP. Stability and dynamics of self-similarity in evolution equations. Journal of Engineering Mathematics. 2010 Jan 1;66(1):11–31.
• Witelski TP. The subtle art of blowing bubbles (News and Views: Fluid Dynamics). Nature Physics. 2009 May;5:315–6.
• Witelski TP, Bowen M. Singular perturbation theory. Scholarpedia. 2009 Apr 7;4:3951–3951.
• Hwang HJ, Witelski TP. Short-time pattern formation in thin film equations. Discrete and Continuous Dynamical Systems. 2009 Mar 1;23(3):867–85.
• Witelski TP. Fluid dynamics: The subtle art of blowing bubbles. Nature Physics. 2009 Jan 1;5(5):315–6.
• Smolka LB, Witelski TP. On the planar extensional motion of an inertially driven liquid sheet. Physics of Fluids. 2009 Jan 1;21(4).
• Gratton MB, Witelski TP. Transient and self-similar dynamics in thin film coarsening. Physica D: Nonlinear Phenomena. 2009 Jan 1;238(23–24):2380–94.
• Peterson E, Shearer M, Witelski TP, Levy R. Stability of traveling waves in thin liquid films driven by gravity and surfactant. In: Tadmor E, Liu J, Tzavaras A, editors. HYPERBOLIC PROBLEMS: THEORY, NUMERICS AND APPLICATIONS, PART 2. AMER MATHEMATICAL SOC; 2009. p. 855-+.
• Aguareles M, Chapman SJ, Witelski T. Interaction of spiral waves in the complex Ginzburg-Landau equation. Physical review letters. 2008 Nov;101(22):224101.
• Santillan ST, Plaut RH, Witelski TP, Virgin LN. Large oscillations of beams and columns including self-weight. International Journal of Non-Linear Mechanics. 2008 Oct 1;43(8):761–71.
• Catllá AJ, Schaeffer DG, Witelski TP, Monson EE, Lin AL. On spiking models for synaptic activity and impulsive differential equations. SIAM Review. 2008 Sep 1;50(3):553–69.
• DiCarlo DA, Juanes R, LaForce T, Witelski TP. Nonmonotonic traveling wave solutions of infiltration into porous media. Water Resources Research. 2008 Feb 1;44(2).
• Gratton MB, Witelski TP. Coarsening of unstable thin films subject to gravity. Physical review E, Statistical, nonlinear, and soft matter physics. 2008 Jan;77(1 Pt 2):016301.
• Aguareles M, Chapman SJ, Witelski TP. Interaction of spiral waves in the Complex Ginzburg-Landau equation. Physical Review Letters. 2008;101(224101).
• Gratton MB, Witelski TP. Coarsening of dewetting thin films subject to gravity. Physical Review E. 2008;77(016301):1–11.
• Levy R, Shearer M, Witelski TP. Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves. European Journal of Applied Mathematics. 2007 Dec 1;18(6):679–708.
• Schaeffer DG, Shearer M, Witelski TP. Boundary-value problems for hyperbolic equations related to steady granular flow. Mathematics and Mechanics of Solids. 2007 Dec 1;12(6):665–99.
• Witelski TP, Shearer M, Levy R. Growing surfactant waves in thin liquid films driven by gravity. Applied Mathematics Research eXpress. 2006 Dec 1;2006.
• Bowen M, Witelski TP. The linear limit of the dipole problem for the thin film equation. SIAM Journal on Applied Mathematics. 2006 Oct 25;66(5):1727–48.
• Munch A, Wagner B, Witelski TP. Lubrication models with small to large slip lengths. Journal of Engineering Mathematics. 2005 Dec;53(3–4):259–83.
• Witelski TP, Rienstra SW. Introduction to practical asymptotics III. Journal of Engineering Mathematics. 2005 Dec 1;53(3–4):199.
• Münch A, Wagner B, Witelski TP. Lubrication models with small to large slip lengths. Journal of Engineering Mathematics. 2005 Dec 1;53(3–4):359–83.
• Haskett RP, Witelski TP, Sur J. Localized Marangoni forcing in driven thin films. Physica D: Nonlinear Phenomena. 2005 Sep 15;209(1-4 SPEC. ISS.):117–34.
• Glasner KB, Witelski TP. Collision versus collapse of droplets in coarsening of dewetting thin films. Physica D: Nonlinear Phenomena. 2005 Sep 15;209(1-4 SPEC. ISS.):80–104.
• Fetzer R, Jacobs K, Münch A, Wagner B, Witelski TP. New slip regimes and the shape of dewetting thin liquid films. Physical review letters. 2005 Sep;95(12):127801.
• Witelski TP. Motion of wetting fronts moving into partially pre-wet soil. Advances in Water Resources. 2005 Jan 1;28(10 SPEC. ISS.):1133–41.
• Smolka LB, Belmonte A, Henderson DM, Witelski TP. Exact solution for the extensional flow of a viscoelastic filament. European Journal of Applied Mathematics. 2004 Dec 1;15(6):679–712.
• Sur J, Witelski TP, Behringer RP. Steady-profile fingering flows in Marangoni driven thin films. Physical review letters. 2004 Dec;93(24):247803.
• Borucki LJ, Witelski T, Please C, Kramer PR, Schwendeman D. A theory of pad conditioning for chemical-mechanical polishing. Journal of Engineering Mathematics. 2004 Dec 1;50(1):1–24.
• Witelski TP, Bernoff AJ, Bertozzi AL. Blowup and dissipation in a critical-case unstable thin film equation. European Journal of Applied Mathematics. 2004 Apr 1;15(2):223–56.
• Witelski TP. Nonlinear Differential Equations, Mechanics and Bifurcation. Discrete and Continuous Dynamical Systems - Series B. 2003 Nov 1;3(4).
• Shearer M, Schaeffer DG, Witelski TP. Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness. Mathematical Models and Methods in Applied Sciences. 2003 Nov 1;13(11):1629–71.
• Witelski TP, Bowen M. ADI schemes for higher-order nonlinear diffusion equations. Applied Numerical Mathematics. 2003 May 1;45(2–3):331–51.
• Witelski TP. Intermediate asymptotics for Richards' equation in a finite layer. Journal of Engineering Mathematics. 2003 Apr 1;45(3–4):379–99.
• Schaeffer DG, Shearer M, Witelski T. One-dimensional solutions of an elastoplasticity model of granular material. Math Models and Methods in Appl Sciences. 2003;13:1629–71.
• Glasner KB, Witelski TP. Coarsening dynamics of dewetting films. Physical review E, Statistical, nonlinear, and soft matter physics. 2003 Jan;67(1 Pt 2):016302.
• Glasner KB, Witelski TP. Coarsening dynamics of dewetting films. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2003 Jan 1;67(1 2):163021–1630212.
• Bernoff AJ, Witelski TP. Linear stability of source-type similarity solutions of the thin film equation. Applied Mathematics Letters. 2002 Jan 1;15(5):599–606.
• Witelski TP. Computing finite-time singularities in interfacial flows. In: Bourlioux A, Gander MJ, Sabidussi G, editors. MODERN METHODS IN SCIENTIFIC COMPUTING AND APPLICATIONS. SPRINGER; 2002. p. 451–87.
• Witelski TP, Schaeffer DG, Shearer M. A discrete model for an ill-posed nonlinear parabolic PDE. Physica D: Nonlinear Phenomena. 2001 Dec 15;160(3–4):189–221.
• Vaynblat D, Lister JR, Witelski TP. Symmetry and self-similarity in rupture and pinchoff: A geometric bifurcation. European Journal of Applied Mathematics. 2001 Dec 1;12(3):209–32.
• Bertozzi AL, Grün G, Witelski TP. Dewetting films: Bifurcations and concentrations. Nonlinearity. 2001 Nov 1;14(6):1569–92.
• Witelski TP, Ono K, Kaper TJ. Critical wave speeds for a family of scalar reaction-diffusion equations. Applied Mathematics Letters. 2001 Jan 1;14(1):65–73.
• Vaynblat D, Lister JR, Witelski TP. Rupture of thin viscous films by van der waals forces: Evolution and self-similarity. Physics of Fluids. 2001 Jan 1;13(5):1130–41.
• Witelski TP, Bernoff AJ. Dynamics of three-dimensional thin film rupture. Physica D: Nonlinear Phenomena. 2000 Dec 1;147(1–2):155–76.
• Witelski TP, Ono K, Kaper TJ. On axisymmetric traveling waves and radial solutions of semi-linear elliptic equations. Natural Resource Modeling. 2000 Jan 1;13(3):339–88.
• Witelski TP, Bernoff AJ. Stability of self-similar solutions for van der Waals driven thin film rupture. Physics of Fluids. 1999 Jan 1;11(9):2443–5.
• Witelski TP, Hendriks F. Large bearing number stability analysis for tango class gas bearing sliders. Tribology Transactions. 1999 Jan 1;42(3):668–74.
• Witelski TP, Hendriks F. Stability of gas bearing sliders for large bearing number: Convective instability of the tapered slider©. Tribology Transactions. 1999 Jan 1;42(1):216–22.
• Witelski TP, Grosberg AY, Tanaka T. On the properties of polymer globules in the high density limit. Journal of Chemical Physics. 1998 Jun 1;108(21):9144–9.
• Witelski TP. Equilibrium interface solutions of a degenerate singular Cahn-Hilliard equation. Applied Mathematics Letters. 1998 Jan 1;11(5):127–33.
• Brenner MP, Witelski TP. On spherically symmetric gravitational collapse. Journal of Statistical Physics. 1998 Jan 1;93(3–4):863–99.
• Witelski TP, Bernoff AJ. Self-similar asymptotics for linear and nonlinear diffusion equations. Studies in Applied Mathematics. 1998 Jan 1;100(2):153–93.
• Bernoff AJ, Bertozzi AL, Witelski TP. Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff. Journal of Statistical Physics. 1998 Jan 1;93(3–4):725–76.
• Witelski TP. Dynamics of air bearing sliders. Physics of Fluids. 1998 Jan 1;10(3):698–708.
• Witelski TP. Horizontal infiltration into wet soil. Water Resources Research. 1998 Jan 1;34(7):1859–63.
• Witelski TP. Similarity solutions of the lubrication equation. Applied Mathematics Letters. 1997 Sep 12;10(5):107–13.
• Witelski TP. Perturbation Analysis for Wetting Fronts in Richards' Equation. Transport in Porous Media. 1997 Jan 1;27(2):121–34.
• Witelski TP. Segregation and mixing in degenerate diffusion in population dynamics. Journal of Mathematical Biology. 1997 Jan 1;35(6):695–712.
• Witelski TP. Traveling wave solutions for case II diffusion in polymers. Journal of Polymer Science, Part B: Polymer Physics. 1996 Jan 15;34(1):141–50.
• Witelski TP. The structure of internal layers for unstable nonlinear diffusion equations. Studies in Applied Mathematics. 1996 Jan 1;97(3):277–300.
• Cohen DS, Witelski TP. Inaccessible states in time-dependent reaction diffusion. Studies in Applied Mathematics. 1996 Jan 1;97(4):301–19.
• Witelski TP. Stopping and merging problems for the porous media equation. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications). 1995 Dec 1;54(3):227–43.
• Witelski TP, Cohen DS. Perturbed reversible systems. Physics Letters A. 1995 Oct 23;207(1–2):83–6.
• Witelski TP, Cohen DS. Forbidden Regions for Shock Formation in Diffusive Systems. Studies in Applied Mathematics. 1995 Oct 1;95(3):297–317.
• Witelski TP. Merging traveling waves for the porous-Fisher's equation. Applied Mathematics Letters. 1995 Jan 1;8(4):57–62.
• Witelski TP. Shocks in nonlinear diffusion. Applied Mathematics Letters. 1995 Jan 1;8(5):27–32.
• Cohen DS, White AB, Witelski TP. Shock formation in a multidimensional viscoelastic diffusive system. SIAM Journal on Applied Mathematics. 1995 Jan 1;55(2):348–68.
• Witelski TP. An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation. Journal of Mathematical Biology. 1994 Nov 1;33(1):1–16.
• Witelski T, Ng P, Ying J, Jundy J, Bove J. An application of pattern recognition and infrared spectroscopy to water analysis. International Journal of Environmental Analytical Chemistry. 1991;44(2):127–36.