CNCS Center for Nonlinear and Complex Systems
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Thomas P. Witelski, Professor of Mathematics and CNCS: Center for nonlinear and complex systems and Professor of Mechanical Engineering and Materials Science

Thomas P. Witelski

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.

Contact Info:
Office Location:  120 Science Drive, Durham, NC 27708-0320
Office Phone:  (919) 660-2841
Email Address: send me a message
Web Pages:  http://fds.duke.edu/db/aas/math/faculty/witelski
http://www.springer.com/us/book/9783319230412

Teaching (Fall 2021):

  • MATH 551.01, APP PART DIFF EQU & COMPX VAR Synopsis
    Physics 259, MWF 05:15 PM-06:05 PM
Teaching (Spring 2022):

  • MATH 575.01, MATHEMATICAL FLUID DYNAM Synopsis
    Physics 205, WF 03:30 PM-04:45 PM
  • MATH 577.01, MATHEMATICAL MODELING Synopsis
    Physics 235, WF 01:45 PM-03:00 PM
Office Hours:

Please email me to request a meeting time
Education:

Ph.D.California Institute of Technology1995
B.S.E.The Cooper Union1991
Specialties:

Applied Math
Applied Math
Research Interests: Fluid Dynamics, Perturbation Methods, Asymptotic Analysis, Nonlinear Ordinary and Partial differential equations

My primary area of expertise is the solution of nonlinear ordinary and partial differential equations via perturbation methods. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in physical systems. Focuses of my work include problems in viscous fluid flow, industrial applications, flow in porous media, mathematical biology, and granular materials. Through my research I am working to extend the understanding of nonlinear diffusion processes in physical systems. Studying problems in a range of different fields has given me a unique opportunity to interact with a diverse set of collaborators and to transfer analytic techniques across the traditional boundaries that separate fields.

Areas of Interest:

Fluid dynamics
Partial differential equations
Asymptotics/Perturbation methods
Industrial and Applied mathematics

Keywords:

Differential equations, Nonlinear • Differential equations, Parabolic • Fluid dynamics • Perturbations, asymptotics • Surface Tension

Current Ph.D. Students   (Former Students)

    Postdocs Mentored

    Undergraduate Research Supervised

    • Veronica Ciocanel (May, 2010 - May, 2012)
      Honorable mention for 2012 Faculty Scholar,
      Thesis: Modeling and numerical simulation of the nonlinear dynamics of the forced planar string pendulum 
    • Jeremy Semko (May, 2009 - May, 2010)
      Thesis: Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface 
    • Lingren Zhang (July, 2006 - September, 2006)
      Thesis: The Motion of Sets of Vortices
      Undergraduate summer research 
    • Qinzheng Tian (July, 2005 - September, 2005)
      Thesis: Simulation of Newtonian fluid fluid between rotating cylinders
      Undergraduate summer research 
    Recent Publications   (More Publications)   (search)

    1. Zhu, H; Zhang, P; Zhong, Z; Xia, J; Rich, J; Mai, J; Su, X; Tian, Z; Bachman, H; Rufo, J; Gu, Y; Kang, P; Chakrabarty, K; Witelski, TP; Huang, TJ, Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices., Science Advances, vol. 7 no. 2 (January, 2021) [doi]  [abs]
    2. Nakad, M; Witelski, T; Domec, JC; Sevanto, S; Katul, G, Taylor dispersion in osmotically driven laminar flows in phloem, Journal of Fluid Mechanics, vol. 913 (January, 2021), Cambridge University Press (CUP) [doi]  [abs]
    3. Aguareles, M; Chapman, SJ; Witelski, T, Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains, Physica D: Nonlinear Phenomena, vol. 414 (December, 2020) [doi]  [abs]
    4. Ji, H; Witelski, T, Steady states and dynamics of a thin-film-type equation with non-conserved mass, European Journal of Applied Mathematics, vol. 31 no. 6 (December, 2020), pp. 968-1001, Cambridge University Press (CUP) [doi]  [abs]
    5. Liu, W; Witelski, TP, Steady states of thin film droplets on chemically heterogeneous substrates, Ima Journal of Applied Mathematics, vol. 85 no. 6 (November, 2020), pp. 980-1020, Oxford University Press (OUP) [doi]  [abs]

    Journal editorial boards

    Other Activities