CNCS Center for Nonlinear and Complex Systems
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Thomas P. Witelski, Professor of Mathematics

Thomas P. Witelski
Contact Info:
Office Location:  295 Physics
Office Phone:  00-1-(919) 660-2841
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~witelski

Teaching (Fall 2013):

  • MATH 551.01, APP PART DIFF EQU & COMPX VAR Synopsis
    Physics 259, MWF 01:40 PM-02:30 PM
Education:

PhD, Applied MathCaltech1995
BS in EngineeringCooper Union1991
DiplomaStuyvesant High School1987
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

Current Ph.D. Students   (Former Students)

Postdocs Mentored

Undergraduate Research Supervised

  • Veronica Ciocanel (May, 2010 - May, 2012)
    2012 Faculty Scholar, Honorable mention, Graduation with Distinction in Mathematics: 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)

  1. S.J.Chapman, P.H.Trinh and T.P. Witelski, Exponential asymptotics for thin film rupture, SIAM Journal on Applied Mathematics, vol. 73 no. 1 (2013), pp. 232-253 [120872012], [doi]
  2. T.P. Witelski, D. Ambrose, A. Bertozzi, A. Layton, ZL. Li, M. Minion, Preface: special issue on fluid dynamics, analysis and numerics, Discrete and Continuous Dynamical Systems Series B, vol. 17 no. 4 (June, 2012), pp. i-ii
  3. R. Wiebe, L.N. Virgin, T. P. Witelski, A parametrically forced nonlinear system with reversible equilibria, International Journal of Bifurcation and Chaos, vol. 22 no. 6 (2012), pp. 1230020 [doi]
  4. Y. Huang, T.P. Witelski, A. L. Bertozzi, Anomalous exponents of self-similar blowup solutions to an aggregation equation in odd dimensions, Applied Mathematics Letters, vol. 25 no. 12 (2012), pp. 2317-2321 [doi]
  5. C. Breward, E. Aydemir, T.P. Witelski, The effect of polar lipids on tear film dynamics, Bulletin of Mathematical Biology, vol. 73 (2011), pp. 1171-1201 [doi]

Journal editorial boards

Other Activities