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Thomas P. Witelski, Professor of Mathematics 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:  295 Physics Bldg, Box 90320, 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.researcherid.com/rid/G-5389-2016

Teaching (Fall 2018):

  • MATH 551.01, APP PART DIFF EQU & COMPX VAR Synopsis
    Hudson 207, MWF 04:55 PM-05:45 PM
Teaching (Spring 2019):
  • MATH 575.01, MATHEMATICAL FLUID DYNAM Synopsis
    Physics 259, TuTh 01:25 PM-02:40 PM
  • MATH 577.01, MATHEMATICAL MODELING Synopsis
    Physics 259, TuTh 10:05 AM-11:20 AM

Office Hours:

Mondays 10:00am-noon and Tuesdays noon-2:30pm

Education:

Ph.D.California Institute of Technology1995
B.S.E.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 • Surface Tension

Current Ph.D. Students   (Former Students)
  • Weifan Liu  

Postdocs Mentored

Undergraduate Researches Supervised
  • Veronica Ciocanel (May, 2010 - May, 2012)
    Honorable mention for 2012 Faculty Scholar, 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)   (search)

  1. 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 Computational Biology, vol. 14 no. 4 (April, 2018), pp. e1006095 [doi]  [abs]
  2. Ji, H; Witelski, TP, Instability and dynamics of volatile thin films, Physical Review Fluids, vol. 3 no. 2 (February, Submitted, 2018) [doi]  [abs]
  3. Gao, Y; Ji, H; Liu, J-G; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol. 350 (July, 2017), pp. 13-25 [doi]
  4. Ji, H; Witelski, TP, Finite-time thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol. 342 (March, 2017), pp. 1-15 [doi]
  5. Gao, Y; Ji, H; Liu, J-G; P. Witelski, T, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete & Continuous Dynamical Systems B, vol. 22 no. 11 (2017), pp. 1-21 [doi]

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