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Thomas P. Witelski, Professor of Mathematics and Pratt School of Engineering

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
Office Phone:  (919) 660-2841
Email Address: send me a message
Web Page:  http://fds.duke.edu/db/aas/math/faculty/witelski

Teaching (Fall 2016):  (typical courses)

  • MATH 553.01, ASYMP/PERTURBATION METHODS Synopsis
    Physics 259, TuTh 04:40 PM-05:55 PM
  • STA 790.01, SPECIAL TOPICS Synopsis
    SEE INSTRU, W 04:40 PM-07:00 PM
    (also cross-listed as MATH 790-71.01)
  • STA 790.02, SPECIAL TOPICS Synopsis
    SEE INSTRU, Tu 04:40 PM-07:00 PM
    (also cross-listed as MATH 790-71.02)
Education:

PhD, Applied MathCaltech1995
Ph.D.California Institute of Technology1995
BS in EngineeringCooper Union1991
B.S.E.Cooper Union1991
DiplomaStuyvesant High School1987
Specialties:

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, dynamical systems, and industrial applications. 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)

Postdocs Mentored

Undergraduate Research 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)

  1. LB Smolka, CK McLaughlin and TP Witelski, Oil capture from a water surface by a falling sphere, Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 497 (2016), pp. 126-132, ISSN 0927-7757 [doi]
  2. P. Sanaei, G.W. Richardson, T. Witelski, L.J. Cummings, Flow and fouling in a pleated membrane filter, Journal of Fluid Mechanics, vol. 795 (2016), pp. 36-59
  3. C. George, L. N. Virgin, T.P. Witelski, Experimental study of regular and chaotic transients in a nonsmooth system, International Journal of Nonlinear Mechanics, vol. 81 (2016), pp. 55-64 [doi]
  4. JA Dijksman, S Mukhopadhyay, C Gaebler, TP Witelski and RP Behringer, Obtaining self-similar scalings in focusing flows., Physical review. E, Statistical, nonlinear, and soft matter physics, vol. 92 no. 4 (2015), pp. 043016, ISSN 1539-3755 [doi]  [abs]
  5. TP Witelski, Preface to the special issue on “Thin films and fluid interfaces”, Journal of Engineering Mathematics, vol. 94 no. 1 (October, 2015), pp. 1-3, ISSN 0022-0833 [doi]
Recent Grant Support

  • FRG: Collaborative:, National Science Foundation, DMS-0968252, 2010/06-2015/05.      
  • CAREER Award, NSF, 2003/09.      
Conferences Organized

Journal editorial boards Other Activities : Statistical and Applied Mathematical Sciences Institute

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320