Thomas P. Witelski, Professor

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
Email Address:
Web Pages:	http://fds.duke.edu/db/aas/math/faculty/witelski https://services.math.duke.edu/~witelski/book_errata.html

Teaching (Fall 2024):  (typical courses)

• MATH 553.01, ASYMP/PERTURBATION METHODS Synopsis

  Physics 227, WF 03:05 PM-04:20 PM

• MATH 577.01, MATHEMATICAL MODELING Synopsis

  Physics 235, MW 01:25 PM-02:40 PM

Office Hours:

Please email me to request a meeting time

Education:

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

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 • Perturbations, asymptotics • Surface Tension

Current Ph.D. Students   (Former Students)

• George Daccache  

Postdocs Mentored

• Jeffrey Wong (September, 2017 - 2021)  
• Saulo Orizaga (September, 2017 - June, 2020)  
• Rachel Levy (July, 2005 - June, 2007)  
• Anne Catlla (2005 - 2008)  
• Anand Jayaraman (September 1, 2004 - August 15, 2005)  
• Sandra Wieland (January 1, 2004 - December, 2004)  
• Linda Smolka (April 8, 2002 - July 1, 2004)  
• Karl Glasner (2001/12-2002/05)  
• Mark Bowen (2000/03-2001/12)  

Undergraduate Research Supervised

• Riley Fisher (January, 2023 - April, 2023)
  Thesis: Pattern formation in evolving domains 
• 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 

Representative Publications   (More Publications)   (search)

1. Witelski, T; Bowen, M, Methods of Mathematical Modelling: Continuous Systems and Differential Equations (September, 2015), pp. 1-305, Springer International Publishing, ISBN 9783319230412 [doi]  [abs] [author's comments]
2. 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]
3. 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]
4. Witelski, TP, Nonlinear dynamics of dewetting thin films, AIMS Mathematics, vol. 5 no. 5 (January, 2020), pp. 4229-4259 [doi]  [abs]
5. Dijksman, JA; Mukhopadhyay, S; Behringer, RP; Witelski, TP, Thermal Marangoni-driven dynamics of spinning liquid films, Physical Review Fluids, vol. 4 no. 8 (August, 2019) [doi]  [abs]
6. Bowen, M; Witelski, TP, Pressure-dipole solutions of the thin-film equation, European Journal of Applied Mathematics, vol. 30 no. 2 (April, 2019), pp. 358-399 [doi]  [abs]
7. 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, vol. 23 no. 10 (December, 2018), pp. 4433-4453, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]

Recent Grant Support

• CAREER Award, NSF, 2003/09.      

Conferences Organized

• TriCAMS: Triangle Computational and Applied Mathematics Symposium 2023, Local organizing committee, November 2023  
• Main organizer. 2016 Mathematical Problems in Industry (MPI) Workshop. Duke University. June 13, 2016 - June 17, 2016, Main organizer, June 13, 2016 - June 17, 2016  
• Member of organizing committee. Dynamics Days 2016 US. Duke University. January 07, 2016 - January 10, 2016, Member of organizing committee, January 7, 2016 - January 10, 2016  
• Member of organizing committee. Flows and Patterns: The Physics of Fluids, Granular Materials, and Soft Matter. Duke University. October 12, 2013 - Oc, Member of organizing committee, October 12, 2013 - October 13, 2013  
• Member of organizing committee. BIRS workshop 12w5035: Thin liquid films and fluid interfaces: models, experiments and applications. December 09, 2012, Member of organizing committee, December 9, 2012 - December 14, 2012  
• Faculty Mentor : Graduate Student Mathematical Modeling Camp 2011 (GSMMC). June 11, 2011 - June 12, 2011, Faculty Mentor : Graduate Student Mathematical Modeling Camp 2011 (GSMMC), June 11, 2011 - June 12, 2011  
• Member of organizing committee : Dynamics Days 2011. January 05, 2011 - January 08, 2011, Member of organizing committee : Dynamics Days 2011, January 5, 2011 - January 8, 2011  
• Chair, organizing committee : FAN2010: Fluid dynamics, Analysis and Numerics (A conference in honor of Thomas Beale). June 28, 2010 - June 30, 2010, Chair, organizing committee : FAN2010: Fluid dynamics, Analysis and Numerics (A conference in honor of Thomas Beale), June 28, 2010 - June 30, 2010  
• Faculty mentor/problem presenter. 2nd UK Graduate Modelling Camp. University of Oxford, Mathematical Institute, OCCAM Oxford Centre for Collaborative , Faculty mentor/problem presenter, April 6, 2010 - April 9, 2010  
• Member of organizing committee : CTMS Workshop: Theory and Applications of Multiscale Modeling. September 11, 2009 - September 12, 2009, Member of organizing committee : CTMS Workshop: Theory and Applications of Multiscale Modeling, September 11, 2009 - September 12, 2009  
• Minisymposium sessions co-organizer : SIAM 2009 Annual meeting, MS65/MS76 Contemporary Applications of Perturbation and Asymptotic Methods I/II. July , Minisymposium sessions co-organizer : SIAM 2009 Annual meeting, MS65/MS76 Contemporary Applications of Perturbation and Asymptotic Methods I/II, July 9, 2009 - July 10, 2009  
• Faculty Mentor. Graduate Student Mathematical Modeling Camp (GSMMC). Rensselaer Polytechnic Institute, Department of Mathematics. June 09, 2009 - June, Faculty Mentor, June 9, 2009 - June 12, 2009  
• Euromech 490 Workshop: Dynamics and Stability of thin liquid films and slender jets, Organising Committee, September 19, 2007 - September 21, 2007  
• Third Annual Graduate Student Mathematical Modeling Camp, Faculty Mentor, June 6, 2006 - June 9, 2006  
• UCLA-IPAM-NSF workshop on Thin Films and Fluid Interfaces, Organizing Committee, January 30, 2006 - February 2, 2006  
• First Annual Graduate Student Mathematical Modeling Camp, Faculty Mentor, June 15, 2004 - June 18, 2004  
• Dynamics Days 2004, Local Organizing Committee + Webmaster, January 2004  
• Nonlinear dynamics of thin films and fluid interfaces, Organizing Committee Member, November-December 2003  
• Nonlinear Differential Equations, Mechanics and Bifurcation 2002: A conference in honor of David G. Schaeffer, Member of organizing committee, 2001-02  
• Minisymposium MS1:Instabilities and Breakdown of Asymptotic Models in Continuum Mechanics, SIAM Conference on Materials Science 2000, Co-Organizer, with Mary Pugh (U-Penn), May 2000  

• Discrete and Continuous Dynamical Systems B
• European Journal of Applied Mathematics

• 
  • Book errata
• Research on fluid dynamics of thin viscous films

• Mathematical Problems in Industry Workshop
• Graduate Student Mathematical Modeling Camp
  

• Applied Math Web Resources guide

• myX: a simple C/C++ programming interface for X11 graphics

• As seen on RateMyProfessors.com
• Tom's favorite integral
• On Google Scholar
• On MathSciNet: 357178