Math @ Duke

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:
Teaching (Spring 2016): (typical courses)
 STA 790.01, SPECIAL TOPICS
Synopsis
 TBA, W 04:40 PM07:00 PM
 STA 790.02, SPECIAL TOPICS
Synopsis
 SEE INSTRU, Tu 04:40 PM07:00 PM
 (also crosslisted as MATH 79071.01)
 Education:
PhD, Applied Math  Caltech  1995 
Ph.D.  California Institute of Technology  1995 
BS in Engineering  Cooper Union  1991 
B.S.E.  Cooper Union  1991 
Diploma  Stuyvesant High School  1987 
 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)
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)
 JA Dijksman, S Mukhopadhyay, C Gaebler, TP Witelski and RP Behringer, Obtaining selfsimilar scalings in focusing flows.,
Physical review. E, Statistical, nonlinear, and soft matter physics, vol. 92 no. 4
(2015),
pp. 043016, ISSN 15393755 [doi] [abs]
 TP Witelski, Preface to the special issue on “Thin films and fluid interfaces”,
Journal of Engineering Mathematics, vol. 94 no. 1
(October, 2015),
pp. 13, ISSN 00220833 [doi]
 T.P. Witelski and M. Bowen, Methods of Mathematical Modelling, Springer Undergraduate Mathematics Series (SUMS)
(2015), ISBN 9783319230412 [9783319230412]
 NS Hall Taylor, IJ Hewitt, JR Ockendon and TP Witelski, A new model for disturbance waves,
International Journal of Multiphase Flow, vol. 66
(November, 2014),
pp. 3845, ISSN 03019322 [doi]
 LB Smolka and TP Witelski, Biaxial extensional motion of an inertially driven radially expanding liquid sheet,
PHYSICS OF FLUIDS, vol. 25 no. 6
(2013), ISSN 10706631 [Gateway.cgi], [doi]
 Recent Grant Support
 FRG: Collaborative:, National Science Foundation, DMS0968252, 2010/062015/05.
 FRG: Collaborative Research: Dynamics of Thin Liquid Films: Mathematics and Experiments, NSF #0968252, 2010/062013/05.
 CAREER Award, NSF, 2003/09.
 Conferences Organized
 Dynamics Days US 2016, organizing committee, January 7, 2016  January 10, 2016
 Organizing Committee : Flows and Patterns: The Physics of Fluids, Granular Materials, and Soft Matter. October 12, 2013  October 13, 2013, Organizing Committee, October 12, 2013  October 13, 2013
 organizing committee : BIRS workshop 12w5035: Thin liquid films and fluid interfaces: models, experiments and applications. December 9, 2012  Decembe, 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, June 11, 2011  June 12, 2011
 member of organizing committee : Dynamics Days 2011. January 5, 2011  January 8, 2011, member of organizing committee, 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, June 28, 2010  June 30, 2010
 Faculty mentor/problem presenter : 2nd UK Graduate Modelling Camp. April 6, 2010  April 9, 2010, 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, September 11, 2009  September 12, 2009
 Minisymposium sessions coorganizer : SIAM 2009 Annual meeting, MS65/MS76 Contemporary Applications of Perturbation and Asymptotic Methods I/II. July, Minisymposium sessions coorganizer, July 9, 2009  July 10, 2009
 Faculty Mentor : Graduate Student Mathematical Modeling Camp 2009. June 9, 2009  June 12, 2009, 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
 UCLAIPAMNSF 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, NovemberDecember 2003
 Nonlinear Differential Equations, Mechanics and Bifurcation 2002: A conference in honor of David G. Schaeffer, Member of organizing committee, 200102
 Minisymposium MS1:Instabilities and Breakdown of Asymptotic Models in Continuum Mechanics, SIAM Conference on Materials Science 2000, CoOrganizer, with Mary Pugh (UPenn), May 2000
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 277080320

