Math @ Duke

Timothy Lucas, Instructor
Please note: Timothy has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
Office Location:  029B Physics Bldg  Office Phone:  (919)6602828  Email Address:   Typical Courses Taught:
 MATH 41, ONE VARIABLE CALCULUS
Synopsis

 MATH 107, LINEAR ALGEBRA & DIFF EQUATION
Synopsis

 MATH 108, ORD & PRTL DIFF EQUATIONS
Synopsis

 MATH 32L, LABORATORY CALCULUS II
Synopsis

 Math 31L, LABORATORY CALCULUS I

 Office Hours:
 TBD
 Education:
PhD in Mathematics  Duke University  2006 
M.A. in Mathematics  Duke University  2001 
B.A. in Mathematics  Occidental College  2000 
 Specialties:

Applied Math
 Research Interests: Numerical Analysis, Partial Differential Equations, Multigrid, Stochastic Differential Equations and Parallel Computing
I am studying a threedimensional system of reactiondiffusion equations with stochastic source terms that arises from an immunology model. I have shown convergence of a first order splitting method for this system. This allows us to take advantage of known numerical methods for the diffusion, reaction and stochastic differential equations. In particular, I have implemented a parallel multigrid scheme for the diffusion.
I am currently working with Dr. William K. Allard in the Mathematics department and Dr. Thomas B. Kepler in the Center for Computational Immunology.
 Keywords:
Numerical Analysis • Partial Differential Equations • Multigrid • Stochastic Differential Equations • Parallel Computing
 Curriculum Vitae
 Recent Publications
 T.A. Lucas, Operator Splitting for an Immunology Model Using ReactionDiffusion Equations with Stochastic Source Terms
(Submitted, Fall, 2007) (Submitted.) [PDF] [abs] [author's comments]
 F. Mitha, T.A. Lucas, F. Feng, T.B. Kepler and C. Chan, The multiscale systems immunology project: Software forcellbased immunological simulation,
Source Code for Biology and Medicine
(Submitted, Fall, 2007) (Submitted.) [PDF] [abs]
 Selected Talks
 Numerical Methods for an Immunology Model Using, January 7, 2008, AMS Session on Applications of Mathematics, San Diego, CA [Immune Cells Responding to MCP1 (sTNFr slices)] [Immune Cells Responding to MCP1 (TNF slices)] [Immune Cells Responding to MCP1 (Volume Rendering)] [Slides without Movies (pdf)]
 Numerical Solutions of an Immunology Model Using ReactionDiffusion
Equations with Stochastic Source Terms, November 8, 2007, Virginia Commonwealth University
 Selected Grant Support
 A Fast Method for the Numerical Simulation of an Immunology Model, National Science Foundation, 0811159 (Submitted).
[Proposal] [Summary]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

