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Math @ Duke



Timothy Lucas, Instructor

Timothy Lucas

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)-660-2828
Email Address: send me a message

Typical Courses Taught:

Office Hours:


PhD in MathematicsDuke University2006
M.A. in MathematicsDuke University2001
B.A. in MathematicsOccidental College2000

Applied Math
Research Interests: Numerical Analysis, Partial Differential Equations, Multigrid, Stochastic Differential Equations and Parallel Computing

I am studying a three-dimensional system of reaction-diffusion 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.


Numerical Analysis • Partial Differential Equations • Multigrid • Stochastic Differential Equations • Parallel Computing

Curriculum Vitae
Recent Publications

  1. T.A. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Submitted, Fall, 2007) (Submitted.) [PDF[abs] [author's comments]
  2. F. Mitha, T.A. Lucas, F. Feng, T.B. Kepler and C. Chan, The multiscale systems immunology project: Software forcell-based immunological simulation, Source Code for Biology and Medicine (Submitted, Fall, 2007) (Submitted.) [PDF[abs]
Selected Talks

  1. 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)]
  2. Numerical Solutions of an Immunology Model Using Reaction-Diffusion 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]
ph: 919.660.2800
fax: 919.660.2821

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