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)-660-2828
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 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.

Keywords:

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]