Timothy Lucas, Instructor

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

Recent Publications

1. T.A. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Submitted, Fall, 2007) (Submitted.)  [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.)  [abs]

Selected Talks

1. Numerical Methods for an Immunology Model Using, January 7, 2008, AMS Session on Applications of Mathematics, San Diego, CA    
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).