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Publications [#70663] of Timothy Lucas

Papers Submitted

  1. T.A. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Fall, 2007) (Submitted.) [PDF]
    (last updated on 2007/11/02)

    Author's Comments:
    Submitted to the SIAM Journal of Numerical Analysis, August 2007

    When immune cells detect foreign molecules, they secrete soluble factors that attract other immune cells to the site of the infection. In this paper, I study numerical solutions to a model of this behavior proposed by Kepler. In this model the soluble factors are governed by a system of reaction-diffusion equations with sources that are centered on the cells. The motion of the model cells is a Langevin process that is biased toward the gradient of the soluble factors. I have shown that the solution to this system exists for all time and remains positive, the supremum is a priori bounded and the derivatives are bounded for finite time. I have also developed a first order split scheme for solving the reaction-diffusion stochastic system. This allows us to make use of known first order schemes for solving the diffusion, the reaction and the stochastic differential equations separately.

    operator splitting • reaction-diffusion • stochastic differential equations
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