Title page for ETD etd-03032009-040651

Type of Document Master's Thesis
Author Weimar, Jörg Richard
URN etd-03032009-040651
Title Cellular automata models for excitable media
Degree Master of Science
Department Computer Science and Applications
Advisory Committee
Advisor Name Title
Tyson, John J. Committee Co-Chair
Watson, Layne T. Committee Co-Chair
Ehrich, Roger W. Committee Member
  • Exciton theory
Date of Defense 1991-05-15
Availability restricted

A cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's.

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