Abstract

Dictyostelium discoideum (Dd) is a model organism, studied for reasons from cell movement to chemotaxis to human disease control. Creating a computer model of the life cycle of Dd has garnered great interest, one part of which is the Aggregation Stage, where thousands of amoeba gather together to form a slug. Chemotaxis is the mechanism through which this is accomplished. This thesis develops two- and three-dimensional alternating direction implicit code which solves the diffusion equation on an adaptive grid. The calculated values for both two and three dimensions are checked against the actual solution and error results are provided. Comparisons are made between the coarse grid with refinement case and a fine grid without refinement case. Also, a non-negativity condition for two dimensions is derived to give a bound on the three major parameters: the diffusion coefficient and the spatial and time discretizations.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2015-11-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd8162

Keywords

Dictyostelium discoideum, Numerical Methods, ADI, Adaptive Grids, Non-negativity condition

Included in

Mathematics Commons

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