Turing patterns in linear chemical reaction systems with nonlinear cross diffusion
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Date
2007
Authors
Franz, David
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007
Abstract
Turing patterns have been studied for over 50 years as a pattern forming mechanism.
To date the current focus has been on the reaction mechanism, with little to no
emphasis on the diffusion terms.
This work focuses on combining the simplest reaction mechanism possible and
the use of nonlinear cross diffusion to form Turing patterns. We start by using two
methods of bifurcation analysis to show that our model can form a Turing instability.
A diffusion model (along with some variants) is then presented along with the results
of numerical simulations. Various tests on both the numerical methods and the model
are done to ensure the accuracy of the results. Finally an additional model that is
closed to mass flow is introduced along with preliminary results.
Description
vi, 55 leaves : ill. ; 29 cm.
Keywords
Dissertations, Academic , Diffusion , Pattern perception , Chemical reactions , Nonlinear waves , Nonlinear theories , Wave mechanics