Main content

The Scientific Way to Simulate Pattern Formation in Reaction-Diffusion Equations

Show simple item record

dc.contributor.advisor Garvie, Marcus
dc.contributor.advisor Kunze, Herb
dc.contributor.author Cleary, Erin
dc.date.accessioned 2013-05-09T19:30:21Z
dc.date.available 2013-05-09T19:30:21Z
dc.date.copyright 2013-05
dc.date.created 2013-04-22
dc.date.issued 2013-05-09
dc.identifier.uri http://hdl.handle.net/10214/6659
dc.description Alexander Graham Bell Canada Graduate Scholarship provides financial support to high calibre scholars who are engaged in master's or doctoral programs in the natural sciences or engineering. en_US
dc.description.abstract For a uniquely defined subset of phase space, solutions of non-linear, coupled reaction-diffusion equations may converge to heterogeneous steady states, organic in appearance. Hence, many theoretical models for pattern formation, as in the theory of morphogenesis, include the mechanics of reaction-diffusion equations. The standard method of simulation for such pattern formation models does not facilitate reproducibility of results, or the verification of convergence to a solution of the problem via the method of mesh refinement. In this thesis we explore a new methodology circumventing the aforementioned issues, which is independent of the choice of programming language. While the new method allows more control over solutions, the user is required to make more choices, which may or may not have a determining effect on the nature of resulting patterns. In an attempt to quantify the extent of the possible effects, we study heterogeneous steady states for two well known reaction-diffusion models, the Gierer-Meinhardt model and the Schnakenberg model. en_US
dc.description.sponsorship Natural Sciences and Engineering Research Council of Canada en_US
dc.language.iso en en_US
dc.subject Turing pattern en_US
dc.subject Finite difference method en_US
dc.subject Numerical methods en_US
dc.subject Turing space en_US
dc.subject Initial data en_US
dc.subject Schnakenberg model en_US
dc.subject Gierer-Meinhardt model en_US
dc.title The Scientific Way to Simulate Pattern Formation in Reaction-Diffusion Equations en_US
dc.type Thesis en_US
dc.degree.programme Mathematics and Statistics en_US
dc.degree.name Master of Science en_US
dc.degree.department Department of Mathematics and Statistics en_US
dc.rights.license All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.


Files in this item

Files Size Format View
Cleray_Erin_201305_MSc.pdf 8.213Mb PDF View/Open

This item appears in the following Collection(s)

Show simple item record