Turing patterns in linear chemical reaction systems with nonlinear cross diffusion

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.

Grantor dc:publisher

Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007

Year dc:date.issued

2007

Authors dc:creator

• Franz, David
• University of Lethbridge. Faculty of Arts and Science

Advisor dc:contributor.supervisor

• Roussel, Marc R.

• Dissertations, Academic
• Diffusion
• Pattern perception
• Chemical reactions
• Nonlinear waves
• Nonlinear theories
• Wave mechanics

Language dc:language.iso

en_US

Identifier

hdl:10133/659

OAI record oai:identifier

https://opus.uleth.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Aopus.uleth.ca%3A10133%2F659