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A Mathematical Model of Discrete Attachment to a Cellulolytic Biofilm using Random DEs

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dc.contributor.advisor Eberl, Hermann
dc.contributor.author Hughes, Jack
dc.date.accessioned 2021-08-30T19:57:49Z
dc.date.available 2021-08-30T19:57:49Z
dc.date.copyright 2021-08
dc.date.created 2021-08-20
dc.identifier.uri https://hdl.handle.net/10214/26321
dc.description.abstract We propose a new mathematical framework for the addition of stochastic attachment to biofilm models via the use of random ordinary differential equations. We focus our approach on a spatially explicit model of cellulolytic biofilm growth and formation that comprises a PDE-ODE coupled system to describe the biomass and carbon respectively. The model equations are discretized in space using a standard finite volume method. We introduce discrete attachment events into the discretized model via an impulse function with a standard stochastic process as input. We solve our model with an implicit ODE solver. We provide basic simulations to investigate the qualitative features of our model. We then perform a grid refinement study to investigate the spatial convergence of our model. We investigate model behaviour while varying key attachment parameters. Lastly, we use our attachment model to provide evidence for a stable travelling wave solution to the original PDE-ODE coupled system. en_US
dc.description.sponsorship Natural Sciences and Engineering Research Council of Canada en_US
dc.language.iso en en_US
dc.publisher University of Guelph en_US
dc.subject attachment en_US
dc.subject cellulolytic biofilms en_US
dc.subject cellulolsic biofilms en_US
dc.subject mathematical model en_US
dc.subject nonlinear diffusion en_US
dc.subject numerical simulation en_US
dc.subject random ordinary differential equations en_US
dc.title A Mathematical Model of Discrete Attachment to a Cellulolytic Biofilm using Random DEs 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.
dc.degree.grantor University of Guelph en_US


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