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

dc.contributor.advisorEberl, Hermann
dc.contributor.authorHughes, Jack
dc.date.accessioned2021-08-30T19:57:49Z
dc.date.available2021-08-30T19:57:49Z
dc.date.copyright2021-08
dc.date.created2021-08-20
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameMaster of Scienceen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractWe 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.sponsorshipNatural Sciences and Engineering Research Council of Canada
dc.identifier.urihttps://hdl.handle.net/10214/26321
dc.language.isoenen_US
dc.publisherUniversity of Guelphen_US
dc.rights.licenseAll items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectattachmenten_US
dc.subjectcellulolytic biofilmsen_US
dc.subjectcellulolsic biofilmsen_US
dc.subjectmathematical modelen_US
dc.subjectnonlinear diffusionen_US
dc.subjectnumerical simulationen_US
dc.subjectrandom ordinary differential equationsen_US
dc.titleA Mathematical Model of Discrete Attachment to a Cellulolytic Biofilm using Random DEsen_US
dc.typeThesisen_US
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