dc.contributor.author | Smith-Roberge, Julien | |
dc.date.accessioned | 2017-04-07T18:54:58Z | |
dc.date.available | 2017-04-07T18:54:58Z | |
dc.date.issued | 2017-04-07T18:54:58Z | |
dc.identifier.uri | http://hdl.handle.net/10222/72825 | |
dc.description.abstract | Recent experiments have shown that patterns can emerge in bacterial colonies programmed to have a drop in diffusion when population densities (detected via a quorum sensing mechanism) are sufficiently large. We examine one partial differential equation model of this system, and construct its non-constant stationary solutions. We demonstrate analytically that these solutions are stable when the diffusion rate of bacteria is large and the diffusion rate of signalling molecules, D_h, is small. We further demonstrate that increasing D_h induces a Hopf bifurcation, resulting in a loss of stability. These results are confirmed by numerical simulations. | en_US |
dc.language.iso | en | en_US |
dc.subject | pattern formation | en_US |
dc.subject | partial differential equations | en_US |
dc.subject | mathematical biology | en_US |
dc.title | Pattern Formation in Bacterial Colonies with Density-Dependent Diffusion | en_US |
dc.type | Thesis | en_US |
dc.date.defence | 2017-04-06 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Master of Science | en_US |
dc.contributor.external-examiner | n/a | en_US |
dc.contributor.graduate-coordinator | David Iron | en_US |
dc.contributor.thesis-reader | Andrew Rutenberg | en_US |
dc.contributor.thesis-reader | Alan Coley | en_US |
dc.contributor.thesis-supervisor | David Iron | en_US |
dc.contributor.thesis-supervisor | Theodore Kolokolnikov | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |