Now showing items 1-6 of 6
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Entire Solutions to Dirichlet Type Problems
(University of Waterloo, 2007-08-02)In this thesis, we examined some Dirichlet type problems of the form: \begin{eqnarray*} \triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\ u & = & f\ {\rm on\ } \psi = 0, \end{eqnarray*} and we were particularly ... -
Long-time behaviour of a coupled PDE model of high intensity focused ultrasound heating of biological tissue
(University of Waterloo, 2021-11-11)High Intensity Focused Ultrasound (HIFU) has emerged as a novel therapeutic modality, for the treatment of various cancers, that is gaining significant traction in clinical oncology. It is a cancer therapy that avoids many ... -
Mathematical Modeling of C elegans L1 aggregation
(University of Waterloo, 2020-01-16)First-stage larvae (L1s) of the nematode Caenorhabditis elegans aggregate after starvation. I develop a mathematical model of this behavior based on the classic Keller-Segel model. In the Keller-Segel model, organisms ... -
Microcolony Dynamics: Motion from Growth, Order, and Incompressibility
(University of Waterloo, 2023-04-27)Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until ... -
Topics in G₂ geometry and geometric flows
(University of Waterloo, 2020-05-15)We study three different problems in this thesis, all related to G₂ structures and geometric flows. In the first problem we study hypersurfaces in a nearly G₂ manifold. We define various quantities associated to such a ... -
The two-space homogenization method
(University of Waterloo, 2012-10-04)In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic ...