Self-avoiding walks on a d-dimensional hypercubic lattice are used to model a polymer interacting with a surface. One can choose to weight the walk by the number of vertices or the number of edges on the surface and define the free energy of the polymer using equilibrium statistical mechanics. We look at the behaviour
of the free energy in the limit that temperature goes to zero and also derive inequalities relating the critical
points of the two weighting schemes. A combined model with weights associated with both the number of vertices and the number of edges on the surface is investigated and the properties of its phase diagram are
explored. Finally, we look at Motzkin paths and partially-directed walks in the combined edge and vertex model and compare their results to the self-avoiding walk’s.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OTU.1807/27359 |
| Date | 31 May 2011 |
| Creators | Rychlewski, Gregory |
| Contributors | Whittington, Stuart |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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