Monte Carlo Simulations of Strand Passage in Unknotted Self-Avoiding Polygons
| dc.contributor.advisor | Soteros, C.E. | |
| dc.creator | Szafron, Michael | |
| dc.date.accessioned | 2024-05-29T21:45:43Z | |
| dc.date.available | 2024-05-29T21:45:43Z | |
| dc.date.issued | 2000 | |
| dc.date.submitted | 2000 | |
| dc.description.abstract | In this thesis, a new Multiple Markov Chain (MMC) Monte Carlo algorithm, based on the BFACF algorithm, is developed to simulate a local strand passage on unknotted self-avoiding polygons, simple models of ring polymers in dilute solution in a good solvent. The algorithm generates unknotted self-avoiding polygons that contain a fixed pattern designed to ensure the viability of the strand passage, that is, changing an over-crossing to an under-crossing or an under-crossing to an over-crossing at the fixed pattern in the unknotted self-avoiding polygons. This new algorithm, referred to as the MMC 8-BFACF algorithm, is a first step in constructing a possible simple model of DNA strand passage induced by the action of a topoisomerase. It will be shown that, in the limit, the algorithm samples uniformly from the whole space of unknotted self-avoiding polygons that contain such a pattern. The rate of convergence of the Multiple Markov Chain (as generated by the MMC 0-BFACF algorithm) to its stationary distribution and the rate of convergence of the individual components of the Multiple Markov chain to their respective marginal stationary distributions will be studied. To study these rates of convergence, as well as properties such as the average length of a polygon in each component of the MMC and the knotting probability after a strand passage about the fixed pattern, a Monte Carlo simulation of the MMC 0-BFACF algorithm will be implemented. | |
| dc.identifier.uri | https://hdl.handle.net/10388/15731 | |
| dc.title | Monte Carlo Simulations of Strand Passage in Unknotted Self-Avoiding Polygons | |
| dc.type.genre | Thesis | |
| thesis.degree.department | Graduate Studies and Research | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of Saskatchewan | en_US |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.Sc.) |