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dc.contributor.advisorSoteros, Chrisen_US
dc.creatorSzafron, Michael Lorneen_US
dc.date.accessioned2009-04-09T23:10:02Zen_US
dc.date.accessioned2013-01-04T04:28:28Z
dc.date.available2010-04-15T08:00:00Zen_US
dc.date.available2013-01-04T04:28:28Z
dc.date.created2009-04en_US
dc.date.issued2009-04-15en_US
dc.date.submittedApril 2009en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-04092009-231002en_US
dc.description.abstractWe study here a model for a strand passage in a ring polymer about a randomly chosen location at which two strands of the polymer have been brought gclose h together. The model is based on ƒ¦-SAPs, which are unknotted self-avoiding polygons in Z^3 that contain a fixed structure ƒ¦ that forces two segments of the polygon to be close together. To study this model, the Composite Markov Chain Monte Carlo (CMCMC) algorithm, referred to as the CMC ƒ¦-BFACF algorithm, that I developed and proved to be ergodic for unknotted ƒ¦-SAPs in my M. Sc. Thesis, is used. Ten simulations (each consisting of 9.6 ~10^10 time steps) of the CMC ƒ¦-BFACF algorithm are performed and the results from a statistical analysis of the simulated data are presented. To this end, a new maximum likelihood method, based on previous work of Berretti and Sokal, is developed for obtaining maximum likelihood estimates of the growth constants and critical exponents associated respectively with the numbers of unknotted (2n)-edge ƒ¦-SAPs, unknotted (2n)-edge successful-strand-passage ƒ¦-SAPs, unknotted (2n)-edge failed-strand-passage ƒ¦-SAPs, and (2n)-edge after-strand-passage-knot-type-K unknotted successful-strand-passage ƒ¦-SAPs. The maximum likelihood estimates are consistent with the result (proved here) that the growth constants are all equal, and provide evidence that the associated critical exponents are all equal. We then investigate the question gGiven that a successful local strand passage occurs at a random location in a (2n)-edge knot-type K ƒ¦-SAP, with what probability will the ƒ¦-SAP have knot-type K f after the strand passage? h. To this end, the CMCMC data is used to obtain estimates for the probability of knotting given a (2n)-edge successful-strand-passage ƒ¦-SAP and the probability of an after-strand-passage polygon having knot-type K given a (2n)-edge successful-strand-passage ƒ¦-SAP. The computed estimates numerically support the unproven conjecture that these probabilities, in the n ¨ ‡ limit, go to a value lying strictly between 0 and 1. We further prove here that the rate of approach to each of these limits (should the limits exist) is less than exponential. We conclude with a study of whether or not there is a difference in the gsize h of an unknotted successful-strand-passage ƒ¦-SAP whose after-strand-passage knot-type is K when compared to the gsize h of a ƒ¦-SAP whose knot-type does not change after strand passage. The two measures of gsize h used are the expected lengths of, and the expected mean-square radius of gyration of, subsets of ƒ¦-SAPs. How these two measures of gsize h behave as a function of a polygon fs length and its after-strand-passage knot-type is investigated.en_US
dc.language.isoen_USen_US
dc.subjectComposite Markov Chain Maximum Likelihood Estimatien_US
dc.subjectKnotting transition probabilitiesen_US
dc.subjectMonte Carlo simulationen_US
dc.titleKnotting statistics after a local strand passage in unknotted self-avoiding polygons in Z3en_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematics and Statisticsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberMillett, K.en_US
dc.contributor.committeeMemberMartin, John R.en_US
dc.contributor.committeeMemberLaverty, William H.en_US
dc.contributor.committeeMemberBunt, Rick B.en_US
dc.contributor.committeeMemberSrinivasan, Rajen_US


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