Knotting Statistics After a Local Strand Passage in Unknotted Self-Avoiding Polygons in Z^3
We then investigate the question gGiven that a successful local strand passage occurs at a random location in a (2n)-edge knot-type K ¦-SAP, with what probability will the ¦-SAP have knot-type Kf 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 ¦-SAP and the probability of an after-strand-passage polygon having knot-type K given a (2n)-edge successful-strand-passage ¦-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 gsizeh of an unknotted successful-strand-passage ¦-SAP whose after-strand-passage knot-type is K when compared to the gsizeh of a ¦-SAP whose knot-type does not change after strand passage. The two measures of gsizeh used are the expected lengths of, and the expected mean-square radius of gyration of, subsets of ¦-SAPs. How these two measures of gsizeh behave as a function of a polygonfs length and its after-strand-passage knot-type is investigated.
Advisor:Soteros, C.; Martin, J. R.; Millett, K.; Bunt, R.; Laverty, W.; Srinivasan, R.
School:University of Saskatchewan
School Location:Canada - Saskatchewan
Source Type:Master's Thesis
Keywords:monte carlo simulation composite markov chain maximum likelihood estimati knotting transition probabilities
Date of Publication:04/15/2009