School of Mathematics and Statistics

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Statistical mechanics of twist-storing polymers

Dagrosa, Eduardo ( 2015)

When double stranded DNA is turned it undergoes a conformational transition which is believed to be similar to the transition that occurs when a rubber coated cable is twisted. In this thesis we use lattice polymers to model such experiments. We consider a lattice ribbon model that was introduced in the 1990s and conclude that the critical structure of these experiments can be obtained by weighting the writhe of self-avoiding walks. We study the latter via exactly solvable toy models and extensively via simulations using the flatPERM and Wang-Landau algorithm. For the physically more relevant situation, one needs to restrict the knot type of the self-avoiding walk. In particular, we will consider unknotted self-avoiding walks. The restriction of the knot type poses several problems. First, the critical structure cannot be obtained from the renormalization group. Second, it becomes significantly more challenging to obtain good data from simulations.