Seminários

Apresentador: Thomas Prellberg, School of Mathematical Sciences, Queen Mary University of London

We review the theory and present results of simulations of winding angle distributions for lattice models of collapsing polymers.

Simulations of interacting self-avoiding walks provide strong numerical evidence for a long-standing prediction of universal scaling of winding angle distributions: the winding angle distribution for N-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as C log N, with C assuming distinct universal values above, at, and below the collapse transition.

In contrast, simulations of interacting self-avoiding trails, which allow crossings, provide strong evidence that while the high temperature swollen state of this model has a winding angle distribution that is also Gaussian, this breaks down at the polymer collapse point and at low temperatures. We provide some evidence that the distributions at the collapse point are well modelled by stretched exponentials.