Yani Zhao, Franco Ferrari
The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. The specific energy and heat capacity of the trefoil, the figure-eight and the $8_1$ knots are calculated at different temperatures and for different lengths. Short-range repulsive interactions between the monomers are assumed. The knots configurations are generated on a three-dimensional cubic lattice and sampled by means of the Wang-Landau algorithm and of the pivot method. The obtained results show that the topological effects play a key role for short-length polymers. Three temperature regimes of the growth rate of the internal energy of the system are distinguished. The method employed to preserve the topology of the knots during the thermal fluctuations allows very fast calculations and can be easily applied to arbitrarily complex knots.
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http://arxiv.org/abs/1209.1717
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