BIRS Workshop Lecture Videos
Random knotting probability of DNA knots and scaling behavior Deguchi, Tetsuo
Random knots are created from the experiment of randomly closing the ends of nicked circular DNA. We evaluate random knotting probability for a very large number of knots by the simulation of self-avoiding polygons of cylindrical segments . Here the radius of cylindrical segments corresponds to the thickness of screening due to counter ions in solution. We evaluate the knotting probabilities for various values of the screening radius. We show that a formula based on the scaling arguments gives good fitting curves to the knotting probability as a function of the number of segments of SAP. The formula is quite useful for composite knots, for which the knotting probability can be derived from those of constituent prime knots. We remark that the formula describes knotting probabilities for some finite numbers of segments, not for infnitely large numbers, although it is based on the scaling analysis which should be good for asymptotically large numbers of segments. Here we remark that finite-size effects are nontrivial in the scaling exponents of polymers . Reference:  E. Uehara and T. Deguchi, in preparation.  E. Uehara and T. Deguchi, Exponents of intrachain correlation for self-avoiding walks and knotted self-avoiding polygons, J. Phys. A: Math. Theor. Vol. 46 (2013) 345001 (28pp).
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