Linking probabilities of off-lattice self-avoiding polygons and the effects of excluded volume
Naomi Hirayama, Kyoichi Tsurusaki, Tetsuo Deguchi · Journal of Physics A Mathematical and Theoretical · 2009
We evaluate numerically the probability of linking, i.e. the probability of a given pair of self-avoiding polygons (SAPs) being entangled and forming a nontrivial link type L . In the simulation we generate pairs of SAPs of N spherical segments of radius r d such that they have no overlaps among the segments and each of the SAPs has the trivial knot type. We evaluate the probability of a self-avoiding pair of SAPs forming a given link type L for various link types with fixed distance R between the centers of mass of the two SAPs. We define normalized distance r by where denotes the square root of the mean square radius of gyration of SAP of the trivial knot 0 1 . We introduce formulae expressing the linking probability as a function of normalized distance r , which gives good fitting curves with respect to χ 2 values. We also investigate the dependence of linking probabilities on the excluded-volume parameter r d and the number of segments, N . Quite interestingly, the graph of linking probability versus normalized distance r shows no N -dependence at a particular value of the excluded volume parameter, r d = 0.2.