Table 1.

Knot transition probabilities in different models

SynergisticRPHJ
Knot transitionsFree, transitionsConfined, this workFree (62)Confined, this workFree (59)
71K0.020.060.660.98
71510.980.920.340.02
713100.0200
52K00.10.490.80.26
52310.50.250.20.130.23
52010.50.650.310.070.51
51K00.060.690.8
513110.940.310.13
41K00.040.160.84
410110.960.840.16
31K00.150.220.870.2
310110.850.780.130.8
  • Topology simplification through the synergistic model proposed in this work is compared with that in RP (62) and HJ (59) models. The confined case is compared with RP simulations performed in this work. K1K denotes transition to any knot K with equal or larger minimal crossing number. Complete table is given in SI Appendix.