Figure 3.

Schematics of the collective order parameter $\left|D\right|$ measuring the linear distance between two prime knots. (a) When both prime components are isolated , the order parameter is given by $\left|D\right|=|d_{1,2}|=|c_1-c_2|$, where $c_i=(e_i+s_i)/2$ is the center of knot i on the chain. Here $e_i$ and $s_i$ stand for the last and the first bead of the i-th isolated prime knot; (b) When the two knots are intertwined, the center of the hosting knot is taken to coincide with the center of the composite knot $c_{1,2}$.