The average shape of the closed trefoil knot fluctuating on a floppy rope.

The average shape of the trefoil knot tied on a floppy, hard rope subject to thermal fluctuations has been determined. The fluctuations of the shape of knots were performed by random bending. As a result of the changing shape procedure large sets of deformed conformations of the initial knot were obtained. Afterwards, these sets were subject to the shape-fitting procedure. It has been found that the conformation is different from the ideal conformation of the knot.

Tightening of the elastic overhand knot.

The process of tightening of the open trefoil knot tied on an elastic filament is analyzed. Evolution of the curvature profile is presented and discussed.

Length of the tightest trefoil knot.

The physical sense of tight knots provided by the SONO algorithm is discussed. A method allowing one to predict their length is presented. An upper bound for the minimum length of a smooth trefoil knot is determined.