Physical knot theory is used to study how geometric and topological characteristics of filamentary structures, such as magnetic flux tubes, vortex filaments, polymers, DNAs, influence their physical properties and functions.
It has applications in various fields of science, including topological fluid dynamics, structural complexity analysis and DNA biology (Kauffman 1991, Ricca 1998).
Such a knot has no thickness or physical properties such as tension or friction.
The traditional model is also studied but with an eye toward properties of specific embeddings ("conformations") of the circle.
Most of the work discussed in this article and in the references below is not concerned with knots tied in physical pieces of rope.