Physical knot theory
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Physical knot theory is the study of mathematical models of knotting phenomena, often motivated by physical considerations from biology, chemistry, and physics (Kauffman 1991). 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 application in various fields of science including topological fluid dynamics, structural complexity analysis and DNA biology (Kauffman 1991, Ricca 1998).
Traditional knot theory models a knot as a simple closed loop in three-dimensional space. Such a knot has no thickness or physical properties such as tension or friction. Physical knot theory incorporates more realistic models. The traditional model is also studied but with an eye toward properties of specific embeddings ("conformations") of the circle. Such properties include ropelength and various knot energies (O’Hara 2003).
- Kauffman, L.H. (1991) Knots and Physics. Series on Knots and Everything 1, World Scientific.
- Kauffman, L.H., Editor (1991) Knots and Applications. Series on Knots and Everything 6, World Scientific.
- O’Hara, J. (2003) Energy of Knots and Conformal Geometry. Series on Knots and Everything 33, World Scientific.
- Ricca, R.L. (1998) Applications of knot theory in fluid mechanics. In Knot Theory (ed. V.F.R. Jones et al.), pp. 321–346. Banach Center Publs. 42, Polish Academy of Sciences, Warsaw.
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