Physical knot theory is the study of

mathematical models A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathemati ...

knot A knot is an intentional complication in Rope, cordage which may be practical or decorative, or both. Practical knots are classified by function, including List of hitch knots, hitches, List of bend knots, bends, List of loop knots, loop knots, ...

ting phenomena, often motivated by considerations from

biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

, and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

(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 applications in various fields of science, including

topological fluid dynamics Topological ideas are relevant to fluid dynamics (including magnetohydrodynamics) at the kinematic level, since any fluid flow involves continuous deformation of any transported scalar or vector field. Problems of stirring and mixing are particular ...

, structural complexity analysis and

DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...

biology (Kauffman 1991, Ricca 1998). Traditional

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

. 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). Most of the work discussed in this article and in the references below is not concerned with knots tied in physical pieces of rope. For the more specific physics of such knots, see Knot: Physical theory of friction knots.

References

* 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. Knot theory {{knottheory-stub