Physical knot theory is the study of mathematical models of knotting phenomena, often motivated by 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 applications 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).
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.
and 20 Related for: Physical knot theory information
Physicalknottheory is the study of mathematical models of knotting phenomena, often motivated by considerations from biology, chemistry, and physics...
In topology, knottheory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope,...
mathematical field of knottheory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence...
Knottheory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs...
significant stimulus in knottheory would arrive later with Sir William Thomson (Lord Kelvin) and his vortex theory of the atom. Different knots are better at different...
mathematics known as knottheory. Knots and knotting have been used and studied throughout history. For example, Chinese knotting is a decorative handicraft...
In physicalknottheory, each realization of a link or knot has an associated ropelength. Intuitively this is the minimal length of an ideally flexible...
In physicalknottheory, a knot energy is a functional on the space of all knot conformations. A conformation of a knot is a particular embedding of a...
subject of knottheory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of...
Current Contents/Physical, Chemical & Earth Sciences Mathematical Reviews Zentralblatt MATH History of knottheory Journal of KnotTheory and Its Ramifications...
the idea of stable, knotted vortices in the ether or aether, it contributed an important mathematical legacy. The vortex theory of the atom was based...
related to, among other things, knottheory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry...
the "Ballantine rings". The first work of knottheory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait....
arrangement of these physical contacts, that are referred to as hard contacts (or h-contacts). Furthermore, chains can fold via knotting (or the formation...
Theory and Beyond, ed. Ted Bastin, Cambridge University Press, 1971. Rovelli, Carlo; Smolin, Lee (1988). "Knottheory and quantum gravity". Physical Review...
§ Introduction). Example applications of braid groups include knottheory, where any knot may be represented as the closure of certain braids (a result...
developed and applied to protein molecules. Knottheory which categorises chain entanglements. The usage of knottheory is limited to a small percentage of proteins...
a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial...
Intersection theory — Invariant theory — Iwasawa theory — K-theory — KK-theory — Knottheory — L-theory — Lie theory — Littlewood–Paley theory — Matrix theory —...