The writhe of open and closed curves

Journal of Physics A: Mathematical and General

Volumn 39, Issue 26, 2006, Pages 8321-8348

  Berger, Mitchell A ^a   Prior, Chris ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745309555     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/26/005     Document Type: Article

References (20)

1. Aldinger J, Klapper I and Tabor M 1995 Formulae for the calculation and estimation of writhe J. Knot Theory Ram. 4 343-72
2. Arnold V I and Khesin B A 1998 Topological Methods in Hydrodynamics (New York: Springer)
3. Berger M A 1993 Energy-crossing number relations for braided magnetic fields Phys. Rev. Lett. 70 705-8
4. Berger M A 2001 Topological invariants in braid theory Lett. Math. Phys. 55 181-92
5. Berger M A and Field G B 1984 The topological properties of magnetic helicity J. Fluid Mech. 147 133-48
6. Clugreanu G 1959 Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants Czech. Math. J. 11 588-625
7. Cantarella J 2005 On comparing the writhe of a smooth curve to the writhe of an inscribed polygon Preprint math/0202236
8. Chmutov S Vand and Duzhin S V 2000 The Kontsevich integral Acta Appl. Math. 66 155-90
9. Fuller F B 1978 Decomposition of the linking of a ribbon: a problem from molecular biology Proc. Natl Acad. Sci. USA 75 3557-61
10. Kontsevich M 1993 Vassiliev's knot invariants Adv. Sov. Math. 16 137-50
11. Maggs A C 2001 Writhing geometry at finite temperature:random walks and geometric phases for stiff polymers J. Chem. Phys. 114 5888-96
12. Moffatt H K 1969 The degree of knottedness of tangled vortex lines J. Fluid Mech. 35 117-29
13. Moffatt H K and Ricca R L 1992 Helicity and the Clugreanu invariant Proc. R. Soc. A 439 411-29
14. Orlandini E, Test M C, Whittington S G, Sumners D W and Janse van Rensburg E J 1994 The writhe of a self-avoiding walk J. Phys. A: Math. Gen. 27 L333-8
15. Rossetto V and Maggs A C 2003 Writhing geometry of open DNA J. Chem. Phys. 118 9864-74
16. Starostin E L 2005 On the Writhing Number of a Non-closed Curve, Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences (Series on Knots and Everything) ed J Calvo, K Millett, E Rawdon and A Stasiak (Singapore: World Scientific) pp 525-45
17. Török T and Kliem B 2005 Confined and ejective eruptions of kink-unstable flux ropes Astrophys. J. 630 L97-100
18. van der Heijden G H M and Thompson J M T 2000 Helical and localised buckling in twisted rods: a unified analysis of the symmetric case Nonlinear Dyn. 21 71-99
19. van der Heijden G H M, Peletier M A and Planque R 2004 A consistent treatment of link and writhe for open rods, and their relation to end rotation Archive Rational Mechanics and Analysis (Berlin: Springer)
20. Vologodskii A V and Marko J F 1997 Extension of torsionally stressed DNA by external force Biophys. J. 73 123-32