Quasi-quantization of writhe in ideal knots

European Physical Journal E

Volumn 6, Issue 2, 2001, Pages 117-121

  Pieranski P ^a   Przybyl S ^a  

^a POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035490769     PISSN: 12928941     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101890170011     Document Type: Article

References (28)

1. P.-G. de Gennes, Macromolecules 17, 703 (1985).
2. M.D. Frank-Kamentskii, A.V. Vologodskii, Sov. Phys. Usp. 24, 679 (1981).
3. A.Y. Grossberg, A.R. Khokhlov, Statistical Physics of Macromolecules (AIP Press, 1994).
4. D.W. Sumners, S.G. Whittington, J. Phys. A 21, 1689 (1988).
5. K. Koniaris, M. Muthukumar, Phys. Rev. Lett. 66, 2211 (1991).
6. T. Deguchi, K. Tsurusaki, J. Knot Theory Ramifications 3, 321 (1994).
7. V. Katritch et al., Phys. Rev. E 61, 5545 (2000).
8. S.A. Wasserman, J.M. Duncan, N.R. Cozzarelli, Science 225, 171 (1985).
9. V.V. Rybenkov, N.R. Cozzarelli, A.V. Vologodskii, Proc. Natl. Acad. Sci. USA 90, 5307 (1993).
10. N.J. Crisona et al., J. Mol. Biol. 243, 437 (1994).
11. A.V. Vologodskii et al., J. Mol. Biol. 278, 1 (1998).
12. G. Cǎlugǎreanu, Rev. Math. Pure Appl. 4, 5 (1959).
13. J.H. White, Am. J. Math. 91, 693 (1969).
14. F.B. Fuller, Proc. Natl. Acad. Sci. USA 68, 815 (1971).
15. A. Stasiak, V. Katritch, L.H. Kauffman (Editors), Ideal Knots (World Scientific, Singapore, 1998).
16. P. Pierański, in [15].
17. L.H. Kauffman, Knots and Physics (World Scientific, Singapore, 1995).
18. The chronology of events which lead to the introduction of the term into the literature on physical knots is given by J. Simon in [15].
19. D. Cimasoni, J. Knot Theory Ramification 10, 387 (2001).
20. V. Katritch et al., Nature 384, 142 (1996).
21. C. Cerf, A. Stasiak, Proc. Nat. Acad. Sci. USA 97, 3795 (2000).
22. D. Rolfsen, Knots and Links (Publish or Perish, Berkeley, 1976). The tables are reproduced in C.C. Adams, The Knot Book (W. H. Freeman and Co., New York, 1994) and J. Przytycki, Wȩzły (Script, Warszawa, 1995) in Polish.
23. D. Rolfsen, Knots and Links (Publish or Perish, Berkeley, 1976). The tables are reproduced in C.C. Adams, The Knot Book (W. H. Freeman and Co., New York, 1994) and J. Przytycki, Wȩzły (Script, Warszawa, 1995) in Polish.
24. D. Rolfsen, Knots and Links (Publish or Perish, Berkeley, 1976). The tables are reproduced in C.C. Adams, The Knot Book (W. H. Freeman and Co., New York, 1994) and J. Przytycki, Wȩzły (Script, Warszawa, 1995) in Polish.
25. E.J. Jense van Rensburg, D.W. Sumners, S.G. Whittington, in [15].
26. T. Maggs, Phys. Rev. Lett. 85, 5472 (2000).
27. M.V. Berry, Nature 326, 277 (1987).
28. A similar problem is encountered in the computer graphics when the surface of the rope shaped into a closed knot is to be polygonized. See R.G. Sharein, Interactive Topological Drawing, thesis, The University of British Columbia, 1998 (unpublished, http://www.pims.math.ca/knotplot/thesis).