Size of knots in ring polymers

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 4, 2007, Pages

  Marcone, B ^a   Orlandini, E ^a   Stella, A L ^a   Zonta, F ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MEASUREMENT THEORY; MONTE CARLO METHODS; PHASE EQUILIBRIA; PROBABILITY DISTRIBUTIONS; TOPOLOGY;

CUBIC LATTICES; POLYGONS; POWER LAW CORRECTION; RING POLYMERS;

POLYMERS;

EID: 34147122537     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.041105     Document Type: Article

References (56)

1. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
2. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
3. B. Alberts, K. Roberts, D. Bray, J. Lewis, M. Raff, and J. D. Watson, The Molecular Biology of the Cell (Garland, New York, 1994).
4. V. V. Rybenkov, N. R. Cozzarelli, and A. V. Vologodskii, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.90.11.5307 90, 5307 (1993).
5. S. Y. Shaw and J. C. Wang, Science SCIEAS 0036-8075 260, 533 (1993).
6. P. Pieransky, S. Kasas, G. Dietler, J. Dubochet, and A. Stasiak, New J. Phys. NJOPFM 1367-2630 3, 10 (2001).
7. W. T. Taylor, Nature (London) NATUAS 0028-0836 392, 916 (2000).
8. R. C. Lua and A. Y. Grosberg, PLOS Comput. Biol. ZZZZZZ 1553-734X 2, e45 (2006).
9. P. Virnau, L. A. Mirny, and M. Kardar, PLOS Comput. Biol. ZZZZZZ 1553-734X 2, e122 (2006).
10. B. Marcone, E. Orlandini, A. L. Stella, and F. Zonta (unpublished).
11. D. W. Sumners and S. G. Whittington, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/21/7/030 21, 1689 (1988).
12. N. Pippenger, Discrete Appl. Math. DAMADU 0166-218X 10.1016/0166-218X(89) 90005-X 25, 273 (1989).
13. E. Orlandini, M. C. Tesi, E. J. Janse van Rensburg, and S. G. Whittington, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/28/010 31, 5953 (1998).
14. B. Marcone, E. Orlandini, A. L. Stella, and F. Zonta, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/1/L03 38, L15 (2005).
15. A. Stasiak, V. Katrich, J. Bednar, D. Michout, and J. Dubochet, Nature (London) NATUAS 0028-0836 10.1038/384122a0 384, 122 (1996).
16. Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinoshita, and H. Itoh, Nature (London) NATUAS 0028-0836 10.1038/20894 399, 446 (1999).
17. X. R. Bao, H. J. Lee, and S. R. Quake, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.265506 91, 265506 (2003).
18. V. Katritch, W. K. Olson, A. Vologodskii, J. Dubochet, and A. Stasiak, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.5545 61, 5545 (2000).
19. E. J. Janse van Rensburg, D. A. W. Sumners, E. Wasserman, and S. G. Whittington, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/25/24/010 25, 6557 (1992).
20. D. Rolfsen, Knots and Links (Publish or Perish, Berkeley, CA, 1990).
21. E. Guitter and E. Orlandini, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/8/006 32, 1359 (1999).
22. R. Metzler, A. Hanke, P. G. Dommersnes, Y. Kantor, and M. Kardar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.188101 88, 188101 (2002).
23. B. Maier and J. O. Rädler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1911 82, 1911 (1999).
24. E. Ben-Naim, Z. A. Daya, P. Vorobieff, and R. E. Ecke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1414 86, 1414 (2001).
25. E. Orlandini, A. L. Stella, and C. Vanderzande, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.031804 68, 031804 (2003).
26. E. Orlandini, A. L. Stella, and C. Vanderzande, J. Stat. Phys. JSTPBS 0022-4715 115, 681 (2004).
27. A. Hanke, R. Metzler, P. G. Dommersnes, Y. Kantor, and M. Kardar, Eur. Phys. J. E EPJSFH 1292-8941 10.1140/epje/i2003-10067-9 12, 347 (2003).
28. C. Vanderzande, Lattice Models of Polymers (Cambridge University Press, Cambridge, 1998).
29. P. Virnau, Y. Kantor, and M. Kardar, J. Am. Chem. Soc. JACSAT 0002-7863 127, 43 (2005).
30. O. Farago, Y. Kantor, and M. Kardar, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00317-0 60, 53 (2002).
31. S. Caracciolo, A. Pellissetto, and A. D. Sokal, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01013668 60, 1 (1990).
32. A. D. Sokal, in Monte Carlo and Molecular Dynamics Simulation in Polymer Science, edited by, K. Binder, (Oxford University Press, New York, 1995).
33. E. J. Janse van Rensburg and S. G. Whittington, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/23/021 24, 5553 (1991).
34. M. C. Tesi, E. J. Janse van Rensburg, E. Orlandini, and S. G. Whittington, J. Stat. Phys. JSTPBS 0022-4715 29, 2451 (1996).
35. E. Orlandini, in Numerical Methods for Polymeric Systems (IMA Volumes in Mathematical and its Applications), edited by, S. Whittington, (Springer, Berlin), Vol. 102.
36. Note that the critical value of Kc for 3D self-avoiding walks has been estimated to be 0.213496 [see A. J. Guttmann, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/14/027 22, 2807 (1989)].
37. N. Madras and G. Slade, The Self Avoiding Walk (Birkhäuser, Berlin, 1993);
38. N. Madras, A. Orlitsky, and L. Shepp, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01020290 58, 159 (1990).
39. A. Yao, H. Marsuda, H. Tsukahara, M. K. Shimamura, and T Deguchi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/37/310 34, 7563 (2001).
40. Y. Kantor and M. Kardar (unpublished).
41. K. Millet, A. Dobay, and A. Stasiak, Macromolecules MAMOBX 0024-9297 10.1021/ma048779a 38, 601 (2005).
42. A. V. Vologodskii, A. V. Lukashin, H. D. Frank-Kamenetskii, and V. V. Anshelevich, Sov. Phys. JETP SPHJAR 0038-5646 66, 2153 (1974).
43. R. Zandi, Y. Kantor, and M. Kardhar (unpublished).
44. E. Carlon, E. Orlandini and A. L. Stella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.198101 88, 198101 (2002).
45. C. Tebaldi, M. De Menech and A. L. Stella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3952 83, 3952 (1999).
46. Since for the distribution in Eq. 1 it is found in general that t (q) =0 for q≤ qc with qc >0, the normalization constraint p (l,N) =1 does not imply D (1-c) =0 i.e., c=1.
47. Y. Diao, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02188227 74, 1247 (1994).
48. K. Koniaris and M. Muthukumar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.2211 66, 2211 (1991);
49. K. Koniaris and M. Muthukumar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.460889 95, 2873 (1991).
50. The symbol τ1 # τ2 refers to the two components composite knot obtained as the connected sum of the two prime knots τ1 and τ2.
51. In spite of this, recent study in Ref. of an off lattice model of polyethylene chains addressed the issue of localization for the 31 knot in the collapsed phase and gave result supporting those of Ref. for SAPs. These authors used methods previously proposed by Koniaris and Muthukumar and by Taylor for the detection and the localization of knots in open chains.
52. R. Guida and J. Zinn-Justin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/40/006 31, 8103 (1998).
53. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.21.3976 21, 3976 (1980);
54. J. C. Le Guillou and J. Zinn-Justin, J. Phys. (France) JOPQAG 0302-0738 50, 1365 (1989).
55. B. Li, N. Madras, and A. D. Sokal, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02178552 80, 661 (1995).
56. A. Dobay, J. Dubochet, K. Millett, P. E. Sottas, and A. Stasiak, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10, 5611 (2003).