The average shape of the closed trefoil knot fluctuating on a floppy rope

  • Marcin Modlinski
  • Sylwester Przybyl
  • Piotr Pieranski
Open Access
Regular Article

Abstract

The average shape of the trefoil knot tied on a floppy, hard rope subject to thermal fluctuations has been determined. The fluctuations of the shape of knots were performed by random bending. As a result of the changing shape procedure large sets of deformed conformations of the initial knot were obtained. Afterwards, these sets were subject to the shape-fitting procedure. It has been found that the conformation is different from the ideal conformation of the knot.

Graphical abstract

Keywords

Soft Matter: Polymers and Polyelectrolytes 

References

  1. 1.
    K.C. Millett, E.J. Rawdon, V.T. Tran, A. Stasiak, J. Chem. Phys. 133, 154113 (2010).ADSCrossRefGoogle Scholar
  2. 2.
    S. Saka, H. Takano, J. Phys. Soc. Jpn. 77, 124802 (2008).ADSCrossRefGoogle Scholar
  3. 3.
    P. Pieranski, S. Przybyl, Phys. Rev. E 64, 318011 (2001).MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Smutny Global radii of curvature, and the biarc approximation of space curves: In pursuit of ideal knot shapes, PhD thesis, École Polytechnique Fédérale de Lausanne (2004).Google Scholar
  5. 5.
    J. Baranska, P. Pieranski, S. Przybyl, E.J. Rawdon, Phys. Rev. E 70, 051810 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    W. Kuhn, Kolloid-Z. 68, 2 (1934).CrossRefGoogle Scholar
  7. 7.
    E. Guitter, E. Orlandini, J. Phys. A 32, 1359 (1999).MathSciNetADSCrossRefMATHGoogle Scholar
  8. 8.
    V. Katritch, W.K. Olson, A. Vologodskii, J. Dubochet, A. Stasiak, Phys. Rev. E 61, 5545 (2000).ADSCrossRefGoogle Scholar
  9. 9.
    R. Metzler, A. Hanke, P.G. Dommersnes, Y. Kantor, M. Kardar, Phys. Rev. Lett. 88, 1881011 (2002).CrossRefGoogle Scholar
  10. 10.
    E. Orlandini, A.L. Stella, C. Vanderzande, J. Stat. Phys. 115, 681 (2004).MathSciNetADSCrossRefMATHGoogle Scholar
  11. 11.
    B. Marcone, E. Orlandini, A.L. Stella, F. Zonta, J. Phys. A: Math. Gen. 38, L15 (2005).MathSciNetADSCrossRefMATHGoogle Scholar
  12. 12.
    E. Orlandini, A.L. Stella, C. Vanderzande, Phys. Biol. 6, 025012 (2009).ADSCrossRefGoogle Scholar
  13. 13.
    E. Ben-Naim, Z.A. Daya, P. Vorobieff, R.E. Ecke, Phys. Rev. Lett. 86, 1414 (2001).ADSCrossRefGoogle Scholar
  14. 14.
    P.G. Dommersnes, Y. Kantor, M. Kardar, Phys. Rev. E 66, 031802 (2002).ADSCrossRefGoogle Scholar
  15. 15.
    A. Amzallag, C. Vaillant, M. Jacob, M. Unser, J. Bednar, J. Kahn, J. Dubochet, A. Stasiak, J.H. Maddocks, Nucl. Acids Res. 34, e125 (2006).CrossRefGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Marcin Modlinski
    • 1
  • Sylwester Przybyl
    • 1
  • Piotr Pieranski
    • 1
  1. 1.Department of Computational PhysicsPoznan University of TechnologyPoznanPoland

Personalised recommendations