Journal of Statistical Physics

, Volume 85, Issue 1–2, pp 103–130 | Cite as

Entanglement complexity of lattice ribbons

  • E. J. Janse van Rensburg
  • E. Orlandini
  • D. W. Sumners
  • M. C. Tesi
  • S. G. Whittington


We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as √n, and similar results hold for the twist and writhe.

Key Words

Ribbon topological entanglement knot link satellite knot writhe double-stranded polymer 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. J. Janse van Rensburg
    • 1
  • E. Orlandini
    • 2
  • D. W. Sumners
    • 3
  • M. C. Tesi
    • 4
  • S. G. Whittington
    • 5
  1. 1.Department of MathematicsYork UniversityNorth YorkCanada
  2. 2.Theoretical PhysicsUniversity of OxfordOxfordU.K.
  3. 3.Department of MathematicsFlorida State UniversityTallahassee
  4. 4.Mathematical InstituteUniversity of OxfordOxfordU.K.
  5. 5.Department of ChemistryUniversity of TorontoTorontoCanada

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