Topology and Geometry in Polymer Science

1. Front Matter

   Pages i-x

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2. Entanglements of Polymers

   • S. F. Edwards

   Pages 1-7

3. Entropic Exponents of Knotted Lattice Polygons

   • Enzo Orlandini, E. J. Janse Van Rensburg, Maria Carla Tesi, S. G. Whittington

   Pages 9-21

4. The Torsion of Three-Dimensional Random Walk*

   • Mikelis G. Bickis

   Pages 23-28

5. Self-Repelling Knots and Local Energy Minima

   • Louis H. Kauffman, Milana Huang, Robert P. Greszczuk

   Pages 29-36

6. Properties of Knot Energies

   • Y. Diao, C. Ernst, E. J. Janse van Rensburg

   Pages 37-47

7. Energy and Thickness of Knots*

   • Jonathan Simon

   Pages 49-65

8. On Distortion and Thickness of Knots*

   • Robert B. Kusnert, John M. Sullivant

   Pages 67-76

9. Percolation of Linked Circles

   • Y. Diao, E. J. Janse van Rensburg

   Pages 79-88

10. Minimal Links in the Cubic Lattice

    • R. Uberti, E. J. Janse van Rensburg, E. Orlandinit, M. C. Tesi, S. G. Whittington

    Pages 89-100

11. Knots in Graphs in Subsets of Z ³

    • C. E. Soteros

    Pages 101-133

12. Topological Entanglement Complexity of Polymer Chains in Confined Geometries

    • Maria Carla Tesi, E. J. Janse van Rensburg, Enzo Orlandini, Stuart G. Whittington

    Pages 135-157

13. Survey of Self-Avoiding Random Surfaces on Cubic Lattices: Issues, Controversies, and Results*

    • T. L. Einsteint, A. L. Stella

    Pages 159-173

14. Computational Methods in Random Surface Simulation

    • Isabel Beichl, Francis Sullivant

    Pages 175-192

15. A Model of Lattice Vesicles

    • E. J. Janse Van Rensburg

    Pages 193-201

16. Back Matter

    Pages 202-206

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This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title. This workshop was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Stuart G. Whittington, De Witt Sumners, and Timothy Lodge for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foun­ dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE This book is the product of a workshop on Topology and Geometry of Polymers, held at the IMA in June 1996. The workshop brought together topologists, combinatorialists, theoretical physicists and polymer scientists, who share an interest in characterizing and predicting the microscopic en­ tanglement properties of polymers, and their effect on macroscopic physical properties.

• Graph
• Polymer
• Sim
• Simulation
• geometry
• mechanics
• model
• combinatorics

• Department of Chemistry, University of Toronto, Toronto, Canada

  Stuart G. Whittington

• Department of Mathematics, Florida State University, Tallahassee, USA

  Witt Sumners

• Department of Chemistry, University of Minnesota, Minneapolis, USA

  Timothy Lodge

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