書誌事項

Random knotting and linking

editors K.C. Millett, D.W. Sumners

(Series on knots and everything, vol. 7)

World Scientific, c1994

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注記

"This volume contains papers presented at the AMS Special Session on Random Knotting and Linking, held at the International Joint Mathematics Meetings of the American Mathematical Society, Canadian Mathematical Society, and the Mathematical Association of America in Vancouver, British Columbia, Canada, August 15-19, 1993" -- Foreword

内容説明・目次

内容説明

This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simple cubic lattice are investigated. The energy of knots is studied both analytically and numerically. Vassiliev invariants are investigated and used in random knot simulations. A mutation scheme which leaves the Jones polynomial unaltered is described. Applications include the investigation of RNA secondary structure using Vassiliev invariants, and the direct experimental measurement of DNA knot probability as a function of salt concentration in random cyclization experiments on linear DNA molecules. The papers in this volume reflect the diversity of interest across science and mathematics in this subject, from topology to statistical mechanics to theoretical chemistry to wet-lab molecular biology.

目次

  • Graph invariants and topology of RNA folding, L.H. Kauffman and Y. Magarshak
  • the functoriality of Vassiliev-type invariants of links, braids and knotted graphs, T. Stanford
  • knotting of regular polygons in 3-space, K. Millett
  • an elementary invariant of knots, R. Randell
  • DNA knot formation in aqueous solutions, S. Shaw and J. Wang
  • energy functions for polygonal knots, J. Simon
  • a statistical study of random knotting using Vassiliev invariants, T. Deguchi and K. Tsurusaki
  • random knots and energy - elementary considerations, G. Buck
  • statistical mechanics and the topology of surfaces in Z(d), E.J. Janse van Rensburg
  • unsplittability of random links, Y. Diao
  • twist sequences and Vassiliev invariants, R. Trapp
  • global mutation of knots, D. Rolfsen
  • on random knots, Y. Diao et al.

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