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. Read more...
Abstract:
The papers in this volume reflect the diversity of interest across science and mathematics in the area of random knotting, from topology and statistical mechanics to theoretical chemistry and wet-lab molecular biology. Read more...
Author(s): Millett, Kenneth C.; Sumners, De Witt L (eds.)
Series: Series on knots and everything 7
Publisher: World Scientific
Year: 1994
Language: English
Pages: 197
Content: 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.
