Knot probability for lattice polygons in confined geometries
- 1 January 1994
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 27 (2) , 347-360
- https://doi.org/10.1088/0305-4470/27/2/019
Abstract
We study the knot probability of polygons confined to slabs or prisms, considered as subsets of the simple cubic lattice. We show rigorously that almost all sufficiently long polygons in a slab are knotted and we use Monte Carlo methods to investigate the behaviour of the knot probability as a function of the width of the slab or prism and the number of edges in the polygon. In addition we consider the effect of solvent quality on the knot probability in these confined geometries.Keywords
This publication has 21 references indexed in Scilit:
- Entanglement complexity of self-avoiding walksJournal of Physics A: General Physics, 1992
- The dimensions of knotted polygonsJournal of Physics A: General Physics, 1991
- Self-entanglement in ring polymersThe Journal of Chemical Physics, 1991
- The knot probability in lattice polygonsJournal of Physics A: General Physics, 1990
- Self-avoiding walks in wedgesJournal of Physics A: General Physics, 1985
- Tight knotsMacromolecules, 1984
- The Knotting of Brownian Motion in 3-SpaceJournal of the London Mathematical Society, 1979
- ‘Monte Carlo’ computer simulation of chain molecules. IMolecular Physics, 1969
- On the Number of Self-Avoiding WalksJournal of Mathematical Physics, 1963
- The number of polygons on a latticeMathematical Proceedings of the Cambridge Philosophical Society, 1961