Geometry and physics of knots

Details

Serval ID
serval:BIB_0E7B92EC5132
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Geometry and physics of knots
Journal
Nature
Author(s)
Katritch V., Bedna  J., Michoud D., Scharein G. S., Dubochet J., Stasiak A.
ISSN
0028-0836
Publication state
Published
Issued date
1996
Peer-reviewed
Oui
Volume
384
Number
6605
Pages
142-145
Language
english
Abstract
KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).
Web of science
Create date
24/01/2008 10:25
Last modification date
20/08/2019 12:35
Usage data