The average crossing number of equilateral random polygons.

Details

Serval ID
serval:BIB_28779
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
The average crossing number of equilateral random polygons.
Journal
Journal of Physics A. Mathematical and General
Author(s)
Diao Y, Dobay A, Kusner RB, Millet K, Sottas PE, Stasiak A
ISSN
0305-4470
Publication state
Published
Issued date
2003
Peer-reviewed
Oui
Volume
36
Number
46
Pages
11561-11574
Language
english
Abstract
In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type -upon cutting, equilibration and reclosure to a new knot type -does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.
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Create date
19/11/2007 13:26
Last modification date
20/08/2019 14:07
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