Eur. Phys. J. B 62, 209-214 (2008)
https://doi.org/10.1140/epjb/e2008-00145-6

Average crossing number of Gaussian and equilateral chains with and without excluded volume

¹ Institute of Theoretical Physics, Heidelberg University, 69118 Heidelberg, Germany
² Institute of Theoretical Physics and Interdisziplinäres Zentrum für Wissenschaftliches Rechnen der Universität Heidelberg, 69118 Heidelberg, Germany

Corresponding author: ^a p.m.diesinger@gmx.de

Received: 9 November 2007
Revised: 1 February 2008
Published online: 11 April 2008

Abstract

We study the influence of excluded volume interactions on the behaviour of the mean average crossing number (mACN) for random off-lattice walks. We investigated Gaussian and equilateral off-lattice random walks with and without ellipsoidal excluded volume up to chain lengths of N = 1500 and equilateral random walks on a cubic lattice up to N = 20000. We find that the excluded volume interactions have a strong influence on the behaviour of the local crossing number 〈 a(l₁,l₂) 〉 at very short distances but only a weak one at large distances. This behaviour is the basis of the proof in [ Y. Diao et al., Math. Gen. 36, 11561 (2003); Y. Diao and C. Ernst, Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences] for the dependence of the mean average crossing number on the chain length N. We show that the data is compatible with an Nln(N)-bahaviour for the mACN, even in the case with excluded volume.