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

P. M. Diesinger () and D. W. Heermann

The European Physical Journal B: Condensed Matter and Complex Systems, 2008, vol. 62, issue 2, 209-214

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(l 1 ,l 2 ) 〉 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Keywords: 61.82.Pv Polymers; organic compounds (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1140/epjb/e2008-00145-6

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