Dobay, Akos; Sottas, Pierre-Edouard; Dubochet, Jacques; Stasiak, Andrzej Predicting optimal lengths of random knots. (English) Zbl 1012.82033 Lett. Math. Phys. 55, No. 3, 239-247 (2001). In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type. Cited in 1 ReviewCited in 5 Documents MSC: 82D60 Statistical mechanics of polymers 57M25 Knots and links in the \(3\)-sphere (MSC2010) 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 92C05 Biophysics Keywords:knots; polymers; scaling laws; DNA; random walks; biophysics PDFBibTeX XMLCite \textit{A. Dobay} et al., Lett. Math. Phys. 55, No. 3, 239--247 (2001; Zbl 1012.82033) Full Text: DOI arXiv