dorsal/arxiv
View SchemaPredicting Optimal Lengths of Random Knots
| Authors | Akos Dobay, Pierre-Edouard Sottas, Jacques Dubochet, Andrzej Stasiak |
|---|---|
| Categories | |
| ArXiv ID | physics/0011061 |
| URL | https://arxiv.org/abs/physics/0011061 |
| Journal | Letters in Mathematical Physics 55:239-247,2001 |
Abstract
In thermally fluctuating long linear polymeric chain in solution, the ends come from time to time into a direct contact or a close vicinity of each other. At such an instance, the chain can be regarded as a closed one and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show their highest occurrence for shorter random walks than more complex knots. However up to now there were 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 the corresponding type.
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"abstract": "In thermally fluctuating long linear polymeric chain in solution, the ends\ncome from time to time into a direct contact or a close vicinity of each other.\nAt such an instance, the chain can be regarded as a closed one and thus will\nform a knot or rather a virtual knot. Several earlier studies of random\nknotting demonstrated that simpler knots show their highest occurrence for\nshorter random walks than more complex knots. However up to now there were no\nrules that could be used to predict the optimal length of a random walk, i.e.\nthe length for which a given knot reaches its highest occurrence. Using\nnumerical simulations, we show here that a power law accurately describes the\nrelation between the optimal lengths of random walks leading to the formation\nof different knots and the previously characterized lengths of ideal knots of\nthe corresponding type.",
"arxiv_id": "physics/0011061",
"authors": [
"Akos Dobay",
"Pierre-Edouard Sottas",
"Jacques Dubochet",
"Andrzej Stasiak"
],
"categories": [
"physics.bio-ph",
"physics.comp-ph"
],
"journal_ref": "Letters in Mathematical Physics 55:239-247,2001",
"title": "Predicting Optimal Lengths of Random Knots",
"url": "https://arxiv.org/abs/physics/0011061"
},
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