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Dobay A, Dubochet J, Millett K, et al. Scaling behavior of random knots. Proc Natl Acad Sci U S A. 2003;100(10):5611-5doi: 10.1073/pnas.0330884100.
Dobay, A., Dubochet, J., Millett, K., Sottas, P. E., & Stasiak, A. (2003). Scaling behavior of random knots. Proceedings of the National Academy of Sciences of the United States of America, 100(10), 5611-5. https://doi.org/10.1073/pnas.0330884100
Dobay, Akos, et al. "Scaling behavior of random knots." Proceedings of the National Academy of Sciences of the United States of America vol. 100,10 (2003): 5611-5. doi: https://doi.org/10.1073/pnas.0330884100
Dobay A, Dubochet J, Millett K, Sottas PE, Stasiak A. Scaling behavior of random knots. Proc Natl Acad Sci U S A. 2003 May 13;100(10):5611-5. doi: 10.1073/pnas.0330884100. Epub 2003 Apr 29. PMID: 16576754; PMCID: PMC156249.
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Proc Natl Acad Sci U S A. 2003 May 13;100(10):5611-5. doi: 10.1073/pnas.0330884100. Epub 2003 Apr 29.

Scaling behavior of random knots.

Proceedings of the National Academy of Sciences of the United States of America

Akos Dobay, Jacques Dubochet, Kenneth Millett, Pierre-Edouard Sottas, Andrzej Stasiak

Affiliations

  1. Laboratory of Ultrastructural Analysis, University of Lausanne, 1015 Lausanne, Switzerland; Department of Mathematics, University of California, Santa Barbara, CA 93106; and Center for Neuromimetic Systems, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland.

PMID: 16576754 PMCID: PMC156249 DOI: 10.1073/pnas.0330884100

Abstract

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

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