Mean unknotting times of random knots and embeddings

Chan, Yao-ban, Owczarek, Aleksander L., Rechnitzer, Andrew and Slade, Gordon (2007) Mean unknotting times of random knots and embeddings. Journal of Statistical Mechanics-Theory and Experiment, 5: P05004.1-P05004.15. doi:10.1088/1742-5468/2007/05/P05004

Author Chan, Yao-ban
Owczarek, Aleksander L.
Rechnitzer, Andrew
Slade, Gordon
Title Mean unknotting times of random knots and embeddings
Journal name Journal of Statistical Mechanics-Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2007-05-01
Year available 2007
Sub-type Article (original research)
DOI 10.1088/1742-5468/2007/05/P05004
Open Access Status Not Open Access
Issue 5
Start page P05004.1
End page P05004.15
Total pages 16
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
We study mean unknotting times of knots and knot embeddings by crossing reversals, in a problem motivated by DNA entanglement. Using self-avoiding polygons (SAPs) and self-avoiding polygon trails (SAPTs) we prove that the mean unknotting time grows exponentially in the length of the SAPT and at least exponentially with the length of the SAP. The proof uses Kesten's pattern theorem, together with results for mean first-passage times in the two-parameter Ehrenfest urn model. We use the pivot algorithm to generate random SAPTs of up to 3000 steps and calculate the corresponding unknotting times, and find that the mean unknotting time grows very slowly, even at moderate lengths. Our methods are quite general - for example, the lower bound on the mean unknotting time applies also to Gaussian random polygons
Keyword Rigorous results in statistical mechanics
Classical Monte Carlo simulations
Stochastic processes (theory)
Mechanical properties (DNA, RNA, membranes bio-polymers) (theory)
Ehrenfest Urn Model
Self Avoiding Walks
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Created: Fri, 13 Sep 2013, 02:13:12 EST by Kay Mackie on behalf of School of Mathematics & Physics