### Abstract

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N
_{0}), where N
_{0} marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N
_{0} for a variety of polymer models. Among models examined, N
_{0} is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

Original language | English (US) |
---|---|

Article number | 005 |

Pages (from-to) | 9081-9092 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 29 |

DOIs | |

State | Published - Jul 21 2006 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*39*(29), 9081-9092. [005]. https://doi.org/10.1088/0305-4470/39/29/005

**The abundance of unknots in various models of polymer loops.** / Moore, N. T.; Grosberg, A. Y.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 39, no. 29, 005, pp. 9081-9092. https://doi.org/10.1088/0305-4470/39/29/005

}

TY - JOUR

T1 - The abundance of unknots in various models of polymer loops

AU - Moore, N. T.

AU - Grosberg, A. Y.

PY - 2006/7/21

Y1 - 2006/7/21

N2 - A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

AB - A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

UR - http://www.scopus.com/inward/record.url?scp=33745826696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745826696&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/29/005

DO - 10.1088/0305-4470/39/29/005

M3 - Article

VL - 39

SP - 9081

EP - 9092

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 29

M1 - 005

ER -