The abundance of unknots in various models of polymer loops

N. T. Moore, A. Y. Grosberg

    Research output: Contribution to journalArticlepeer-review


    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/N0), where N0 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 N0 for a variety of polymer models. Among models examined, N0 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 languageEnglish (US)
    Article number005
    Pages (from-to)9081-9092
    Number of pages12
    JournalJournal of Physics A: Mathematical and General
    Issue number29
    StatePublished - Jul 21 2006

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • General Physics and Astronomy


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