Worm-like polymer loops and Fourier knots

S. M. Rappaport, Y. Rabin, A. Yu Grosberg

    Research output: Contribution to journalArticlepeer-review


    Every smooth closed curve can be represented by a suitable Fourier sum as a function of an arbitrary parameter τ. We show that the ensemble of curves generated by randomly chosen Fourier coefficients with amplitudes inversely proportional to spatial frequency (with a smooth exponential cutoff) can be accurately mapped on the physical ensemble of inextensible worm-like polymer loops. The τ → s mapping of the curve parameter τ on the arc length s of the inextensible polymer is achieved at the expense of coupling all Fourier harmonics in a non-trivial fashion. We characterize the obtained ensemble of conformations by looking at tangent-tangent and position-position correlations. Measures of correlation on the scale of the entire loop yield a larger persistence length than that calculated from the tangent-tangent correlation function at small length scales. The topological properties of the ensemble, randomly generated worm-like loops, are shown to be similar to those of other polymer models.

    Original languageEnglish (US)
    Article numberL04
    Pages (from-to)L507-L513
    JournalJournal of Physics A: Mathematical and General
    Issue number30
    StatePublished - Jul 28 2006

    ASJC Scopus subject areas

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


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