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Center for Nonlinear Studies |
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. We show that this is a direct consequence of the infinite smoothness of the Fourier representation which gives rise to curves with finite curvature and torsion. The topological properties of the ensemble are shown to be similar to those of other polymer models.