Eigenfunction approach to the persistent random walk in two dimensions

Details Eigenfunction approach to the persistent random walk in two dimensions Eigenfunction approach to the persistent random walk in two dimensions

2003-04-10

arxiv.org/abs/cond-mat/0304241v1

Physics

Condensed Matter

Soft Condensed Matter

14 pages, 9 figures

Scientific paper

The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a step depends on the relative orientation towards the preceding step. For all but the shortest walks, the proposed method provides a rapidly converging, numerically stable algorithm that is particularly useful for the precise study of intermediate-size chains that have not yet approached the diffusion limit. As a practical application, we examine the force-extension diagram of various planar polymer chains. With increasing joint stiffness, a marked transition from rubber-like behaviour to a form of elastic response resembling that of a flexible rod is observed.

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