Knots and Random Walks in Vibrated Granular Chains

Details Knots and Random Walks in Vibrated Granular Chains Knots and Random Walks in Vibrated Granular Chains

2000-12-08

arxiv.org/abs/cond-mat/0012145v1

Phys. Rev. Lett. 86, 1414 (2001)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.86.1414

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.

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