Knots and Random Walks in Vibrated Granular Chains

Preprint

8 December 2000

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/0012145

Abstract

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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Version 1, 2000-12-08, ArXiv
Published version: Physical Review Letters, 86 (8), 1414.

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