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Knots and Random Walks in Vibrated Granular Chains

E. Ben-Naim·Z. A. Daya·P. Vorobieff·R. E. Ecke
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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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E. Ben-Naim, Z. A. Daya, P. Vorobieff, R. E. Ecke. 2000-12-08. Knots and Random Walks in Vibrated Granular Chains. https://doi.org/10.1103/physrevlett.86.1414

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