Physical Sciences and Mathematics Commons^™

Knots And Random Walks In Vibrated Granular Chains, E. Ben-Naim, Z.A. Daya, P. Vorobieff, R.E. Ecke

Eli Ben-Naim

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.