Knots and Random Walks in Vibrated Granular Chains

E. Ben-Naim; Z. A. Daya; P. Vorobieff; R. E. Ecke

doi:10.1103/PhysRevLett.86.1414

Knots and Random Walks in Vibrated Granular Chains

E. Ben-Naim, Z. A. Daya, P. Vorobieff, and R. E. Ecke

Phys. Rev. Lett. 86, 1414 – Published 19 February 2001

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 theoretical values.

Received 31 July 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1414

Authors & Affiliations

E. Ben-Naim^1,2, Z. A. Daya^2,3, P. Vorobieff^2,4, and R. E. Ecke^2,3

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
²Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
³Condensed Matter & Thermal Physics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
⁴Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131