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Observations of metastable states of the free swelling knots and directional motion of tensioned knots in vibrated bead chains

  • Y. C. ChouEmail author
Regular Article
  • 18 Downloads

Abstract.

The free swelling of knots and the directional motion of knots under tension were studied in vertically vibrated bead chains. A metastable state of swelling was observed in the strongly vibrated two-end-free bead chains, as predicted by Grosberg and Rabin (Phys. Rev. Lett. 99, 217801 (2007)). Knots in the two-end-fixed chains were found to move directionally. The direction of motion could be changed by flipping the knot over. The velocity of motion depended on the tension in the bead chain. The effects of tension on the motion of knots were studied in one-end-fixed chains. The directional reptation might have been influenced by the random motion of the leading arc of the knot. The knots might move in a forced-reptation manner under the interaction with a simulated translocase.

Graphical abstract

Keywords

Flowing Matter: Granular Materials 

Supplementary material

10189_2019_11841_MOESM1_ESM.mp4 (10.6 mb)
Swelling and untying of a $5_{1}$ knot in a both-end-free chain, $\Gamma = 2.5$ G.
10189_2019_11841_MOESM2_ESM.mp4 (29.7 mb)
A metastable $3_{1}$ knot in a both-end-free chain for $\Gamma = 4.5$ G.
10189_2019_11841_MOESM3_ESM.mp4 (19.8 mb)
Motion of a $3_{1}$ knot in a 90-bead chain with both ends fixed at the vibrational acceleration $\Gamma = 3.0$ G. The leading arc is to the left of the images.
10189_2019_11841_MOESM4_ESM.mp4 (16.6 mb)
Motion of a $3_{1}$ knot in a bead chain under a tension of 140 mgw for $\Gamma = 4.0$ G. The leading arc is to the free end.
10189_2019_11841_MOESM5_ESM.mp4 (3.4 mb)
Pushing and untying of a $3_{1}$ knot in a linear chain by a simulated helicase for $\Gamma = 3.0$ G.
10189_2019_11841_MOESM6_ESM.mp4 (10.3 mb)
Tightening of a $4_{1}$ knot in a circular chain by a simulated helicase at $\Gamma = 4.0$ G.

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Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsNational Tsing-Hua UniversityHsinchuTaiwan

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