Advanced Undergraduate Laboratory

Department of Physics

University of Toronto

KNOT: Knots and topological transformations in vibrating chains

How knots tied in metal chains untie themselves when vibrated is way to study how important macromolecules such as polymers and DNA tangle and untangle. In this seemly simple experiment you will explore the challenging mechanics and thermodynamics of linear chains. The experiment is originally based on Knots and Random Walks in Vibrated Granular Chains, E. Ben-Naim et al., Phys. Rev. Lett. 86 (2001) 1414.

Write-Up in PDF Format or Microsoft Word Format.

(The experiment is currently located in MP239; last write-up revision: April 2012.)

Additional resources:

• Possibly useful Python software which you can use/modify:
  • Numerical solution of Ben-Naim's equations (3) and (4): unknotting_time.py.
  • A simple Monte Carlo simulation of Ben-Naim's unknotting model: knot_random_walk.py.
  • A vPython simulation of a beaded chain unknotting on a vibrating plate: beaded_chain.py.
  • Windows-only Python software that uses a webcam to measure and plot the radius of gyration of a beaded chain in real time, written by students Jamie Woodbury and Anselm Hui: RealTime_ROG.zip.
• MMA 1220 accelerometer specifications.
• Some example unknotting and knotting videos: Unknot_5.wmv, Unknot_8.wmv, Unknot_9.wmv, Knot_1.avi
• Older MatLab software written by student Nikita Reznik to measure the radius of gyration of a reflective chain as it lies on a black background.
  • gyration.m , gyration.asv , gyration.fig : Matlab code for measuring radius of gyration, and two supporting files.
  • Documentation written by Nikita Reznik: Microsoft Word, PDF

Physics student, Myles Casey-Nestor, working on the Knots experiment in November 2011.

Last updated on 26 February 2013