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Time-dependent knotting of agitated chains.

Ingrid Gendron1, Katherine Savard1, Xavier Capaldi1

  • 1Physics Department, McGill University, 3600 rue University, Montreal, Canada.

Physical Review. E
|April 17, 2021
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Researchers studied how agitated strings form knots, finding knotting probability saturates but longer strings create more complex knots. This provides insights into microscale knotting dynamics using macroscale models.

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Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Knotting phenomena are observed across various scales, from polymer chains to cosmic strings.
  • Understanding knot formation dynamics is crucial for fields like materials science and statistical physics.
  • Macroscale models offer a tractable approach to study complex topological phenomena.

Purpose of the Study:

  • To present an experimental setup for macroscale knot formation using agitated strings.
  • To analyze knotting probability, complexity, and dynamics in a controlled experimental setting.
  • To investigate the relationship between chain length, confinement, and knot complexity.

Main Methods:

  • Utilizing a confined tumbling apparatus to induce knot formation in agitated strings.
  • Developing a software interface for processing and analyzing complex knot data.
  • Characterizing knots based on crossing number and topological complexity.

Main Results:

  • Knotting probability saturates below 80% within 100 seconds of tumbling initiation.
  • Saturation probability remains constant for chain lengths above a critical threshold.
  • Longer chains, despite confinement, form knots with higher complexity due to increased loop accessibility.

Conclusions:

  • The observed saturation indicates nonequilibrium conditions in the knot formation process.
  • Chain length is a key factor in determining knot complexity, even when overall knotting probability saturates.
  • This experimental system provides a powerful tool for studying knot theory and dynamics.